in a class of 50 students , 20 play baseball , 15 play cricket and 11 play football . 7 play both baseball and cricket , 4 play cricket and football and 5 play baseball and football . if 18 students do not play any of these given sports , how many students play exactly two of these sports ?

Explanation: notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { cricket } + { football } - { hc + ch + hf } + { all three } + { neither } for more checkadvanced overlapping sets problems [ / color ] 50 = 20 + 15 + 11 - ( 7 + 4 + 5 ) + { all three } + 18 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a .

add(subtract(5, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), add(subtract(7, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), subtract(4, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18)))))

<gadget id="calculator">20 + 15</gadget>
<output>35</output>
<gadget id="calculator">35 + 11</gadget>
<output>46</output>
<gadget id="calculator">7 + 4</gadget>
<output>11</output>
<gadget id="calculator">11 + 5</gadget>
<output>16</output>
<gadget id="calculator">46 - 16</gadget>
<output>30</output>
<gadget id="calculator">30 + 18</gadget>
<output>48</output>
<gadget id="calculator">50 - 48</gadget>
<output>2</output>
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
<gadget id="calculator">7 - 2</gadget>
<output>5</output>
<gadget id="calculator">4 - 2</gadget>
<output>2</output>
<gadget id="calculator">5 + 2</gadget>
<output>7</output>
<gadget id="calculator">3 + 7</gadget>
<output>10</output>
<result>10</result>


the speed of a train is 90 kmph . what is the distance covered by it in 10 minutes ?

Explanation: "90 * 10 / 60 = 15 kmph answer : a"

<gadget id="calculator">10 / 60</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 90</gadget>
<output>15</output>
<result>15</result>


a positive number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x ?

Explanation: "sq rt ( 5 x / 3 ) = x = > 5 x / 3 = x ^ 2 = > x = 5 / 3 ans - d"

<gadget id="calculator">5 / 3</gadget>
<output>5/3 = around 1.666667</output>
<result>5/3 = around 1.666667</result>


the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 2001 , the price of commodity x was rs . 4.20 and that of y was rs . 6.30 , in which year commodity x will cost 40 paise more than the commodity y ?

Explanation: "suppose commodity x will cost 40 paise more than y after z years . then , ( 4.20 + 0.40 z ) - ( 6.30 + 0.15 z ) = 0.40 0.25 z = 0.40 + 2.10 z = 2.50 / 0.25 = 250 / 25 = 10 . therefore , x will cost 40 paise more than y 10 years after 2001 i . e . , 2011 . answer is d ."

add(2001, divide(add(divide(40, const_100), subtract(6.30, 4.20)), subtract(divide(40, const_100), divide(15, const_100))))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">6.3 - 4.2</gadget>
<output>2.1</output>
<gadget id="calculator">(2/5) + 2.1</gadget>
<output>2.5</output>
<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(2/5) - (3/20)</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">2.5 / (1/4)</gadget>
<output>10</output>
<gadget id="calculator">2_001 + 10</gadget>
<output>2_011</output>
<result>2_011</result>


if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 13 . what is the value of f ( 6 ) ?

Explanation: "since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 13 then f ( 5 ) = 13 - 5 = 8 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 8 - 6 = 2 . answer : d . questions on funtions to practice :"

<gadget id="calculator">1 + 4</gadget>
<output>5</output>
<gadget id="calculator">13 - 5</gadget>
<output>8</output>
<gadget id="calculator">8 - 6</gadget>
<output>2</output>
<result>2</result>


what will be the area of a semi - circle of 14 metres diameter ?

Explanation: area of semicircle = ½ π r 2 = ½ × 22 ⁄ 7 × 7 × 7 = 77 m 2 answer b

<gadget id="calculator">14 / 2</gadget>
<output>7</output>
<gadget id="calculator">pi * (7 ** 2)</gadget>
<output>49*pi = around 153.93804</output>
<gadget id="calculator">(49*pi) / 2</gadget>
<output>49*pi/2 = around 76.96902</output>
<result>49*pi/2 = around 76.96902</result>


the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 2200 for a computer table , then what was the cost price of the computer table ?

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 2200 ( 100 / 110 ) = rs . 2000 answer : b"

divide(2200, add(const_1, divide(10, const_100)))

<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">2_200 / (11/10)</gadget>
<output>2_000</output>
<result>2_000</result>


one fourth of a solution that was 10 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?

Explanation: "say the second solution ( which was 1 / 4 th of total ) was x % salt , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : b ."

multiply(subtract(multiply(divide(16, const_100), const_4), subtract(multiply(divide(10, const_100), const_4), divide(10, const_100))), const_100)

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>
<gadget id="calculator">(4/25) * 4</gadget>
<output>16/25 = around 0.64</output>
<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/10) * 4</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) - (1/10)</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(16/25) - (3/10)</gadget>
<output>17/50 = around 0.34</output>
<gadget id="calculator">(17/50) * 100</gadget>
<output>34</output>
<result>34</result>


if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 85 , what is the value of c â ˆ ’ a ?

Explanation: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 170 - - 2 subtracting 1 from 2 we have c - a = 80 ; answer : b"

it can not be determined from the information given

subtract(multiply(85, const_2), multiply(45, const_2))

<gadget id="calculator">85 * 2</gadget>
<output>170</output>
<gadget id="calculator">45 * 2</gadget>
<output>90</output>
<gadget id="calculator">170 - 90</gadget>
<output>80</output>
<result>80</result>


3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 4 pumps work to empty the tank in 1 day ?

Explanation: the required number of working hours per day x , more pumps , less working hours per day ( indirect ) less days , more working hours per day ( indirect ) pumps 4 : 3 , days 1 : 2 } : : 8 : x therefore 4 * 1 * x = 3 * 2 * 8 , x = ( 3 * 2 * 8 ) / 4 x = 12 correct answer ( d )

<gadget id="calculator">3 * 8</gadget>
<output>24</output>
<gadget id="calculator">24 * 2</gadget>
<output>48</output>
<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>


peter invests a sum of money and gets back an amount of $ 810 in 3 years . david invests an equal amount of money and gets an amount of $ 854 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?

Explanation: since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 854 - 810 = 44 interest earned for 3 years = 44 * 3 = 132 amount invested = 815 - 132 = 683 answer : b

subtract(810, multiply(divide(subtract(854, 810), subtract(divide(4, const_100), divide(3, const_100))), divide(3, const_100)))

<gadget id="calculator">854 - 810</gadget>
<output>44</output>
<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">3 / 100</gadget>
<output>3/100 = around 0.03</output>
<gadget id="calculator">(1/25) - (3/100)</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">44 / (1/100)</gadget>
<output>4_400</output>
<gadget id="calculator">4_400 * (3/100)</gadget>
<output>132</output>
<gadget id="calculator">810 - 132</gadget>
<output>678</output>
<result>678</result>


a envelop weight 9.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?

Explanation: "800 * 9.2 7360.0 gm 7.36 kg answer : e"

<gadget id="calculator">9.2 * 800</gadget>
<output>7_360</output>
<gadget id="calculator">7_360 / 1_000</gadget>
<output>184/25 = around 7.36</output>
<result>184/25 = around 7.36</result>


what least number should be added to 1022 , so that the sum is completely divisible by 25 ?

Explanation: "1022 ã · 25 = 40 with remainder = 22 22 + 3 = 25 . hence 3 should be added to 1022 so that the sum will be divisible by 25 answer : option b"

<gadget id="calculator">1_022 % 25</gadget>
<output>22</output>
<gadget id="calculator">25 - 22</gadget>
<output>3</output>
<result>3</result>


a hostel had provisions for 250 men for 44 days . if 50 men left the hostel , how long will the food last at the same rate ?

Explanation: "a hostel had provisions for 250 men for 44 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 44 250 × 44 = 200 x 5 × 44 = 4 x x = 5 × 11 = 55 answer a"

divide(multiply(250, 44), subtract(250, 50))

<gadget id="calculator">250 * 44</gadget>
<output>11_000</output>
<gadget id="calculator">250 - 50</gadget>
<output>200</output>
<gadget id="calculator">11_000 / 200</gadget>
<output>55</output>
<result>55</result>


the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8339 for a computer table , then what was the cost price of the computer table ?

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8339 ( 100 / 124 ) = rs . 6725 . answer : c"

divide(8339, add(const_1, divide(24, const_100)))

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>
<gadget id="calculator">1 + (6/25)</gadget>
<output>31/25 = around 1.24</output>
<gadget id="calculator">8_339 / (31/25)</gadget>
<output>6_725</output>
<result>6_725</result>


Explanation: "63 + 5 * 12 / ( 180 / 3 ) = 63 + 5 * 12 / ( 60 ) = 63 + ( 5 * 12 ) / 60 = 63 + 1 = 64 . answer : d"

add(63, divide(multiply(5, 12), divide(180, 3)))

<gadget id="calculator">5 * 12</gadget>
<output>60</output>
<gadget id="calculator">180 / 3</gadget>
<output>60</output>
<gadget id="calculator">60 / 60</gadget>
<output>1</output>
<gadget id="calculator">63 + 1</gadget>
<output>64</output>
<result>64</result>


a hen leaps 3 leaps for every 2 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?

Explanation: "given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 3 / 3 * 2 = 2 : 1 ' ' answer : 2 : 1 ;"

<gadget id="calculator">3 / 2</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(3/2) / (3/4)</gadget>
<output>2</output>
<result>2</result>


praveen starts business with rs . 3640 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari ’ s contribution in the capital ?

Explanation: "let hari ’ s capital be rs . x . then , 3640 * 12 / 7 x = 2 / 3 = > 14 x = 131040 = > x = 9360 . answer : e"

divide(divide(3640, subtract(const_1, divide(5, const_12))), divide(2, 3))

<gadget id="calculator">5 / 12</gadget>
<output>5/12 = around 0.416667</output>
<gadget id="calculator">1 - (5/12)</gadget>
<output>7/12 = around 0.583333</output>
<gadget id="calculator">3_640 / (7/12)</gadget>
<output>6_240</output>
<gadget id="calculator">2 / 3</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">6_240 / (2/3)</gadget>
<output>9_360</output>
<result>9_360</result>


how many positive integers q between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ?

