Question: a can give b 100 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">1_000 - 200</gadget>
<output>800</output>

<gadget id="calculator">1_000 * 800</gadget>
<output>800_000</output>

<gadget id="calculator">1_000 - 100</gadget>
<output>900</output>

<gadget id="calculator">800_000 / 900</gadget>
<output>8_000/9 = around 888.888889</output>

<gadget id="calculator">1_000 - (8_000/9)</gadget>
<output>1_000/9 = around 111.111111</output>
<result>1_000/9 = around 111.111111</result>

Choices:
A. 111.12 m
B. 221.12 m
C. 271.12 m
D. 611.12 m
E. 191.12 m

subtract(multiply(const_100, const_10), divide(multiply(multiply(const_100, const_10), subtract(multiply(const_100, const_10), 200)), subtract(multiply(const_100, const_10), 100)))

Explanation: "explanation : a runs 1000 m while b runs 900 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . b can give c = 1000 - 888.88 = 111.12 m . answer : a"


Question: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 961 . find the cost of each ice - cream cup ?

<gadget id="calculator">16 * 6</gadget>
<output>96</output>

<gadget id="calculator">961 - 96</gadget>
<output>865</output>

<gadget id="calculator">5 * 45</gadget>
<output>225</output>

<gadget id="calculator">865 - 225</gadget>
<output>640</output>

<gadget id="calculator">7 * 70</gadget>
<output>490</output>

<gadget id="calculator">640 - 490</gadget>
<output>150</output>

<gadget id="calculator">150 / 6</gadget>
<output>25</output>
<result>25</result>

Choices:
A. rs . 25
B. rs . 22.50
C. rs . 20
D. rs . 17.50
E. none of these

divide(subtract(subtract(subtract(961, multiply(16, 6)), multiply(5, 45)), multiply(7, 70)), 6)

Explanation: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 961 96 + 225 + 490 + 6 x = 961 6 x = 150 = > x = 25 . answer : a"


Question: a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 20 - sided polygon have ?

<gadget id="calculator">20 - 3</gadget>
<output>17</output>

<gadget id="calculator">17 * 20</gadget>
<output>340</output>

<gadget id="calculator">340 / 2</gadget>
<output>170</output>
<result>170</result>

Choices:
A. 875
B. 170
C. 1425
D. 2025
E. 2500

divide(multiply(subtract(20, const_3), 20), const_2)

Explanation: there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 20 . plugging it in , we get 170 diagonals ! answer ( b ) .


Question: a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . what is the greatest two digit prime saturated integer ?

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">100 - 10</gadget>
<output>90</output>

<gadget id="calculator">6 + 90</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 99
B. 98
C. 97
D. 96
E. 95

add(multiply(const_2, const_3), subtract(const_100, const_10))

Explanation: "clearly d a number is said to be prime saturated if the product of all the different positive prime factors of z is less than the square root of z . 96 has more number of smaller prime factor thats the clue ! ! = d"


Question: find large number from below question the difference of two numbers is 1311 . on dividing the larger number by the smaller , we get 11 as quotient and the 11 as remainder

<gadget id="calculator">1_311 - 11</gadget>
<output>1_300</output>

<gadget id="calculator">11 - 1</gadget>
<output>10</output>

<gadget id="calculator">1_300 / 10</gadget>
<output>130</output>

<gadget id="calculator">130 * 11</gadget>
<output>1_430</output>
<result>1_430</result>

Choices:
A. 1209
B. 1324
C. 1441
D. 1300
E. 1635

multiply(divide(subtract(1311, 11), subtract(11, const_1)), 11)

Explanation: "let the smaller number be x . then larger number = ( x + 1311 ) . x + 1311 = 11 x + 11 10 x = 1300 x = 130 large number = 130 + 1311 = 1441 answer : c"


Question: 1 blue dice and 2 red dice are thrown . . . . what is the probability that the no . appeared on blue dice is always greater than both the no . appeared on the 2 red dice . .

<gadget id="calculator">1 ** 2</gadget>
<output>1</output>

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

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

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">5 + 9</gadget>
<output>14</output>

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

<gadget id="calculator">14 + 16</gadget>
<output>30</output>

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

<gadget id="calculator">5 ** 2</gadget>
<output>25</output>

<gadget id="calculator">30 + 25</gadget>
<output>55</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

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

<gadget id="calculator">12 ** 2</gadget>
<output>144</output>

<gadget id="calculator">12 * 5</gadget>
<output>60</output>

<gadget id="calculator">60 + 12</gadget>
<output>72</output>

<gadget id="calculator">144 + 72</gadget>
<output>216</output>

<gadget id="calculator">55 / 216</gadget>
<output>55/216 = around 0.25463</output>
<result>55/216 = around 0.25463</result>

Choices:
A. 55 / 216
B. 56 / 216
C. 57 / 216
D. 54 / 216
E. 53 / 216

divide(add(add(add(add(power(1, const_2), power(2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_3, const_2), const_2)), add(power(multiply(multiply(const_3, const_2), const_2), const_2), add(multiply(multiply(multiply(const_3, const_2), const_2), add(power(1, const_2), power(2, const_2))), multiply(multiply(const_3, const_2), const_2))))

Explanation: if the no . on blue dice is 2 then 2 red dice can take ( 1,1 ) value = 1 ^ 2 if the no . on blue dice is 3 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) = 2 ^ 2 if the no . on blue dice is 4 then 2 red dice can take ( 1,1 ) ( 1,2 ) ( 2,1 ) ( 2,2 ) ( 1,3 ) ( 2,3 ) ( 3,2 ) ( 3,1 ) ( 3,3 ) = 3 ^ 2 similarly , if the no . on blue dice is 5 then 2 red dice can take = 4 ^ 2 and if the no . on blue dice is 6 then 2 red dice can take = 5 ^ 2 therefor , probability = total no . of favourable outcome / total no . of possible outcome = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 / 216 = 55 / 216 answer : a


Question: excluding stoppages , the speed of the bus is 54 kmph and including stoppages , it is 36 kmph . for how many minutes does the bus stop per hr

<gadget id="calculator">36 / 54</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">(1/3) * 60</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 12 min
B. 11 min
C. 13 min
D. 19 min
E. 20 min

multiply(subtract(const_1, divide(36, 54)), const_60)

Explanation: due to stoppages , it covers 18 km less . time taken to cover 18 km is [ 18 / 54 * 60 ] min = 20 min answer is e .


