initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many q women are currently in the room ?

Explanation: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number q = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"

multiply(2, subtract(divide(multiply(5, subtract(14, 2)), 4), 3))

<gadget id="calculator">14 - 2</gadget>
<output>12</output>
<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">60 / 4</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<gadget id="calculator">2 * 12</gadget>
<output>24</output>
<result>24</result>


a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 225.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?

Explanation: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 225 = > 125 * s = 150 = > s = 1.2 answer d"

<gadget id="calculator">125 * 0.6</gadget>
<output>75</output>
<gadget id="calculator">225 - 75</gadget>
<output>150</output>
<gadget id="calculator">150 / 125</gadget>
<output>6/5 = around 1.2</output>
<result>6/5 = around 1.2</result>


a and b invests rs . 3000 and rs . 5500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?

Explanation: "( 3 * 6 + 6 * 6 ) : ( 5.5 * 12 ) 54 : 66 = > 9 : 11 answer : e"

divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(5500, add(6, 6)))

<gadget id="calculator">3_000 * 6</gadget>
<output>18_000</output>
<gadget id="calculator">3_000 * 2</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 * 6</gadget>
<output>36_000</output>
<gadget id="calculator">18_000 + 36_000</gadget>
<output>54_000</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">5_500 * 12</gadget>
<output>66_000</output>
<gadget id="calculator">54_000 / 66_000</gadget>
<output>9/11 = around 0.818182</output>
<result>9/11 = around 0.818182</result>


if a lends rs . 3150 to b at 8 % per annum and b lends the same sum to c at 12.5 % per annum then the gain of b in a period of 2 years is ?

Explanation: "( 3150 * 4.5 * 2 ) / 100 = > 283.5 answer : c"

subtract(divide(multiply(multiply(3150, 12.5), 2), const_100), divide(multiply(multiply(3150, 8), 2), const_100))

<gadget id="calculator">3_150 * 12.5</gadget>
<output>39_375</output>
<gadget id="calculator">39_375 * 2</gadget>
<output>78_750</output>
<gadget id="calculator">78_750 / 100</gadget>
<output>1_575/2 = around 787.5</output>
<gadget id="calculator">3_150 * 8</gadget>
<output>25_200</output>
<gadget id="calculator">25_200 * 2</gadget>
<output>50_400</output>
<gadget id="calculator">50_400 / 100</gadget>
<output>504</output>
<gadget id="calculator">(1_575/2) - 504</gadget>
<output>567/2 = around 283.5</output>
<result>567/2 = around 283.5</result>


apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 663 and for 36 kgs of apples is 726 then the cost of first 10 kgs of apples is

Explanation: ans : by framing equations we get 30 l + 3 q = 663 30 l + 6 q = 726 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 20 cost of 10 kgs of apples = 10 x 20 = 200 answer : c

multiply(divide(subtract(663, multiply(subtract(33, 30), divide(subtract(726, 663), subtract(36, 33)))), 30), 10)

<gadget id="calculator">33 - 30</gadget>
<output>3</output>
<gadget id="calculator">726 - 663</gadget>
<output>63</output>
<gadget id="calculator">36 - 33</gadget>
<output>3</output>
<gadget id="calculator">63 / 3</gadget>
<output>21</output>
<gadget id="calculator">3 * 21</gadget>
<output>63</output>
<gadget id="calculator">663 - 63</gadget>
<output>600</output>
<gadget id="calculator">600 / 30</gadget>
<output>20</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<result>200</result>


a rower can row 7 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?

Explanation: let x be the distance to big rock . time = x / 5 + x / 9 = 1 x = 45 / 14 = 3.21 km the answer is d .

multiply(divide(subtract(7, 2), add(add(7, 2), subtract(7, 2))), add(7, 2))

<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">7 + 2</gadget>
<output>9</output>
<gadget id="calculator">9 + 5</gadget>
<output>14</output>
<gadget id="calculator">5 / 14</gadget>
<output>5/14 = around 0.357143</output>
<gadget id="calculator">(5/14) * 9</gadget>
<output>45/14 = around 3.214286</output>
<result>45/14 = around 3.214286</result>


a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a women alone in 18 days , how long will a boy take to complete the work ?

Explanation: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 womans 1 day ’ s work = 1 / 18 ( 1 man + 1 woman ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 boys 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the boy alone can finish the work in 9 days . answer : option c"

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/6) + (1/18)</gadget>
<output>2/9 = around 0.222222</output>
<gadget id="calculator">(1/3) - (2/9)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


the least number which should be added to 1789 so that the sum is exactly divisible by 5 , 6 , 4 and 3 is ?

Explanation: l . c . m . of 5 , 6 , 4 and 3 = 60 . on dividing 1789 by 60 , the remainder is 49 . number to be added = ( 60 - 49 ) = 11 b )

subtract(multiply(3, multiply(4, 5)), multiply(subtract(divide(1789, multiply(3, multiply(4, 5))), subtract(multiply(const_3, const_10), const_1)), multiply(3, multiply(4, 5))))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">3 * 20</gadget>
<output>60</output>
<gadget id="calculator">1_789 / 60</gadget>
<output>1_789/60 = around 29.816667</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">30 - 1</gadget>
<output>29</output>
<gadget id="calculator">(1_789/60) - 29</gadget>
<output>49/60 = around 0.816667</output>
<gadget id="calculator">(49/60) * 60</gadget>
<output>49</output>
<gadget id="calculator">60 - 49</gadget>
<output>11</output>
<result>11</result>


i chose a number and divide it by 8 . then i subtracted 160 from the result and got 12 . what was the number i chose ?

Explanation: "let x be the number i chose , then x / 8 − 160 = 12 x / 8 = 172 x = 1376 answer is a ."

<gadget id="calculator">160 + 12</gadget>
<output>172</output>
<gadget id="calculator">172 * 8</gadget>
<output>1_376</output>
<result>1_376</result>


a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 40 , how many horses are there ?

Explanation: legs 8 * 4 = 32 now half on their horses so remaining on the walk so 4 men 4 men has 8 legs so , 8 + 32 = 40 legs walking answer : a

divide(40, add(const_4, divide(const_2, const_2)))

<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>


workers at a campaign office have 3000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?

Explanation: "( 1 / 5 ) * 3000 = 600 remaining = 3000 - 600 = 2400 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2400 = 600 remaining now = 2400 - 600 = 1800 answer : option a"

subtract(subtract(3000, divide(3000, 5)), divide(subtract(3000, divide(3000, 5)), 4))

<gadget id="calculator">3_000 / 5</gadget>
<output>600</output>
<gadget id="calculator">3_000 - 600</gadget>
<output>2_400</output>
<gadget id="calculator">2_400 / 4</gadget>
<output>600</output>
<gadget id="calculator">2_400 - 600</gadget>
<output>1_800</output>
<result>1_800</result>


the diagonal of a rhombus are 70 m and 160 m . its area is :

Explanation: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 70 ã — 160 ) cm ( power ) 2 = 70 ã — 80 = 5600 cm ( power ) 2 answer is c ."

<gadget id="calculator">(70 * 160) / 2</gadget>
<output>5_600</output>
<result>5_600</result>


50 % of a number is more than 40 % of 120 by 180 . find the number ?

Explanation: "( 50 / 100 ) * x – ( 40 / 100 ) * 120 = 180 1 / 2 x = 228 x = 456 answer : a"

divide(multiply(add(divide(multiply(120, 40), const_100), 180), const_100), 50)

<gadget id="calculator">120 * 40</gadget>
<output>4_800</output>
<gadget id="calculator">4_800 / 100</gadget>
<output>48</output>
<gadget id="calculator">48 + 180</gadget>
<output>228</output>
<gadget id="calculator">228 * 100</gadget>
<output>22_800</output>
<gadget id="calculator">22_800 / 50</gadget>
<output>456</output>
<result>456</result>


sheela deposits rs . 5000 in bank savings account . if this is 20 % of her monthly income . what is her monthly income in ?

Explanation: "explanation : 20 % of income = rs . 5000 100 % of income = 5000 x 100 / 20 = rs . 25000 answer : c"

<gadget id="calculator">5_000 * 100</gadget>
<output>500_000</output>
<gadget id="calculator">500_000 / 20</gadget>
<output>25_000</output>
<result>25_000</result>


there are 4 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?

Explanation: "each person is one participant of 4 games . so there are in all 4 * 4 = 16 instances of one participant games . but each game has 2 participants so total number of games = 16 / 2 = 8 b"

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


a 24 ' ' x 24 ' ' square metal plate needs to be fixed by a carpenter on to a wooden board . the carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square . each nail is at the same distance from the neighboring nails . how many nails does the carpenter use ?

Explanation: every corner will have one , 4 corners will have 4 + and for 4 sides 23 no of nails = 4 + ( 4 * 23 ) = 96 answer : c

add(multiply(subtract(25, const_2), const_4), const_4)

<gadget id="calculator">25 - 2</gadget>
<output>23</output>
<gadget id="calculator">23 * 4</gadget>
<output>92</output>
<gadget id="calculator">92 + 4</gadget>
<output>96</output>
<result>96</result>


let the number which when multiplied by 15 is increased by 280 .

Explanation: "solution let the number be x . then , 15 x - x = 280 ‹ = › 14 x = 280 x ‹ = › 20 . answer b"

<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">280 / 14</gadget>
<output>20</output>
<result>20</result>


in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 105 ?

Explanation: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 105 5 x - 20 = 105 5 x = 125 x = 25 the answer is b ."

<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">2 + 4</gadget>
<output>6</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">12 + 8</gadget>
<output>20</output>
<gadget id="calculator">105 - 20</gadget>
<output>85</output>
<gadget id="calculator">85 / 5</gadget>
<output>17</output>
<gadget id="calculator">17 + 8</gadget>
<output>25</output>
<result>25</result>


4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ?

