s is a positive integer and multiple of 2 ; p = 4 ^ s , what is the remainder when p is divided by 10 ?

Explanation: it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b .

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>
<gadget id="calculator">16 % 10</gadget>
<output>6</output>
<result>6</result>


if the sum of two numbers is 22 and the sum of their squares is 386 , then the product of the numbers is

Explanation: "sol . let the numbers be x and y . then , ( x + y ) = 22 and x 2 + y 2 = 386 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 22 ) 2 - 386 = 484 - 386 = 98 xy = 49 . answer b"

divide(subtract(power(22, const_2), 386), const_2)

<gadget id="calculator">22 ** 2</gadget>
<output>484</output>
<gadget id="calculator">484 - 386</gadget>
<output>98</output>
<gadget id="calculator">98 / 2</gadget>
<output>49</output>
<result>49</result>


a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 80 percent of the drive from the center , what percent of the round - trip has the technician completed ?

Explanation: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 80 % of 50 % i . e 40 % . so he completed 50 + 40 = 90 % of total trip . e"

add(divide(const_100, const_2), divide(multiply(80, divide(const_100, const_2)), const_100))

<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<gadget id="calculator">80 * 50</gadget>
<output>4_000</output>
<gadget id="calculator">4_000 / 100</gadget>
<output>40</output>
<gadget id="calculator">50 + 40</gadget>
<output>90</output>
<result>90</result>


if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 15 - m ) then m = ?

Explanation: "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 15 - m ) = 4 ^ ( ( 15 - m ) / 2 ) therefore , m = ( 15 - m ) / 2 2 m = 15 - m m = 5 answer d"

<gadget id="calculator">2 + 1</gadget>
<output>3</output>
<gadget id="calculator">15 / 3</gadget>
<output>5</output>
<result>5</result>


$ 378 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?

Explanation: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 378 x = 54 4 x = 216 the answer is c ."

multiply(divide(378, add(add(divide(const_1, const_2), const_1), const_2)), const_2)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) + 1</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(3/2) + 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">378 / (7/2)</gadget>
<output>108</output>
<gadget id="calculator">108 * 2</gadget>
<output>216</output>
<result>216</result>


harkamal purchased 8 kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?

Explanation: "cost of 8 kg grapes = 75 × 8 = 600 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 600 + 495 = 1095 . e )"

<gadget id="calculator">8 * 75</gadget>
<output>600</output>
<gadget id="calculator">9 * 55</gadget>
<output>495</output>
<gadget id="calculator">600 + 495</gadget>
<output>1_095</output>
<result>1_095</result>


if the side length of square b is sqrt ( 5 ) times that of square a , the area of square b is how many times the area of square a ?

Explanation: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 5 ) x ) ^ 2 = 5 x ^ 2 . the answer is e ."

<gadget id="calculator">5 ** (1/2)</gadget>
<output>sqrt(5) = around 2.236068</output>
<gadget id="calculator">(sqrt(5)) ** 2</gadget>
<output>5</output>
<result>5</result>


a certain quantity of 50 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?

Explanation: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 15 % . therefore , 15 out of 25 is 3 / 5 and e is the answer ."

inverse(add(divide(subtract(35, 25), subtract(50, 35)), const_1))

<gadget id="calculator">35 - 25</gadget>
<output>10</output>
<gadget id="calculator">50 - 35</gadget>
<output>15</output>
<gadget id="calculator">10 / 15</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) + 1</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">1 / (5/3)</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>


a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?

Explanation: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.2 x ) = 0.96 x . the difference is 4 % . the answer is d ."

multiply(subtract(const_1, multiply(add(divide(20, const_100), const_1), divide(80, const_100))), const_100)

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) + 1</gadget>
<output>6/5 = around 1.2</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(6/5) * (4/5)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">1 - (24/25)</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">(1/25) * 100</gadget>
<output>4</output>
<result>4</result>


there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?

Explanation: amount left = 0.5 x − 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x − 4 = 8 ⇒ x = 24 for third store , amount left = 24 so 12 x − 4 = 24 ⇒ x = 56 for second store , amount left = 56 so 0.5 x − 4 = 56 ⇒ x = 120 for first store , amount left = 120 so 0.5 x − 4 = 120 ⇒ x = 248 so he entered first store with 248 . answer : a

multiply(add(multiply(add(multiply(add(multiply(add(multiply(4, const_2), 4), const_2), 4), const_2), 4), const_2), 4), const_2)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 4</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<gadget id="calculator">24 + 4</gadget>
<output>28</output>
<gadget id="calculator">28 * 2</gadget>
<output>56</output>
<gadget id="calculator">56 + 4</gadget>
<output>60</output>
<gadget id="calculator">60 * 2</gadget>
<output>120</output>
<gadget id="calculator">120 + 4</gadget>
<output>124</output>
<gadget id="calculator">124 * 2</gadget>
<output>248</output>
<result>248</result>


3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :

Explanation: original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a .

divide(subtract(divide(const_1, const_2), divide(const_1, 3)), divide(const_1, 3))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/2) - (1/3)</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) / (1/3)</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>


two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?

Explanation: solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 350 x 18 / 25 ) sec = 252 sec . answer d

multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(45, 40)))

<gadget id="calculator">200 + 150</gadget>
<output>350</output>
<gadget id="calculator">350 / 1_000</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">45 - 40</gadget>
<output>5</output>
<gadget id="calculator">(7/20) / 5</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">3_600 * (7/100)</gadget>
<output>252</output>
<result>252</result>


a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 35 . find the profit percentage ?

Explanation: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 175 ( 35 * 5 ) profit percentage = ( 175 - 100 ) / 100 * 100 = 75 % answer : c"

subtract(multiply(35, add(const_4, const_1)), multiply(25, const_4))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">35 * 5</gadget>
<output>175</output>
<gadget id="calculator">25 * 4</gadget>
<output>100</output>
<gadget id="calculator">175 - 100</gadget>
<output>75</output>
<result>75</result>


how many 1 / 8 s are there in 37 1 / 2 ?

Explanation: "required number = ( 75 / 2 ) / ( 1 / 8 ) = ( 75 / 2 x 8 / 1 ) = 300 . answer : a"

divide(add(37, divide(1, 2)), divide(1, 8))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">37 + (1/2)</gadget>
<output>75/2 = around 37.5</output>
<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">(75/2) / (1/8)</gadget>
<output>300</output>
<result>300</result>


in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz

Explanation: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 5 = 8 : 10 - - > qy = 4.0 . answer : c ."

<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 / 10</gadget>
<output>4</output>
<result>4</result>


the average runs of a cricket player of 10 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?

Explanation: "explanation : average after 11 innings = 24 required number of runs = ( 24 * 11 ) – ( 20 * 10 ) = 264 – 200 = 64 answer : c"

subtract(multiply(add(10, const_1), add(20, 4)), multiply(20, 10))

<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<gadget id="calculator">20 + 4</gadget>
<output>24</output>
<gadget id="calculator">11 * 24</gadget>
<output>264</output>
<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">264 - 200</gadget>
<output>64</output>
<result>64</result>


the sum of the even numbers between 1 and k is 79 * 80 , where k is an odd number , then k =

Explanation: "the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e ."

<gadget id="calculator">79 * 2</gadget>
<output>158</output>
<gadget id="calculator">158 + 1</gadget>
<output>159</output>
<result>159</result>


how long does a train 125 m long running at the speed of 78 km / hr takes to cross a bridge 125 m length ?

Explanation: "speed = 78 * 5 / 18 = 21.7 m / sec total distance covered = 125 + 125 = 250 m . required time = 250 / 21.7 ' = 11.5 sec . answer : c"

<gadget id="calculator">125 + 125</gadget>
<output>250</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">78 * (5/18)</gadget>
<output>65/3 = around 21.666667</output>
<gadget id="calculator">250 / (65/3)</gadget>
<output>150/13 = around 11.538462</output>
<result>150/13 = around 11.538462</result>


ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?

Explanation: ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )

multiply(subtract(multiply(const_2, 15), 15), 3)

<gadget id="calculator">2 * 15</gadget>
<output>30</output>
<gadget id="calculator">30 - 15</gadget>
<output>15</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<result>45</result>


a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of this son is

Explanation: "explanation : let ' s son age is x , then father age is x + 30 . = > 2 ( x + 2 ) = ( x + 30 + 2 ) = > 2 x + 4 = x + 32 = > x = 28 years option a"

divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1))

<gadget id="calculator">2 * 2</gadget>
<output>4</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">30 - 2</gadget>
<output>28</output>
<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">28 / 1</gadget>
<output>28</output>
<result>28</result>


the length of the bridge , which a train 110 meters long and travelling at 45 km / hr can cross in 30 seconds , is :

Explanation: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 110 + x ) / 30 = 25 / 2 = = > 2 ( 110 + x ) = 750 = = > x = 265 m . answer : option a"

subtract(multiply(divide(multiply(45, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 110)

<gadget id="calculator">1_000 / 1</gadget>
<output>1_000</output>
<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>
<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>
<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>
<gadget id="calculator">375 - 110</gadget>
<output>265</output>
<result>265</result>


cole drove from home to work at an average speed of 60 kmh . he then returned home at an average speed of 100 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?