Explanation: 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the integers ending in 5 ( already took out those ending in 0 ) . take out 10 integers ( 2 ? 5 , ? = 0 to 9 ) , leaving us with 40 integers . 4 ) now the painstaking part . we have to remove the remaining numbers that are multiples of 3 . those are 201 , 207 , 213 , 219 , 231 , 237 , 243 , 249 , 261 , 267 , 273 , 279 , 291 , and 297 . . . a total of 14 numbers . 26 numbers left ! 6 ) answer choice e .

subtract(subtract(subtract(add(subtract(300, 200), const_1), add(subtract(divide(300, 2), divide(200, 2)), const_1)), floor(add(subtract(add(subtract(divide(300, 3), divide(200, 3)), const_1), add(add(const_10, 5), 2)), const_1))), subtract(add(subtract(divide(300, 5), divide(200, 5)), const_1), add(const_10, 5)))

<gadget id="calculator">300 - 200</gadget>
<output>100</output>
<gadget id="calculator">100 + 1</gadget>
<output>101</output>
<gadget id="calculator">300 / 2</gadget>
<output>150</output>
<gadget id="calculator">200 / 2</gadget>
<output>100</output>
<gadget id="calculator">150 - 100</gadget>
<output>50</output>
<gadget id="calculator">50 + 1</gadget>
<output>51</output>
<gadget id="calculator">101 - 51</gadget>
<output>50</output>
<gadget id="calculator">300 / 3</gadget>
<output>100</output>
<gadget id="calculator">200 / 3</gadget>
<output>200/3 = around 66.666667</output>
<gadget id="calculator">100 - (200/3)</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">(100/3) + 1</gadget>
<output>103/3 = around 34.333333</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">15 + 2</gadget>
<output>17</output>
<gadget id="calculator">(103/3) - 17</gadget>
<output>52/3 = around 17.333333</output>
<gadget id="calculator">(52/3) + 1</gadget>
<output>55/3 = around 18.333333</output>
<gadget id="calculator">floor(55/3)</gadget>
<output>18</output>
<gadget id="calculator">50 - 18</gadget>
<output>32</output>
<gadget id="calculator">300 / 5</gadget>
<output>60</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<gadget id="calculator">60 - 40</gadget>
<output>20</output>
<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">21 - 15</gadget>
<output>6</output>
<gadget id="calculator">32 - 6</gadget>
<output>26</output>
<result>26</result>


rs . 850 becomes rs . 956 in 3 years at a certain rate of simple interest . if the rate of interest is increased by 4 % , what amount will rs . 850 become in 3 years ?

Explanation: "solution s . i . = rs . ( 956 - 850 ) = rs . 106 rate = ( 100 x 106 / 850 x 3 ) = 212 / 51 % new rate = ( 212 / 51 + 4 ) % = 416 / 51 % new s . i . = rs . ( 850 x 416 / 51 x 3 / 100 ) rs . 208 . ∴ new amount = rs . ( 850 + 208 ) = rs . 1058 . answer c"

add(850, divide(multiply(multiply(850, add(divide(multiply(subtract(956, 850), const_100), multiply(850, 3)), 4)), 3), const_100))

<gadget id="calculator">956 - 850</gadget>
<output>106</output>
<gadget id="calculator">106 * 100</gadget>
<output>10_600</output>
<gadget id="calculator">850 * 3</gadget>
<output>2_550</output>
<gadget id="calculator">10_600 / 2_550</gadget>
<output>212/51 = around 4.156863</output>
<gadget id="calculator">(212/51) + 4</gadget>
<output>416/51 = around 8.156863</output>
<gadget id="calculator">850 * (416/51)</gadget>
<output>20_800/3 = around 6_933.333333</output>
<gadget id="calculator">(20_800/3) * 3</gadget>
<output>20_800</output>
<gadget id="calculator">20_800 / 100</gadget>
<output>208</output>
<gadget id="calculator">850 + 208</gadget>
<output>1_058</output>
<result>1_058</result>


it takes ten minutes to load a certain video on a cellphone , and fifteen seconds to load that same video on a laptop . if the two devices were connected so that they operated in concert at their respective rates , how many seconds would it take them to load the video , rounded to the nearest hundredth ?

Explanation: "the laptop can load the video at a rate of 1 / 15 of the video per second . the phone can load the video at a rate of 1 / ( 60 * 10 ) = 1 / 600 of the video per second . the combined rate is 1 / 15 + 1 / 600 = 41 / 600 of the video per second . the time required to load the video is 600 / 41 = 14.63 seconds . the answer is d ."

subtract(inverse(add(inverse(multiply(add(add(const_2, const_3), const_4), const_60)), inverse(add(multiply(const_3, const_4), const_3)))), divide(subtract(multiply(multiply(const_4, const_4), const_3), const_2), multiply(const_100, const_100)))

<gadget id="calculator">2 + 3</gadget>
<output>5</output>
<gadget id="calculator">5 + 4</gadget>
<output>9</output>
<gadget id="calculator">9 * 60</gadget>
<output>540</output>
<gadget id="calculator">1 / 540</gadget>
<output>1/540 = around 0.001852</output>
<gadget id="calculator">3 * 4</gadget>
<output>12</output>
<gadget id="calculator">12 + 3</gadget>
<output>15</output>
<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/540) + (1/15)</gadget>
<output>37/540 = around 0.068519</output>
<gadget id="calculator">1 / (37/540)</gadget>
<output>540/37 = around 14.594595</output>
<gadget id="calculator">4 * 4</gadget>
<output>16</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">48 - 2</gadget>
<output>46</output>
<gadget id="calculator">100 * 100</gadget>
<output>10_000</output>
<gadget id="calculator">46 / 10_000</gadget>
<output>23/5_000 = around 0.0046</output>
<gadget id="calculator">(540/37) - (23/5_000)</gadget>
<output>2_699_149/185_000 = around 14.589995</output>
<result>2_699_149/185_000 = around 14.589995</result>


a certain scholarship committee awarded scholarships in the amounts of $ 1250 , $ 2500 and $ 4000 . the committee awarded twice as many $ 2500 scholarships as $ 4000 and it awarded 3 times as many $ 1250 scholarships as $ 2500 scholarships . if the total of $ 75000 was awarded in $ 1250 scholarships , how many $ 4000 scholarships were awarded ?

Explanation: since the starting point is given as the $ 4000 scholarship , assume $ 4000 scholarships to be x by the given information , $ 2500 scholarships = 2 x and $ 1250 scholarships = 6 x gievn : total $ 1250 scholarships = $ 75000 6 x * 1250 = 75000 solve for x = 10 option d

divide(divide(75000, 1250), multiply(const_2, 3))

<gadget id="calculator">75_000 / 1_250</gadget>
<output>60</output>
<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">60 / 6</gadget>
<output>10</output>
<result>10</result>


in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 6 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]

Explanation: "a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 6 eggs - - > 6 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 12 eggs = 12 / 12 * 33 = 33 cents . answer : c ."

multiply(divide(divide(6, divide(const_1, const_2)), const_12), multiply(0.33, 100))

<gadget id="calculator">1 / 2</gadget>
<output>1/2 = around 0.5</output>
<gadget id="calculator">6 / (1/2)</gadget>
<output>12</output>
<gadget id="calculator">12 / 12</gadget>
<output>1</output>
<gadget id="calculator">0.33 * 100</gadget>
<output>33</output>
<gadget id="calculator">1 * 33</gadget>
<output>33</output>
<result>33</result>


a pupil ' s marks were wrongly entered as 73 instead of 40 . 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 = ( 73 - 40 ) = > x / 2 = 33 = > x = 66 . answer : c"

<gadget id="calculator">73 - 40</gadget>
<output>33</output>
<gadget id="calculator">33 * 2</gadget>
<output>66</output>
<result>66</result>


a baseball card decreased in value 25 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?

Explanation: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 25 / 100 ) * 100 = 75 after second year , value of baseball card = ( 1 - 10 / 100 ) * 75 = 67.5 total percent decrease of the card ' s value over the two years = ( 100 - 67.5 ) / 100 * 100 % = 31.5 % answer c"

subtract(const_100, multiply(multiply(subtract(const_1, divide(10, const_100)), subtract(const_1, divide(25, const_100))), const_100))

<gadget id="calculator">10 / 100</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 - (1/4)</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">(9/10) * (3/4)</gadget>
<output>27/40 = around 0.675</output>
<gadget id="calculator">(27/40) * 100</gadget>
<output>135/2 = around 67.5</output>
<gadget id="calculator">100 - (135/2)</gadget>
<output>65/2 = around 32.5</output>
<result>65/2 = around 32.5</result>


if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?

Explanation: "total nos of ways in which we can choose n = 96 n ( n + 1 ) ( n + 2 ) will be divisible by 8 ? case 1 : n = odd then n + 2 = odd & n + 1 will be even i . e this needs get divided by 8 , hence is a multiple of 8 so we have 8 . . 96 = 12 multiples to fill the n + 1 pos hence 12 ways case 2 : n is even then n + 2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n = 2 . . . . 96 ( all even nos ) i . e 48 nos total = 48 + 12 = 60 ways so reqd p = 60 / 96 = 5 / 8 ; answer : d"

divide(add(divide(96, 2), divide(96, 8)), 96)

<gadget id="calculator">96 / 2</gadget>
<output>48</output>
<gadget id="calculator">96 / 8</gadget>
<output>12</output>
<gadget id="calculator">48 + 12</gadget>
<output>60</output>
<gadget id="calculator">60 / 96</gadget>
<output>5/8 = around 0.625</output>
<result>5/8 = around 0.625</result>


a dealer offers a cash discount of 16 % and still makes a profit of 25 % when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?