Question: a 150 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?

<gadget id="calculator">150 / 18</gadget>
<output>25/3 = around 8.333333</output>

<gadget id="calculator">(25/3) * 39</gadget>
<output>325</output>

<gadget id="calculator">325 - 150</gadget>
<output>175</output>
<result>175</result>

Choices:
A. 300
B. 175
C. 360
D. 370
E. 380

subtract(multiply(speed(150, 18), 39), 150)

Explanation: "speed = 150 / 18 = 25 / 3 m / sec . let the length of the platform be x meters . then , ( x + 150 ) / 39 = 25 / 3 = > x = 325 m . l = 325 - 150 = 175 m answer : option b"


Question: a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 35 , how many coins of each type are there ?

<gadget id="calculator">1 / 4</gadget>
<output>1/4 = around 0.25</output>

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

<gadget id="calculator">(1/4) + (1/2)</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) + 1</gadget>
<output>7/4 = around 1.75</output>

<gadget id="calculator">35 / (7/4)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 20 coins
B. 30 coins
C. 28 coins
D. 25 coins
E. none of these

divide(35, add(add(inverse(const_4), inverse(const_2)), const_1))

Explanation: "let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 35 ⇒ 1.75 x = 35 ⇒ x = 20 coins answer a"


Question: a girl scout was selling boxes of cookies . in a month , she sold both boxes of chocolate chip cookies ( $ 1.25 each ) and boxes of plain cookies ( $ 0.75 each ) . altogether , she sold 1,585 boxes for a combined value of $ 1 , 588.25 . how many boxes of plain cookies did she sell ?

<gadget id="calculator">1_000 + 588.25</gadget>
<output>1_588.25</output>

<gadget id="calculator">1_588.25 / 2</gadget>
<output>794.125</output>
<result>794.125</result>

Choices:
A. 0
B. 233
C. 500
D. 695
E. 786

Explanation: "let # plain cookies sold be x then # chocolate cookies = ( total cookies - x ) equating for x ( 0.75 ) * x + ( 1.25 ) * ( 1585 - x ) = 1588.25 = > x = 786 first get the difference of the revenue to the number of boxes . 1588.25 - 1585 = 3.25 now you know that the difference between plain cookies boxes and chocolate cookies boxes is small . we now divide the revenue by two . 1588.25 / 2 = ~ 794 because the difference between the possible answers is big , this leaves us with choice e ."


Question: how many positive even integers less than 100 contain digits 5 or 7 ?

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

Choices:
A. 10
B. 17
C. 18
D. 19
E. 20

Explanation: "two digit numbers : 5 at tens place : 50 , 52,54 , 56,58 7 at tens place : 70 , 72,74 , 76,78 if 5 and 7 is at units place , the number cant be even total : 5 + 5 = 10 answer a"


Question: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 10 km ?

<gadget id="calculator">4 - 2</gadget>
<output>2</output>

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

Choices:
A. 3
B. 5
C. 8
D. 9
E. 6

Explanation: "m = 4 s = 2 us = 4 - 2 = 2 d = 10 t = 10 / 2 = 5 answer : b"


Question: the price of a certain painting increased by 25 % during the first year and decreased by 15 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?

<gadget id="calculator">25 - 15</gadget>
<output>10</output>

<gadget id="calculator">15 * 25</gadget>
<output>375</output>

<gadget id="calculator">375 / 100</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">10 - (15/4)</gadget>
<output>25/4 = around 6.25</output>

<gadget id="calculator">(25/4) + 100</gadget>
<output>425/4 = around 106.25</output>
<result>425/4 = around 106.25</result>

Choices:
A. 109 %
B. 106.25 %
C. 120 %
D. 115 %
E. 110 %

add(subtract(subtract(25, 15), divide(multiply(15, 25), const_100)), const_100)

Explanation: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 25 = 125 price at the end of year 2 = 125 - 125 * 0.15 = 125 * 0.85 = 106.25 hence required answer = ( 106.25 / 100 ) * 100 % = 106.25 % answer is b ."


Question: rs . 1010 / - distributed among a , b and c such that on decreasing their shares by rs . 25 , rs . 10 and rs . 15 respectively , the balance money would be divided among them in the ratio 3 : 2 : 5 . then , c ’ s share is : ?

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

<gadget id="calculator">35 + 15</gadget>
<output>50</output>

<gadget id="calculator">1_010 - 50</gadget>
<output>960</output>

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

<gadget id="calculator">5 + 5</gadget>
<output>10</output>

<gadget id="calculator">960 / 10</gadget>
<output>96</output>

<gadget id="calculator">5 * 96</gadget>
<output>480</output>

<gadget id="calculator">480 + 15</gadget>
<output>495</output>
<result>495</result>

Choices:
A. rs . 485
B. rs . 495 / -
C. rs . 575
D. rs . 685
E. rs . 592

Explanation: a : b : c = 3 : 2 : 5 total parts = 10 c ' s share is = 5 parts 10 - - - - - > rs . 960 / - 3 - - - - - > rs . 480 / - a ' s total = 480 + 15 = rs . 495 / - b )


Question: a is twice as good a work man as b and together they finish a piece of work in 36 days . the number of days taken by b alone to finish the work is :

<gadget id="calculator">1 / 36</gadget>
<output>1/36 = around 0.027778</output>

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

<gadget id="calculator">(1/36) / 3</gadget>
<output>1/108 = around 0.009259</output>

<gadget id="calculator">1 / (1/108)</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 100 days .
B. 108 days .
C. 98 days .
D. 47 days .
E. 103 days .

Explanation: solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 2 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 36 divide 1 / 36 in the ratio 2 : 1 . ∴ b ’ s 1 day ’ s work = ( 1 / 36 x 1 / 3 ) = 1 / 108 hence , b alone can finish the work in 108 days . answer b


Question: 5 % of ( 25 % of $ 1600 ) is ?