Explanation: probability of getting two same faces : 1 and 1 / 6 for other two faces , probabilities : 5 / 6 and 4 / 6 respectively . the dice combinations can be arranged in 4 ! / 2 ! ways total probability = 1 * 1 / 6 * 5 / 6 * 4 / 6 * 4 ! / 2 ! = 5 / 9 answer : b

divide(multiply(multiply(multiply(choose(4, 2), const_6), const_5), const_4), power(const_6, const_4))

<gadget id="calculator">binomial(4, 2)</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 * 5</gadget>
<output>180</output>
<gadget id="calculator">180 * 4</gadget>
<output>720</output>
<gadget id="calculator">6 ** 4</gadget>
<output>1_296</output>
<gadget id="calculator">720 / 1_296</gadget>
<output>5/9 = around 0.555556</output>
<result>5/9 = around 0.555556</result>


a boat having a length 7 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :

Explanation: "volume of water displaced = ( 7 x 3 x 0.01 ) m 3 = 0.21 m 3 . mass of man = volume of water displaced x density of water = ( 0.21 x 1000 ) kg = 210 kg . answer : e"

multiply(multiply(multiply(7, 3), divide(1, const_100)), const_1000)

<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">21 * (1/100)</gadget>
<output>21/100 = around 0.21</output>
<gadget id="calculator">(21/100) * 1_000</gadget>
<output>210</output>
<result>210</result>


in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 50 overs to reach the target of 282 runs ?

Explanation: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 50 run rate needed = 250 / 50 = 5 answer : option d"

divide(subtract(282, multiply(10, 3.2)), 50)

<gadget id="calculator">10 * 3.2</gadget>
<output>32</output>
<gadget id="calculator">282 - 32</gadget>
<output>250</output>
<gadget id="calculator">250 / 50</gadget>
<output>5</output>
<result>5</result>


the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 0.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?

Explanation: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 0.50 + 0.50 ( x − 2 ) = 0.50 + . 5 * 3 = 0.5 + 1.5 = 2 $ answer a"

add(0.50, multiply(0.50, subtract(add(divide(subtract(18, 2), 4), const_1), 2)))

<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<gadget id="calculator">16 / 4</gadget>
<output>4</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">0.5 * 3</gadget>
<output>1.5</output>
<gadget id="calculator">0.5 + 1.5</gadget>
<output>2</output>
<result>2</result>


if a : b : : 3 : 7 , then what is ( 5 a + 2 b ) : ( a - 2 b ) ?

Explanation: "a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 2 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 2 ] / [ ( 3 / 7 ) - 2 ] = - 29 / 11 answer : d"

divide(add(multiply(5, 3), multiply(7, 2)), subtract(3, multiply(2, 7)))

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<gadget id="calculator">15 + 14</gadget>
<output>29</output>
<gadget id="calculator">2 * 7</gadget>
<output>14</output>
<gadget id="calculator">3 - 14</gadget>
<output>-11</output>
<gadget id="calculator">29 / (-11)</gadget>
<output>-29/11 = around -2.636364</output>
<result>-29/11 = around -2.636364</result>


in a group of 100 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?

Explanation: number of people whose age is less than 20 is given by 100 - 90 = 10 probability p that a person selected at random from the group is less than 20 is given by 10 / 100 = 0.1 correct answer a

<gadget id="calculator">100 - 90</gadget>
<output>10</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<result>1/10 = around 0.1</result>


an article is bought for rs . 1200 and sold for rs . 800 , find the loss percent ?

Explanation: "1200 - - - - 400 100 - - - - ? = > 33 % answer : c"

subtract(const_100, divide(multiply(800, const_100), 1200))

<gadget id="calculator">800 * 100</gadget>
<output>80_000</output>
<gadget id="calculator">80_000 / 1_200</gadget>
<output>200/3 = around 66.666667</output>
<gadget id="calculator">100 - (200/3)</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


how much is 80 % of 45 is greater than 4 / 5 of 25 ?

Explanation: "( 80 / 100 ) * 45 â € “ ( 4 / 5 ) * 25 36 - 20 = 16 answer : c"

subtract(multiply(45, divide(80, const_100)), multiply(divide(4, 5), 25))

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">45 * (4/5)</gadget>
<output>36</output>
<gadget id="calculator">4 / 5</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) * 25</gadget>
<output>20</output>
<gadget id="calculator">36 - 20</gadget>
<output>16</output>
<result>16</result>


if p ( a ) = 5 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .

Explanation: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 5 / 7 . 2 / 5 p ( a n b ) = 2 / 7 . d"

<gadget id="calculator">5 / 7</gadget>
<output>5/7 = around 0.714286</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(5/7) * (2/5)</gadget>
<output>2/7 = around 0.285714</output>
<result>2/7 = around 0.285714</result>


in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?

Explanation: "20 * 10 * 5 = 1000 answer : b"

<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 5</gadget>
<output>1_000</output>
<result>1_000</result>


in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 3 / 5 of the way by bus , and the remaining 2 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?

Explanation: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 3 x + 3 / 5 x + 2 x - 1 / 3 x - 3 / 5 x = 2 x = 30 km option : a"

multiply(2, inverse(subtract(1, add(divide(1, 3), divide(3, 5)))))

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(1/3) + (3/5)</gadget>
<output>14/15 = around 0.933333</output>
<gadget id="calculator">1 - (14/15)</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">1 / (1/15)</gadget>
<output>15</output>
<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<result>30</result>


a factory produces 6500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?

Explanation: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 6500 / 5 = 1300 toys correct answer c"

<gadget id="calculator">6_500 / 5</gadget>
<output>1_300</output>
<result>1_300</result>


the charge for a single room at hotel p is 20 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?

Explanation: "let rate in r = 100 x then p = 80 x g = 100 y p = 90 y thus 80 x = 90 y or x = 1.125 y ans r = 112.5 y so increase = 12.5 % answer : c"

multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 20), subtract(const_100, 10)), const_100)), multiply(divide(subtract(const_100, 20), subtract(const_100, 10)), const_100)), const_100)

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">80 / 90</gadget>
<output>8/9 = around 0.888889</output>
<gadget id="calculator">(8/9) * 100</gadget>
<output>800/9 = around 88.888889</output>
<gadget id="calculator">100 - (800/9)</gadget>
<output>100/9 = around 11.111111</output>
<gadget id="calculator">(100/9) / (800/9)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 144 ) . what is the slope of line m ?

Explanation: the midpoint of ( 2,8 ) and ( 14,4 ) is ( 8,6 ) . the slope of a line through ( 0 , - 2 ) and ( 8,6 ) is ( 6 - ( - 2 ) ) / ( 8 - 0 ) = 8 / 8 = 1 the answer is d .

divide(divide(add(8, reminder(144, const_10)), const_2), subtract(divide(add(2, divide(subtract(144, reminder(144, const_10)), const_10)), const_2), 2))

<gadget id="calculator">144 % 10</gadget>
<output>4</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 / 2</gadget>
<output>6</output>
<gadget id="calculator">144 - 4</gadget>
<output>140</output>
<gadget id="calculator">140 / 10</gadget>
<output>14</output>
<gadget id="calculator">2 + 14</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">6 / 6</gadget>
<output>1</output>
<result>1</result>


the average weight of a , b and c is 60 kg . if the average weight of a and b be 70 kg and that of b and c be 50 kg , then the weight of b is :

Explanation: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 60 x 3 ) = 180 â € ¦ . ( i ) a + b = ( 70 x 2 ) = 140 â € ¦ . ( ii ) b + c = ( 50 x 2 ) = 100 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 240 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 60 . b â € ™ s weight = 60 kg . answer b"

subtract(add(multiply(70, const_2), multiply(50, const_2)), multiply(60, const_3))

<gadget id="calculator">70 * 2</gadget>
<output>140</output>
<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">140 + 100</gadget>
<output>240</output>
<gadget id="calculator">60 * 3</gadget>
<output>180</output>
<gadget id="calculator">240 - 180</gadget>
<output>60</output>
<result>60</result>


length of a rectangular plot is 22 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?

Explanation: "let breadth = x metres . then , length = ( x + 22 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 22 ) + x ] = 200 2 x + 22 = 100 2 x = 78 x = 39 . hence , length = x + 22 = 61 m b"

divide(add(divide(5300, 26.50), multiply(const_2, 22)), const_4)

<gadget id="calculator">5_300 / 26.5</gadget>
<output>200</output>
<gadget id="calculator">2 * 22</gadget>
<output>44</output>
<gadget id="calculator">200 + 44</gadget>
<output>244</output>
<gadget id="calculator">244 / 4</gadget>
<output>61</output>
<result>61</result>


a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 600 , what is the reduced price for kg ?

Explanation: "600 * ( 20 / 100 ) = 120 - - - - 4 ? - - - - 1 = > rs . 30 answer : d"

divide(divide(multiply(600, 20), const_100), 4)

<gadget id="calculator">600 * 20</gadget>
<output>12_000</output>
<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>
<gadget id="calculator">120 / 4</gadget>
<output>30</output>
<result>30</result>


after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 2500 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?

Explanation: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 2500 = 18000 exp in % = 100 - 10 = 90 % , 18000 = 90 % saving = 10 % = 18000 x 10 / 90 = rs . 2000 answer : c"

<gadget id="calculator">5_000 + 1_500</gadget>
<output>6_500</output>
<gadget id="calculator">6_500 + 4_500</gadget>
<output>11_000</output>
<gadget id="calculator">11_000 + 2_500</gadget>
<output>13_500</output>
<gadget id="calculator">13_500 + 2_000</gadget>
<output>15_500</output>
<gadget id="calculator">15_500 + 2_500</gadget>
<output>18_000</output>
<gadget id="calculator">18_000 * 100</gadget>
<output>1_800_000</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">1_800_000 / 90</gadget>
<output>20_000</output>
<gadget id="calculator">20_000 - 18_000</gadget>
<output>2_000</output>
<result>2_000</result>


jim drove 384 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?