Explanation: "let the distance one way be x time from home to work = x / 60 time from work to home = x / 100 total time = 2 hrs ( x / 60 ) + ( x / 100 ) = 2 solving for x , we get x = 75 time from home to work in minutes = ( 75 ) * 60 / 60 = 75 minutes ans = d"

multiply(divide(multiply(100, 2), add(60, 100)), const_60)

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<gadget id="calculator">60 + 100</gadget>
<output>160</output>
<gadget id="calculator">200 / 160</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">(5/4) * 60</gadget>
<output>75</output>
<result>75</result>


if the radius of a circle is decreased 50 % , what happens to the area ?

Explanation: "area of square = pi * radius ^ 2 new radius = 0.5 * old radius so new area = ( 0.5 ) ^ 2 old area = > 0.25 of old area = > 25 % old area ans : c"

subtract(const_100, multiply(power(divide(50, const_100), const_2), const_100))

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<gadget id="calculator">100 - 25</gadget>
<output>75</output>
<result>75</result>


calculate the ratio between x and y if 90 % of x equal to 60 % of y ?

Explanation: "explanation : 90 x = 60 y x : y = 90 : 60 = 3 : 2 answer : c"

<gadget id="calculator">90 / 60</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>


find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 15 cm and 5 cm ?

Explanation: "1 / 2 * 50 ( 15 + 5 ) = 500 cm 2 answer : e"

multiply(multiply(divide(const_1, const_2), add(5, 15)), 50)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">5 + 15</gadget>
<output>20</output>
<gadget id="calculator">(1/2) * 20</gadget>
<output>10</output>
<gadget id="calculator">10 * 50</gadget>
<output>500</output>
<result>500</result>


a right circular cone is exactly fitted inside a cube in such away that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube . if the volume of the cube is 343 cc , what approximately is the volume of the cone ?

Explanation: edge of the cube = 3 √ 334 = 7 cm ∴ radius of cone = 3.5 cm height = 7 cm volume of cone = 1 ⁄ 3 π r 2 h 1 ⁄ 3 π r 2 h = 1 ⁄ 3 × 22 ⁄ 7 × ( 3.5 ) 2 × 7 = 1 ⁄ 3 × 22 × 12.25 ≈ 90 sec answer b

<gadget id="calculator">343 ** (1/3)</gadget>
<output>7</output>
<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>
<gadget id="calculator">pi * ((7/2) ** 2) * 7 / 3</gadget>
<output>343*pi/12 = around 89.79719</output>
<result>343*pi/12 = around 89.79719</result>


if the given two numbers are respectively 7 % and 28 % of a third number , then what percentage is the first of the second ?

Explanation: "here , l = 7 and m = 28 therefore , first number = l / m x 100 % of second number = 7 / 28 x 100 % of second number = 25 % of second number answer : b"

multiply(divide(divide(7, const_100), divide(28, const_100)), const_100)

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>
<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/100) / (7/25)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) * 100</gadget>
<output>25</output>
<result>25</result>


a pupil ' s marks were wrongly entered as 83 instead of 53 . due to 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 = ( 83 - 53 ) = > x / 2 = 30 = > x = 60 . answer : c"

<gadget id="calculator">83 - 53</gadget>
<output>30</output>
<gadget id="calculator">30 * 2</gadget>
<output>60</output>
<result>60</result>


the area of a rhombus is equal to the area of a rectangle whose length is 20 cm and the breadth is 10 cm . if one of the diagonals is 32 cm what is the length of other diagonal ?

Explanation: area of rectangle = 20 x 10 = 200 cm â ² let ' l ' the length of other diagonal = 0.5 x 32 xl = 200 which gives x = 12.5 cm answer : b

divide(multiply(rectangle_area(20, 10), const_2), 32)

<gadget id="calculator">20 * 10</gadget>
<output>200</output>
<gadget id="calculator">200 * 2</gadget>
<output>400</output>
<gadget id="calculator">400 / 32</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


if the simple interest on a certain amount in at 4 % rate 5 years amounted to rs . 2160 less than the principal . what was the principal ?

Explanation: p - 2160 = ( p * 5 * 4 ) / 100 p = 2700 answer : c

divide(2160, 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">2_160 / (4/5)</gadget>
<output>2_700</output>
<result>2_700</result>


a certain bus driver is paid a regular rate of $ 16 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 948 in total compensation , how many total hours did he work that week ?

Explanation: "for 40 hrs = 40 * 16 = 640 excess = 948 - 640 = 308 for extra hours = . 75 ( 16 ) = 12 + 16 = 28 number of extra hrs = 308 / 28 = 77 / 7 = 11 total hrs = 40 + 11 = 51 answer e 51"

add(40, divide(subtract(948, multiply(16, 40)), divide(multiply(16, add(const_100, 75)), const_100)))

<gadget id="calculator">16 * 40</gadget>
<output>640</output>
<gadget id="calculator">948 - 640</gadget>
<output>308</output>
<gadget id="calculator">100 + 75</gadget>
<output>175</output>
<gadget id="calculator">16 * 175</gadget>
<output>2_800</output>
<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>
<gadget id="calculator">308 / 28</gadget>
<output>11</output>
<gadget id="calculator">40 + 11</gadget>
<output>51</output>
<result>51</result>


a line has a slope of 3 / 4 and intersects the point w ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?

Explanation: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point w of intersection is ( 40,0 ) . a is the correct answer ."

multiply(negate(divide(subtract(negate(39), multiply(negate(12), divide(3, 4))), divide(3, 4))), const_10)

<gadget id="calculator">-39</gadget>
<output>-39</output>
<gadget id="calculator">-12</gadget>
<output>-12</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(-12) * (3/4)</gadget>
<output>-9</output>
<gadget id="calculator">(-39) - (-9)</gadget>
<output>-30</output>
<gadget id="calculator">(-30) / (3/4)</gadget>
<output>-40</output>
<gadget id="calculator">-(-40)</gadget>
<output>40</output>
<gadget id="calculator">40 * 10</gadget>
<output>400</output>
<result>400</result>


a salesman commission is 5 % on all sales upto $ 10000 and 4 % on all sales exceeding this . he remits $ 31100 to his parent company after deducting his commission . find the total sales ?

Explanation: let his total sales be x total sales - commission = $ 31100 x - [ ( 5 % of 10000 ) + 4 % of ( x - 10000 ) ] = 31100 x - 500 - ( x - 10000 ) / 25 = 31100 x = 32500 answer is b

divide(add(31100, subtract(divide(multiply(5, 10000), const_100), divide(multiply(4, 10000), const_100))), subtract(const_1, divide(4, const_100)))

<gadget id="calculator">5 * 10_000</gadget>
<output>50_000</output>
<gadget id="calculator">50_000 / 100</gadget>
<output>500</output>
<gadget id="calculator">4 * 10_000</gadget>
<output>40_000</output>
<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>
<gadget id="calculator">500 - 400</gadget>
<output>100</output>
<gadget id="calculator">31_100 + 100</gadget>
<output>31_200</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 - (1/25)</gadget>
<output>24/25 = around 0.96</output>
<gadget id="calculator">31_200 / (24/25)</gadget>
<output>32_500</output>
<result>32_500</result>


how much 60 % of 50 is greater than 34 % of 30 ?

Explanation: ( 60 / 100 ) * 50 – ( 34 / 100 ) * 30 30 - 10.2 = 19.8 answer : b

subtract(divide(multiply(60, 50), const_100), divide(multiply(34, 30), const_100))

<gadget id="calculator">60 * 50</gadget>
<output>3_000</output>
<gadget id="calculator">3_000 / 100</gadget>
<output>30</output>
<gadget id="calculator">34 * 30</gadget>
<output>1_020</output>
<gadget id="calculator">1_020 / 100</gadget>
<output>51/5 = around 10.2</output>
<gadget id="calculator">30 - (51/5)</gadget>
<output>99/5 = around 19.8</output>
<result>99/5 = around 19.8</result>


a man can row 5 kmph in still water . when the river is running at 2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

Explanation: "m = 5 s = 2 ds = 7 us = 3 x / 7 + x / 3 = 1 x = 2.1 d = 2.1 * 2 = 4.2 answer : d"

multiply(divide(multiply(add(5, 2), subtract(5, 2)), add(add(5, 2), subtract(5, 2))), const_2)

<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">7 + 3</gadget>
<output>10</output>
<gadget id="calculator">21 / 10</gadget>
<output>21/10 = around 2.1</output>
<gadget id="calculator">(21/10) * 2</gadget>
<output>21/5 = around 4.2</output>
<result>21/5 = around 4.2</result>


how long does a truck of 200 m long traveling at 60 kmph takes to cross a bridge of 180 m in length ?