<gadget id="calculator">1_600 * 25</gadget>
<output>40_000</output>

<gadget id="calculator">40_000 / 100</gadget>
<output>400</output>

<gadget id="calculator">400 * 5</gadget>
<output>2_000</output>

<gadget id="calculator">2_000 / 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. $ 20
B. $ 30
C. $ 45
D. $ 15
E. $ 60

divide(multiply(divide(multiply(1600, 25), const_100), 5), const_100)

Explanation: 5 % of ( 25 % of $ 1600 ) = 5 / 100 ( 25 / 100 * 1600 ) = $ 20 answer is a


Question: how many diagonals does a 60 - sided convex polygon have ?

Choices:
A. 960
B. 1280
C. 1710
D. 2560
E. 3420

divide(factorial(60), multiply(factorial(subtract(60, const_2)), factorial(const_2)))

Explanation: "a 60 - sided convex polygon has 60 vertices . if we examine a single vertex , we can see that we can connect it with 57 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 60 vertices can be connected with 57 vertices to create a diagonal then the total number of diagonals would be ( 60 ) ( 57 ) = 3420 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3420 by 2 to get 1710 . the answer is c ."


Question: rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount ?

<gadget id="calculator">5 / 4</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">10 / 9</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(5/4) + (10/9)</gadget>
<output>85/36 = around 2.361111</output>

<gadget id="calculator">(85/36) + 1</gadget>
<output>121/36 = around 3.361111</output>

<gadget id="calculator">1_210 / (121/36)</gadget>
<output>360</output>

<gadget id="calculator">360 * (10/9)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. rs . 300
B. rs . 400
C. rs . 480
D. rs . 500
E. rs . 520

multiply(divide(1210, add(add(divide(5, 4), divide(10, 9)), const_1)), divide(10, 9))

Explanation: p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b


Question: a fruit drink is made of orange , watermelon , and grape juice , where 35 percent of the drink is orange juice and 35 percent is watermelon juice . if the drink is made with 45 ounces of grape juice , how many ounces is the drink total ?

<gadget id="calculator">45 * 35</gadget>
<output>1_575</output>

<gadget id="calculator">35 + 35</gadget>
<output>70</output>

<gadget id="calculator">100 - 70</gadget>
<output>30</output>

<gadget id="calculator">1_575 / 30</gadget>
<output>105/2 = around 52.5</output>

<gadget id="calculator">45 + (105/2)</gadget>
<output>195/2 = around 97.5</output>

<gadget id="calculator">(195/2) + (105/2)</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 120
B. 140
C. 150
D. 180
E. 200

add(add(45, divide(multiply(45, 35), subtract(const_100, add(35, 35)))), divide(multiply(45, 35), subtract(const_100, add(35, 35))))

Explanation: "let the total number of ounces in the drink be x . % of orange = 35 % % of watermelon = 35 % % of grape = 100 % - 70 % = 30 % 0.30 x = 45 x = 150 therefore there are a total of 150 ounces in the drink . the answer is c ."


Question: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 24 , then v =

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>

<gadget id="calculator">36 / (2/3)</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 45
B. 48
C. 51
D. 54
E. 57

divide(divide(24, subtract(const_1, divide(const_1, 3))), subtract(const_1, divide(const_1, 3)))

Explanation: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 24 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 54 the answer is d ."


Question: the least perfect square , which is divisible by each of 21,36 and 66 is

<gadget id="calculator">3 + 4</gadget>
<output>7</output>

<gadget id="calculator">7 ** 2</gadget>
<output>49</output>

<gadget id="calculator">66 / 3</gadget>
<output>22</output>

<gadget id="calculator">22 / 2</gadget>
<output>11</output>

<gadget id="calculator">11 ** 2</gadget>
<output>121</output>

<gadget id="calculator">49 * 121</gadget>
<output>5_929</output>

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

<gadget id="calculator">5_929 * 4</gadget>
<output>23_716</output>

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">23_716 * 9</gadget>
<output>213_444</output>
<result>213_444</result>

Choices:
A. 213444
B. 214344
C. 214434
D. 213443
E. none of these

multiply(multiply(multiply(power(add(const_3, const_4), const_2), power(divide(divide(66, const_3), const_2), const_2)), power(const_2, const_2)), power(const_3, const_2))

Explanation: l . c . m . of 21 , 36 , 66 = 2772 . now , 2772 = 2 x 2 x 3 x 3 x 7 x 11 to make it a perfect square , it must be multiplied by 7 x 11 . so , required number = 22 x 32 x 72 x 112 = 213444 answer a


Question: if w / x = 2 / 3 and w / y = 6 / 15 , then ( x + y ) / y =

<gadget id="calculator">6 / 2</gadget>
<output>3</output>

<gadget id="calculator">15 / 3</gadget>
<output>5</output>

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) + 1</gadget>
<output>8/5 = around 1.6</output>
<result>8/5 = around 1.6</result>

Choices:
A. 4 / 5
B. 6 / 5
C. 7 / 5
D. 8 / 5
E. 9 / 5

add(divide(divide(6, 2), divide(15, 3)), const_1)

Explanation: w / x = 2 / 3 = > x = 3 / 2 w and w / y = 6 / 15 = > y = 15 / 6 w ( x + y ) / y = ( 3 / 2 w + 15 / 6 w ) / 15 / 6 w = 4 w / ( 15 / 6 w ) = 8 / 5 correct option : d


Question: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500,000 ?

<gadget id="calculator">6 - 4</gadget>
<output>2</output>

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

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

Choices:
A. 160
B. 200
C. 240
D. 300
E. 480

multiply(multiply(subtract(6, const_4), const_10), const_10)

Explanation: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .


Question: a trader sold an article on a certain price with 40 % profit . if he sold double of previous selling price then find its profit %

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">2 * 140</gadget>
<output>280</output>

<gadget id="calculator">280 - 100</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 140 %
B. 180 %
C. 120 %
D. 100 %
E. 150 %

subtract(multiply(const_2, add(const_100, 40)), const_100)

Explanation: "let cost price = 100 % selling price = 140 % new s . p . = 280 % p % = 280 - 100 = 180 % answer is b"


Question: the average price of an decoration piece increases over the years . if from 1990 to 1996 , the price of the decoration piece increased by 13 % and from 1996 to 2001 it increased by 20 % , what is the price of the decoration piece in 2001 if the price in 1990 was $ 11500 ?

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">1 + (1/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">13 / 100</gadget>
<output>13/100 = around 0.13</output>

<gadget id="calculator">1 + (13/100)</gadget>
<output>113/100 = around 1.13</output>

<gadget id="calculator">(113/100) * 11_500</gadget>
<output>12_995</output>

<gadget id="calculator">(6/5) * 12_995</gadget>
<output>15_594</output>
<result>15_594</result>

Choices:
A. $ 15594 .
B. $ 15322 .
C. $ 14786 .
D. $ 14543 .
E. $ 12988 .

multiply(add(const_1, divide(20, const_100)), multiply(add(const_1, divide(13, const_100)), 11500))

Explanation: whenever you have a question in which a value is increased by x % and then increased by y % then the overall effective increase = ( x + y + xy / 100 ) % the effective increase = 13 + 20 + ( 13 × 20 / 100 ) = 35.6 % this is a little more 33 % or 1 / 3 the original value . the quickest way to solve this question is to use approximation . 11500 + 1 / 3 ( 12000 ) = 15500 therefore option a is the answer . i selected 12000 because it ' s value is a little more 11500 and it ' s easier to divide by 3 ( ie to calculate 1 / 3 or 33 % ) .


Question: a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many h cubes are painted on only 2 faces ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">27 ** (1/3)</gadget>
<output>3</output>

<gadget id="calculator">4 * 3</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 8
C. 6
D. 10
E. 16

multiply(const_4, power(27, divide(const_1, const_3)))

Explanation: "1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . h = 4 + 4 + 4 = 12 . answer a"


Question: the length of a rectangle is increased by 15 % and its breadth is decreased by 20 % . what is the effect on its area ?

<gadget id="calculator">15 + 100</gadget>
<output>115</output>

<gadget id="calculator">100 - 20</gadget>
<output>80</output>

<gadget id="calculator">115 * 80</gadget>
<output>9_200</output>
<result>9_200</result>

Choices:
A. 1288
B. 1299
C. 1000
D. 10000
E. 9200

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

Explanation: "100 * 100 = 10000 115 * 80 = 9200 answer : e"


Question: how many seconds will a train 150 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?

<gadget id="calculator">150 + 150</gadget>
<output>300</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">300 / 10</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 28 sec
B. 23 sec
C. 29 sec
D. 30 sec
E. 36 sec

Explanation: "d d = 150 + 150 = 300 s = 36 * 5 / 18 = 10 mps t = 300 / 10 = 30 sec"


Question: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 8.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?

<gadget id="calculator">8.8 - 3.2</gadget>
<output>5.6</output>

<gadget id="calculator">2 ** (1/2)</gadget>
<output>sqrt(2) = around 1.414214</output>

<gadget id="calculator">(sqrt(2)) - 1</gadget>
<output>-1 + sqrt(2) = around 0.414214</output>

<gadget id="calculator">5 + (-1 + sqrt(2))</gadget>
<output>sqrt(2) + 4 = around 5.414214</output>

<gadget id="calculator">5.6 / (sqrt(2) + 4)</gadget>
<output>5.6/(sqrt(2) + 4) = around 1.034315</output>

<gadget id="calculator">(5.6/(sqrt(2) + 4)) * 5</gadget>
<output>28.0/(sqrt(2) + 4) = around 5.171573</output>

<gadget id="calculator">3.2 + (28.0/(sqrt(2) + 4))</gadget>
<output>3.2 + 28.0/(sqrt(2) + 4) = around 8.371573</output>
<result>3.2 + 28.0/(sqrt(2) + 4) = around 8.371573</result>

Choices:
A. $ 8.40
B. $ 5.10
C. $ 5.30
D. $ 5.50
E. $ 5.60

add(3.20, multiply(divide(subtract(8.80, 3.20), add(5, subtract(sqrt(2), 1))), 5))

Explanation: "i tried using time / rate approach : - initial price difference = 8.80 - 3.20 = 5.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 5.6 = t ( 5.4 x ) - > t = ( 5.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 5.6 / 5.4 = 8.4 answer a ."


Question: find the area of the quadrilateral of one of its diagonals is 28 cm and its off sets 9 cm and 6 cm ?

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

<gadget id="calculator">6 + 9</gadget>
<output>15</output>

<gadget id="calculator">(1/2) * 15</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(15/2) * 28</gadget>
<output>210</output>
<result>210</result>

Choices:
A. 210 cm 2
B. 150 cm 2
C. 168 cm 2
D. 198 cm 2
E. 987 cm 2

multiply(multiply(divide(const_1, const_2), add(6, 9)), 28)

Explanation: "1 / 2 * 28 ( 9 + 6 ) = 210 cm 2 answer : a"


Question: when the price of a product was decreased by 20 % , the number sold increased by 60 % . what was the effect on the total revenue ?

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 + (3/5)</gadget>
<output>8/5 = around 1.6</output>

<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">(8/5) * (4/5)</gadget>
<output>32/25 = around 1.28</output>

<gadget id="calculator">(32/25) - 1</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) * 100</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28 %
B. 32 %
C. 35 %
D. 45 %
E. 52 %

multiply(subtract(multiply(add(const_1, divide(60, const_100)), divide(subtract(const_100, 20), const_100)), const_1), const_100)

Explanation: let the price of the product be $ 100 and let original sale be 100 pieces then , total revenue = 100 * 100 = $ 10000 new revenue = 80 * 160 = $ 12800 increase in revenue = 2800 * 100 / 10000 = 28 % answer is a


Question: in a rare coin collection , all coins are either pure gold or pure silver , and there is initially one gold coin for every 3 silver coins . with the addition of 15 more gold coins to the collection , the ratio of gold coins to silver coins is 1 to 2 . based on this information , how many total coins are there now in this collection ( after the acquisition ) ?