Explanation: "the number of miles to drive to finish his journey is given by 1200 - 384 = 816 miles correct answer d"

<gadget id="calculator">1_200 - 384</gadget>
<output>816</output>
<result>816</result>


find the product of the local value and absolute value of 4 in 564823

Explanation: explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 x 4 = 16000 answer : option c

<gadget id="calculator">4 * 1_000</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 * 4</gadget>
<output>16_000</output>
<result>16_000</result>


the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 60 . the banker â € ™ s discount is

Explanation: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 60 x 100 / 10 x 3 ) = rs . 200 . b . d = rs ( 200 + 60 ) = rs . 260 . answer e"

add(divide(multiply(60, const_100), multiply(3, 10)), 60)

<gadget id="calculator">60 * 100</gadget>
<output>6_000</output>
<gadget id="calculator">3 * 10</gadget>
<output>30</output>
<gadget id="calculator">6_000 / 30</gadget>
<output>200</output>
<gadget id="calculator">200 + 60</gadget>
<output>260</output>
<result>260</result>


robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?

Explanation: "let original salary be $ 100 salary after decreasing 70 % = 100 - 100 x 70 / 100 = $ 30 salary after increasing 70 % on $ 30 = 30 + 30 x 70 / 100 = $ 51 percentage of loss = 100 - 51 = 49 % answer : e"

multiply(divide(subtract(multiply(const_100, const_100), multiply(subtract(const_100, 70), add(const_100, 70))), multiply(const_100, const_100)), const_100)

<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">100 - 70</gadget>
<output>30</output>
<gadget id="calculator">100 + 70</gadget>
<output>170</output>
<gadget id="calculator">30 * 170</gadget>
<output>5_100</output>
<gadget id="calculator">10_000 - 5_100</gadget>
<output>4_900</output>
<gadget id="calculator">4_900 / 10_000</gadget>
<output>49/100 = around 0.49</output>
<gadget id="calculator">(49/100) * 100</gadget>
<output>49</output>
<result>49</result>


the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number e ?

Explanation: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = e answer : b"

divide(30, subtract(add(const_1, divide(12.5, const_100)), subtract(const_1, divide(25, const_100))))

<gadget id="calculator">12.5 / 100</gadget>
<output>0.125</output>
<gadget id="calculator">1 + 0.125</gadget>
<output>1.125</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1.125 - (3/4)</gadget>
<output>0.375</output>
<gadget id="calculator">30 / 0.375</gadget>
<output>80</output>
<result>80</result>


what is the remainder when you divide 2 ^ 200 - 3 by 7 ?

Explanation: answer is a . this is very similar to the 32 ^ 32 ^ 32 - 3 divided by 7 question .

<gadget id="calculator">200 * 2</gadget>
<output>400</output>
<gadget id="calculator">400 % 3</gadget>
<output>1</output>
<result>1</result>


if ( log 5 5 ) ( log 4 9 ) ( log 3 2 ) is equal to

Explanation: solution given expression = log 9 / log 4 × log 2 / log 3 ‹ = › log 3 ² / log 2 ² × log 2 / log 3 = 2 log 3 / 2 log 2 × log 2 / log 3 = 1 . answer a

<gadget id="calculator">log(5)</gadget>
<output>log(5) = around 1.609438</output>
<gadget id="calculator">log(5) / log(5)</gadget>
<output>1</output>
<result>1</result>


the total marks obtained by a student in mathematics and physics is 32 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

Explanation: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 32 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 32 + 20 ) / 2 = 26 . answer : b"

<gadget id="calculator">32 + 20</gadget>
<output>52</output>
<gadget id="calculator">52 / 2</gadget>
<output>26</output>
<result>26</result>


in the rectangular coordinate system , if the line x = 4 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?

Explanation: "x = 4 y + 5 , and thus y = x / 4 - 5 / 4 the slope is 1 / 4 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 4 and thus p = 1 / 2 the answer is c ."

<gadget id="calculator">2 / 4</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


the average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student . the weight of the student is

Explanation: explanation : let the weight of student be x kg . given , difference in average weight = 8 kg = > ( 96 - x ) / 4 = 8 = > x = 64 answer : c

<gadget id="calculator">4 * 8</gadget>
<output>32</output>
<gadget id="calculator">96 - 32</gadget>
<output>64</output>
<result>64</result>


if 4 men working 10 hours a day earn rs . 800 per week , then 9 men working 6 hours a day will earn how much per week ?

Explanation: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 800 : x hence 4 * 10 * x = 9 * 6 * 800 or x = 9 * 6 * 800 / 4 * 10 = 1080 answer : c"

multiply(divide(multiply(9, 6), multiply(4, 10)), 800)

<gadget id="calculator">9 * 6</gadget>
<output>54</output>
<gadget id="calculator">4 * 10</gadget>
<output>40</output>
<gadget id="calculator">54 / 40</gadget>
<output>27/20 = around 1.35</output>
<gadget id="calculator">(27/20) * 800</gadget>
<output>1_080</output>
<result>1_080</result>


in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ?

Explanation: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 4.5 + 4.5 = 9 area = 1 / 2 * 16 * 9 = 72 b is the answer"

rhombus_area(multiply(8, const_2), multiply(4.5, const_2))

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">4.5 * 2</gadget>
<output>9</output>
<gadget id="calculator">(16 * 9) / 2</gadget>
<output>72</output>
<result>72</result>


a theater box office sold an average ( arithmetic mean ) of 63 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 78 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?

Explanation: deviation from the mean for the daytime staff = 78 - 63 = 15 . deviation from the mean for the evening staff = 63 - 60 = 3 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 3 : 15 = 1 : 5 . the answer is c .

divide(subtract(63, 60), subtract(78, 63))

<gadget id="calculator">63 - 60</gadget>
<output>3</output>
<gadget id="calculator">78 - 63</gadget>
<output>15</output>
<gadget id="calculator">3 / 15</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


a train running at the speed of 100 km / hr crosses a pole in 9 sec . what is the length of the train ?

Explanation: "speed = 100 * 5 / 18 = 250 / 9 m / sec length of the train = speed * time = 250 / 9 * 9 = 250 m answer : b"

multiply(divide(multiply(100, const_1000), const_3600), 9)

<gadget id="calculator">100 * 1_000</gadget>
<output>100_000</output>
<gadget id="calculator">100_000 / 3_600</gadget>
<output>250/9 = around 27.777778</output>
<gadget id="calculator">(250/9) * 9</gadget>
<output>250</output>
<result>250</result>


an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 45 meters . how many times did the ball bounce ?

Explanation: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 going up = 1 - - > total = 45 ( caught ) no of bounce = 4 answer : b"

<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>


average between 2 sets of numbers is closer to the set with more no ' s ?

Explanation: "if on a test three people answered 90 % of the questions correctly and two people answered 80 % correctly , then the average for the group is not 85 % but rather 3 × 90 + 2 × 805 = 4305 = 86.3 × 90 + 2 × 805 = 4305 = 86 . here , 90 has a weight of 3 = > it occurs 3 times . whereas 80 has a weight of 2 = > it occurs 2 times . so the average is closer to 90 than to 80 as we have just calculated . b"

<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">8 * 10</gadget>
<output>80</output>
<result>80</result>


a merchant marks his goods up by 30 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?

Explanation: "let the price be 100 . the price becomes 130 after a 30 % markup . now a discount of 10 % on 130 . profit = 117 - 100 17 % answer a"

subtract(subtract(add(30, const_100), divide(multiply(add(30, const_100), 10), const_100)), const_100)

<gadget id="calculator">30 + 100</gadget>
<output>130</output>
<gadget id="calculator">130 * 10</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 / 100</gadget>
<output>13</output>
<gadget id="calculator">130 - 13</gadget>
<output>117</output>
<gadget id="calculator">117 - 100</gadget>
<output>17</output>
<result>17</result>


elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 46 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?

Explanation: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 46 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 46 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 46 i . e . x = 30 i . e . fixed monthly charge , y = 16 answer : option d"

<gadget id="calculator">46 * 2</gadget>
<output>92</output>
<gadget id="calculator">92 - 76</gadget>
<output>16</output>
<result>16</result>


if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 18 days , then c alone can do it in ?

Explanation: "c 9 days c = 1 / 4 - 1 / 12 – 1 / 18 = 1 / 9 = > 9 days"

divide(const_1, subtract(subtract(const_0_25, divide(const_1, 12)), divide(const_1, 18)))

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/4) - (1/12)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 / 18</gadget>
<output>1/18 = around 0.055556</output>
<gadget id="calculator">(1/6) - (1/18)</gadget>
<output>1/9 = around 0.111111</output>
<gadget id="calculator">1 / (1/9)</gadget>
<output>9</output>
<result>9</result>


on a certain day , tim invested $ 600 at 10 percent annual interest , compounded annually , and lana invested 800 at 5 percent annual interest , compounded annually . the total amount of interest earned by tim ’ s investment in the first 2 years was how much greater than the total amount of interest earned by lana ’ s investment in the first 2 years ?