Explanation: "given cash discount - 16 % profit - 25 % items sold - 60 price sold at = list price of 50 assume list price = $ 10 total invoice = $ 500 - 16 % cash discount = $ 420 let cost price of 60 items be x so total cost = 60 * x given the shopkeeper had a profit of 25 % 60 * x * 125 / 100 = 420 or x = $ 7 * 4 / 5 = $ 28 / 5 which means his products were listed at $ 10 which is a 78 + ( 4 / 7 ) % markup over $ 28 / 5 answer e"

multiply(subtract(divide(divide(divide(add(const_100, 25), const_100), subtract(const_1, divide(subtract(60, 50), 60))), divide(subtract(const_100, 16), const_100)), const_1), const_100)

<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">60 - 50</gadget>
<output>10</output>
<gadget id="calculator">10 / 60</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">1 - (1/6)</gadget>
<output>5/6 = around 0.833333</output>
<gadget id="calculator">(5/4) / (5/6)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">100 - 16</gadget>
<output>84</output>
<gadget id="calculator">84 / 100</gadget>
<output>21/25 = around 0.84</output>
<gadget id="calculator">(3/2) / (21/25)</gadget>
<output>25/14 = around 1.785714</output>
<gadget id="calculator">(25/14) - 1</gadget>
<output>11/14 = around 0.785714</output>
<gadget id="calculator">(11/14) * 100</gadget>
<output>550/7 = around 78.571429</output>
<result>550/7 = around 78.571429</result>


if n divided by 8 has a remainder of 1 , what is the remainder when 3 times n is divided by 8 ?

Explanation: as per question = > n = 8 p + 1 for some integer p hence 3 n = > 24 q + 3 = > remainder = > 3 for some integer q hence b

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


the volume of a cube is 2197 cc . find its surface .

Explanation: a 3 = 2197 = > a = 13 6 a 2 = 6 * 13 * 13 = 1014 answer : b

<gadget id="calculator">2_197 ** (1/3)</gadget>
<output>13</output>
<gadget id="calculator">6 * (13 ** 2)</gadget>
<output>1_014</output>
<result>1_014</result>


15 business executives and 3 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?

Explanation: "there are 15 business exec and in each handshake 2 business execs are involved . hence 15 c 2 = 105 also , each of 15 exec will shake hand with every 3 other chairmen for total of 45 handshake . total = 45 + 105 = 150 ans : a"

add(divide(multiply(15, subtract(15, const_1)), const_2), multiply(15, 3))

<gadget id="calculator">15 - 1</gadget>
<output>14</output>
<gadget id="calculator">15 * 14</gadget>
<output>210</output>
<gadget id="calculator">210 / 2</gadget>
<output>105</output>
<gadget id="calculator">15 * 3</gadget>
<output>45</output>
<gadget id="calculator">105 + 45</gadget>
<output>150</output>
<result>150</result>


a is twice as fast as b . if b alone can do a piece of work in 18 days , in what time can a and b together complete the work ?

Explanation: "a can do the work in 18 / 2 i . e . , 9 days . a and b ' s one day ' s work = 1 / 9 + 1 / 18 = ( 2 + 1 ) / 18 = 1 / 6 so a and b together can do the work in 6 days . answer : d"

inverse(add(divide(const_1, 18), multiply(divide(const_1, 18), const_2)))

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


the area of a triangle is with base 5.5 m and height 6 m ?

Explanation: "1 / 2 * 5.5 * 6 = 16.5 m 2 answer : b"

<gadget id="calculator">(5.5 * 6) / 2</gadget>
<output>16.5</output>
<result>16.5</result>


the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 8400 for a computer table , then what was the cost price of the computer table ?

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8400 ( 100 / 125 ) = rs . 6720 . answer : d"

divide(8400, add(const_1, divide(25, const_100)))

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">1 + (1/4)</gadget>
<output>5/4 = around 1.25</output>
<gadget id="calculator">8_400 / (5/4)</gadget>
<output>6_720</output>
<result>6_720</result>


the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 11 . the larger of the two numbers is :

Explanation: "clearly , the numbers are ( 23 x 10 ) and ( 23 x 11 ) . larger number = ( 23 x 11 ) = 253 . answer : option b"

<gadget id="calculator">23 * 11</gadget>
<output>253</output>
<result>253</result>


tim and é lan are 60 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?

Explanation: tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice c meet the 2 : 1 ( tim : elan = 40 : 20 ) ratio of maintaining total distance traveled 60 miles so correct answer c

<gadget id="calculator">5 + 10</gadget>
<output>15</output>
<gadget id="calculator">10 / 15</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 60</gadget>
<output>40</output>
<result>40</result>


if y is 90 % greater than x , than x is what % less than y ?

Explanation: "y = 1.9 x x = y / 1.9 = 10 y / 19 x is 9 / 19 less which is 47.4 % less than y . the answer is d ."

multiply(divide(90, add(90, const_100)), const_100)

<gadget id="calculator">90 + 100</gadget>
<output>190</output>
<gadget id="calculator">90 / 190</gadget>
<output>9/19 = around 0.473684</output>
<gadget id="calculator">(9/19) * 100</gadget>
<output>900/19 = around 47.368421</output>
<result>900/19 = around 47.368421</result>


what is the length of a bridge ( in meters ) , which a train 166 meters long and travelling at 45 km / h can cross in 40 seconds ?

Explanation: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 166 = 334 meters the answer is d ."

subtract(multiply(multiply(45, const_0_2778), 40), 166)

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>
<gadget id="calculator">45 * (5/18)</gadget>
<output>25/2 = around 12.5</output>
<gadget id="calculator">(25/2) * 40</gadget>
<output>500</output>
<gadget id="calculator">500 - 166</gadget>
<output>334</output>
<result>334</result>


the average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?

Explanation: "solution total weight increased = ( 10 x 4.2 ) kg = 42 kg . weight of new person = ( 65 + 42 ) kg = 107 kg . answer a"

<gadget id="calculator">10 * 4.2</gadget>
<output>42</output>
<gadget id="calculator">65 + 42</gadget>
<output>107</output>
<result>107</result>


a certain class of students is being divided into teams . the class can either be divided into 8 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?

Explanation: "let total no of students in the class be n so , we are told that n is divisible by both 8 24 so , lets find the least common multiple of 8 24 , ie 24 so our answer is ( d ) 24"

<gadget id="calculator">lcm(8, 24)</gadget>
<output>24</output>
<result>24</result>


in a games hour 4 different types of players came to the ground ? cricket 11 , hokey 15 , football 21 , softball 15 . how many players are present in the ground ?

Explanation: "total number of players = 11 + 15 + 21 + 15 = 62 answer is c"

<gadget id="calculator">11 + 15</gadget>
<output>26</output>
<gadget id="calculator">21 + 15</gadget>
<output>36</output>
<gadget id="calculator">26 + 36</gadget>
<output>62</output>
<result>62</result>


a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 275.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?

Explanation: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 275 = > 125 * s = 200 = > s = 1.6 answer e"

<gadget id="calculator">125 * 0.6</gadget>
<output>75</output>
<gadget id="calculator">275 - 75</gadget>
<output>200</output>
<gadget id="calculator">200 / 125</gadget>
<output>8/5 = around 1.6</output>
<result>8/5 = around 1.6</result>


a batsman makes a score of 50 runs in the 6 th inning and thus increases his average by 2 . find his average after 6 th inning .

Explanation: "let the average after 6 th inning = x then , average after 5 th inning = x - 2 5 ( x - 2 ) + 50 = 6 x x = 10 - 50 = 40 answer is a"

<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">50 - 12</gadget>
<output>38</output>
<gadget id="calculator">38 + 2</gadget>
<output>40</output>
<result>40</result>


the distance between two cities a and b is 330 km . a train starts from a at 8 a . m . and travels towards b at 60 km / hr . another train starts from b at 9 a . m . and travels towards a at 75 km / hr . at what time do they meet ?

Explanation: "suppose they meet x hrs after 8 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 330 60 x + 75 ( x - 1 ) = 330 = > x = 3 so , they meet at ( 8 + 3 ) i . e . , 11 a . m . answer : c"

<gadget id="calculator">330 + 75</gadget>
<output>405</output>
<gadget id="calculator">60 + 75</gadget>
<output>135</output>
<gadget id="calculator">405 / 135</gadget>
<output>3</output>
<gadget id="calculator">3 + 8</gadget>
<output>11</output>
<result>11</result>


a high school has 360 students 1 / 2 attend the arithmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 3 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .

Explanation: "basically , this question is asking you to figure out how many students are being double - counted . a - club has 180 members ( 1 / 2 of 360 ) b - club has 225 members ( 5 / 8 of 360 ) c - club has 270 members ( 3 / 4 of 360 ) we can create an equation to solve this : 180 + 225 + 270 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 135 ) . 180 + 225 + 270 = 360 + x + 270 x = 405 - 360 = 45 a"

subtract(subtract(add(add(divide(multiply(360, 1), 2), divide(multiply(360, 5), 8)), divide(multiply(360, 3), 4)), multiply(divide(multiply(360, 3), 8), 2)), 360)

<gadget id="calculator">360 * 1</gadget>
<output>360</output>
<gadget id="calculator">360 / 2</gadget>
<output>180</output>
<gadget id="calculator">360 * 5</gadget>
<output>1_800</output>
<gadget id="calculator">1_800 / 8</gadget>
<output>225</output>
<gadget id="calculator">180 + 225</gadget>
<output>405</output>
<gadget id="calculator">360 * 3</gadget>
<output>1_080</output>
<gadget id="calculator">1_080 / 4</gadget>
<output>270</output>
<gadget id="calculator">405 + 270</gadget>
<output>675</output>
<gadget id="calculator">1_080 / 8</gadget>
<output>135</output>
<gadget id="calculator">135 * 2</gadget>
<output>270</output>
<gadget id="calculator">675 - 270</gadget>
<output>405</output>
<gadget id="calculator">405 - 360</gadget>
<output>45</output>
<result>45</result>


the cash difference between the selling prices of an article at a profit of 8 % and 6 % is rs . 3 . the ratio of the two selling prices is ?

Explanation: "let c . p . of the article be rs . x . then , required ratio = 108 % of x / 106 % of x = 108 / 106 = 54 / 53 = 54 : 53 answer : d"

divide(add(const_100, 8), add(const_100, 6))

<gadget id="calculator">100 + 8</gadget>
<output>108</output>
<gadget id="calculator">100 + 6</gadget>
<output>106</output>
<gadget id="calculator">108 / 106</gadget>
<output>54/53 = around 1.018868</output>
<result>54/53 = around 1.018868</result>


reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 588 as interest at the end of the loan period , what was the rate of interest ?