<gadget id="calculator">2 * 15</gadget>
<output>30</output>

<gadget id="calculator">30 * 3</gadget>
<output>90</output>

<gadget id="calculator">90 + 30</gadget>
<output>120</output>

<gadget id="calculator">120 + 15</gadget>
<output>135</output>
<result>135</result>

Choices:
A. 124
B. 135
C. 146
D. 157
E. 168

add(add(multiply(multiply(2, 15), 3), multiply(2, 15)), 15)

Explanation: initially the number of gold coins and silver coins is 2 k and 6 k . after adding gold coins , the number of coins is 3 k and 6 k . thus k = 15 and the total number of coins is 9 k = 135 . the answer is b .


Question: a student has to obtain 35 % of the total marks to pass . he got 100 marks and failed by 40 marks . the maximum marks are ?

<gadget id="calculator">100 + 40</gadget>
<output>140</output>

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">140 / (7/20)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 280
B. 400
C. 420
D. 480
E. 520

divide(add(100, 40), divide(35, const_100))

Explanation: "let the maximum marks be x then , 35 % of x = 100 + 40 35 x / 100 = 140 35 x = 140 * 100 = 14000 x = 400 answer is b"


Question: if a : b = 3 : 4 , b : c = 7 : 9 , c : d = 5 : 7 , find a : d ?

<gadget id="calculator">3 * 7</gadget>
<output>21</output>

<gadget id="calculator">21 * 5</gadget>
<output>105</output>

<gadget id="calculator">4 * 9</gadget>
<output>36</output>

<gadget id="calculator">36 * 7</gadget>
<output>252</output>

<gadget id="calculator">105 / 252</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>

Choices:
A. 5 / 12
B. 5 / 15
C. 5 / 10
D. 5 / 11
E. 5 / 13

divide(multiply(multiply(3, 7), 5), multiply(multiply(4, 9), 7))

Explanation: "a / d = ( 3 / 4 ) * ( 7 / 9 ) * ( 5 / 7 ) = > 5 / 12 answer : a"


Question: the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?

<gadget id="calculator">40 - 4</gadget>
<output>36</output>

<gadget id="calculator">12 * 36</gadget>
<output>432</output>

<gadget id="calculator">12 * 32</gadget>
<output>384</output>

<gadget id="calculator">432 - 384</gadget>
<output>48</output>

<gadget id="calculator">48 / 4</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 8
B. 12
C. 15
D. 17
E. 18

divide(subtract(multiply(12, subtract(40, 4)), multiply(12, 32)), 4)

Explanation: "let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b"


Question: a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 12 days before the completion of the work . in how many days was the work completed ?

<gadget id="calculator">1 / 24</gadget>
<output>1/24 = around 0.041667</output>

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">(1/24) + (1/30)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(3/40) * 12</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>

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

<gadget id="calculator">2 * 12</gadget>
<output>24</output>

<gadget id="calculator">5 * 24</gadget>
<output>120</output>

<gadget id="calculator">1 / 120</gadget>
<output>1/120 = around 0.008333</output>

<gadget id="calculator">(1/120) + (3/40)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/10) / (1/12)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">(6/5) + 12</gadget>
<output>66/5 = around 13.2</output>
<result>66/5 = around 13.2</result>

Choices:
A. 13 days
B. 16 days
C. 18 days
D. 11 days
E. 38 days

add(divide(subtract(const_1, multiply(add(divide(const_1, 24), divide(const_1, 30)), 12)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, 12))), add(divide(const_1, 24), divide(const_1, 30)))), 12)

Explanation: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 12 days = 12 * ( 1 / 24 + 1 / 30 ) = 9 / 10 remaining work = 1 / 10 the number of days required for this initial work = 1 days . the total number of days required = 12 + 1 = 13 days . answer : a"


Question: the total marks obtained by a student in mathematics and physics is 30 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .

<gadget id="calculator">30 + 20</gadget>
<output>50</output>

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

Choices:
A. 40
B. 30
C. 25
D. data inadequate
E. none of these .

Explanation: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 30 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 30 + 20 ) / 2 = 25 . answer : c"


Question: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1540 in all from both of them as interest . the rate of interest per annum is ?

<gadget id="calculator">5_000 * 2</gadget>
<output>10_000</output>

<gadget id="calculator">3_000 * 4</gadget>
<output>12_000</output>

<gadget id="calculator">10_000 + 12_000</gadget>
<output>22_000</output>

<gadget id="calculator">1_540 / 22_000</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">(7/100) * 100</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 7 %
B. 12 %
C. 74 %
D. 10 %
E. 45 %

multiply(divide(1540, add(multiply(5000, 2), multiply(3000, 4))), const_100)

Explanation: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1540 100 r + 120 r = 1540 r = 7 % answer : a"


Question: solve for x and check : 25 x = 675

<gadget id="calculator">675 / 25</gadget>
<output>27</output>

<gadget id="calculator">25 * 27</gadget>
<output>675</output>
<result>675</result>

Choices:
A. 675
B. 725
C. 895
D. 1025
E. none of these

Explanation: "solution : dividing each side by 25 , we obtain ( 25 x / 675 ) = ( 675 / 25 ) therefore : x = 27 check : 25 x = 675 ( 25 * 27 ) = 675 675 = 675 answer : a"


Question: given that x and y are events such that z ( x ) = 0.02 z ( y ) = 0.10 z ( xny ) = 0.10 z ( x | y ) = find z ( x | y ) and z ( x | y )

<gadget id="calculator">0.1 / 0.02</gadget>
<output>5</output>

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

Choices:
A. 1 / 5
B. 1 / 6
C. 1 / 6
D. 1 / 4
E. 1 / 2

Explanation: here , x and y are events z ( x | y ) = z ( xny ) / z ( y ) = 0.10 / 0.10 = 1 q ( g | h ) = z ( xny ) / z ( x ) = 0.4 / 0.02 = 1 / 5 answer is a


Question: a jar contains a mixture of ab in the ratio 4 : 1 . when 40 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