Explanation: compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 600 ( 1.10 ) ^ 2 = 600 ( 1.21 ) = 726 and lana would have 800 ( 1.05 ) ^ 2 = 800 ( 1.1025 ) = 882 thus , tim earned 126 dollars , while lana earned 82 dollars the difference is $ 44 and the answer is c .

subtract(subtract(multiply(600, power(add(const_1, divide(10, const_100)), 2)), 600), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 800), 800))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>
<gadget id="calculator">600 * (121/100)</gadget>
<output>726</output>
<gadget id="calculator">726 - 600</gadget>
<output>126</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>
<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>
<gadget id="calculator">(441/400) * 800</gadget>
<output>882</output>
<gadget id="calculator">882 - 800</gadget>
<output>82</output>
<gadget id="calculator">126 - 82</gadget>
<output>44</output>
<result>44</result>


today mary ’ s father is 4 times as old as mary . 3 years ago , he was 5 times as old . how old is mary today ?

Explanation: dad ' s age = 4 m 5 * ( m - 3 ) = 4 m - 3 m = 12 the answer is d .

<gadget id="calculator">5 * 3</gadget>
<output>15</output>
<gadget id="calculator">15 - 3</gadget>
<output>12</output>
<result>12</result>


a horse is tethered to one corner of a rectangular grassy field 42 m by 26 m with a rope 16 m long . over how much area of the field can it graze ?

Explanation: "area of the shaded portion = 1 ⁄ 4 × π × ( 16 ) 2 = 201 m 2 answer c"

divide(multiply(power(16, const_2), const_pi), const_4)

<gadget id="calculator">16 ** 2</gadget>
<output>256</output>
<gadget id="calculator">256 * pi</gadget>
<output>256*pi = around 804.247719</output>
<gadget id="calculator">(256*pi) / 4</gadget>
<output>64*pi = around 201.06193</output>
<result>64*pi = around 201.06193</result>


a batsman in his 17 th innings makes a score of 85 and their by increasing his average by 3 . what is his average after the 17 thinnings ?

Explanation: "16 x + 85 = 17 ( x + 3 ) x = 34 + 3 = 37 answer : d"

<gadget id="calculator">17 * 3</gadget>
<output>51</output>
<gadget id="calculator">85 - 51</gadget>
<output>34</output>
<gadget id="calculator">34 + 3</gadget>
<output>37</output>
<result>37</result>


the average ( arithmetic mean ) of 4 different integers is 76 . if the largest integer is 90 , what is the least possible value of the smallest integer ?

Explanation: "total of integers = 76 * 4 = 3004 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 304 - ( 90 + 89 + 88 ) = 304 - 267 = 37 answer : e"

subtract(subtract(subtract(multiply(76, 4), 90), subtract(90, const_1)), subtract(90, const_2))

<gadget id="calculator">76 * 4</gadget>
<output>304</output>
<gadget id="calculator">304 - 90</gadget>
<output>214</output>
<gadget id="calculator">90 - 1</gadget>
<output>89</output>
<gadget id="calculator">214 - 89</gadget>
<output>125</output>
<gadget id="calculator">90 - 2</gadget>
<output>88</output>
<gadget id="calculator">125 - 88</gadget>
<output>37</output>
<result>37</result>


a certain elevator has a safe weight limit of 2,000 pounds . what is the greatest possible number of people who can safely ride on the elevator at one time with the average ( arithmetic mean ) weight of half the riders being 200 pounds and the average weight of the others being 230 pounds ?

Explanation: lets assume there are 2 x people . half of them have average weight of 200 and other half has 230 . maximum weight is = 2000 so 200 * x + 230 * x = 2000 = > 430 x = 2000 = > x is approximately equal to 5 . so total people is 2 * 5 = 10 we are not taking 10 as answer because say 10 th person has minimum of 200 weight then 200 * 5 + 230 * 5 = 2150 ( which is more than 2000 ) answer c .

multiply(divide(multiply(const_10, 200), add(200, 230)), const_2)

<gadget id="calculator">10 * 200</gadget>
<output>2_000</output>
<gadget id="calculator">200 + 230</gadget>
<output>430</output>
<gadget id="calculator">2_000 / 430</gadget>
<output>200/43 = around 4.651163</output>
<gadget id="calculator">(200/43) * 2</gadget>
<output>400/43 = around 9.302326</output>
<result>400/43 = around 9.302326</result>


the average salary of all the workers in a workshop is $ 8000 . the average salary of 7 technicians is $ 12000 and the average salary of the rest is $ 6000 . the total number of workers in the shop is ?

Explanation: let the total number of workers be x 8000 x = 12000 * 7 + 6000 ( x - 7 ) x = 21 answer is c

divide(subtract(multiply(7, 12000), multiply(6000, 7)), subtract(8000, 6000))

<gadget id="calculator">7 * 12_000</gadget>
<output>84_000</output>
<gadget id="calculator">6_000 * 7</gadget>
<output>42_000</output>
<gadget id="calculator">84_000 - 42_000</gadget>
<output>42_000</output>
<gadget id="calculator">8_000 - 6_000</gadget>
<output>2_000</output>
<gadget id="calculator">42_000 / 2_000</gadget>
<output>21</output>
<result>21</result>


a farmer grows broccoli in his farm that is in the shape of a square . each broccoli takes 1 square foot of area in his garden . this year , he has increased his output by 101 broccoli when compared to last year . the shape of the area used for growing the broccoli has remained a square in both these years . how many broccoli did he produce this year ?

Explanation: explanatory answer the shape of the area used for growing broccoli has remained a square in both the years . let the side of the square area used for growing broccoli this year be x ft . therefore , the area of the ground used for cultivation this year = x 2 sq . ft . let the side of the square area used for growing broccoli last year be y ft . therefore , the area of the ground used for cultivation last year = y 2 sq . ft . as the number of broccoli grown has increased by 101 , the area would have increased by 101 sq ft because each broccoli takes 1 sq ft space . hence , x 2 - y 2 = 101 ( x + y ) ( x - y ) = 101 . 101 is a prime number and hence it will have only two factors . i . e . , 101 and 1 . therefore , 101 can be expressed as product of 2 numbers in only way = 101 * 1 i . e . , ( x + y ) ( x - y ) = 101 * 1 so , ( x + y ) should be 101 and ( x - y ) should be 1 . solving the two equations we get x = 51 and y = 50 . therefore , number of broccoli produced this year = x 2 = 512 = 2601 . alternative approach : use answer choices the area in both the years are squares of two numbers . that rules out choice a , c and d . as 2400,1987 and 2000 are not the square of any number . check choice b : if this year ' s produce is 2601 , last year ' s produce would have been 2601 - 101 = 2500 2500 is the square of 50 . so , 2601 is the answer . choice b

power(divide(add(101, 1), const_2), const_2)

<gadget id="calculator">101 + 1</gadget>
<output>102</output>
<gadget id="calculator">102 / 2</gadget>
<output>51</output>
<gadget id="calculator">51 ** 2</gadget>
<output>2_601</output>
<result>2_601</result>


a person can swim in still water at 10 km / h . if the speed of water 8 km / h , how many hours will the man take to swim back against the current for 16 km ?

Explanation: "m = 10 s = 8 us = 10 - 8 = 2 d = 16 t = 16 / 2 = 8 answer : d"

<gadget id="calculator">10 - 8</gadget>
<output>2</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


90 students represent x percent of the boys at jones elementary school . if the boys at jones elementary make up 60 % of the total school population of x students , what is x ?

Explanation: "90 = x / 100 * 60 / 100 * x = > x ^ 2 = 9 * 10000 / 6 = > x = 122 a"

sqrt(divide(multiply(90, const_100), divide(60, const_100)))

<gadget id="calculator">90 * 100</gadget>
<output>9_000</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">9_000 / (3/5)</gadget>
<output>15_000</output>
<gadget id="calculator">15_000 ** (1/2)</gadget>
<output>50*sqrt(6) = around 122.474487</output>
<result>50*sqrt(6) = around 122.474487</result>


maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 65 kilometers , maxwell ' s walking speed is 2 km / h , and brad ' s running speed is 3 km / h . what is the distance traveled by maxwell when they meet in the middle ?

Explanation: "consider max starts from point a and brad starts from point b and move towards each other . assume they shall meet at point o after time ' t ' . the question asks us to find oa . from the question stem we can make out : - distance oa = 50 km - distance ob = > 2 xt = 65 - 3 xt ( i . e distance = speed x time ) = > 5 t = 65 hence t = 13 oa = 2 x 13 = 26 km answer : e"

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">65 / 5</gadget>
<output>13</output>
<gadget id="calculator">2 * 13</gadget>
<output>26</output>
<result>26</result>


the odds in favour of an events are 3 : 5 . the probability of occurrence of the event is

Explanation: number of cases favourable to e = 3 total number of cases = 3 + 5 = 8 p ( e ) = 3 / 8 answer is a

<gadget id="calculator">3 + 5</gadget>
<output>8</output>
<gadget id="calculator">3 / 8</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>


if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 3 other contributions made before john ' s , what is the size of his donation ?

Explanation: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 3 people . so $ 75 . but , he also has to put in the average for himself ( the fourth person ) , so add $ 75 . so $ 150 is your answer . answer b"

add(subtract(multiply(add(3, const_1), 75), multiply(add(3, const_1), 50)), 50)

<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">4 * 75</gadget>
<output>300</output>
<gadget id="calculator">4 * 50</gadget>
<output>200</output>
<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<gadget id="calculator">100 + 50</gadget>
<output>150</output>
<result>150</result>


in a class of 40 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?

Explanation: 26 + 20 - 17 = 29 40 - 29 = 11 play neither answer is d

<gadget id="calculator">26 + 20</gadget>
<output>46</output>
<gadget id="calculator">46 - 17</gadget>
<output>29</output>
<gadget id="calculator">40 - 29</gadget>
<output>11</output>
<result>11</result>


seller selling an apple for rs . 18 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?