Explanation: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 588 12 r 2 = 588 r 2 = 49 r = 7 . answer : b"

<gadget id="calculator">588 * 100</gadget>
<output>58_800</output>
<gadget id="calculator">58_800 / 1_200</gadget>
<output>49</output>
<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>
<result>7</result>


Explanation: "substitute y by 2 in x + 5 y = 24 x + 5 ( 2 ) = 24 x + 10 = 24 if we substitute x by 14 in x + 10 = 24 , we have 14 + 10 = 24 . hence x = 14 correct answer e"

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">24 - 10</gadget>
<output>14</output>
<result>14</result>


the wages earned by robin is 20 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?

Explanation: "let wage of erica = 10 wage of robin = 1.2 * 10 = 12 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 12 ) / 12 * 100 % = 4 / 12 * 100 % = 33 % answer b"

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

<gadget id="calculator">100 + 60</gadget>
<output>160</output>
<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">160 - 120</gadget>
<output>40</output>
<gadget id="calculator">40 / 120</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>


there are two numbers . if 10 % of the first number is added to the second number , then the second number increases to its 6 - fifth . what is the ratio of the first number to the second number ?

Explanation: let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e .

divide(divide(const_1, divide(10, const_2)), divide(const_1, 10))

<gadget id="calculator">10 / 2</gadget>
<output>5</output>
<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>
<gadget id="calculator">(1/5) / (1/10)</gadget>
<output>2</output>
<result>2</result>


each child has 2 pencils and 13 skittles . if there are 6 children , how many pencils are there in total ?

Explanation: 2 * 6 = 12 . answer is b .

<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<result>12</result>


a reduction of 40 % in the price of bananas would enable a man to obtain 60 more for rs . 40 , what is reduced price per dozen ?

Explanation: "40 * ( 40 / 100 ) = 16 - - - 60 ? - - - 12 = > rs . 3.2 answer : c"

multiply(const_12, divide(multiply(40, divide(40, const_100)), 60))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">40 * (2/5)</gadget>
<output>16</output>
<gadget id="calculator">16 / 60</gadget>
<output>4/15 = around 0.266667</output>
<gadget id="calculator">12 * (4/15)</gadget>
<output>16/5 = around 3.2</output>
<result>16/5 = around 3.2</result>


in a fuel station the service costs $ 2.05 per car , every liter of fuel costs 0.6 $ . assuming that you fill up 3 mini - vans and 2 trucks , how much money will the fuel cost to all the cars owners total , if a mini - van ' s tank is 70 liters and a truck ' s tank is 120 % bigger and they are all empty - ?

Explanation: "service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 70 = 210 litre fuel in 2 trucks = 2 * 70 ( 1 + 120 / 100 ) = 308 total fuel ( van + truck ) = 518 litre total fuel cost = 518 * 0.6 = 310.8 total cost = fuel + service = 310.8 + 10.25 = 321.05 answer is b"

add(multiply(multiply(add(70, divide(multiply(70, 120), const_100)), 2), 0.6), multiply(multiply(70, 3), 0.6))

<gadget id="calculator">70 * 120</gadget>
<output>8_400</output>
<gadget id="calculator">8_400 / 100</gadget>
<output>84</output>
<gadget id="calculator">70 + 84</gadget>
<output>154</output>
<gadget id="calculator">154 * 2</gadget>
<output>308</output>
<gadget id="calculator">308 * 0.6</gadget>
<output>184.8</output>
<gadget id="calculator">70 * 3</gadget>
<output>210</output>
<gadget id="calculator">210 * 0.6</gadget>
<output>126</output>
<gadget id="calculator">184.8 + 126</gadget>
<output>310.8</output>
<result>310.8</result>


a man two flats for $ 675958 each . on one he gains 16 % while on the other he loses 16 % . how much does he gain or lose in the whole transaction ?

Explanation: "in such a case there is always a loss loss % = ( 16 / 10 ) ^ 2 = 64 / 25 = 2.56 % answer is b"

multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 16)), 675958), multiply(divide(const_100, subtract(const_100, 16)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 16)), 675958), multiply(divide(const_100, subtract(const_100, 16)), 675958))), const_100)


a rectangular lawn of dimensions 120 m * 60 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?

Explanation: "area = ( l + b – d ) d ( 120 + 60 – 10 ) 10 = > 1700 m 2 1700 * 3 = rs . 5100 answer : a"

multiply(multiply(subtract(add(120, 60), 10), 10), 3)

<gadget id="calculator">120 + 60</gadget>
<output>180</output>
<gadget id="calculator">180 - 10</gadget>
<output>170</output>
<gadget id="calculator">170 * 10</gadget>
<output>1_700</output>
<gadget id="calculator">1_700 * 3</gadget>
<output>5_100</output>
<result>5_100</result>


the sum of the first 50 positive even integers is 2550 . what is the sum of the even integers from 502 to 600 inclusive ?

Explanation: "2 + 4 + 6 + 8 + . . . + 100 = 2550 502 + 504 + . . . + 600 = 50 ( 500 ) + ( 2 + 4 + . . . + 100 ) = 25,000 + 2550 = 27,550 the answer is b ."

multiply(divide(add(600, 502), const_2), add(divide(subtract(600, 502), const_2), const_1))

<gadget id="calculator">600 + 502</gadget>
<output>1_102</output>
<gadget id="calculator">1_102 / 2</gadget>
<output>551</output>
<gadget id="calculator">600 - 502</gadget>
<output>98</output>
<gadget id="calculator">98 / 2</gadget>
<output>49</output>
<gadget id="calculator">49 + 1</gadget>
<output>50</output>
<gadget id="calculator">551 * 50</gadget>
<output>27_550</output>
<result>27_550</result>


when x is multiplied by 3 , the result is 18 more than the result of subtracting x from 70 . what is the value of x ?

Explanation: "the equation that can be formed is : 3 x - 18 = 70 - x or , 4 x = 88 or , x = 22 . e answer ."

<gadget id="calculator">70 + 18</gadget>
<output>88</output>
<gadget id="calculator">3 + 1</gadget>
<output>4</output>
<gadget id="calculator">88 / 4</gadget>
<output>22</output>
<result>22</result>


10 men can complete a work in 7 days . but 10 women need 14 days to complete the same work . how many days will 5 men and 10 women need to complete the work ?

Explanation: work done by 10 men in 1 day = 1 / 7 work done by 1 man in 1 day = ( 1 / 7 ) / 10 = 1 / 70 work done by 10 women in 1 day = 1 / 14 work done by 1 woman in 1 day = 1 / 140 work done by 5 men and 10 women in 1 day = 5 × ( 1 / 70 ) + 10 × ( 1 / 140 ) = 5 / 70 + 10 / 140 = 1 / 7 = 5 men and 10 women can complete the work in 7 days answer : option c

inverse(add(multiply(10, inverse(multiply(14, 10))), multiply(5, divide(inverse(7), 10))))

<gadget id="calculator">14 * 10</gadget>
<output>140</output>
<gadget id="calculator">1 / 140</gadget>
<output>1/140 = around 0.007143</output>
<gadget id="calculator">10 * (1/140)</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">(1/7) / 10</gadget>
<output>1/70 = around 0.014286</output>
<gadget id="calculator">5 * (1/70)</gadget>
<output>1/14 = around 0.071429</output>
<gadget id="calculator">(1/14) + (1/14)</gadget>
<output>1/7 = around 0.142857</output>
<gadget id="calculator">1 / (1/7)</gadget>
<output>7</output>
<result>7</result>


vijay sells a cupboard at 10 % below cost price . had he got rs . 1500 more , he would have made a profit of 10 % . what is the cost price of the cupboard ?

Explanation: "explanation : cost price = 1500 / ( 0.10 + 0.10 ) = 1500 / 0.20 = rs . 7500 answer b"

divide(1500, divide(subtract(add(const_100, 10), subtract(const_100, 10)), const_100))

<gadget id="calculator">100 + 10</gadget>
<output>110</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">110 - 90</gadget>
<output>20</output>
<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1_500 / (1/5)</gadget>
<output>7_500</output>
<result>7_500</result>


there has been successive increases of 20 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?

Explanation: "let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.2 * p = x * p y = x / ( 1.1 * 1.2 ) which is about 0.76 x which is a decrease of about 24 % . the answer is c ."

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

<gadget id="calculator">100 + 20</gadget>
<output>120</output>
<gadget id="calculator">120 * 10</gadget>
<output>1_200</output>
<gadget id="calculator">1_200 / 100</gadget>
<output>12</output>
<gadget id="calculator">120 + 12</gadget>
<output>132</output>
<gadget id="calculator">100 / 132</gadget>
<output>25/33 = around 0.757576</output>
<gadget id="calculator">1 - (25/33)</gadget>
<output>8/33 = around 0.242424</output>
<gadget id="calculator">(8/33) * 100</gadget>
<output>800/33 = around 24.242424</output>
<result>800/33 = around 24.242424</result>


the length of a rectangle is increased by 35 % and its breadth is decreased by 20 % . what is the effect on its area ?

Explanation: "100 * 100 = 10000 135 * 80 = 10800 answer : a"

multiply(add(35, const_100), subtract(const_100, 20))

<gadget id="calculator">35 + 100</gadget>
<output>135</output>
<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">135 * 80</gadget>
<output>10_800</output>
<result>10_800</result>


Explanation: "25 * 18 / 5 = 90 kmph answer : c"

<gadget id="calculator">25 / 1_000</gadget>
<output>1/40 = around 0.025</output>
<gadget id="calculator">(1/40) * 3_600</gadget>
<output>90</output>
<result>90</result>


a can finish a work in 24 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?