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

<gadget id="calculator">6 + 4</gadget>
<output>10</output>

<gadget id="calculator">6 - 1</gadget>
<output>5</output>

<gadget id="calculator">40 / 5</gadget>
<output>8</output>

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

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

<gadget id="calculator">80 / 5</gadget>
<output>16</output>

<gadget id="calculator">16 * 4</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 12
B. 15
C. 16
D. 64
E. 25

multiply(divide(multiply(add(multiply(3, const_2), multiply(2, const_2)), divide(40, subtract(multiply(3, const_2), 1))), add(4, 1)), 4)

Explanation: 40 litres of mixture that is replaced will contain 32 litres of a and 8 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 32 ] / [ k - 8 + 40 ] = 2 / 3 = > 12 k - 96 = 2 k - 16 + 80 = > 10 k = 160 solve for k which is k = 16 so initial volume of liquid a = 4 k = 64 litres answer : d


Question: the length of a rectangle is 3 times its width . if the width of the rectangle is 6 inches , what is the rectangle ' s area , in square inches ?

<gadget id="calculator">3 * 6</gadget>
<output>18</output>

<gadget id="calculator">6 * 18</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 30 square inches
B. 108 square inches
C. 68 square inches
D. 89 square inches
E. 92 square inches

Explanation: "if the width is 6 in and the length is 3 times the width , then the length is 3 * 6 = 18 in the area is given by 6 * 18 = 108 square inches correct answer b"


Question: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2500 . the difference between the profit shares of a and c is ?

<gadget id="calculator">12_000 / 10_000</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">8_000 / 10_000</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(6/5) - (4/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 2_500</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 621
B. 276
C. 236
D. 1000
E. 211

Explanation: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2500 = > 5 parts out of 15 parts is rs . 2500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2500 ) = rs . 1000 answer : d"


Question: a truck drives 80 miles on local roads at 30 mph , and 50 miles on the highway at 60 mph , the truck also take a hour lunch break . what is the average speed of the entire trip ?

<gadget id="calculator">80 + 60</gadget>
<output>140</output>

<gadget id="calculator">50 / 60</gadget>
<output>5/6 = around 0.833333</output>

<gadget id="calculator">80 / 30</gadget>
<output>8/3 = around 2.666667</output>

<gadget id="calculator">(5/6) + (8/3)</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">(7/2) + 1</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">140 / (9/2)</gadget>
<output>280/9 = around 31.111111</output>
<result>280/9 = around 31.111111</result>

Choices:
A. 30 mph
B. 29 mph
C. 28 mph
D. 31 mph
E. 23 mph

divide(add(80, 60), add(add(divide(50, 60), divide(80, 30)), const_1))

Explanation: so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 80 miles , and v = 30 mph so we can obtain time : 30 * t = 80 or t = 80 / 30 = 2.6 hours the needed time to cover 80 miles in the same way we should divide 50 to 60 to find the needed time to cover 50 miles , so t = 0.8 hours so the total time for covering total distance would be 2.6 + 0.8 + 1 ( lunch time ) = 4.4 hours and total distance is 80 + 50 = 130 miles final stage : average speed is total distance divide to total time : 130 / 4.4 = 29.5 miles per hour rounding up to 30 . . . .


Question: carrey rented a car for rs . 20 plus rs . 0.25 per kilometer driven . samuel rented a car for rs . 24 plus rs . 0.16 per kilometer driven . if each drove d km . and each was charged exactly the same amount for the rental , then d equals ?

<gadget id="calculator">24 - 20</gadget>
<output>4</output>

<gadget id="calculator">0.25 - 0.16</gadget>
<output>0.09</output>

<gadget id="calculator">4 / 0.09</gadget>
<output>44.444444</output>
<result>44.444444</result>

Choices:
A. 44.4
B. 44.8
C. 1
D. 19
E. 44.11

divide(subtract(24, 20), subtract(0.25, 0.16))

Explanation: explanation : 20 + 0.25 × d = 24 + 0.16 d solving we get d = 44.4 answer : a


Question: the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 24 ?

<gadget id="calculator">24 / 6</gadget>
<output>4</output>

<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 44
B. 46
C. 48
D. 50
E. 52

Explanation: $ 24 = 4 * $ 6 the number of doughnuts is 4 * 12 = 48 the answer is c .


Question: the speed of the boat in still water in 12 kmph . it can travel downstream through 48 kms in 3 hrs . in what time would it cover the same distance upstream ?

<gadget id="calculator">48 / 3</gadget>
<output>16</output>

<gadget id="calculator">16 - 12</gadget>
<output>4</output>

<gadget id="calculator">12 - 4</gadget>
<output>8</output>

<gadget id="calculator">48 / 8</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 8 hours
B. 6 hours
C. 4 hours
D. 5 hours
E. 6 hours

divide(48, subtract(12, subtract(divide(48, 3), 12)))

Explanation: "still water = 12 km / hr downstream = 48 / 3 = 16 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 16 / 2 = 8 km / hr so time taken in upstream = 48 / 8 = 6 hrs answer : e"


Question: on a sum of money , the simple interest for 2 years is rs . 326 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is

<gadget id="calculator">326 / 2</gadget>
<output>163</output>

<gadget id="calculator">340 - 163</gadget>
<output>177</output>

<gadget id="calculator">177 - 163</gadget>
<output>14</output>

<gadget id="calculator">100 * 14</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 / 163</gadget>
<output>1_400/163 = around 8.588957</output>
<result>1_400/163 = around 8.588957</result>

Choices:
A. 15 %
B. 14.25 %
C. 8.58 %
D. 10.5 %
E. 11.5 %

divide(multiply(const_100, subtract(subtract(340, divide(326, 2)), divide(326, 2))), divide(326, 2))

Explanation: "explanation : the difference between compound interest and simple interest on rs . p for 2 years at r % per annum = ( r ã — si ) / ( 2 ã — 100 ) difference between the compound interest and simple interest = 340 - 326 = 14 ( r ã — si ) / ( 2 ã — 100 ) = 14 ( r ã — 326 ) / ( 2 ã — 100 ) = 14 r = 8.58 % answer : option c"


Question: in a certain supermarket , a triangular display of cans is arranged in 9 rows , numbered 1 through 9 from top to bottom . each successively numbered row contains 3 more cans than the row immediately above it . if there are fewer than 120 cans in the entire display , how many cans are in the seventh row ?