Explanation: "sp = 18 loss = cp 19 loss = cp − sp = cp − 18 ⇒ cp 19 = cp − 18 ⇒ 18 cp 19 = 18 ⇒ cp 19 = 1 ⇒ cp = 19 c"

<gadget id="calculator">18 + 1</gadget>
<output>19</output>
<result>19</result>


if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 8 , what is the least possible value of n ?

Explanation: we need 3 factors of 2 , so n must be at least 4 . therefore , the answer is b .

<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>


a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 250 per month . what is his monthly salary ?

Explanation: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 250 = > 6250 answer : d"

divide(multiply(250, const_100), subtract(const_100, add(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(20, const_100)))))

<gadget id="calculator">250 * 100</gadget>
<output>25_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">80 * (1/5)</gadget>
<output>16</output>
<gadget id="calculator">80 + 16</gadget>
<output>96</output>
<gadget id="calculator">100 - 96</gadget>
<output>4</output>
<gadget id="calculator">25_000 / 4</gadget>
<output>6_250</output>
<result>6_250</result>


if 15 students in a class average 75 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?

Explanation: "( 15 * 75 + 10 * 90 ) / 25 = 81 % the answer is b ."

divide(add(multiply(15, 75), multiply(10, 90)), 25)

<gadget id="calculator">15 * 75</gadget>
<output>1_125</output>
<gadget id="calculator">10 * 90</gadget>
<output>900</output>
<gadget id="calculator">1_125 + 900</gadget>
<output>2_025</output>
<gadget id="calculator">2_025 / 25</gadget>
<output>81</output>
<result>81</result>


in a 100 m race a beats b by 25 m b beats c by 4 then a beats c by

Explanation: a : b = 100 : 75 b : c = 100 : 96 . a : c = ( a / b x b / c ) = ( 100 / 75 x 100 / 96 ) = 100 / 72 = 100 : 72 . a beats c by ( 100 - 72 ) m = 28 m . answer : e

subtract(100, divide(100, multiply(divide(100, subtract(100, 25)), divide(100, subtract(100, 4)))))

<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<gadget id="calculator">100 / 75</gadget>
<output>4/3 = around 1.333333</output>
<gadget id="calculator">100 - 4</gadget>
<output>96</output>
<gadget id="calculator">100 / 96</gadget>
<output>25/24 = around 1.041667</output>
<gadget id="calculator">(4/3) * (25/24)</gadget>
<output>25/18 = around 1.388889</output>
<gadget id="calculator">100 / (25/18)</gadget>
<output>72</output>
<gadget id="calculator">100 - 72</gadget>
<output>28</output>
<result>28</result>


for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 50 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?

Explanation: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 50 / 100 ) * 300 = 100 + 150 = 250 % comission = ( 250 / 800 ) * 100 = 31.3 ~ 31 % answer is e"

multiply(divide(add(multiply(divide(20, const_100), 500), multiply(divide(50, const_100), subtract(800, 500))), 800), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 500</gadget>
<output>100</output>
<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">800 - 500</gadget>
<output>300</output>
<gadget id="calculator">(1/2) * 300</gadget>
<output>150</output>
<gadget id="calculator">100 + 150</gadget>
<output>250</output>
<gadget id="calculator">250 / 800</gadget>
<output>5/16 = around 0.3125</output>
<gadget id="calculator">(5/16) * 100</gadget>
<output>125/4 = around 31.25</output>
<result>125/4 = around 31.25</result>


a man swims downstream 60 km and upstream 100 km taking 10 hours each time , what is the speed of the man in still water ?

Explanation: "60 - - - 10 ds = 6 ? - - - - 1 100 - - - - 10 us = 10 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : d"

divide(add(divide(100, 10), divide(60, 10)), const_2)

<gadget id="calculator">100 / 10</gadget>
<output>10</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<gadget id="calculator">10 + 6</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


a light flashes every 30 seconds , how many times will it flash in ? of an hour ?

Explanation: 1 flash = 30 sec for 1 min = 2 flashes so for 1 hour = 2 * 60 = 120 flashes . answer : e

<gadget id="calculator">3_600 / 30</gadget>
<output>120</output>
<result>120</result>


tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 100 ?

Explanation: "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is e"

divide(subtract(multiply(100, 30), 1800), subtract(100, 50))

<gadget id="calculator">100 * 30</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 - 1_800</gadget>
<output>1_200</output>
<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<gadget id="calculator">1_200 / 50</gadget>
<output>24</output>
<result>24</result>


at an election 2 candidates are participated and a candidate got 20 % of votes and defeated by 500 . and 10 votes are invalid . find the total polled votes ?

Explanation: "winner votes = 100 - 20 = 80 polled votes = [ ( 100 * 500 ) / 2 * 80 - 100 ] + 10 = 843 ( approximately ) answer is a"

divide(add(500, 10), subtract(const_1, divide(multiply(20, 2), const_100)))

<gadget id="calculator">500 + 10</gadget>
<output>510</output>
<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">510 / (3/5)</gadget>
<output>850</output>
<result>850</result>


a cat chases a rat 6 hours after the rat runs . cat takes 4 hours to reach the rat . if the average speed of the cat is 90 kmph , what s the average speed of the rat ?

Explanation: cat take 10 hours and rat take 4 hours . . . then distance chased by them is 90 * 4 . so speed of rat is ( 90 * 4 ) / 10 = 36 kmph . answer is d

<gadget id="calculator">90 * 4</gadget>
<output>360</output>
<gadget id="calculator">4 + 6</gadget>
<output>10</output>
<gadget id="calculator">360 / 10</gadget>
<output>36</output>
<result>36</result>


average of 5 consecutive even numbers is 35 . find the greatest number in these 5 numbers ?

Explanation: 39 option ' c '

divide(add(multiply(5, 35), add(add(add(add(const_2, const_2), const_2), const_2), add(add(add(const_2, const_2), const_2), add(add(const_2, const_2), const_2)))), 5)

<gadget id="calculator">5 * 35</gadget>
<output>175</output>
<gadget id="calculator">2 + 2</gadget>
<output>4</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 2</gadget>
<output>8</output>
<gadget id="calculator">6 + 6</gadget>
<output>12</output>
<gadget id="calculator">8 + 12</gadget>
<output>20</output>
<gadget id="calculator">175 + 20</gadget>
<output>195</output>
<gadget id="calculator">195 / 5</gadget>
<output>39</output>
<result>39</result>


a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . what is the area of the wall photo , in square inches ?

Explanation: this question is an example of a ' punch out ' question - we have to find the area of everything , then ' punch out ' the part that we do n ' t want . we ' re told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . we ' re asked for the area of the wall photo , in square inches . area of a rectangle = ( length ) ( width ) so the area of the wall photo is . . . ( 8 ) ( 12 ) = 96 the wall photo ' adds ' 2 inches to the top , bottom , left and right ' sides ' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we ' punch out ' the area of the paper , we ' ll be left with the area of the wall photo : 192 - 96 = 96 final answer : a

subtract(multiply(multiply(8, 2), 12), rectangle_area(8, 12))

<gadget id="calculator">8 * 2</gadget>
<output>16</output>
<gadget id="calculator">16 * 12</gadget>
<output>192</output>
<gadget id="calculator">8 * 12</gadget>
<output>96</output>
<gadget id="calculator">192 - 96</gadget>
<output>96</output>
<result>96</result>


the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle

Explanation: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : option b"

<gadget id="calculator">(2.5 * 36) / 2</gadget>
<output>45</output>
<result>45</result>


john found that the average of 15 no . ' s is 40 . if 10 is added to each number then the mean of number is ?

Explanation: ( x + x 1 + . . . x 14 ) / 15 = 40 50 option a

<gadget id="calculator">40 + 10</gadget>
<output>50</output>
<result>50</result>


a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 2000 in march , how many cars does he need to sell in april in order to double his march earnings ?

Explanation: 1000 + 200 x = 4000 x = 15 cars . the answer is b .

divide(subtract(multiply(2000, const_2), 1000), 200)

<gadget id="calculator">2_000 * 2</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 - 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 200</gadget>
<output>15</output>
<result>15</result>


barbata invests $ 2200 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?

Explanation: "let the additional invested amount for 8 % interest be x ; equation will be ; 2200 + 0.05 * 2200 + x + 0.08 x = 2200 + x + 0.06 ( 2200 + x ) 0.05 * 2200 + 0.08 x = 0.06 x + 0.06 * 2200 0.02 x = 2200 ( 0.06 - 0.05 ) x = 2200 * 0.01 / 0.02 = 1100 ans : ` ` a ' '"

divide(subtract(multiply(divide(6, const_100), 2200), multiply(2200, divide(5, const_100))), subtract(divide(8, const_100), divide(6, const_100)))

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">(3/50) * 2_200</gadget>
<output>132</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">2_200 * (1/20)</gadget>
<output>110</output>
<gadget id="calculator">132 - 110</gadget>
<output>22</output>
<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) - (3/50)</gadget>
<output>1/50 = around 0.02</output>
<gadget id="calculator">22 / (1/50)</gadget>
<output>1_100</output>
<result>1_100</result>


24 lbs of coffee p and 25 lbs of coffee v are mixed to make coffee x and y . the ratio of p to v in coffee x is 4 to 1 , in y is 1 to 5 . how much of p is contained in the mixture x ?