Explanation: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 24 therefore 1 work is done by a in ( 24 x 1 ) = 8 days . e"

divide(multiply(multiply(divide(const_1, 15), 10), 24), const_2)

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>
<gadget id="calculator">(1/15) * 10</gadget>
<output>2/3 = around 0.666667</output>
<gadget id="calculator">(2/3) * 24</gadget>
<output>16</output>
<gadget id="calculator">16 / 2</gadget>
<output>8</output>
<result>8</result>


a satellite is composed of 30 modular units , each of which is equipped with a set of sensors , some of which have been upgraded . each unit contains the same number of non - upgraded sensors . if the number of non - upgraded sensors on one unit is 1 / 6 the total number of upgraded sensors on the entire satellite , what fraction of the sensors on the satellite have been upgraded ?

Explanation: "let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 30 ( x / 6 ) = 5 x . the fraction of sensors which have been upgraded is x / ( x + 5 x ) = x / 6 x = 1 / 6 the answer is c ."

divide(30, add(30, multiply(30, multiply(divide(1, 6), 30))))

<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/6) * 30</gadget>
<output>5</output>
<gadget id="calculator">30 * 5</gadget>
<output>150</output>
<gadget id="calculator">30 + 150</gadget>
<output>180</output>
<gadget id="calculator">30 / 180</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


a certain class of students is being divided into teams . the class can either be divided into 16 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?

Explanation: "let total no of students in the class be n so , we are told that n is divisible by both 16 24 so , lets find the least common multiple of 16 24 , ie 48 so our answer is ( c ) 48"

<gadget id="calculator">lcm(16, 24)</gadget>
<output>48</output>
<result>48</result>


if 5 % more is gained by selling an article for rs . 350 than by selling it for rs . 320 , the cost of the article is

Explanation: "explanation : let c . p . be rs . x . then , 5 % of x = 350 - 320 = 30 x / 20 = 30 = > x = 600 answer : e"

divide(subtract(350, 320), divide(5, const_100))

<gadget id="calculator">350 - 320</gadget>
<output>30</output>
<gadget id="calculator">5 / 100</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">30 / (1/20)</gadget>
<output>600</output>
<result>600</result>


a hall 36 m long and 15 m broad is to be paved with stones , each measuring 5 dm by 5 dm . the number of stones required is :

Explanation: "area of the hall = 3600 * 1500 area of each stone = ( 50 * 50 ) therefore , number of stones = ( 3600 * 1500 / 50 * 50 ) = 2160 answer : d"

divide(multiply(36, 15), divide(multiply(5, 5), const_100))

<gadget id="calculator">36 * 15</gadget>
<output>540</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>
<gadget id="calculator">540 / (1/4)</gadget>
<output>2_160</output>
<result>2_160</result>


before leaving home for the town of madison , pete checks a map which shows that madison is 6 inches from his current location , gardensquare . pete arrives in madison 2.5 hours later and drove at an average speed of 60 miles per hour . at what scale , in inches per mile , is the map drawn ?

Explanation: "pete covered 2.5 * 60 = 150 miles which correspond to 6 inches on the map - - > scale in inches per mile is 6 / 150 = 1 / 25 . answer : a ."

divide(const_1, multiply(divide(2.5, 6), 60))

<gadget id="calculator">2.5 / 6</gadget>
<output>0.416667</output>
<gadget id="calculator">0.416667 * 60</gadget>
<output>25.00002</output>
<gadget id="calculator">1 / 25.00002</gadget>
<output>0.04</output>
<result>0.04</result>


a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 480 less than the sum lent . what was the sum lent ?

Explanation: "p - 480 = ( p * 5 * 8 ) / 100 p = 800 the answer is b ."

divide(480, subtract(const_1, divide(multiply(5, 8), const_100)))

<gadget id="calculator">5 * 8</gadget>
<output>40</output>
<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">480 / (3/5)</gadget>
<output>800</output>
<result>800</result>


all numbers from 1 to 200 ( in decimal system ) are written in base 6 and base 7 systems . how many of the numbers will have a non - zero units digit in both base 6 and base 7 notations ?

Explanation: detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a

subtract(200, subtract(add(divide(200, 6), divide(200, 7)), divide(200, multiply(6, 7))))

<gadget id="calculator">200 / 6</gadget>
<output>100/3 = around 33.333333</output>
<gadget id="calculator">200 / 7</gadget>
<output>200/7 = around 28.571429</output>
<gadget id="calculator">(100/3) + (200/7)</gadget>
<output>1_300/21 = around 61.904762</output>
<gadget id="calculator">6 * 7</gadget>
<output>42</output>
<gadget id="calculator">200 / 42</gadget>
<output>100/21 = around 4.761905</output>
<gadget id="calculator">(1_300/21) - (100/21)</gadget>
<output>400/7 = around 57.142857</output>
<gadget id="calculator">200 - (400/7)</gadget>
<output>1_000/7 = around 142.857143</output>
<result>1_000/7 = around 142.857143</result>


an urn contains 6 red , 5 blue and 2 green marbles . if 2 marbles are picked at random , what is the probability that both are red ?

Explanation: option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b

divide(divide(multiply(6, 5), const_2), divide(multiply(add(add(6, 5), 2), subtract(add(add(6, 5), 2), const_1)), const_2))

<gadget id="calculator">6 * 5</gadget>
<output>30</output>
<gadget id="calculator">30 / 2</gadget>
<output>15</output>
<gadget id="calculator">6 + 5</gadget>
<output>11</output>
<gadget id="calculator">11 + 2</gadget>
<output>13</output>
<gadget id="calculator">13 - 1</gadget>
<output>12</output>
<gadget id="calculator">13 * 12</gadget>
<output>156</output>
<gadget id="calculator">156 / 2</gadget>
<output>78</output>
<gadget id="calculator">15 / 78</gadget>
<output>5/26 = around 0.192308</output>
<result>5/26 = around 0.192308</result>


if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 30 % of m is equal to what percent of 200 % of j ?

Explanation: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 30 % of 350 , comes out to be 105 . . . . 200 % of 10 is 20 . . . . ( 105 * 100 ) / 20 = 525 . . . . ans : c"

multiply(divide(multiply(divide(multiply(multiply(125, 150), 175), multiply(multiply(25, 50), 75)), 30), 200), const_100)

<gadget id="calculator">125 * 150</gadget>
<output>18_750</output>
<gadget id="calculator">18_750 * 175</gadget>
<output>3_281_250</output>
<gadget id="calculator">25 * 50</gadget>
<output>1_250</output>
<gadget id="calculator">1_250 * 75</gadget>
<output>93_750</output>
<gadget id="calculator">3_281_250 / 93_750</gadget>
<output>35</output>
<gadget id="calculator">35 * 30</gadget>
<output>1_050</output>
<gadget id="calculator">1_050 / 200</gadget>
<output>21/4 = around 5.25</output>
<gadget id="calculator">(21/4) * 100</gadget>
<output>525</output>
<result>525</result>


Explanation: "2 x + 1 = - 15 x = - 8 a"

<gadget id="calculator">15 + 1</gadget>
<output>16</output>
<gadget id="calculator">-16</gadget>
<output>-16</output>
<gadget id="calculator">(-16) / 2</gadget>
<output>-8</output>
<result>-8</result>


a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 556 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?

Explanation: "total weekly income over 5 weeks = $ 556 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2220 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2220 = $ 1280 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1280 - $ 700 = $ 580 for 2 weeks avg weekly commission = $ 290 answer b"

<gadget id="calculator">500 * 7</gadget>
<output>3_500</output>
<gadget id="calculator">556 + 413</gadget>
<output>969</output>
<gadget id="calculator">436 + 420</gadget>
<output>856</output>
<gadget id="calculator">969 + 856</gadget>
<output>1_825</output>
<gadget id="calculator">1_825 + 395</gadget>
<output>2_220</output>
<gadget id="calculator">3_500 - 2_220</gadget>
<output>1_280</output>
<gadget id="calculator">1_280 / 2</gadget>
<output>640</output>
<gadget id="calculator">640 - 350</gadget>
<output>290</output>
<result>290</result>


a man can row 4.8 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?

Explanation: "speed of boat in still water ( b ) = 4.8 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.6 km / hr . answer : e"

divide(subtract(multiply(4.8, const_2), 4.8), const_3)

<gadget id="calculator">4.8 * 2</gadget>
<output>9.6</output>
<gadget id="calculator">9.6 - 4.8</gadget>
<output>4.8</output>
<gadget id="calculator">4.8 / 3</gadget>
<output>1.6</output>
<result>1.6</result>


125 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ?

Explanation: "milk = 3 / 5 * 125 = 75 liters water = 50 liters 75 : ( 50 + p ) = 3 : 4 150 + 3 p = 400 = > p = 50 50 liters of water are to be added for the ratio become 3 : 4 . answer : d"

<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">125 / 5</gadget>
<output>25</output>
<gadget id="calculator">25 * 2</gadget>
<output>50</output>
<result>50</result>


a pupil ' s marks were wrongly entered as 35 instead of 23 . due to that the average marks for the class got increased by half . the number of pupils in the class is :

Explanation: let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 35 - 23 ) = > x / 2 = 12 = > x = 24 . answer : e

<gadget id="calculator">35 - 23</gadget>
<output>12</output>
<gadget id="calculator">12 * 2</gadget>
<output>24</output>
<result>24</result>


the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 400 resolutions ?

Explanation: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 400 * 2 * 22 / 7 * 22.4 = 56320 cm = 563.2 m answer : e"

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), 400), 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 * 400</gadget>
<output>56_320</output>
<gadget id="calculator">56_320 / 100</gadget>
<output>2_816/5 = around 563.2</output>
<result>2_816/5 = around 563.2</result>


q is as much younger than r as he is older than t . if the sum of the ages of r and t is 50 years , what is definitely the difference between r and q ' s age ?

Explanation: explanation : given r – q = q – t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c

<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<result>25</result>


if x and y are integers , what is the least positive number of 24 x + 21 y ?

Explanation: "24 x + 21 y = 3 ( 8 x + 7 y ) which will be a minimum positive number when 8 x + 7 y = 1 . 8 ( 1 ) + 7 ( - 1 ) = 1 then 3 ( 8 x + 7 y ) can have a minimum positive value of 3 . the answer is a ."

<gadget id="calculator">24 - 21</gadget>
<output>3</output>
<result>3</result>


the average of runs of a cricket player of 20 innings was 32 . how many runs must he make in his next innings so as to increase his average of runs by 3 ?