<gadget id="calculator">3 + 3</gadget>
<output>6</output>

<gadget id="calculator">6 * 3</gadget>
<output>18</output>

<gadget id="calculator">9 - 1</gadget>
<output>8</output>

<gadget id="calculator">3 * 8</gadget>
<output>24</output>

<gadget id="calculator">24 / 2</gadget>
<output>12</output>

<gadget id="calculator">12 * 9</gadget>
<output>108</output>

<gadget id="calculator">120 - 108</gadget>
<output>12</output>

<gadget id="calculator">12 / 9</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">floor(4/3)</gadget>
<output>1</output>

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

Choices:
A. 13
B. 15
C. 17
D. 19
E. 21

add(multiply(add(3, 3), 3), floor(divide(subtract(120, multiply(divide(multiply(3, subtract(9, 1)), const_2), 9)), 9)))

Explanation: "let x be the number of cans in row 1 . the total number of cans is x + ( x + 3 ) + . . . + ( x + 24 ) = 9 x + 3 ( 1 + 2 + . . . + 8 ) = 9 x + 3 ( 8 ) ( 9 ) / 2 = 9 x + 108 since the total is less than 120 , x must equal 1 . the number of cans in the 7 th row is 1 + 3 ( 6 ) = 19 the answer is d ."


Question: the length of a rectangle is 3 times its width . if the width of the rectangle is 4 inches , what is the rectangle ' s area , in square inches ?

<gadget id="calculator">3 * 4</gadget>
<output>12</output>

<gadget id="calculator">4 * 12</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 30 square inches
B. 75 square inches
C. 68 square inches
D. 48 square inches
E. 92 square inches

Explanation: "if the width is 4 in and the length is 3 times the width , then the length is 3 * 4 = 12 in the area is given by 4 * 12 = 48 square inches correct answer d"


Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.7 years . the ration of the number of boys to the number of girls in the class is ?

<gadget id="calculator">15.8 - 15.7</gadget>
<output>0.1</output>

<gadget id="calculator">16.4 - 15.8</gadget>
<output>0.6</output>

<gadget id="calculator">0.1 / 0.6</gadget>
<output>0.166667</output>
<result>0.166667</result>

Choices:
A. 1 : 6
B. 2 : 3
C. 2 : 5
D. 2 : 1
E. 2 : 4

Explanation: "let the ratio be k : 1 . then , k * 16.4 + 1 * 15.7 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.7 ) = k = 0.1 / 0.6 = 1 / 6 required ratio = 1 / 6 : 1 = 1 : 6 . answer : a"


Question: a man walking at a rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge is ?

<gadget id="calculator">5 * 1_000</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 / 60</gadget>
<output>250/3 = around 83.333333</output>

<gadget id="calculator">(250/3) * 15</gadget>
<output>1_250</output>
<result>1_250</result>

Choices:
A. 1250 m
B. 1310 m
C. 1500 m
D. 1000 m
E. 1195 m

multiply(divide(multiply(5, const_1000), const_60), 15)

Explanation: "speed = 5 * 5 / 18 = 25 / 18 m / sec distance covered in 15 minutes = 25 / 18 * 15 * 60 = 1250 m answer is a"


Question: the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 11 . if p invested the money for 5 months , find for how much time did q invest the money ?

<gadget id="calculator">7 / 5</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">11 / 7</gadget>
<output>11/7 = around 1.571429</output>

<gadget id="calculator">(7/5) * (11/7)</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">(11/5) * 5</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 19
B. 17
C. 13
D. 11
E. 12

multiply(multiply(divide(7, 5), divide(11, 7)), 5)

Explanation: "7 * 5 : 5 * x = 7 : 11 x = 11 answer : d"


Question: a fair price shopkeeper takes 10 % profit on his goods . he lost 30 % goods during theft . his loss percent is :

<gadget id="calculator">100 + 10</gadget>
<output>110</output>

<gadget id="calculator">110 * 30</gadget>
<output>3_300</output>

<gadget id="calculator">3_300 / 100</gadget>
<output>33</output>

<gadget id="calculator">110 - 33</gadget>
<output>77</output>

<gadget id="calculator">100 - 77</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23 %
B. 42 %
C. 32 %
D. 12 %
E. 22 %

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

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 70 . s . p . of each item = rs . 1.10 total sale = 1.10 * 70 = rs . 77 hence , loss % = 23 / 100 * 100 = 23 % answer : a"


Question: how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?

<gadget id="calculator">63 - 3</gadget>
<output>60</output>

<gadget id="calculator">10 / 36</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">60 * (5/18)</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">500 / (50/3)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 22
B. 30
C. 88
D. 26
E. 12

divide(500, multiply(subtract(63, 3), const_0_2778))

Explanation: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 500 * 3 / 50 = 30 sec . answer : b"


Question: the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is

<gadget id="calculator">21 + 23</gadget>
<output>44</output>

<gadget id="calculator">44 / 2</gadget>
<output>22</output>

<gadget id="calculator">1 * 10</gadget>
<output>10</output>

<gadget id="calculator">22 + 10</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 22
B. 30
C. 99
D. 38
E. 32

add(divide(add(21, 23), const_2), multiply(const_1, 10))

Explanation: "total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e"


Question: if 64 ( 8 ^ x ) = 1 then x =

<gadget id="calculator">1 / 64</gadget>
<output>1/64 = around 0.015625</output>

<gadget id="calculator">log(1/64)</gadget>
<output>-log(64) = around -4.158883</output>

<gadget id="calculator">log(8)</gadget>
<output>log(8) = around 2.079442</output>

<gadget id="calculator">(-log(64)) / log(8)</gadget>
<output>-log(64)/log(8) = around -2</output>
<result>-log(64)/log(8) = around -2</result>

Choices:
A. 2
B. – 1
C. 0
D. 1
E. - 2

Explanation: "8 ^ x = 1 / 64 8 ^ x = 1 / 8 ^ 2 8 ^ x = 8 ^ - 2 x = - 2 e"


Question: the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?