Explanation: let there be 4 x lbs of p in x and x lbs of v in x let there be y lbs of p in y and 5 y lbs of v in y now total p is 4 x + y = 24 and total q is x + 5 y = 25 solving the two equations , we get x = 5 and y = 4 mixture x has 4 x lbs of p = 4 x = 4 * 5 = 20 lbs answer : b

multiply(divide(subtract(multiply(24, 5), 25), subtract(24, 5)), 4)

<gadget id="calculator">24 * 5</gadget>
<output>120</output>
<gadget id="calculator">120 - 25</gadget>
<output>95</output>
<gadget id="calculator">24 - 5</gadget>
<output>19</output>
<gadget id="calculator">95 / 19</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<result>20</result>


the average of 10 numbers is 0 . in those 10 , at the least , how many may be greater than or equal to zero ?

Explanation: explanation : average of 10 numbers = 0 sum of 10 numbers = ( 0 x 10 ) = 0 . it is quite possible that 9 of these numbers may be negative and if there sum is - a , then 10 th number is ( a ) . answer : b

<gadget id="calculator">0 + 1</gadget>
<output>1</output>
<result>1</result>


if x + y = 260 , x - y = 200 , for integers of x and y , y = ?

Explanation: "x + y = 260 x - y = 200 2 x = 60 x = 30 y = 230 answer is b"

<gadget id="calculator">260 + 200</gadget>
<output>460</output>
<gadget id="calculator">460 / 2</gadget>
<output>230</output>
<result>230</result>


a man can row 24 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?

Explanation: "let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 24 x = 12 rate of upstream = 12 rate of downstream = 36 rate of stream 1 / 2 ( 36 - 12 ) = 12 kmph answer is b ."

divide(multiply(24, const_2), add(const_3, const_1))

<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>


a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 36.00 , how much did he pay for it ?

Explanation: "let the cost price of book = x selling price of book = 36 $ markup % = 20 ( 120 / 100 ) x = 36 = > x = 30 answer d"

subtract(36.00, multiply(divide(20, const_100), 36.00))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 36</gadget>
<output>36/5 = around 7.2</output>
<gadget id="calculator">36 - (36/5)</gadget>
<output>144/5 = around 28.8</output>
<result>144/5 = around 28.8</result>


the hcf of two numbers is 42 and the other two factors of their lcm are 10 and 20 . what is the largest number .

Explanation: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 10 & 20 then the numbers are ( 42 * 10 ) and ( 42 x 20 ) = 420 and 840 answer : option c"

<gadget id="calculator">42 * 20</gadget>
<output>840</output>
<result>840</result>


suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 92 runs thereby increasing his average by 4 runs . what is his average after the 17 th innings ?

Explanation: to improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings . thus , the average after the 17 th innings = 92 - 64 = 28 . answer : c

divide(subtract(92, multiply(16, 4)), subtract(17, 16))

<gadget id="calculator">16 * 4</gadget>
<output>64</output>
<gadget id="calculator">92 - 64</gadget>
<output>28</output>
<gadget id="calculator">17 - 16</gadget>
<output>1</output>
<gadget id="calculator">28 / 1</gadget>
<output>28</output>
<result>28</result>


a dog have birth to 12 puppies , 2 female and 10 male . what is the ratio of the female puppies to the male ?

Explanation: if female is 2 and male is 10 , then 1 / 5 . so ratio of female to male is = 2 / 10 = 1 / 5 answer : a

<gadget id="calculator">2 / 10</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


a box contains 6 black , 8 red and 4 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?

Explanation: "explanation : total marbles in a box = 6 black + 8 red + 4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random . therefore , n ( s ) = 18 c 2 = 153 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 2 + 8 c 2 + 4 c 2 = 15 + 28 + 6 = 49 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 49 / 153 answer : a"

divide(add(add(const_3.0, 4), add(const_10, add(const_3.0, 2))), multiply(add(const_10, 8), 4))

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">7 + 15</gadget>
<output>22</output>
<gadget id="calculator">10 + 8</gadget>
<output>18</output>
<gadget id="calculator">18 * 4</gadget>
<output>72</output>
<gadget id="calculator">22 / 72</gadget>
<output>11/36 = around 0.305556</output>
<result>11/36 = around 0.305556</result>


a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be

Explanation: "explanation : let number of hens = h and number of cows = c number of heads = 48 = > h + c = 48 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 48 = > c = 20 substituting the value of c in equation 1 , we get h + 20 = 48 = > h = 48 - 20 = 28 i . e . , number of hens = 28 answer : e"

divide(subtract(multiply(48, const_4), 136), const_2)

<gadget id="calculator">48 * 4</gadget>
<output>192</output>
<gadget id="calculator">192 - 136</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


the average of 25 results is 20 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?

Explanation: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 20 or , x = 128 . answer : option a"

subtract(subtract(multiply(25, 20), multiply(12, 17)), multiply(12, 14))

<gadget id="calculator">25 * 20</gadget>
<output>500</output>
<gadget id="calculator">12 * 17</gadget>
<output>204</output>
<gadget id="calculator">500 - 204</gadget>
<output>296</output>
<gadget id="calculator">12 * 14</gadget>
<output>168</output>
<gadget id="calculator">296 - 168</gadget>
<output>128</output>
<result>128</result>


if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be

Explanation: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .

multiply(divide(divide(divide(divide(add(add(multiply(const_3, const_1000), divide(const_100, const_2)), const_100), const_2), power(add(const_3, const_2), const_2)), const_3), const_3), const_2)

<gadget id="calculator">3 * 1_000</gadget>
<output>3_000</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">3_000 + 50</gadget>
<output>3_050</output>
<gadget id="calculator">3_050 + 100</gadget>
<output>3_150</output>
<gadget id="calculator">3_150 / 2</gadget>
<output>1_575</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 ** 2</gadget>
<output>25</output>
<gadget id="calculator">1_575 / 25</gadget>
<output>63</output>
<gadget id="calculator">63 / 3</gadget>
<output>21</output>
<gadget id="calculator">21 / 3</gadget>
<output>7</output>
<gadget id="calculator">7 * 2</gadget>
<output>14</output>
<result>14</result>


x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14190 ?

Explanation: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14190 ã — 16 / 55 = rs . 4128 . share of z in the profit is rs . 4128 . option d"

multiply(multiply(48000, subtract(multiply(const_3, 4), 4)), divide(14190, add(add(multiply(36000, multiply(const_3, 4)), multiply(42000, multiply(const_3, 4))), multiply(48000, subtract(multiply(const_3, 4), 4)))))

<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 - 4</gadget>
<output>8</output>
<gadget id="calculator">48_000 * 8</gadget>
<output>384_000</output>
<gadget id="calculator">36_000 * 12</gadget>
<output>432_000</output>
<gadget id="calculator">42_000 * 12</gadget>
<output>504_000</output>
<gadget id="calculator">432_000 + 504_000</gadget>
<output>936_000</output>
<gadget id="calculator">936_000 + 384_000</gadget>
<output>1_320_000</output>
<gadget id="calculator">14_190 / 1_320_000</gadget>
<output>43/4_000 = around 0.01075</output>
<gadget id="calculator">384_000 * (43/4_000)</gadget>
<output>4_128</output>
<result>4_128</result>


there are 250 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?

Explanation: "the number of nurses at the hospital is ( 3 / 5 ) * 250 = 150 . the answer is e ."

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">250 / 5</gadget>
<output>50</output>
<gadget id="calculator">50 * 3</gadget>
<output>150</output>
<result>150</result>


in an examination , 300 students appeared . out of these students ; 26 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .

Explanation: "the number of students with first division = 26 % of 300 = 26 / 100 × 300 = 7800 / 100 = 78 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 78 + 162 ) = 60 answer : d"

divide(multiply(300, subtract(const_100, add(26, 54))), const_100)

<gadget id="calculator">26 + 54</gadget>
<output>80</output>
<gadget id="calculator">100 - 80</gadget>
<output>20</output>
<gadget id="calculator">300 * 20</gadget>
<output>6_000</output>
<gadget id="calculator">6_000 / 100</gadget>
<output>60</output>
<result>60</result>


on a certain transatlantic crossing , 30 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?

Explanation: "0.30 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.30 p = 0.40 ( rt ) rt / p = 3 / 4 = 75 % answer - e"

divide(30, divide(subtract(const_100, 60), const_100))

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">30 / (2/5)</gadget>
<output>75</output>
<result>75</result>


students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio d of men to women ?

Explanation: ( a ) d = 184 x 5 + 170 x 2 = 1260 . a

divide(subtract(180, 170), subtract(184, 180))

<gadget id="calculator">180 - 170</gadget>
<output>10</output>
<gadget id="calculator">184 - 180</gadget>
<output>4</output>
<gadget id="calculator">10 / 4</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>


at what rate of compound interest per annum will a sum of $ 1200 becomes 1348.32 in 2 years ?

Explanation: "let the rate be r % p . a . 1200 * ( 1 + r / 100 ) ^ 2 = 1348.32 ( 1 + r / 100 ) ^ 2 = 134832 / 120000 = 11236 / 10000 ( 1 + r / 100 ) ^ 2 = ( 106 / 100 ) ^ 2 1 + r / 100 = 106 / 100 r = 6 % answer is b"

subtract(sqrt(divide(multiply(1348.32, const_100), divide(1200, const_100))), sqrt(divide(multiply(1200, const_100), divide(1200, const_100))))

<gadget id="calculator">1_348.32 * 100</gadget>
<output>134_832</output>
<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>
<gadget id="calculator">134_832 / 12</gadget>
<output>11_236</output>
<gadget id="calculator">11_236 ** (1/2)</gadget>
<output>106</output>
<gadget id="calculator">1_200 * 100</gadget>
<output>120_000</output>
<gadget id="calculator">120_000 / 12</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 ** (1/2)</gadget>
<output>100</output>
<gadget id="calculator">106 - 100</gadget>
<output>6</output>
<result>6</result>


the food in a camp lasts for 10 men for 50 days . if 10 more men join , how many days will the food last ?