Explanation: d = 200 + 180 = 380 m s = 60 * 5 / 18 = 50 / 3 t = 380 * 3 / 50 = 22.8 sec answer : c

<gadget id="calculator">200 + 180</gadget>
<output>380</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">380 / (50/3)</gadget>
<output>114/5 = around 22.8</output>
<result>114/5 = around 22.8</result>


difference between the length & breadth of a rectangle is 10 m . if its perimeter is 206 m , then its area is ?

Explanation: solving the two equations , we get : l = 30 and b = 40 . area = ( l x b ) = ( 30 x 40 ) m 2 = 1200 m ^ 2 d

multiply(multiply(10, const_4), multiply(10, const_3))

<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">40 * 30</gadget>
<output>1_200</output>
<result>1_200</result>


for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?

Explanation: "factorization of 45 = 3 * 3 * 5 factorization of 80 = 5 * 2 ^ 4 means the smallest value of k is \ sqrt { 3 ^ 2 * 5 * 2 ^ 4 } = 3 * 5 * 2 ^ 2 k ^ 3 = 3 ^ 3 * 5 ^ 3 * 2 ^ 6 * x = 3 ^ 3 * 2 * 4000 * x where x can be any integer k ^ 3 / 4000 = 3 ^ 3 * 2 * x = 54 x which obviously has different units digit depending on x answer : d"

divide(multiply(multiply(multiply(3, 2), multiply(3, 2)), multiply(3, 2)), const_4)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">36 * 6</gadget>
<output>216</output>
<gadget id="calculator">216 / 4</gadget>
<output>54</output>
<result>54</result>


paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 40 % of his income to sam and 60 % of his income to quentin , quentin ' s new income would be what fraction of sam ' s new income ?

Explanation: make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 7.6 and q 10.8 so 10.8 / 7.6 = 2.7 / 1.9 ans : e

divide(add(multiply(60, const_100), multiply(60, subtract(const_100, 20))), add(multiply(40, const_100), multiply(add(40, 20), 60)))

<gadget id="calculator">60 * 100</gadget>
<output>6_000</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">60 * 80</gadget>
<output>4_800</output>
<gadget id="calculator">6_000 + 4_800</gadget>
<output>10_800</output>
<gadget id="calculator">40 * 100</gadget>
<output>4_000</output>
<gadget id="calculator">40 + 20</gadget>
<output>60</output>
<gadget id="calculator">60 * 60</gadget>
<output>3_600</output>
<gadget id="calculator">4_000 + 3_600</gadget>
<output>7_600</output>
<gadget id="calculator">10_800 / 7_600</gadget>
<output>27/19 = around 1.421053</output>
<result>27/19 = around 1.421053</result>


Explanation: "let p = 3 , q = 7 then 2 * 3 + 7 = 13 so 2 p + q = 13 . answer : c"

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">6 + 7</gadget>
<output>13</output>
<result>13</result>


in a box of 9 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

Explanation: "# defective pens = 2 # good pens = 7 probability of the 1 st pen being good = 7 / 9 probability of the 2 nd pen being good = 6 / 8 total probability = 7 / 9 * 6 / 8 = 7 / 12 the answer is d ."

multiply(divide(subtract(9, 2), 9), divide(subtract(subtract(9, 2), const_1), subtract(9, const_1)))

<gadget id="calculator">9 - 2</gadget>
<output>7</output>
<gadget id="calculator">7 / 9</gadget>
<output>7/9 = around 0.777778</output>
<gadget id="calculator">7 - 1</gadget>
<output>6</output>
<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">6 / 8</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(7/9) * (3/4)</gadget>
<output>7/12 = around 0.583333</output>
<result>7/12 = around 0.583333</result>


if 36 men can do a piece of work in 25 hours , in how mwny hours will 15 men do it ?

Explanation: "explanation : let the required no of hours be x . then less men , more hours ( indirct proportion ) \ inline \ fn _ jvn \ therefore 15 : 36 : : 25 : x \ inline \ fn _ jvn \ leftrightarrow ( 15 x x ) = ( 36 x 25 ) \ inline \ fn _ jvn \ leftrightarrow \ inline \ fn _ jvn x = \ frac { 36 \ times 25 } { 15 } = 60 hence , 15 men can do it in 60 hours . answer : c ) 60"

<gadget id="calculator">36 * 25</gadget>
<output>900</output>
<gadget id="calculator">900 / 15</gadget>
<output>60</output>
<result>60</result>


last year the price range ( per kg ) for 100 varieties of apples in wholesale market was $ 100 . if the prices of each of the 100 varieties increased by 10 percent this year over what it was last year , what is the range of the wholesale prices of the 1000 varieties of apples this year ?

Explanation: let the lowest price be x . therefore , highest price is x + 100 . now price of each variety is increased by 10 % . therefore the price will remain arranged in the same order as before . or lowest price = 1.1 x and highest = 1.1 * ( x + 100 ) or range = highest - lowest = 1.1 * ( x + 100 ) - 1.1 x = 110 , hence , c

multiply(100, divide(add(10, const_100), const_100))

<gadget id="calculator">10 + 100</gadget>
<output>110</output>
<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>
<gadget id="calculator">100 * (11/10)</gadget>
<output>110</output>
<result>110</result>


the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?

Explanation: "explanation : let the c . p . of the article be rs . x given that % profit earned by selling article at rs . 1920 = % loss incurred by selling article at rs . 1280 ( 1920 − x / x ) ∗ 100 = ( x − 1280 / x ) ∗ 100 = > 1920 - x = x - 1280 = > 2 x = 3200 = > x = 1600 s . p . for 25 % profit = rs . 1600 + 25 % of rs . 1600 = rs . 1600 * ( 125 / 100 ) = rs . 2000 answer : a"

multiply(divide(add(const_100, 25), const_100), divide(add(1920, 1280), const_2))

<gadget id="calculator">100 + 25</gadget>
<output>125</output>
<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">1_920 + 1_280</gadget>
<output>3_200</output>
<gadget id="calculator">3_200 / 2</gadget>
<output>1_600</output>
<gadget id="calculator">(5/4) * 1_600</gadget>
<output>2_000</output>
<result>2_000</result>


the tailor has a 10 meter long piece of fabric for which to sew a ball room dress . she has to cuts this fabric into strips of 200 centimeters each . how long will it take the tailor to complete this tasks if each 200 centimeter took 5 minutes to cut ?

Explanation: the tailors would need to cut the fabric 49 times thus the total amount spent would be 245 minutes . the answer is d

multiply(subtract(divide(multiply(10, const_1000), 200), const_1), 5)

<gadget id="calculator">10 * 1_000</gadget>
<output>10_000</output>
<gadget id="calculator">10_000 / 200</gadget>
<output>50</output>
<gadget id="calculator">50 - 1</gadget>
<output>49</output>
<gadget id="calculator">49 * 5</gadget>
<output>245</output>
<result>245</result>


in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 4720 votes were polled , then how many valid votes did b get ?

Explanation: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 4720 32.5 k = 32.5 k / 100 k * 4720 = 1534 the number of valid votes polled in favour of b is 1534 . answer : a"

divide(subtract(multiply(subtract(const_1, divide(20, const_100)), 4720), divide(multiply(15, 4720), const_100)), const_2)

<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">(4/5) * 4_720</gadget>
<output>3_776</output>
<gadget id="calculator">15 * 4_720</gadget>
<output>70_800</output>
<gadget id="calculator">70_800 / 100</gadget>
<output>708</output>
<gadget id="calculator">3_776 - 708</gadget>
<output>3_068</output>
<gadget id="calculator">3_068 / 2</gadget>
<output>1_534</output>
<result>1_534</result>


if $ 1088 are divided between worker a and worker b in the ratio 5 : 11 , what is the share that worker b will get ?

Explanation: "worker b will get 11 / 16 = 68.75 % the answer is d ."

<gadget id="calculator">5 + 11</gadget>
<output>16</output>
<gadget id="calculator">1_088 / 16</gadget>
<output>68</output>
<result>68</result>


the average age of 6 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years . find the average age of the women ?

Explanation: "20 + 24 + 6 * 2 = 56 / 2 = 28 answer : e"

divide(add(add(20, 24), multiply(6, 2)), const_2)

<gadget id="calculator">20 + 24</gadget>
<output>44</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">44 + 12</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<result>28</result>


operation # is defined as : a # b = 4 a ^ 2 + 4 b ^ 2 + 8 ab for all non - negative integers . what is the value of ( a + b ) + 4 , when a # b = 100 ?

Explanation: official solution : ( b ) we know that a # b = 100 and a # b = 4 a ² + 4 b ² + 8 ab . so 4 a ² + 4 b ² + 8 ab = 100 we can see that 4 a ² + 4 b ² + 8 ab is a well - known formula for ( 2 a + 2 b ) ² . therefore ( 2 a + 2 b ) ² = 100 . ( 2 a + 2 b ) is non - negative number , since both a and b are non - negative numbers . so we can conclude that 2 ( a + b ) = 10 . ( a + b ) + 4 = 10 / 2 + 4 = 9 . the correct answer is b .

<gadget id="calculator">100 / 4</gadget>
<output>25</output>
<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<result>9</result>


the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 500 per sq . metre .