Explanation: "average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 3 = 35 runs total runs = new avg x new no . of innings = 35 * 21 = 735 runs made in the 11 th inning = 735 - 640 = 95 answer : a"

subtract(multiply(add(20, const_1), add(3, 32)), multiply(20, 32))

<gadget id="calculator">20 + 1</gadget>
<output>21</output>
<gadget id="calculator">3 + 32</gadget>
<output>35</output>
<gadget id="calculator">21 * 35</gadget>
<output>735</output>
<gadget id="calculator">20 * 32</gadget>
<output>640</output>
<gadget id="calculator">735 - 640</gadget>
<output>95</output>
<result>95</result>


a sum of money deposited at c . i . amounts to rs . 500 in 3 years and to rs . 650 in 4 years . find the rate percent ?

Explanation: "500 - - - 150 100 - - - ? = > 30 % answer : b"

multiply(divide(subtract(650, 500), 500), const_100)

<gadget id="calculator">650 - 500</gadget>
<output>150</output>
<gadget id="calculator">150 / 500</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>


joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?

Explanation: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 36400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 364 so we have 1 , 3 , 9 , 27 . . . . . 36400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 364 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 364 x - 2 = 1 - 3 ^ n - 728 = 1 - 3 ^ n - 729 = - 3 ^ n 729 = 3 ^ n ( negatives cancel out ) 729 can also be re written as 3 ^ 6 therefore ; 3 ^ 6 = 3 ^ n thus n = 6 ( a )"

divide(log(add(divide(multiply(36400, const_2), 100), const_1)), log(const_3))

<gadget id="calculator">36_400 * 2</gadget>
<output>72_800</output>
<gadget id="calculator">72_800 / 100</gadget>
<output>728</output>
<gadget id="calculator">728 + 1</gadget>
<output>729</output>
<gadget id="calculator">log(729)</gadget>
<output>log(729) = around 6.591674</output>
<gadget id="calculator">log(3)</gadget>
<output>log(3) = around 1.098612</output>
<gadget id="calculator">log(729) / log(3)</gadget>
<output>log(729)/log(3) = around 6</output>
<result>log(729)/log(3) = around 6</result>


a big container is 35 % full with water . if 16 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?

Explanation: "16 liters is 40 % of the capacity c . 16 = 0.4 c c = 16 / 0.4 = 40 liters . the answer is b ."

divide(16, subtract(divide(3, 4), divide(35, const_100)))

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>
<gadget id="calculator">(3/4) - (7/20)</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">16 / (2/5)</gadget>
<output>40</output>
<result>40</result>


in objective test a correct ans score 4 marks and on a wrong ans 2 marks are - - - . a student score 480 marks from 150 question . how many ans were correct ?

Explanation: let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b

<gadget id="calculator">150 * 2</gadget>
<output>300</output>
<gadget id="calculator">480 + 300</gadget>
<output>780</output>
<gadget id="calculator">4 + 2</gadget>
<output>6</output>
<gadget id="calculator">780 / 6</gadget>
<output>130</output>
<result>130</result>


a number when divided by a certain divisor left remainder 251 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?

Explanation: "easy solution : n = dq 1 + 251 2 n = 2 dq 1 + 502 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 390 d * some integer = 390 checking all options only ( c ) syncs with it . answer c"

<gadget id="calculator">251 * 2</gadget>
<output>502</output>
<gadget id="calculator">502 - 112</gadget>
<output>390</output>
<result>390</result>


excluding stoppages , the average speed of a bus is 120 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?

Explanation: "in 1 hr , the bus covers 120 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 120 - 40 ) km i . e 80 km at 120 km / hr . stoppage time = 80 / 120 hrs = 40 min answer : e"

subtract(multiply(const_1, const_60), multiply(divide(40, 120), const_60))

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<gadget id="calculator">40 / 120</gadget>
<output>1/3 = around 0.333333</output>
<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>
<gadget id="calculator">60 - 20</gadget>
<output>40</output>
<result>40</result>


consider a lady took a loan from a bank at the rate of 12 % p . a . simple interest . after 3 years she had to pay rs . 9900 interest only for the period . the principal amount borrowed by her was

Explanation: "explanation : principal = rs . ( 100 × 9900 / 12 × 3 ) = > rs . 27500 . answer : b"

divide(9900, divide(multiply(3, 12), const_100))

<gadget id="calculator">3 * 12</gadget>
<output>36</output>
<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>
<gadget id="calculator">9_900 / (9/25)</gadget>
<output>27_500</output>
<result>27_500</result>


if the cost price is 96 % of the selling price , then what is the profit percent ?

Explanation: "let s . p . = $ 100 c . p . = $ 96 profit = $ 4 profit % = 4 / 96 * 100 = 25 / 6 = 4.17 % answer is a"

multiply(divide(subtract(const_100, 96), 96), const_100)

<gadget id="calculator">100 - 96</gadget>
<output>4</output>
<gadget id="calculator">4 / 96</gadget>
<output>1/24 = around 0.041667</output>
<gadget id="calculator">(1/24) * 100</gadget>
<output>25/6 = around 4.166667</output>
<result>25/6 = around 4.166667</result>


how many multiples of 5 are there between 70 and 358 ?

Explanation: "5 * 14 = 70 5 * 71 = 355 total no of multiples = ( 71 - 14 ) + 1 = 57 + 1 = 58 answer is e ."

add(divide(subtract(358, 70), 5), const_1)

<gadget id="calculator">358 - 70</gadget>
<output>288</output>
<gadget id="calculator">288 / 5</gadget>
<output>288/5 = around 57.6</output>
<gadget id="calculator">(288/5) + 1</gadget>
<output>293/5 = around 58.6</output>
<result>293/5 = around 58.6</result>


a sum of money deposited at c . i . amounts to rs . 5000 in 5 years and to rs . 5750 in 6 years . find the rate percent ?

Explanation: 5000 - - - 750 100 - - - ? = > 15 % answer : d

multiply(divide(subtract(5750, 5000), 5000), const_100)

<gadget id="calculator">5_750 - 5_000</gadget>
<output>750</output>
<gadget id="calculator">750 / 5_000</gadget>
<output>3/20 = around 0.15</output>
<gadget id="calculator">(3/20) * 100</gadget>
<output>15</output>
<result>15</result>


renu can do a piece of work in 6 days , but with the help of her friend suma , she can do it in 5 days . in what time suma can do it alone ?

Explanation: renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 5 - 1 / 6 = 1 / 30 suma can do it alone in 30 days . answer : e

inverse(subtract(divide(const_1, 5), divide(const_1, 6)))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<gadget id="calculator">(1/5) - (1/6)</gadget>
<output>1/30 = around 0.033333</output>
<gadget id="calculator">1 / (1/30)</gadget>
<output>30</output>
<result>30</result>


if 5 machines can produce 20 units in 10 hours , how long would it take 20 machines to produce 160 units ?

Explanation: "here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 160 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 160 units is ' 8 times ' 20 , we need ' 8 times ' more time . ( 2.5 hours ) ( 8 times ) = 20 hours final answer : [ reveal ] spoiler : c"

divide(160, multiply(divide(divide(20, 10), 5), 20))

<gadget id="calculator">20 / 10</gadget>
<output>2</output>
<gadget id="calculator">2 / 5</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">(2/5) * 20</gadget>
<output>8</output>
<gadget id="calculator">160 / 8</gadget>
<output>20</output>
<result>20</result>


a policeman noticed a criminal from a distance of 200 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?

Explanation: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 200 - 50 ) m = 150 m . answer : d"

subtract(200, multiply(divide(3, const_60), const_1000))

<gadget id="calculator">3 / 60</gadget>
<output>1/20 = around 0.05</output>
<gadget id="calculator">(1/20) * 1_000</gadget>
<output>50</output>
<gadget id="calculator">200 - 50</gadget>
<output>150</output>
<result>150</result>


the average of 6 no . ' s is 3.95 . the average of 2 of them is 4 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?

Explanation: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4 * 2 ) + ( 3.85 * 2 ) ] = 8 required average = ( 8 / 2 ) = 4 e"

divide(subtract(multiply(6, 3.95), add(multiply(2, 4), multiply(2, 3.85))), 2)

<gadget id="calculator">6 * 3.95</gadget>
<output>23.7</output>
<gadget id="calculator">2 * 4</gadget>
<output>8</output>
<gadget id="calculator">2 * 3.85</gadget>
<output>7.7</output>
<gadget id="calculator">8 + 7.7</gadget>
<output>15.7</output>
<gadget id="calculator">23.7 - 15.7</gadget>
<output>8</output>
<gadget id="calculator">8 / 2</gadget>
<output>4</output>
<result>4</result>


the population of a town increased from 50000 to 80000 in a decade . the average percent increase of population per year is :

Explanation: solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % â ˆ ´ required average = ( 60 / 10 ) % = 6 % answer c

divide(multiply(divide(subtract(80000, 50000), 50000), const_100), const_10)

<gadget id="calculator">80_000 - 50_000</gadget>
<output>30_000</output>
<gadget id="calculator">30_000 / 50_000</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<gadget id="calculator">60 / 10</gadget>
<output>6</output>
<result>6</result>


carina has 130 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?

Explanation: "lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 130 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 130 - > y = 120 / 15 . = 8 d"

divide(subtract(130, multiply(5, 2)), add(10, 5))

<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">130 - 10</gadget>
<output>120</output>
<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<gadget id="calculator">120 / 15</gadget>
<output>8</output>
<result>8</result>


if x = 1 / q and y = ( 2 / q ) - 6 , then for what value of q , x is equal to y ?

Explanation: explanation : x = y < = > 1 / q = ( 2 / q ) - 6 < = > 1 / q = 6 < = > q = 1 / 6 . answer : b

<gadget id="calculator">2 - 1</gadget>
<output>1</output>
<gadget id="calculator">1 / 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>


a watch was sold at a loss of 10 % . if it was sold for rs . 140 more , there would have been a gain of 4 % . what is the cost price ?