Explanation: "one man can consume the same food in 10 * 50 = 500 days . 10 more men join , the total number of men = 20 the number of days the food will last = 500 / 20 = 25 days . answer : b"

<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<gadget id="calculator">10 + 10</gadget>
<output>20</output>
<gadget id="calculator">500 / 20</gadget>
<output>25</output>
<result>25</result>


a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 6 miles per day and it will take them two days , how many miles long is the route down the mountain ?

Explanation: "on the way down , the rate is 1.5 * 6 = 9 miles per day . the distance of the route down the mountain is 2 * 9 = 18 miles . the answer is c ."

multiply(multiply(6, const_2), divide(const_3, const_2))

<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">12 * (3/2)</gadget>
<output>18</output>
<result>18</result>


equal amount of water were poured into two empty jars of different capacities , which made one jar 1 / 3 full and other jar 1 / 2 full . if the water in the jar with lesser capacity is then poured into the jar with greater capacity , what fraction of the larger jar will be filled with water ?

Explanation: same amount of water made bigger jar 1 / 3 full , thenthe same amount of water ( stored for a while in smaller jar ) were added to bigger jar , so bigger jar is 1 / 3 + 1 / 3 = 2 / 3 full . answer : a .

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<result>2/3 = around 0.666667</result>


a certain candy manufacturer reduced the weight of candy bar m by 5 percent buy left the price unchanged . what was the resulting percent increase in the price per ounce of candy bar m ?

Explanation: assume 1 oz candy cost $ 1 before . now price remain same $ 1 but weight of candy reduces to 0.95 oz new price of candy = 1 / 0.95 = 1.052 price increase 5.2 % d

subtract(multiply(divide(const_1, subtract(const_1, divide(5, const_100))), const_100), const_100)

<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>
<gadget id="calculator">1 / (19/20)</gadget>
<output>20/19 = around 1.052632</output>
<gadget id="calculator">(20/19) * 100</gadget>
<output>2_000/19 = around 105.263158</output>
<gadget id="calculator">(2_000/19) - 100</gadget>
<output>100/19 = around 5.263158</output>
<result>100/19 = around 5.263158</result>


mary ' s income is 60 percent more than tim ' s income , and tim ' s income is 60 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?

Explanation: "juan ' s income = 100 ( assume ) ; tim ' s income = 40 ( 60 percent less than juan ' s income ) ; mary ' s income = 64 ( 60 percent more than tim ' s income ) . thus , mary ' s income ( 64 ) is 64 % of juan ' s income ( 100 ) . answer : a ."

multiply(multiply(subtract(const_1, divide(60, const_100)), add(const_1, divide(60, const_100))), const_100)

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>
<gadget id="calculator">(2/5) * (8/5)</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">(16/25) * 100</gadget>
<output>64</output>
<result>64</result>


12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 7 .

Explanation: d = d * q + r d = 17 * 9 + 7 d = 153 + 7 d = 160 answer e

<gadget id="calculator">17 * 9</gadget>
<output>153</output>
<gadget id="calculator">153 + 7</gadget>
<output>160</output>
<result>160</result>


if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs 1920 less than the principal . what was the principal ?

Explanation: "p - 1920 = ( p * 5 * 4 ) / 100 p = 2400 answer : e"

divide(1920, subtract(const_1, divide(multiply(4, 5), const_100)))

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">1_920 / (4/5)</gadget>
<output>2_400</output>
<result>2_400</result>


the diagonals of a rhombus are 15 cm and 20 cm . find its area ?

Explanation: "1 / 2 * 15 * 20 = 150 answer : c"

<gadget id="calculator">(15 * 20) / 2</gadget>
<output>150</output>
<result>150</result>


if 1 / ( x + 4 ) + 1 / ( x - 4 ) = 1 / ( x - 4 ) , what is the value of x ?

Explanation: "if we solve the question , we get x = 4 . option : b"

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<result>4</result>


the average of 9 observations was 8 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?

Explanation: explanation : 1 to 9 = 8 * 9 = 72 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 72 = 18 option a

subtract(add(multiply(10, 5), multiply(8, 5)), multiply(8, 9))

<gadget id="calculator">10 * 5</gadget>
<output>50</output>
<gadget id="calculator">8 * 5</gadget>
<output>40</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<gadget id="calculator">8 * 9</gadget>
<output>72</output>
<gadget id="calculator">90 - 72</gadget>
<output>18</output>
<result>18</result>


sophia finished 2 / 3 of a book . she calculated that she finished 30 more pages than she has yet to read . how long is her book ?

Explanation: "let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 30 1 / 3 * x = 30 x = 90 so the book is 90 pages long . answer is a ."

divide(30, subtract(const_1, divide(2, 3)))

<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">1 - (2/3)</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">30 / (1/3)</gadget>
<output>90</output>
<result>90</result>


Explanation: let 3252 / 3257 be the original fraction . notice that it is a positive proper fraction . hence adding the same constant to both the numerator and the denominator will increase the fraction as the fraction will move closer to one . hence we just have to pick the number that adds the greatest value to both the numerator and the denominator . options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3351 ) e ) 1 - ( 5 / 3458 ) answer : c

divide(subtract(const_3600, multiply(const_3, const_3)), subtract(const_3600, const_4))

<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">3_600 - 9</gadget>
<output>3_591</output>
<gadget id="calculator">3_600 - 4</gadget>
<output>3_596</output>
<gadget id="calculator">3_591 / 3_596</gadget>
<output>3_591/3_596 = around 0.99861</output>
<result>3_591/3_596 = around 0.99861</result>


if there are 200 questions in a 3 hr examination . among these questions are 100 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?

Explanation: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 100 x + 100 * 2 x = 180 x = 180 / 300 x = 0.6 time taken for type a problem = 100 * 2 * 0.6 = 120 min answer : e"

multiply(multiply(const_2, divide(multiply(3, const_60), add(subtract(200, 100), multiply(const_2, 100)))), 100)

<gadget id="calculator">3 * 60</gadget>
<output>180</output>
<gadget id="calculator">200 - 100</gadget>
<output>100</output>
<gadget id="calculator">2 * 100</gadget>
<output>200</output>
<gadget id="calculator">100 + 200</gadget>
<output>300</output>
<gadget id="calculator">180 / 300</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">2 * (3/5)</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">(6/5) * 100</gadget>
<output>120</output>
<result>120</result>


a and b are 90 km apart they start to move each other simultaneously a at speed 10 and b at 5 km / hr if every hour they double their speed what is distance that a pass until he meet b ?

Explanation: in 2 hours a covers ( 10 + 20 ) = 30 km b covers ( 5 + 10 ) = 15 km , total covered = 45 in the next hour they have to cover ( 90 - 45 ) km with the speeds 40 km / hr and 20 km / hr respectively let them take another t hrs to meet so sum of the distance to be covered by both is 45 km ( 40 * t ) + ( 20 * t ) = 45 km gives t = ( 3 / 4 ) hrs we need to fid out the distance covered by a which equals to = 30 + ( 40 * ( 3 / 4 ) ) = 60 km answer : d

<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 * 2</gadget>
<output>30</output>
<gadget id="calculator">15 + 30</gadget>
<output>45</output>
<gadget id="calculator">15 + 45</gadget>
<output>60</output>
<result>60</result>


a card board of size 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the card box . find the total number of pins used .

Explanation: total 35 pins are there and 4 sides of card board . . . so 35 x 4 = 140 now in the rectangle 4 vertices have 4 pins which is common to the sides . . . . so 140 - 4 = 136 answer : b

add(const_100, subtract(multiply(subtract(const_10, const_1), add(const_4, const_1)), const_10))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">9 * 5</gadget>
<output>45</output>
<gadget id="calculator">45 - 10</gadget>
<output>35</output>
<gadget id="calculator">100 + 35</gadget>
<output>135</output>
<result>135</result>


a cistern can be filled by a tap in 2 hours while it can be emptied by another tap in 4 hours . if both the taps are opened simultaneously then after how much time will the cistern get filled ?

Explanation: "net part filled in 1 hour 1 / 2 - 1 / 4 = 1 / 4 the cistern will be filled in 4 hr answer is e"

divide(const_1, subtract(divide(const_1, 2), divide(const_1, 4)))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/2) - (1/4)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 / (1/4)</gadget>
<output>4</output>
<result>4</result>


evaluate combination 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) !

Explanation: explanation : ncr = n ! / ( r ) ! ( n − r ) ! 98 c 96 = 98 ! / ( 96 ) ! ( 2 ) ! = 98 ∗ 97 * 96 ! / ( 96 ) ! ( 2 ) ! = 98 * 97 / 2 ∗ 1 = 4753 option b

divide(multiply(98, subtract(98, const_1)), 2)

<gadget id="calculator">98 - 1</gadget>
<output>97</output>
<gadget id="calculator">98 * 97</gadget>
<output>9_506</output>
<gadget id="calculator">9_506 / 2</gadget>
<output>4_753</output>
<result>4_753</result>


a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 4 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?

Explanation: 3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 4 = 84 . the minimum number of horses and ponies is 164 . the answer is d .

add(add(lcm(10, multiply(divide(10, 5), 8)), 4), lcm(10, multiply(divide(10, 5), 8)))

<gadget id="calculator">10 / 5</gadget>
<output>2</output>
<gadget id="calculator">2 * 8</gadget>
<output>16</output>
<gadget id="calculator">lcm(10, 16)</gadget>
<output>80</output>
<gadget id="calculator">80 + 4</gadget>
<output>84</output>
<gadget id="calculator">84 + 80</gadget>
<output>164</output>
<result>164</result>


there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 8 other amateurs , what is the total number of chess games possible to be played in the tournament ?