Explanation: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 500 hence , total cost = 5.5 × 3.75 × 500 = $ 10312.50 a"

<gadget id="calculator">5.5 * 3.75</gadget>
<output>20.625</output>
<gadget id="calculator">500 * 20.625</gadget>
<output>10_312.5</output>
<result>10_312.5</result>


a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?

Explanation: "we have : l = 20 ft and lb = 10 sq . ft . so , b = 0.5 ft . length of fencing = ( l + 2 b ) = ( 20 + 1 ) ft = 21 ft . answer : d"

add(multiply(divide(10, 20), const_2), 20)

<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(1/2) * 2</gadget>
<output>1</output>
<gadget id="calculator">1 + 20</gadget>
<output>21</output>
<result>21</result>


each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum k in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is

Explanation: the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the “ 1 – x ” technique : what ’ s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn ’ t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don ’ t ) and in which z retains value ( while x and y don ’ t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it ’ s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated — and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .

subtract(add(multiply(20, const_2), multiply(20, 3)), const_10)

<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">20 * 3</gadget>
<output>60</output>
<gadget id="calculator">40 + 60</gadget>
<output>100</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<result>90</result>


a ferry can transport 50 tons of vehicles . automobiles range in weight from 1,600 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?

Explanation: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d

divide(multiply(multiply(50, const_2), const_1000), add(add(add(add(add(add(const_1000, const_100), const_100), const_100), const_100), const_100), const_100))

<gadget id="calculator">50 * 2</gadget>
<output>100</output>
<gadget id="calculator">100 * 1_000</gadget>
<output>100_000</output>
<gadget id="calculator">1_000 + 100</gadget>
<output>1_100</output>
<gadget id="calculator">1_100 + 100</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 + 100</gadget>
<output>1_300</output>
<gadget id="calculator">1_300 + 100</gadget>
<output>1_400</output>
<gadget id="calculator">1_400 + 100</gadget>
<output>1_500</output>
<gadget id="calculator">1_500 + 100</gadget>
<output>1_600</output>
<gadget id="calculator">100_000 / 1_600</gadget>
<output>125/2 = around 62.5</output>
<result>125/2 = around 62.5</result>


what is the ratio between perimeters of two squares one having 8 times the diagonal then the other ?

Explanation: "d = 8 d d = d a √ 2 = 8 d a √ 2 = d a = 8 d / √ 2 a = d / √ 2 = > 8 : 1 answer : d"

<gadget id="calculator">8 / 8</gadget>
<output>1</output>
<gadget id="calculator">8 / 1</gadget>
<output>8</output>
<result>8</result>


a bank pays interest to its customers on the last day of the year . the interest paid to a customer is calculated as 10 % of the average monthly balance maintained by the customer . john is a customer at the bank . on the last day , when the interest was accumulated into his account , his bank balance doubled to $ 5080 . what is the average monthly balance maintained by john in his account during the year ?

Explanation: bank balance is doubled with accumulation of interest tp 5080 . . this means interest is 5080 / 2 = 2540 for entire year . . although since interest is 10 % of avg monthly balance , it becomes 25400 . . d

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">5_080 * 5</gadget>
<output>25_400</output>
<result>25_400</result>


a bus 75 m long is running with a speed of 21 km / hr . in what time will it pass a woman who is walking at 3 km / hr in the direction opposite to that in which the bus is going ?

Explanation: "speed of bus relative to woman = 21 + 3 = 24 km / hr . = 24 * 5 / 18 = 20 / 3 m / sec . time taken to pass the woman = 75 * 3 / 20 = 11.25 sec . answer : c"

divide(divide(multiply(75, const_3600), add(21, 3)), const_1000)

<gadget id="calculator">75 * 3_600</gadget>
<output>270_000</output>
<gadget id="calculator">21 + 3</gadget>
<output>24</output>
<gadget id="calculator">270_000 / 24</gadget>
<output>11_250</output>
<gadget id="calculator">11_250 / 1_000</gadget>
<output>45/4 = around 11.25</output>
<result>45/4 = around 11.25</result>


reeya obtained 40 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average

Explanation: "explanation : ( 40 + 60 + 70 + 80 + 80 / 5 ) = 66 option a"

<gadget id="calculator">40 + 60</gadget>
<output>100</output>
<gadget id="calculator">100 + 70</gadget>
<output>170</output>
<gadget id="calculator">170 + 80</gadget>
<output>250</output>
<gadget id="calculator">250 + 80</gadget>
<output>330</output>
<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">330 / 5</gadget>
<output>66</output>
<result>66</result>


the distance from city a to city b is 100 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?

Explanation: "the time it takes bob to drive to city b is 100 / 40 = 2.5 hours . alice needs to take less than 2 hours for the trip . alice needs to exceed a constant speed of 100 / 2 = 50 miles per hour . the answer is c ."

divide(100, subtract(divide(100, 40), divide(30, const_60)))

<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">30 / 60</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(5/2) - (1/2)</gadget>
<output>2</output>
<gadget id="calculator">100 / 2</gadget>
<output>50</output>
<result>50</result>


when positive integer k is divided by 5 , the remainder is 2 . when k is divided by 6 , the remainder is 5 . if k is less than 24 , what is the remainder when k is divided by 7 ?

Explanation: "cant think of a straight approach but here is how i solved it : k is divided by 5 and remainder is 2 . this means k = 5 n + 2 ( n is an integer ) so the possible values of k = { 2 , 7 , 12 , 17 , 22 } ( less than 24 ) secondly , if k is divided by 6 , the remainder is 5 = > k = 6 m + 5 so the possible value set for k = { 5 , 11 , 17 , 23 } ( less than 24 ) 17 is the only common number in both the sets . hence k = 17 answer : d"

<gadget id="calculator">12 + 5</gadget>
<output>17</output>
<gadget id="calculator">17 % 7</gadget>
<output>3</output>
<result>3</result>


is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , then how old is b ?

Explanation: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 = > x = 6 hence , b ' s age = 2 x = 12 years . answer : e"

multiply(divide(subtract(32, const_2), add(const_3, const_2)), const_2)

<gadget id="calculator">32 - 2</gadget>
<output>30</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">30 / 5</gadget>
<output>6</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<result>12</result>


how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 132 m length ?

Explanation: "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 132 = 242 m . required time = 242 / 20 = 12.1 sec . answer : b"

<gadget id="calculator">110 + 132</gadget>
<output>242</output>
<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">72 * (5/18)</gadget>
<output>20</output>
<gadget id="calculator">242 / 20</gadget>
<output>121/10 = around 12.1</output>
<result>121/10 = around 12.1</result>


mary ' s income is 60 % more than tim ' s income and tim ' s income is 60 % less than juan ' s income . what % of juan ' s income is mary ' s income .

Explanation: "even i got 96 % j = 100 t = 100 * 0.4 = 40 m = 40 * 1.6 = 64 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 64 * 100 / 100 = 64 ans : c"

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

<gadget id="calculator">100 - 60</gadget>
<output>40</output>
<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>
<gadget id="calculator">40 + 24</gadget>
<output>64</output>
<result>64</result>


11 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?

Explanation: "no . of ways of picking 2 biology books ( from 11 books ) = 11 c 2 = ( 11 * 10 ) / 2 = 55 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 55 * 28 = 1540 ( option e )"

multiply(divide(divide(factorial(11), factorial(subtract(11, 2))), 2), divide(divide(factorial(8), factorial(subtract(8, 2))), 2))

<gadget id="calculator">factorial(11)</gadget>
<output>39_916_800</output>
<gadget id="calculator">11 - 2</gadget>
<output>9</output>
<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>
<gadget id="calculator">39_916_800 / 362_880</gadget>
<output>110</output>
<gadget id="calculator">110 / 2</gadget>
<output>55</output>
<gadget id="calculator">factorial(8)</gadget>
<output>40_320</output>
<gadget id="calculator">8 - 2</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">40_320 / 720</gadget>
<output>56</output>
<gadget id="calculator">56 / 2</gadget>
<output>28</output>
<gadget id="calculator">55 * 28</gadget>
<output>1_540</output>
<result>1_540</result>


pipe a can fill the tank in 30 minutes and pipe b can empty the tank in 90 minutes . how long it will take to fill the tank if both pipes are operating together ?

Explanation: pipe a fills 1 / 30 th of the tank in a minute and pipe b empties 1 / 90 th of the tank ( 1 / 30 ) - ( 1 / 90 ) = ( 1 / x ) 2 / 90 = 1 / x = > x = 45 answer : d

divide(const_1, subtract(divide(const_1, 30), divide(const_1, 90)))

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>
<gadget id="calculator">(1/30) - (1/90)</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">1 / (1/45)</gadget>
<output>45</output>
<result>45</result>


an electric pump can fill a tank in 4 hours . because of a leak in the tank , it took 8 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?

Explanation: work done by the leak in 1 hour = 1 / 4 - 1 / 8 = 1 / 8 the leak will empty the tank in 8 hours answer is c

<gadget id="calculator">8 / 1</gadget>
<output>8</output>
<result>8</result>


at the wholesale store you can buy an 8 - pack of hot dogs for $ 1.55 , a 20 - pack for $ 3.05 , and a 250 - pack for $ 22.95 . what is the greatest number of hot dogs you can buy at this store with $ 203 ?