Explanation: "explanation : 90 % 104 % - - - - - - - - 14 % - - - - 140 100 % - - - - ? = > rs . 1000 a )"

divide(multiply(140, const_100), subtract(add(const_100, 4), subtract(const_100, 10)))

<gadget id="calculator">140 * 100</gadget>
<output>14_000</output>
<gadget id="calculator">100 + 4</gadget>
<output>104</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">104 - 90</gadget>
<output>14</output>
<gadget id="calculator">14_000 / 14</gadget>
<output>1_000</output>
<result>1_000</result>


arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 50 days .

Explanation: they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 50 * 6 / 10 = 30 days . answer : d

subtract(50, multiply(divide(50, 10), 4))

<gadget id="calculator">50 / 10</gadget>
<output>5</output>
<gadget id="calculator">5 * 4</gadget>
<output>20</output>
<gadget id="calculator">50 - 20</gadget>
<output>30</output>
<result>30</result>


a certain telescope increases the visual range at a particular location from 70 kilometers to 150 kilometers . by what percent is the visual range increased by using the telescope ?

Explanation: "original visual range = 70 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 70 ) / 70 * 100 % = 8 / 7 * 100 % = 114.28 % answer e"

multiply(divide(subtract(150, 70), 70), const_100)

<gadget id="calculator">150 - 70</gadget>
<output>80</output>
<gadget id="calculator">80 / 70</gadget>
<output>8/7 = around 1.142857</output>
<gadget id="calculator">(8/7) * 100</gadget>
<output>800/7 = around 114.285714</output>
<result>800/7 = around 114.285714</result>


find the simple interest on rs . 68,000 at 16 2 / 3 % per annum for 9 months .

Explanation: "p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is a ."

multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))

<gadget id="calculator">2 * 3</gadget>
<output>6</output>
<gadget id="calculator">6 * 100</gadget>
<output>600</output>
<gadget id="calculator">600 * 100</gadget>
<output>60_000</output>
<gadget id="calculator">3 * 3</gadget>
<output>9</output>
<gadget id="calculator">9 * 100</gadget>
<output>900</output>
<gadget id="calculator">3 + 2</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">900 * 10</gadget>
<output>9_000</output>
<gadget id="calculator">60_000 + 9_000</gadget>
<output>69_000</output>
<gadget id="calculator">16 * 3</gadget>
<output>48</output>
<gadget id="calculator">48 + 2</gadget>
<output>50</output>
<gadget id="calculator">50 / 3</gadget>
<output>50/3 = around 16.666667</output>
<gadget id="calculator">69_000 * (50/3)</gadget>
<output>1_150_000</output>
<gadget id="calculator">2 * 6</gadget>
<output>12</output>
<gadget id="calculator">9 / 12</gadget>
<output>3/4 = around 0.75</output>
<gadget id="calculator">1_150_000 * (3/4)</gadget>
<output>862_500</output>
<gadget id="calculator">1 / 100</gadget>
<output>1/100 = around 0.01</output>
<gadget id="calculator">862_500 * (1/100)</gadget>
<output>8_625</output>
<result>8_625</result>


three cubes of iron whose edges are 6 cm , 8 cm and 10 cm respectively are melted and formed into a single cube . the edge of the new cube formed is

Explanation: sol . volume of the new cube = ( 63 + 83 + 103 ) cm 3 = 1728 cm 3 . let the edge of the new cube be a cm . ∴ a 3 = 1728 ⇒ a = 12 . answer b

<gadget id="calculator">10 ** 3</gadget>
<output>1_000</output>
<gadget id="calculator">6 ** 3</gadget>
<output>216</output>
<gadget id="calculator">8 ** 3</gadget>
<output>512</output>
<gadget id="calculator">216 + 512</gadget>
<output>728</output>
<gadget id="calculator">1_000 + 728</gadget>
<output>1_728</output>
<gadget id="calculator">1_728 ** (1/3)</gadget>
<output>12</output>
<result>12</result>


after 6 games , team b had an average of 75 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

Explanation: "( 6 * 75 ) + 47 + x > 500 450 + 47 + x > 500 497 + x > 500 = > x > 3 option d"

<gadget id="calculator">6 * 75</gadget>
<output>450</output>
<gadget id="calculator">450 + 47</gadget>
<output>497</output>
<gadget id="calculator">500 - 497</gadget>
<output>3</output>
<result>3</result>


if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?

Explanation: ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) has one appearance of 3 ( in the 6 ) and no appearances of 5 . thus n must include at least 3 ^ 2 * 5 ^ 2 = 9 * 25 = 225 the answer is e .

add(add(add(add(add(multiply(multiply(5, 7), 2), multiply(multiply(5, 7), 2)), multiply(multiply(5, 7), 2)), 7), const_4), const_4)

<gadget id="calculator">5 * 7</gadget>
<output>35</output>
<gadget id="calculator">35 * 2</gadget>
<output>70</output>
<gadget id="calculator">70 + 70</gadget>
<output>140</output>
<gadget id="calculator">140 + 70</gadget>
<output>210</output>
<gadget id="calculator">210 + 7</gadget>
<output>217</output>
<gadget id="calculator">217 + 4</gadget>
<output>221</output>
<gadget id="calculator">221 + 4</gadget>
<output>225</output>
<result>225</result>


there are 20 poles with a constant distance between each pole . a car takes 26 second to reach the 12 th pole . how much will it take to reach the last pole .

Explanation: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 26 seconds 1 pole ( 26 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 26 / 11 ) seconds = 44.9091 seconds answer : b"

<gadget id="calculator">26 / 12</gadget>
<output>13/6 = around 2.166667</output>
<gadget id="calculator">(13/6) * 20</gadget>
<output>130/3 = around 43.333333</output>
<result>130/3 = around 43.333333</result>


p has $ 21 more than what q and r together would have had if both b and c had 1 / 5 of what p has . how much does p have ?

Explanation: "p = ( 2 / 5 ) * p + 21 ( 3 / 5 ) * p = 21 p = 35 the answer is a ."

divide(21, subtract(1, multiply(divide(1, 5), const_2)))

<gadget id="calculator">1 / 5</gadget>
<output>1/5 = around 0.2</output>
<gadget id="calculator">(1/5) * 2</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">1 - (2/5)</gadget>
<output>3/5 = around 0.6</output>
<gadget id="calculator">21 / (3/5)</gadget>
<output>35</output>
<result>35</result>


a large box contains 18 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?

Explanation: "the number of chocolate bars is equal to 18 ? 25 = 450 correct answer c"

<gadget id="calculator">18 * 25</gadget>
<output>450</output>
<result>450</result>


because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 5 times as much as mork did , what was their combined tax rate ?

Explanation: "say morks income is - 100 so tax paid will be 40 say mindys income is 5 * 100 = 500 so tax paid is 30 % * 500 = 150 total tax paid = 40 + 150 = 190 . combined tax % will be 190 / 100 + 500 = 31.67 %"

multiply(const_100, divide(add(divide(40, const_100), multiply(5, divide(30, const_100))), add(const_1, 5)))

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>
<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>
<gadget id="calculator">5 * (3/10)</gadget>
<output>3/2 = around 1.5</output>
<gadget id="calculator">(2/5) + (3/2)</gadget>
<output>19/10 = around 1.9</output>
<gadget id="calculator">1 + 5</gadget>
<output>6</output>
<gadget id="calculator">(19/10) / 6</gadget>
<output>19/60 = around 0.316667</output>
<gadget id="calculator">100 * (19/60)</gadget>
<output>95/3 = around 31.666667</output>
<result>95/3 = around 31.666667</result>


find the number which is nearest to 3105 and is exactly divisible by 21 .

Explanation: "sol . on dividing 3105 by 21 , we get 18 as remainder . number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . option b"

<gadget id="calculator">3_105 % 21</gadget>
<output>18</output>
<gadget id="calculator">21 - 18</gadget>
<output>3</output>
<gadget id="calculator">3_105 + 3</gadget>
<output>3_108</output>
<result>3_108</result>


how many terminating zeroes r does 200 ! have ?

Explanation: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c

add(divide(200, add(const_4, const_1)), divide(200, multiply(add(const_4, const_1), add(const_4, const_1))))

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">200 / 5</gadget>
<output>40</output>
<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">200 / 25</gadget>
<output>8</output>
<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<result>48</result>


a girl walking at the rate of 9 km per hour crosses a square field diagonally in 12 seconds . the area of the field is :

Explanation: distance covered in ( 9 × 1000 ) / ( 3600 ) × 12 = 30 m diagonal of squarre field = 30 m . area of square field = 30 ( power ) 2 / 2 = 900 / 2 = 450 sq . m answer is c .

divide(multiply(multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10))), multiply(12, divide(multiply(9, const_1000), multiply(const_360, const_10)))), const_2)

<gadget id="calculator">9 * 1_000</gadget>
<output>9_000</output>
<gadget id="calculator">360 * 10</gadget>
<output>3_600</output>
<gadget id="calculator">9_000 / 3_600</gadget>
<output>5/2 = around 2.5</output>
<gadget id="calculator">12 * (5/2)</gadget>
<output>30</output>
<gadget id="calculator">30 * 30</gadget>
<output>900</output>
<gadget id="calculator">900 / 2</gadget>
<output>450</output>
<result>450</result>


the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle

Explanation: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : option c"

<gadget id="calculator">(2.5 * 40) / 2</gadget>
<output>50</output>
<result>50</result>


the probability that event b occurs is 0.6 , and the probability that events a and b both occur is 0.25 . if the probability that either event a or event b occurs is 0.4 , what is the probability that event a will occur ?

Explanation: p ( a or b ) = p ( a ) + p ( b ) - p ( a n b ) 0.4 = 0.6 + p ( a ) - 0.25 p ( a ) = 0.05 ans : a

<gadget id="calculator">0.25 + 0.4</gadget>
<output>0.65</output>
<gadget id="calculator">0.65 - 0.6</gadget>
<output>0.05</output>
<result>0.05</result>


if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?

Explanation: since 2 xy prime e factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .

multiply(multiply(2, add(const_1, const_1)), add(const_1, const_1))

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


in a certain group of 10 developers , 4 developers code only in python and the rest program in either ruby on rails or php - but not both . if a developer organization is to choose a 3 - member team , which must have at least 1 developer who codes in python , how many different programming teams can be chosen ?