Explanation: "method 2 : each person is one participant of 4 games . so there are in all 8 * 5 = 40 instances of one participant games . but each game has 2 participants so total number of games = 40 / 2 = 20 b"

<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<result>20</result>


the speed of a train is 90 kmph . what is the distance covered by it in 12 minutes ?

Explanation: 90 * 12 / 60 = 18 kmph answer : b

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 90</gadget>
<output>18</output>
<result>18</result>


in a chess competition involving some men and women , every player needs to play exactly one game with every other player . it was found that in 45 games , both the players were women and in 190 games , both players were men . what is the number of games in which one person was a man and other person was a woman ?

Explanation: this is similar to handshake problem , if there are nn people , then number of handshakes = 1 + 2 + . . . n = n ∗ ( n − 1 ) / 2 no . of women be xx and given x ∗ ( x − 1 ) / 2 = 45 this gives x = 10 | | | y no . of men : solve y ∗ ( y − 1 ) / 2 = 190 . this gives y = 20 so total men vs . women = 10 * 20 = 200 . answer is d

multiply(divide(add(const_1, sqrt(add(const_1, multiply(multiply(45, const_2), const_4)))), const_2), divide(add(const_1, sqrt(add(const_1, multiply(multiply(190, const_2), const_4)))), const_2))

<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">90 * 4</gadget>
<output>360</output>
<gadget id="calculator">1 + 360</gadget>
<output>361</output>
<gadget id="calculator">361 ** (1/2)</gadget>
<output>19</output>
<gadget id="calculator">1 + 19</gadget>
<output>20</output>
<gadget id="calculator">20 / 2</gadget>
<output>10</output>
<gadget id="calculator">190 * 2</gadget>
<output>380</output>
<gadget id="calculator">380 * 4</gadget>
<output>1_520</output>
<gadget id="calculator">1 + 1_520</gadget>
<output>1_521</output>
<gadget id="calculator">1_521 ** (1/2)</gadget>
<output>39</output>
<gadget id="calculator">1 + 39</gadget>
<output>40</output>
<gadget id="calculator">40 / 2</gadget>
<output>20</output>
<gadget id="calculator">10 * 20</gadget>
<output>200</output>
<result>200</result>


11 is subtracted from 40 % of a number and results is 23 . what is the number ?

Explanation: "( 40 / 100 ) * x â € “ 11 = 23 4 x = 340 x = 85 answer : d"

divide(add(11, 23), divide(40, const_100))

<gadget id="calculator">11 + 23</gadget>
<output>34</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">34 / (2/5)</gadget>
<output>85</output>
<result>85</result>


in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required is :

Explanation: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 8 : : 12 : x = > 8 x 15 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 8 x 15 ) = > x = 8 answer : d"

divide(divide(multiply(multiply(12, 8), 10), 15), 8)

<gadget id="calculator">12 * 8</gadget>
<output>96</output>
<gadget id="calculator">96 * 10</gadget>
<output>960</output>
<gadget id="calculator">960 / 15</gadget>
<output>64</output>
<gadget id="calculator">64 / 8</gadget>
<output>8</output>
<result>8</result>


what is the maximum number of pieces of birthday cake of size 4 ” by 4 ” that can be cut from a cake 20 ” by 20 ” ?

Explanation: "each length = 20 ' ' each piece = 4 ' ' cake could be divided to maximum of 25 pieces answer : e"

divide(multiply(20, 20), multiply(4, 4))

<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">400 / 16</gadget>
<output>25</output>
<result>25</result>


the present worth of rs . 845 due in 2 years at 4 % per annum compound interest is

Explanation: "solution present worth = rs . [ 845 / ( 1 + 4 / 100 ) ² ] = rs . ( 845 x 25 / 26 x 25 / 26 ) = rs . 781.25 answer c"

divide(845, power(add(divide(4, const_100), const_1), 2))

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) + 1</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>
<gadget id="calculator">845 / (676/625)</gadget>
<output>3_125/4 = around 781.25</output>
<result>3_125/4 = around 781.25</result>


on the first of the year , james invested x dollars at proudstar bank in an account that yields 4 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

Explanation: per quarter , interest = 4 % so for a year , interest = 16 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 16.25 % answer = 16.25 % = answer : d

<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<result>16</result>


if a store owner increases a product ’ s price by 20 percent and then increases this price by another 15 percent , what percent of the original price is the total price increase ?

Explanation: let the initial price be 100 1 st increase = 20 % the price now is 120 2 nd increase of 15 % on 120 = 18 final price = 138 , total increase = 38 % answer : c

add(multiply(add(multiply(const_100, divide(20, const_100)), const_100), divide(15, const_100)), multiply(const_100, divide(20, const_100)))

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">100 * (1/5)</gadget>
<output>20</output>
<gadget id="calculator">20 + 100</gadget>
<output>120</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">120 * (3/20)</gadget>
<output>18</output>
<gadget id="calculator">18 + 20</gadget>
<output>38</output>
<result>38</result>


if 5 students are made to sit in a row , then 6 do n ' t have seats . if 12 students are made to sit in a row , then 3 rows are empty . how many students have to sit a row such that each row has equal number of students and all students are seated ?

Explanation: let there be a rows . then 5 a + 6 = 12 ( a - 3 ) [ equating the number of students ] = > a = 6 and total number of students = 36 therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated . option ( e )

divide(add(multiply(12, 3), 6), subtract(12, 5))

<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 + 6</gadget>
<output>42</output>
<gadget id="calculator">12 - 5</gadget>
<output>7</output>
<gadget id="calculator">42 / 7</gadget>
<output>6</output>
<result>6</result>


a pupil ' s marks were wrongly entered as 85 instead of 33 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

Explanation: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 85 - 33 ) = > x / 2 = 52 = > x = 104 . answer : b"

<gadget id="calculator">85 - 33</gadget>
<output>52</output>
<gadget id="calculator">52 * 2</gadget>
<output>104</output>
<result>104</result>


if the ratio of two number is 6 : 7 and lcm of the number is 450 then what is the number .

Explanation: "product of two no = lcm * hcf 6 x * 7 x = 450 * x x = 11 answer : a"

<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">450 / 42</gadget>
<output>75/7 = around 10.714286</output>
<result>75/7 = around 10.714286</result>


jim is able to sell a hand - carved statue for $ 620 which was a 25 % profit over his cost . how much did the statue originally cost him ?

Explanation: "620 = 1.25 * x x = 620 / 1.25 = 496.00 which rounds to $ 496.00 , which is ( a ) ."

divide(620, add(divide(25, const_100), const_1))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">620 / (5/4)</gadget>
<output>496</output>
<result>496</result>


praveen starts business with rs . 3780 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?

Explanation: "let hari ’ s capital be rs . x . then , 3780 * 12 / 7 x = 2 / 3 = > 14 x = 136080 = > x = 9720 . answer : d"

divide(divide(3780, subtract(const_1, divide(5, const_12))), divide(2, 3))

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">1 - (5/12)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">3_780 / (7/12)</gadget>
<output>6_480</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">6_480 / (2/3)</gadget>
<output>9_720</output>
<result>9_720</result>


a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are ?

Explanation: "let the maximum marks be x then , 33 % of x = 125 + 40 33 x / 100 = 165 x = 500 answer is c"

divide(add(125, 40), divide(33, const_100))

<gadget id="calculator">125 + 40</gadget>
<output>165</output>
<gadget id="calculator">33 / 100</gadget>
<output>33/100 = around 0.33</output>
<gadget id="calculator">165 / (33/100)</gadget>
<output>500</output>
<result>500</result>


the telephone company wants to add an area code composed of 2 letters to every phone number . in order to do so , the company chose a special sign language containing 524 different signs . if the company used 522 of the signs fully and two remained unused , how many additional area codes can be created if the company uses all 524 signs ?

Explanation: # of 2 - letter codes possible from 524 different signs = 524 * 524 . # of 2 - letter codes possible from 522 different signs = 522 * 522 . the difference = 524 ^ 2 - 522 ^ 2 = ( 524 - 522 ) ( 524 + 522 ) = 2092 . answer : c .

multiply(multiply(522, subtract(524, 522)), subtract(524, 522))

<gadget id="calculator">524 - 522</gadget>
<output>2</output>
<gadget id="calculator">522 * 2</gadget>
<output>1_044</output>
<gadget id="calculator">1_044 * 2</gadget>
<output>2_088</output>
<result>2_088</result>


a case contains c cartons . each carton contains b boxes , and each box contains 200 paper clips . how many paper clips are contained in 2 cases ?

Explanation: "2 cases * c cartons / case * b boxes / carton * 200 clips / box = 400 bc paper clips the answer is c ."

<gadget id="calculator">2 * 200</gadget>
<output>400</output>
<result>400</result>


what is the value of x ^ 2 yz − xyz ^ 2 , if x = − 2 , y = 1 , and z = 1 ?

Explanation: 4 * 1 * 1 - ( - 2 * 1 * 1 ) = 4 + 2 = 6 ans : a

multiply(multiply(multiply(negate(2), 1), 1), subtract(negate(2), 1))

<gadget id="calculator">-2</gadget>
<output>-2</output>
<gadget id="calculator">(-2) * 1</gadget>
<output>-2</output>
<gadget id="calculator">(-2) - 1</gadget>
<output>-3</output>
<gadget id="calculator">(-2) * (-3)</gadget>
<output>6</output>
<result>6</result>


Explanation: "explanation : 2.205 / 0.3 = 22.05 / 3 = 7.35 . answer : option a"

<gadget id="calculator">2.205 / 0.3</gadget>
<output>7.35</output>
<result>7.35</result>