Explanation: "i think it should be d . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 6 20 - pack for 3.05 * 5 = $ 18.30 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2120"

<gadget id="calculator">203 / 22.95</gadget>
<output>8.845316</output>
<gadget id="calculator">8.845316 * 250</gadget>
<output>2_211.329</output>
<result>2_211.329</result>


if 3 girls can do 3 times of a particular work in 3 days , then , 7 girls can do 7 times of that work in

Explanation: answer : option ' d ' that is , 1 girl can do one time of the work in 3 days . therefore , 7 girls can do 7 times work in the same 3 days itself .

<gadget id="calculator">3 / 3</gadget>
<output>1</output>
<gadget id="calculator">1 * 3</gadget>
<output>3</output>
<result>3</result>


a sum fetched a total simple interest of 4043.25 at the rate of 9 % . p . a . in 5 years . what is the sum ?

Explanation: "principal = ( 100 x 4043.25 ) / ( 9 x 5 ) = 404325 / 45 = 8985 . answer b"

divide(divide(multiply(4043.25, const_100), 9), 5)

<gadget id="calculator">4_043.25 * 100</gadget>
<output>404_325</output>
<gadget id="calculator">404_325 / 9</gadget>
<output>44_925</output>
<gadget id="calculator">44_925 / 5</gadget>
<output>8_985</output>
<result>8_985</result>


arun is travelling on his cycle and has calculated to reach point a at 2 pm if he travels at 10 kmph . he will reach there at 12 noon if he travels at 15 kmph . at what speed must he travel to reach a at 1 pm ?

Explanation: let distance be x km travelling at 10 kmph reach at 2 pm travelling at 15 kmph reach at 12 noon = > time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs x / 10 - x / 15 = 2 3 x - 2 x * 30 x = 60 time needed if travelled at 10 kmph = 60 / 10 = 6 hrs = > reach at 1 pm = > ( 6 - 1 ) = 5 hrs req speed = 60 / 5 = 12 kmph answer b

<gadget id="calculator">15 + 10</gadget>
<output>25</output>
<gadget id="calculator">25 / 2</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>


rs . 600 amounts to rs . 900 in 3 years at simple interest . if the interest is increased by 4 % , it would amount to how much ?

Explanation: "( 600 * 3 * 4 ) / 100 = 72 600 + 72 = 672 answer : a"

multiply(power(add(const_1, divide(4, const_100)), 3), 600)

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>
<gadget id="calculator">(26/25) ** 3</gadget>
<output>17_576/15_625 = around 1.124864</output>
<gadget id="calculator">(17_576/15_625) * 600</gadget>
<output>421_824/625 = around 674.9184</output>
<result>421_824/625 = around 674.9184</result>


the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions .

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84403 cm = 844.03 m answer : b"

divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 600), const_100)

<gadget id="calculator">3 + 4</gadget>
<output>7</output>
<gadget id="calculator">7 * 3</gadget>
<output>21</output>
<gadget id="calculator">21 + 1</gadget>
<output>22</output>
<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>
<gadget id="calculator">(22/7) * 22.4</gadget>
<output>70.4</output>
<gadget id="calculator">70.4 * 2</gadget>
<output>140.8</output>
<gadget id="calculator">140.8 * 600</gadget>
<output>84_480</output>
<gadget id="calculator">84_480 / 100</gadget>
<output>4_224/5 = around 844.8</output>
<result>4_224/5 = around 844.8</result>


a certain bag contains 100 balls â € ” 50 white , 25 green , 10 yellow , 7 red , and 8 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?

Explanation: according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 25 + 10 ) / 100 = 85 / 100 = 0.85 . answer is b

<gadget id="calculator">7 + 8</gadget>
<output>15</output>
<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>
<result>17/20 = around 0.85</result>


a 1 k . m . long wire is held by n poles . if one pole is removed , the length of the gap becomes 12 / 3 m . what is the number of poles initially ?

Explanation: length after removing pole is 12 / 3 = 4 then before removing pole is 2 ( ' coz | 2 | 2 | is | 4 | ) i . e . gap between two poles is 2 m 1 km = 1000 m then split 1000 m by 2 m = > we have 500 sections or gaps then no . of poles is 500 + 1 st pole = 501 poles therefore n = 501 . answer : b

subtract(add(add(add(add(multiply(multiply(12, 3), const_12), const_10), multiply(const_10, const_4)), const_10), const_10), 1)

<gadget id="calculator">12 * 3</gadget>
<output>36</output>
<gadget id="calculator">36 * 12</gadget>
<output>432</output>
<gadget id="calculator">432 + 10</gadget>
<output>442</output>
<gadget id="calculator">10 * 4</gadget>
<output>40</output>
<gadget id="calculator">442 + 40</gadget>
<output>482</output>
<gadget id="calculator">482 + 10</gadget>
<output>492</output>
<gadget id="calculator">492 + 10</gadget>
<output>502</output>
<gadget id="calculator">502 - 1</gadget>
<output>501</output>
<result>501</result>


a certain deep blue paint contains 45 percent blue pigment and 55 percent red pigment by weight . a certain green paint contains 35 percent blue pigment and 65 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?

Explanation: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 55 = 2.75 grams of red pigment

multiply(divide(55, multiply(const_100, const_2)), 10)

<gadget id="calculator">100 * 2</gadget>
<output>200</output>
<gadget id="calculator">55 / 200</gadget>
<output>11/40 = around 0.275</output>
<gadget id="calculator">(11/40) * 10</gadget>
<output>11/4 = around 2.75</output>
<result>11/4 = around 2.75</result>


the average expenditure of a labourer for 6 months was 95 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i

Explanation: "income of 6 months = ( 6 × 95 ) – debt = 570 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 840 average monthly income = 840 ÷ 10 = 84 answer e"

divide(add(add(multiply(95, 6), multiply(60, 4)), 30), add(6, 4))

<gadget id="calculator">95 * 6</gadget>
<output>570</output>
<gadget id="calculator">60 * 4</gadget>
<output>240</output>
<gadget id="calculator">570 + 240</gadget>
<output>810</output>
<gadget id="calculator">810 + 30</gadget>
<output>840</output>
<gadget id="calculator">6 + 4</gadget>
<output>10</output>
<gadget id="calculator">840 / 10</gadget>
<output>84</output>
<result>84</result>


if 60 % of 3 / 5 of a number is 18 , then the number is ?

Explanation: "let the number be x . then 60 % of 3 / 5 of x = 18 60 / 100 * 3 / 5 * x = 18 x = ( 18 * 25 / 9 ) = 50 required number = 50 . correct option : d"

divide(18, multiply(divide(60, const_100), divide(3, 5)))

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * (3/5)</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">18 / (9/25)</gadget>
<output>50</output>
<result>50</result>


a driver just filled the car ' s gas tank with 18 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?

Explanation: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 18 ) + x = 0.1 ( 18 + x ) 0.9 x = 1.8 - 0.9 x = 1 liter the answer is a ."

divide(multiply(18, 5), subtract(const_100, 10))

<gadget id="calculator">18 * 5</gadget>
<output>90</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">90 / 90</gadget>
<output>1</output>
<result>1</result>


in covering a distance of 30 km , arun takes 22 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?

Explanation: explanation : if arun doubles his speed , he needs 3 hour less . double speed means half time . hence , half of the time required by arun to cover 30 km = 3 hour i . e . , time required by arun to cover 30 km = 6 hour arun ' s speed = 30 / 6 = 5 kmph answer is b

divide(30, multiply(add(1, const_2), const_2))

<gadget id="calculator">1 + 2</gadget>
<output>3</output>
<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">30 / 6</gadget>
<output>5</output>
<result>5</result>


in the new budget the price of wheat rose by 8 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?

Explanation: reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b

multiply(divide(divide(8, const_100), add(divide(8, const_100), const_1)), const_100)

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>
<gadget id="calculator">(2/25) + 1</gadget>
<output>27/25 = around 1.08</output>
<gadget id="calculator">(2/25) / (27/25)</gadget>
<output>2/27 = around 0.074074</output>
<gadget id="calculator">(2/27) * 100</gadget>
<output>200/27 = around 7.407407</output>
<result>200/27 = around 7.407407</result>


find the length of the wire required to go 12 times round a square field containing 104976 m 2 .

Explanation: "a 2 = 104976 = > a = 324 4 a = 1296 1296 * 12 = 15552 answer : e"

<gadget id="calculator">104_976 ** (1/2)</gadget>
<output>324</output>
<gadget id="calculator">4 * 324</gadget>
<output>1_296</output>
<gadget id="calculator">1_296 * 12</gadget>
<output>15_552</output>
<result>15_552</result>


a , b and c started a business with a total investment of rs . 72000 . a invests rs . 6000 more than b and b invests rs . 3000 less than c . if the total profit at the end of a year is rs . 8640 , find a ' s share .