Explanation: two ways . . . 1 ) total ways = 10 c 3 = 10 ! / 7 ! 3 ! = 120 . . ways without python developer = 6 c 3 = 6 ! / 3 ! 3 ! = 20 . . ways of at least one python developer = 120 - 20 = 100 . . 2 ) ways of selecting only one = 4 * 6 c 2 = 4 * 15 = 60 . . ways of selecting only two = 4 c 2 * 6 c 1 = 6 * 6 = 36 . . ways of selecting all three = 4 c 3 = 4 = 4 . . total = 60 + 36 + 4 = 100 . . . answer : a

subtract(divide(factorial(10), multiply(factorial(subtract(10, 3)), factorial(3))), divide(factorial(subtract(10, 4)), multiply(factorial(3), factorial(3))))

<gadget id="calculator">factorial(10)</gadget>
<output>3_628_800</output>
<gadget id="calculator">10 - 3</gadget>
<output>7</output>
<gadget id="calculator">factorial(7)</gadget>
<output>5_040</output>
<gadget id="calculator">factorial(3)</gadget>
<output>6</output>
<gadget id="calculator">5_040 * 6</gadget>
<output>30_240</output>
<gadget id="calculator">3_628_800 / 30_240</gadget>
<output>120</output>
<gadget id="calculator">10 - 4</gadget>
<output>6</output>
<gadget id="calculator">factorial(6)</gadget>
<output>720</output>
<gadget id="calculator">6 * 6</gadget>
<output>36</output>
<gadget id="calculator">720 / 36</gadget>
<output>20</output>
<gadget id="calculator">120 - 20</gadget>
<output>100</output>
<result>100</result>


a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 920 gm . for a kg . his gain is … % .

Explanation: "his percentage gain is 100 * 80 / 920 as he is gaining 80 units for his purchase of 920 units . so 8.69 % . answer : e"

multiply(subtract(inverse(divide(920, multiply(multiply(add(const_4, const_1), const_2), const_100))), const_1), const_100)

<gadget id="calculator">4 + 1</gadget>
<output>5</output>
<gadget id="calculator">5 * 2</gadget>
<output>10</output>
<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">920 / 1_000</gadget>
<output>23/25 = around 0.92</output>
<gadget id="calculator">1 / (23/25)</gadget>
<output>25/23 = around 1.086957</output>
<gadget id="calculator">(25/23) - 1</gadget>
<output>2/23 = around 0.086957</output>
<gadget id="calculator">(2/23) * 100</gadget>
<output>200/23 = around 8.695652</output>
<result>200/23 = around 8.695652</result>


5.40 can be expressed in terms of percentage as

Explanation: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.40 * 100 = 540 answer : option d"

<gadget id="calculator">5.4 * 100</gadget>
<output>540</output>
<result>540</result>


a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 25.00 ?

Explanation: "for retail price = $ 25 first maximum discounted price = 25 - 30 % of 25 = 25 - 7.5 = 17.5 price after additional discount of 20 % = 17.5 - 20 % of 17.5 = 17.5 - 3.5 = 14 answer : option a"

multiply(divide(subtract(const_100, 20), const_100), multiply(divide(subtract(const_100, 30), const_100), 25.00))

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>
<gadget id="calculator">100 - 30</gadget>
<output>70</output>
<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>
<gadget id="calculator">(7/10) * 25</gadget>
<output>35/2 = around 17.5</output>
<gadget id="calculator">(4/5) * (35/2)</gadget>
<output>14</output>
<result>14</result>


a number is mistakenly divided by 5 instead of being multiplied by 5 . find the percentage change in the result due t this mistake .

Explanation: lets take a number 20 20 / 5 = 4 20 * 5 = 100 diff = 100 - 4 = 96 % answer : a

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

<gadget id="calculator">5 * 5</gadget>
<output>25</output>
<gadget id="calculator">25 - 1</gadget>
<output>24</output>
<gadget id="calculator">100 / 25</gadget>
<output>4</output>
<gadget id="calculator">24 * 4</gadget>
<output>96</output>
<result>96</result>


the first , second and third terms of the proportion are 56 , 16 , 49 . find the fourth term .

Explanation: explanation : let the fourth term be x . thus 56 , 16 , 49 , x are in proportion . product of extreme terms = 56 x product of mean terms = 16 x 49 since , the numbers make up a proportion therefore , 56 x = 16 49 or , x = ( 16 49 ) / 56 or , x = 14 therefore , the fourth term of the proportion is 14 . answer : b

<gadget id="calculator">49 * 16</gadget>
<output>784</output>
<gadget id="calculator">784 / 56</gadget>
<output>14</output>
<result>14</result>


during a sale , the price of a pair of shoes is marked down 10 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?

Explanation: "assume the price = 100 price during sale = 90 price after sale = 100 percent increase = 10 / 90 * 100 = 11 % approx . correct option : c"

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

<gadget id="calculator">10 * 100</gadget>
<output>1_000</output>
<gadget id="calculator">100 - 10</gadget>
<output>90</output>
<gadget id="calculator">1_000 / 90</gadget>
<output>100/9 = around 11.111111</output>
<result>100/9 = around 11.111111</result>


sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 324 per week . how much does she earn in dollars per hour ?

Explanation: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 324 . hourly wage = 324 / 36 = 9 answer : c ) 9"

divide(324, add(multiply(8, const_3), multiply(6, const_2)))

<gadget id="calculator">8 * 3</gadget>
<output>24</output>
<gadget id="calculator">6 * 2</gadget>
<output>12</output>
<gadget id="calculator">24 + 12</gadget>
<output>36</output>
<gadget id="calculator">324 / 36</gadget>
<output>9</output>
<result>9</result>


determine the value of 3 * 27 / 31 + 81 / 93

Explanation: solution : both fractions should be reduced before performing arithmetic operations . we get 3 * 27 / 31 + 3.27 / 3.31 = 3 * 27 / 31 + 27 / 31 = 4 * 27 / 31 = 151 / 31 answer d

divide(add(subtract(add(81, multiply(27, 3)), subtract(93, 81)), const_1), 31)

<gadget id="calculator">27 * 3</gadget>
<output>81</output>
<gadget id="calculator">81 + 81</gadget>
<output>162</output>
<gadget id="calculator">93 - 81</gadget>
<output>12</output>
<gadget id="calculator">162 - 12</gadget>
<output>150</output>
<gadget id="calculator">150 + 1</gadget>
<output>151</output>
<gadget id="calculator">151 / 31</gadget>
<output>151/31 = around 4.870968</output>
<result>151/31 = around 4.870968</result>


in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds e in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?

Explanation: "1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out e : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b"

add(const_10, divide(add(25, 25), const_2))

<gadget id="calculator">25 + 25</gadget>
<output>50</output>
<gadget id="calculator">50 / 2</gadget>
<output>25</output>
<gadget id="calculator">10 + 25</gadget>
<output>35</output>
<result>35</result>


what is the smallest integer t greater than 1 that leaves a remainder of 1 when divided by any of the integers 6 , 8 , and 10 ?

Explanation: or u can just use the answer choices here . since the answers are already arranged in ascending order , the first number which gives remainder t as 1 for all three is the correct answer . in the given question , the first number which gives a remainder of 1 for 6,8 and 10 is 121 . c

<gadget id="calculator">lcm(6, 8)</gadget>
<output>24</output>
<gadget id="calculator">lcm(24, 10)</gadget>
<output>120</output>
<gadget id="calculator">120 + 1</gadget>
<output>121</output>
<result>121</result>


a train 150 m long running at 72 kmph crosses a platform in 20 sec . what is the length of the platform ?

Explanation: "e 250 e = 72 * 5 / 18 = 20 = 400 â € “ 150 = 250"

subtract(multiply(20, multiply(72, const_0_2778)), 150)

<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">20 * 20</gadget>
<output>400</output>
<gadget id="calculator">400 - 150</gadget>
<output>250</output>
<result>250</result>


the smallest number when increased by ` ` 1 ` ` is exactly divisible by 2 , 8 , 24 , 36 is :

Explanation: lcm = 72 72 - 1 = 71 answer : a

<gadget id="calculator">lcm(24, 36)</gadget>
<output>72</output>
<gadget id="calculator">72 - 1</gadget>
<output>71</output>
<result>71</result>


a person bought 135 glass bowls at a rate of rs . 15 per bowl . he sold 115 of them at rs . 18 and the remaining broke . what is the percentage gain for a ?

Explanation: "cp = 135 * 15 = 2025 and sp = 115 * 18 = 2070 gain % = 100 * ( 2070 - 2025 ) / 2025 = 20 / 9 answer : c"

multiply(divide(subtract(multiply(115, 18), multiply(135, 15)), multiply(135, 15)), const_100)

<gadget id="calculator">115 * 18</gadget>
<output>2_070</output>
<gadget id="calculator">135 * 15</gadget>
<output>2_025</output>
<gadget id="calculator">2_070 - 2_025</gadget>
<output>45</output>
<gadget id="calculator">45 / 2_025</gadget>
<output>1/45 = around 0.022222</output>
<gadget id="calculator">(1/45) * 100</gadget>
<output>20/9 = around 2.222222</output>
<result>20/9 = around 2.222222</result>


the maximum number of students among them 1200 pens and 820 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils ?

Explanation: "number of pens = 1200 number of pencils = 820 required number of students = h . c . f . of 1200 and 820 = 20 answer is b"

<gadget id="calculator">gcd(1_200, 820)</gadget>
<output>20</output>
<result>20</result>


in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 50 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 is the approximate number of fish in the pond ?

Explanation: this is a rather straight forward ratio problem . 1 . 80 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 80 / x thus , x = 2000 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . d

<gadget id="calculator">2 / 50</gadget>
<output>1/25 = around 0.04</output>
<gadget id="calculator">80 / (1/25)</gadget>
<output>2_000</output>
<result>2_000</result>


a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what w percent of the list price is the lowest possible sale price ?

Explanation: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which w is 40 % of 80 hence , d is the answer"

<gadget id="calculator">80 / 2</gadget>
<output>40</output>
<result>40</result>