Explanation: explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 9 / 24 ) × 8640 ] = rs . 3240 answer : option a

<gadget id="calculator">6_000 + 3_000</gadget>
<output>9_000</output>
<gadget id="calculator">72_000 - 9_000</gadget>
<output>63_000</output>
<gadget id="calculator">63_000 / 3</gadget>
<output>21_000</output>
<gadget id="calculator">21_000 + 6_000</gadget>
<output>27_000</output>
<gadget id="calculator">27_000 / 72_000</gadget>
<output>3/8 = around 0.375</output>
<gadget id="calculator">8_640 * (3/8)</gadget>
<output>3_240</output>
<result>3_240</result>


a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction e of the sum of the 21 numbers in the list ?

Explanation: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 1 / 6 answer b"

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))

<gadget id="calculator">1 * 1</gadget>
<output>1</output>
<gadget id="calculator">20 / 4</gadget>
<output>5</output>
<gadget id="calculator">5 + 21</gadget>
<output>26</output>
<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>
<gadget id="calculator">(13/2) * 2</gadget>
<output>13</output>
<gadget id="calculator">13 - 4</gadget>
<output>9</output>
<gadget id="calculator">9 - 3</gadget>
<output>6</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


the s . i . on a certain sum of money for 5 years at 6 % per annum is half the c . i . on rs . 3000 for 2 years at 15 % per annum . the sum placed on s . i . is ?

Explanation: c . i . = [ 3000 * ( 1 + 15 / 100 ) 2 - 3000 ] = ( 3000 * 23 / 20 * 23 / 20 - 3000 ) = rs . 967.5 . sum = ( 483.75 * 100 ) / ( 5 * 6 ) = rs . 1612.5 answer : c

divide(divide(subtract(multiply(3000, power(add(const_1, divide(15, const_100)), 2)), 3000), const_2), multiply(5, divide(6, const_100)))

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>
<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>
<gadget id="calculator">3_000 * (529/400)</gadget>
<output>7_935/2 = around 3_967.5</output>
<gadget id="calculator">(7_935/2) - 3_000</gadget>
<output>1_935/2 = around 967.5</output>
<gadget id="calculator">(1_935/2) / 2</gadget>
<output>1_935/4 = around 483.75</output>
<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>
<gadget id="calculator">5 * (3/50)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(1_935/4) / (3/10)</gadget>
<output>3_225/2 = around 1_612.5</output>
<result>3_225/2 = around 1_612.5</result>


what is rate of interest if principal . amount be 400 , simple interest 80 and time 2 year .

Explanation: "s . i = ( p * r * t ) / 100 80 = 800 r / 100 r = 80 / 8 = 10 % answer a"

multiply(divide(80, multiply(400, 2)), const_100)

<gadget id="calculator">400 * 2</gadget>
<output>800</output>
<gadget id="calculator">80 / 800</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>


if 0.20 : x : : 4 : 2 , then x is equal to

Explanation: "sol . ( x × 4 ) = ( 0.20 × 2 ) ⇒ x = 0.4 / 4 = 0.1 . answer c"

<gadget id="calculator">0.2 * 2</gadget>
<output>0.4</output>
<gadget id="calculator">0.4 / 4</gadget>
<output>0.1</output>
<result>0.1</result>


along a yard 225 metres long , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees

Explanation: "explanation : 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 option b"

<gadget id="calculator">26 - 1</gadget>
<output>25</output>
<gadget id="calculator">225 / 25</gadget>
<output>9</output>
<result>9</result>


a retailer marks her goods in such a way that the profit made by selling 50 articles is equal to the selling price of 20 articles . what is the percentage of profit made by the retailer ?

Explanation: let cost price = x profit = y selling price = x + y 50 y = 20 ( x + y ) 30 y = 20 x percentage profit = y / x ∗ 100 = 20 / 30 ∗ 100 = 66.667 answer = a

multiply(subtract(divide(50, subtract(50, 20)), const_1), const_100)

<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<gadget id="calculator">50 / 30</gadget>
<output>5/3 = around 1.666667</output>
<gadget id="calculator">(5/3) - 1</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>


a basket contains 10 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?

Explanation: "the total number of ways to choose 2 apples is 10 c 2 = 45 the number of ways that include the spoiled apple is 9 c 1 = 9 p ( the spoiled apple is included ) = 9 / 45 = 1 / 5 the answer is e ."

divide(choose(subtract(10, 1), 1), choose(10, 2))

<gadget id="calculator">10 - 1</gadget>
<output>9</output>
<gadget id="calculator">binomial(9, 1)</gadget>
<output>9</output>
<gadget id="calculator">binomial(10, 2)</gadget>
<output>45</output>
<gadget id="calculator">9 / 45</gadget>
<output>1/5 = around 0.2</output>
<result>1/5 = around 0.2</result>


Explanation: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is first term = 90 ; total terms = 85 ; difference = 5 90 + ( 84 ) 5 = 510 ans e"

add(90, multiply(subtract(85, const_1), 5))

<gadget id="calculator">85 - 1</gadget>
<output>84</output>
<gadget id="calculator">84 * 5</gadget>
<output>420</output>
<gadget id="calculator">90 + 420</gadget>
<output>510</output>
<result>510</result>


a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 191 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?

Explanation: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 191 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 191 ( x + y ) ( x - y ) = 191 191 is a prime number and thus it will be ( 96 + 95 ) * ( 96 - 95 ) . thus x = 96 and y = 95 x ^ 2 = 96 ^ 2 = 9216 the answer is c ."

power(add(divide(191, const_2), add(const_0_25, const_0_25)), const_2)

<gadget id="calculator">191 / 2</gadget>
<output>191/2 = around 95.5</output>
<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(191/2) + (1/2)</gadget>
<output>96</output>
<gadget id="calculator">96 ** 2</gadget>
<output>9_216</output>
<result>9_216</result>


a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a .

Explanation: "( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = 240 answer : a"

multiply(divide(630, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>
<gadget id="calculator">3_000 - 1_000</gadget>
<output>2_000</output>
<gadget id="calculator">12 - 8</gadget>
<output>4</output>
<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>
<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>
<gadget id="calculator">4_000 + 1_000</gadget>
<output>5_000</output>
<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>
<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>
<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>
<gadget id="calculator">630 / 84_000</gadget>
<output>3/400 = around 0.0075</output>
<gadget id="calculator">(3/400) * 32_000</gadget>
<output>240</output>
<result>240</result>


on a certain day , tim invested $ 1,000 at 10 percent annual interest , compounded annually , and lana invested 2,000 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 1,000 ( 1.10 ) ^ 2 = 1,000 ( 1.21 ) = 1,210 and lana would have 2,000 ( 1.05 ) ^ 2 = 2,000 ( 1.1025 ) = 2,205 thus , tim earned 210 dollars , while lana earned 205 dollars the difference is $ 5 and the answer is a ."

subtract(subtract(multiply(1,000, power(add(const_1, divide(10, const_100)), 2)), 1,000), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 2,000), 2,000))

<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">1_000 * (121/100)</gadget>
<output>1_210</output>
<gadget id="calculator">1_210 - 1_000</gadget>
<output>210</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) * 2_000</gadget>
<output>2_205</output>
<gadget id="calculator">2_205 - 2_000</gadget>
<output>205</output>
<gadget id="calculator">210 - 205</gadget>
<output>5</output>
<result>5</result>


what is the angle between the minute and the hour hand of the clock which shows 12 : 24 ?

Explanation: at 12 : 24 - minute hand will be at 24 * 6 = 144 degrees from position of 12 . - hour hand will move by 2 * 6 = 12 degree during the same time so the difference between the two hands will be 144 - 12 = 132 degrees . answer : e

subtract(multiply(24, multiply(const_3, const_2)), 12)

<gadget id="calculator">3 * 2</gadget>
<output>6</output>
<gadget id="calculator">24 * 6</gadget>
<output>144</output>
<gadget id="calculator">144 - 12</gadget>
<output>132</output>
<result>132</result>


find the value of ( 70 + 28 / 100 ) × 100

Explanation: ( 7000 + 28 ) / 100 * 100 = 7028 answer : a

multiply(add(divide(28, 100), 70), const_100)

<gadget id="calculator">28 / 100</gadget>
<output>7/25 = around 0.28</output>
<gadget id="calculator">(7/25) + 70</gadget>
<output>1_757/25 = around 70.28</output>
<gadget id="calculator">(1_757/25) * 100</gadget>
<output>7_028</output>
<result>7_028</result>


a train with 120 wagons crosses john who is going in the same direction , in 36 seconds . it travels for half an hour from the time it starts ove ( who is also riding on his horse ) coming from the opposite direction in 24 seconds . in how much time after the train has crossed the mike do the john meets to mike ? rtaking the john ( he is riding on the horse ) before it starts overtaking the mike

Explanation: let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e

subtract(divide(multiply(subtract(divide(add(36, 24), subtract(36, 24)), const_1), multiply(multiply(const_10, const_3), const_60)), const_2), 24)

<gadget id="calculator">36 + 24</gadget>
<output>60</output>
<gadget id="calculator">36 - 24</gadget>
<output>12</output>
<gadget id="calculator">60 / 12</gadget>
<output>5</output>
<gadget id="calculator">5 - 1</gadget>
<output>4</output>
<gadget id="calculator">10 * 3</gadget>
<output>30</output>
<gadget id="calculator">30 * 60</gadget>
<output>1_800</output>
<gadget id="calculator">4 * 1_800</gadget>
<output>7_200</output>
<gadget id="calculator">7_200 / 2</gadget>
<output>3_600</output>
<gadget id="calculator">3_600 - 24</gadget>
<output>3_576</output>
<result>3_576</result>


the ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5808 sq cm . what is the ratio of the width and the area of the rectangle ?

Explanation: "let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 5808 12 x ^ 2 = 5808 x ^ 2 = 484 x = 22 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 88 the answer is d ."

divide(divide(sqrt(multiply(3, 5808)), const_2), 5808)

<gadget id="calculator">3 * 5_808</gadget>
<output>17_424</output>
<gadget id="calculator">17_424 ** (1/2)</gadget>
<output>132</output>
<gadget id="calculator">132 / 2</gadget>
<output>66</output>
<gadget id="calculator">66 / 5_808</gadget>
<output>1/88 = around 0.011364</output>
<result>1/88 = around 0.011364</result>


a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 990 grams . find the profit percent .

Explanation: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 990 100 + g / 100 + 0 = 1000 / 990 100 + g = 100 / 99 * 100 g = 1.01 answer : c"

multiply(divide(subtract(multiply(add(add(const_4, const_1), add(const_4, const_1)), const_100), 990), 990), const_100)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 + 5</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">1_000 - 990</gadget>
<output>10</output>
<gadget id="calculator">10 / 990</gadget>
<output>1/99 = around 0.010101</output>
<gadget id="calculator">(1/99) * 100</gadget>
<output>100/99 = around 1.010101</output>
<result>100/99 = around 1.010101</result>


a basket contains 9 apples , of which 1 is spoiled and the rest are good . if we select 2 apples from the basket simultaneously and at random , what is the probability that the 2 apples selected will include the spoiled apple ?

Explanation: the total number of ways to choose 2 apples is 9 c 2 = 36 the number of ways that include the spoiled apple is 8 c 1 = 8 p ( the spoiled apple is included ) = 8 / 36 = 2 / 9 the answer is d .

divide(choose(subtract(9, 1), 1), choose(9, 2))

<gadget id="calculator">9 - 1</gadget>
<output>8</output>
<gadget id="calculator">binomial(8, 1)</gadget>
<output>8</output>
<gadget id="calculator">binomial(9, 2)</gadget>
<output>36</output>
<gadget id="calculator">8 / 36</gadget>
<output>2/9 = around 0.222222</output>
<result>2/9 = around 0.222222</result>


26 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?

Explanation: "think of 100 people total : from the first fact , 26 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 26 equals the number of fair haired men , which is 39 men with fair hair . add this 39 to the 26 women and get 65 fair haired men and women out of 100 total men and women . 65 % e"

<gadget id="calculator">26 / 40</gadget>
<output>13/20 = around 0.65</output>
<gadget id="calculator">(13/20) * 100</gadget>
<output>65</output>
<result>65</result>


a work as fast as b . if b can complete a work in 24 days independently , the number of days in which a and b can together finish the work in ?

Explanation: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 24 a + b 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 a and b can finish the work in 8 days answer is c"

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">2 * (1/24)</gadget>
<output>1/12 = around 0.083333</output>
<gadget id="calculator">(1/24) + (1/12)</gadget>
<output>1/8 = around 0.125</output>
<gadget id="calculator">1 / (1/8)</gadget>
<output>8</output>
<result>8</result>


Explanation: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 = > 4 x 2 ^ 2 n = 4 ^ 20 = 2 ^ 40 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 40 = > 2 ^ ( 2 n + 2 ) = 2 ^ 40 = > 2 n + 2 = 40 = > n = 19 so . answer will be c ."

<gadget id="calculator">20 * 2</gadget>
<output>40</output>
<gadget id="calculator">40 - 2</gadget>
<output>38</output>
<gadget id="calculator">38 / 2</gadget>
<output>19</output>
<result>19</result>


in a division sum , the remainder is 8 and the divisor is 6 times the quotient and is obtained by adding 3 to the thrice of the remainder . the dividend is :

Explanation: "diver = ( 8 * 3 ) + 3 = 27 6 * quotient = 27 quotient = 4.5 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 4.5 ) + 8 = 129.5 b"

add(multiply(add(multiply(8, const_3), 3), divide(add(multiply(8, const_3), 3), 6)), 8)

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">24 + 3</gadget>
<output>27</output>
<gadget id="calculator">27 / 6</gadget>
<output>9/2 = around 4.5</output>
<gadget id="calculator">27 * (9/2)</gadget>
<output>243/2 = around 121.5</output>
<gadget id="calculator">(243/2) + 8</gadget>
<output>259/2 = around 129.5</output>
<result>259/2 = around 129.5</result>


a rectangular swimming pool is 20 feet by 20 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 576 square feet . what is the width of the deck ?

Explanation: "let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 24 has unit digit 6 . . . . . . . . . . hold b ) 2.5 feet . . . . . . . . . 25 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 26 has unit digit 6 . . . . . . . . . . . elimate ( area is more than stipulated ) d ) 4 feet . . . . . . . . . . . . 28 * 28 has unit digit 4 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : a"

divide(subtract(sqrt(add(power(subtract(20, const_1), const_2), subtract(576, rectangle_area(20, 20)))), subtract(20, const_1)), const_2)

<gadget id="calculator">20 - 1</gadget>
<output>19</output>
<gadget id="calculator">19 ** 2</gadget>
<output>361</output>
<gadget id="calculator">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">576 - 400</gadget>
<output>176</output>
<gadget id="calculator">361 + 176</gadget>
<output>537</output>
<gadget id="calculator">537 ** (1/2)</gadget>
<output>sqrt(537) = around 23.17326</output>
<gadget id="calculator">(sqrt(537)) - 19</gadget>
<output>-19 + sqrt(537) = around 4.17326</output>
<gadget id="calculator">(-19 + sqrt(537)) / 2</gadget>
<output>-19/2 + sqrt(537)/2 = around 2.08663</output>
<result>-19/2 + sqrt(537)/2 = around 2.08663</result>


a circle graph shows how the budget of a certain company was spent : 61 percent for salaries , 10 percent for research and development , 6 percent for utilities , 5 percent for equipment , 3 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the percent of the budget it represents , how many degrees of the circle are used to represent transportation ?

Explanation: the percent of the budget for transportation is 100 - ( 61 + 10 + 6 + 5 + 3 ) = 15 % 100 % of the circle is 360 degrees . then ( 15 % / 100 % ) * 360 = 54 degrees the answer is c .

divide(multiply(const_360, subtract(const_100, add(add(add(add(61, 10), 6), 5), 3))), const_100)

<gadget id="calculator">61 + 10</gadget>
<output>71</output>
<gadget id="calculator">71 + 6</gadget>
<output>77</output>
<gadget id="calculator">77 + 5</gadget>
<output>82</output>
<gadget id="calculator">82 + 3</gadget>
<output>85</output>
<gadget id="calculator">100 - 85</gadget>
<output>15</output>
<gadget id="calculator">360 * 15</gadget>
<output>5_400</output>
<gadget id="calculator">5_400 / 100</gadget>
<output>54</output>
<result>54</result>


10 stickers numbered 1 to 10 are placed in a bowl , mixed up thoroughly and then one sticker is drawn randomly . if it is known that the number on the drawn sticker is more than 3 , what is the probability that it is an even number ?

Explanation: let a be the event ‘ the number on the card drawn is even ’ and b be the event ‘ the number on the card drawn is greater than 3 ’ . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )

multiply(divide(const_4, 10), divide(10, subtract(10, 3)))

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">10 / 7</gadget>
<output>10/7 = around 1.428571</output>
<gadget id="calculator">(2/5) * (10/7)</gadget>
<output>4/7 = around 0.571429</output>
<result>4/7 = around 0.571429</result>


for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score w for the exam ?

Explanation: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a ."

divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))

<gadget id="calculator">58 * 3</gadget>
<output>174</output>
<gadget id="calculator">98 * 2</gadget>
<output>196</output>
<gadget id="calculator">174 + 196</gadget>
<output>370</output>
<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">370 / 5</gadget>
<output>74</output>
<result>74</result>


tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 9 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?

Explanation: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 9 = 144 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 144 pi / 200 pi = 0.72 a"

multiply(multiply(power(divide(8, 10), const_2), divide(9, 8)), const_100)

<gadget id="calculator">8 / 10</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">(4/5) ** 2</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">9 / 8</gadget>
<output>9/8 = around 1.125</output>
<gadget id="calculator">(16/25) * (9/8)</gadget>
<output>18/25 = around 0.72</output>
<gadget id="calculator">(18/25) * 100</gadget>
<output>72</output>
<result>72</result>


220 metres long yard , 21 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees

Explanation: "21 trees have 20 gaps between them , required distance ( 220 / 20 ) = 11 d"

divide(220, add(subtract(21, 2), const_1))

<gadget id="calculator">21 - 2</gadget>
<output>19</output>
<gadget id="calculator">19 + 1</gadget>
<output>20</output>
<gadget id="calculator">220 / 20</gadget>
<output>11</output>
<result>11</result>


the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 10 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 10 = 50 km imo , correct answer is ` ` d . ' '"

multiply(60, divide(multiply(5, 10), 60))

<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">60 * (5/6)</gadget>
<output>50</output>
<result>50</result>


a student travels from his house to school at 10 km / hr and reaches school 1 hour late . the next day he travels 12 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?

Explanation: let x be the distance from his house to the school . x / 10 = x / 12 + 2 6 x = 5 x + 120 x = 120 km the answer is e .

multiply(multiply(10, 12), divide(subtract(12, 10), add(1, 1)))

<gadget id="calculator">10 * 12</gadget>
<output>120</output>
<gadget id="calculator">12 - 10</gadget>
<output>2</output>
<gadget id="calculator">1 + 1</gadget>
<output>2</output>
<gadget id="calculator">2 / 2</gadget>
<output>1</output>
<gadget id="calculator">120 * 1</gadget>
<output>120</output>
<result>120</result>


two bullet trains of equal lengths take 10 seconds and 30 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

Explanation: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 30 m / sec = 4 m / sec . relative speed = ( 12 + 4 ) = 16 m / sec . required time = ( 120 + 120 ) / 16 sec = 15 sec . d"

<gadget id="calculator">120 + 120</gadget>
<output>240</output>
<gadget id="calculator">120 / 10</gadget>
<output>12</output>
<gadget id="calculator">120 / 30</gadget>
<output>4</output>
<gadget id="calculator">12 + 4</gadget>
<output>16</output>
<gadget id="calculator">240 / 16</gadget>
<output>15</output>
<result>15</result>


kathleen can paint a room in 2 hours , and anthony can paint an identical room in 7 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?

Explanation: ( 1 / 2 + 1 / 7 ) t = 2 t = 28 / 9 answer : a

multiply(divide(const_1, add(divide(const_1, 2), divide(const_1, 7))), const_2)

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/2) + (1/7)</gadget>
<output>9/14 = around 0.642857</output>
<gadget id="calculator">1 / (9/14)</gadget>
<output>14/9 = around 1.555556</output>
<gadget id="calculator">(14/9) * 2</gadget>
<output>28/9 = around 3.111111</output>
<result>28/9 = around 3.111111</result>


according to a recent student poll , 4 / 6 out of 24 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?

Explanation: "16 students are interested , 8 are not interested prob = 1 - 8 c 2 / 24 c 2 = 1 - ( 8 * 7 / ( 24 * 23 ) ) = 1 - 7 / 69 = 62 / 69 answer : d"

divide(subtract(choose(24, const_2), choose(subtract(24, multiply(24, divide(4, 6))), const_2)), choose(24, const_2))

<gadget id="calculator">binomial(24, 2)</gadget>
<output>276</output>
<gadget id="calculator">4 / 6</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">24 * (2/3)</gadget>
<output>16</output>
<gadget id="calculator">24 - 16</gadget>
<output>8</output>
<gadget id="calculator">binomial(8, 2)</gadget>
<output>28</output>
<gadget id="calculator">276 - 28</gadget>
<output>248</output>
<gadget id="calculator">248 / 276</gadget>
<output>62/69 = around 0.898551</output>
<result>62/69 = around 0.898551</result>


in school there are some bicycles and 4 wheeler wagons . one tuesday there are 190 wheels in the campus . how many bicycles are there ?

Explanation: let no . of bicycles be x & no . of wagons be y so , 2 x + 4 y = 190 by solving , we get no . of bicycles = 39 ( wheels = > 2 * 39 = 78 ) no . of wagons = 28 ( wheels = > 4 * 28 = 112 ) answer : e

multiply(divide(190, add(multiply(4, const_2), const_2)), const_2)

<gadget id="calculator">4 * 2</gadget>
<output>8</output>
<gadget id="calculator">8 + 2</gadget>
<output>10</output>
<gadget id="calculator">190 / 10</gadget>
<output>19</output>
<gadget id="calculator">19 * 2</gadget>
<output>38</output>
<result>38</result>


in a certain pond , 90.00001 fish were caught , tagged , and returned to the pond . a few days later , 90 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?

Explanation: "the percent of tagged fish in the second catch is 2 / 90 * 100 = 2.22 % . we are told that 2.22 % approximates the percent of tagged fish in the pond . since there are 90 tagged fish , then we have 0.022 x = 90 - - > x = 4,091 . answer : e ."

<gadget id="calculator">2 / 90</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">90.00001 / (1/45)</gadget>
<output>4_050.00045</output>
<result>4_050.00045</result>


in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 5 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight

Explanation: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 5 of the garden is green , so , since all the flowers must be either green or yellow , we know that 4 / 5 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 4 / 5 * 1 / 2 = 2 / 5 , or c ."

multiply(subtract(1, divide(1, 5)), divide(1, 2))

<gadget id="calculator">1 / 5</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 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">(4/5) * (1/2)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>


in what time will a railway train 110 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

Explanation: "t = 110 / 36 * 18 / 5 = 11 sec answer : d"

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>
<gadget id="calculator">110 / 10</gadget>
<output>11</output>
<result>11</result>


there are two groups of students in the sixth grade . there are 45 students in group a , and 55 students in group b . if , on a particular day , 20 % of the students in group a forget their homework , and 40 % of the students in group b forget their homework , then what percentage of the sixth graders forgot their homework ?

Explanation: "number of students in group a = 45 students who forget homework in group a = 20 % of 45 = 9 students number of students in group b = 55 students who forget homework in group b = 40 % of 55 = 22 students total number of students = 45 + 55 = 100 students who forgot homework = 9 + 22 = 31 students percentage of students who forget homework = 31 / 100 * 100 = 31 % answer : d"

multiply(divide(add(divide(multiply(45, 20), const_100), divide(multiply(55, 40), const_100)), add(45, 55)), const_100)

<gadget id="calculator">45 * 20</gadget>
<output>900</output>
<gadget id="calculator">900 / 100</gadget>
<output>9</output>
<gadget id="calculator">55 * 40</gadget>
<output>2_200</output>
<gadget id="calculator">2_200 / 100</gadget>
<output>22</output>
<gadget id="calculator">9 + 22</gadget>
<output>31</output>
<gadget id="calculator">45 + 55</gadget>
<output>100</output>
<gadget id="calculator">31 / 100</gadget>
<output>31/100 = around 0.31</output>
<gadget id="calculator">(31/100) * 100</gadget>
<output>31</output>
<result>31</result>


in a factory , an average of 50 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 43 sets / day . the average production per day for day last 5 days is ?

Explanation: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 43 - 25 x 50 = 40 ∴ average for last 5 days = 40 / 5 = 8 c"

divide(subtract(multiply(add(25, 5), 43), multiply(25, 50)), 5)

<gadget id="calculator">25 + 5</gadget>
<output>30</output>
<gadget id="calculator">30 * 43</gadget>
<output>1_290</output>
<gadget id="calculator">25 * 50</gadget>
<output>1_250</output>
<gadget id="calculator">1_290 - 1_250</gadget>
<output>40</output>
<gadget id="calculator">40 / 5</gadget>
<output>8</output>
<result>8</result>


find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1904 ?

Explanation: "1904 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1700 . answer : a"

divide(1904, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1))

<gadget id="calculator">2 * 5</gadget>
<output>10</output>
<gadget id="calculator">10 + 2</gadget>
<output>12</output>
<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>
<gadget id="calculator">(12/5) * 5</gadget>
<output>12</output>
<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>
<gadget id="calculator">(3/25) + 1</gadget>
<output>28/25 = around 1.12</output>
<gadget id="calculator">1_904 / (28/25)</gadget>
<output>1_700</output>
<result>1_700</result>


the overall age of x and y is 11 year greater than the overall age of y and z . z is how many decades younger that x ?

Explanation: "a 11 ( x + y ) â € “ ( y + z ) = 11 x â € “ z = 11"

<gadget id="calculator">11 / 1</gadget>
<output>11</output>
<result>11</result>


the mean of 50 observations was 36 . it was found later that an observation 47 was wrongly taken as 23 . the corrected new mean is

Explanation: "solution correct sum = ( 36 x 50 + 47 - 23 ) = 1824 . â ˆ ´ correct mean = 1824 / 50 = 36.48 . answer d"

divide(add(multiply(36, 50), subtract(subtract(50, const_2), 23)), 50)

<gadget id="calculator">36 * 50</gadget>
<output>1_800</output>
<gadget id="calculator">50 - 2</gadget>
<output>48</output>
<gadget id="calculator">48 - 23</gadget>
<output>25</output>
<gadget id="calculator">1_800 + 25</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 / 50</gadget>
<output>73/2 = around 36.5</output>
<result>73/2 = around 36.5</result>