<gadget id="calculator">12 * 6</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 27 sq . m
B. 126 sq . m
C. 84 sq . m
D. 18 sq . m
E. 72 sq . m

Explanation: a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e )


Question: pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?

<gadget id="calculator">30 / 6</gadget>
<output>5</output>

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

<gadget id="calculator">4 * 24</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 18
B. 27
C. 96
D. 27
E. 21

multiply(subtract(divide(30, 6), const_1), 24)

Explanation: "let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c"


Question: the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?

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

Choices:
A. 3
B. 5
C. 6
D. 7
E. 8

Explanation: "q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"


Question: a fair price shopkeeper takes 10 % profit on his goods . he lost 70 % goods during theft . his loss percent is :

<gadget id="calculator">100 + 10</gadget>
<output>110</output>

<gadget id="calculator">110 * 70</gadget>
<output>7_700</output>

<gadget id="calculator">7_700 / 100</gadget>
<output>77</output>

<gadget id="calculator">110 - 77</gadget>
<output>33</output>

<gadget id="calculator">100 - 33</gadget>
<output>67</output>
<result>67</result>

Choices:
A. 72 %
B. 42 %
C. 32 %
D. 67 %
E. 22 %

subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 70), const_100)))

Explanation: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 30 . s . p . of each item = rs . 1.10 total sale = 1.10 * 30 = rs . 33 hence , loss % = 67 / 100 * 100 = 67 % answer : d"


Question: the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?

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

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

<gadget id="calculator">40 - 8</gadget>
<output>32</output>

<gadget id="calculator">5 - 3</gadget>
<output>2</output>

<gadget id="calculator">32 / 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 11
B. 13
C. 14
D. 16
E. 10

divide(subtract(multiply(add(const_4, const_1), 8), 8), subtract(add(const_4, const_1), const_3))

Explanation: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d"


Question: 13 buckets of water fill a tank when the capacity of each bucket is 42 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 6 litres ?

<gadget id="calculator">42 * 13</gadget>
<output>546</output>

<gadget id="calculator">546 / 6</gadget>
<output>91</output>
<result>91</result>

Choices:
A. 91
B. 80
C. 96
D. 98
E. 90

Explanation: "capacity of the tank = ( 13 ã — 42 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 ã — 42 / 6 = 13 ã — 7 = 91 answer is a"


Question: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 22 seconds . the ratio of their speeds is ?

<gadget id="calculator">27 - 22</gadget>
<output>5</output>

<gadget id="calculator">22 - 17</gadget>
<output>5</output>

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

Choices:
A. 3 / 1
B. 3 / 1
C. 1 / 1
D. 3 / 5
E. 5 / 2

divide(subtract(27, 22), subtract(22, 17))

Explanation: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 22 = = > 27 x + 17 y = 22 x + 22 y = = > 5 x = 5 y = = > x / y = 1 / 1 . answer : c"


Question: exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

<gadget id="calculator">7 * 9</gadget>
<output>63</output>

<gadget id="calculator">63 * 3</gadget>
<output>189</output>

<gadget id="calculator">189 / 7</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 27
B. 35
C. 39
D. 60
E. 65

Explanation: "the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a ."


Question: the product of two successive numbers is 7832 . which is the smaller of the two numbers ?

<gadget id="calculator">7_832 ** (1/2)</gadget>
<output>2*sqrt(1958) = around 88.498588</output>
<result>2*sqrt(1958) = around 88.498588</result>

Choices:
A. 78
B. 68
C. 88
D. 97
E. 37

Explanation: "c 88 from the given alternatives , 88 × 89 = 7832 ∴ smaller number = 88"


Question: the value of 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 is

<gadget id="calculator">3.6 * 0.48</gadget>
<output>1.728</output>

<gadget id="calculator">1.728 * 2.5</gadget>
<output>4.32</output>

<gadget id="calculator">0.12 * 0.09</gadget>
<output>0.0108</output>

<gadget id="calculator">0.0108 * 0.5</gadget>
<output>0.0054</output>

<gadget id="calculator">4.32 / 0.0054</gadget>
<output>800</output>
<result>800</result>

Choices:
A. 80
B. 800
C. 8000
D. 80000
E. none of these

divide(multiply(multiply(3.6, 0.48), 2.50), multiply(multiply(0.12, 0.09), 0.5))

Explanation: "solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b"


Question: two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 30 hr . if all pipes are opened simultaneously , then the cistern will be filled in

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/10) + (1/12)</gadget>
<output>11/60 = around 0.183333</output>

<gadget id="calculator">1 / 30</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">(11/60) - (1/30)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">1 / (3/20)</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>

Choices:
A. 6.67 hr
B. 8 hr
C. 8.5 hr
D. 10 hr
E. none of these

inverse(subtract(add(divide(const_1, 10), divide(const_1, 12)), divide(const_1, 30)))

Explanation: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 30 = 3 / 20 hence , tank will be filled in 20 / 3 = 6.67 hour option ( a )"


Question: if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?

<gadget id="calculator">7 / 2</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">1 / 8</gadget>
<output>1/8 = around 0.125</output>

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

<gadget id="calculator">(1/8) + (1/2)</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">(7/2) * (5/8)</gadget>
<output>35/16 = around 2.1875</output>

<gadget id="calculator">1 - (5/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">(35/16) / (3/8)</gadget>
<output>35/6 = around 5.833333</output>

<gadget id="calculator">(35/6) + (7/2)</gadget>
<output>28/3 = around 9.333333</output>
<result>28/3 = around 9.333333</result>

Choices:
A. 7.33 cm
B. 6.33 cm
C. 5.33 cm
D. 9.33 cm
E. 8.33 cm

add(divide(multiply(divide(7, 2), add(divide(1, 8), divide(1, 2))), subtract(const_1, add(divide(1, 8), divide(1, 2)))), divide(7, 2))

Explanation: ( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d


Question: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?

<gadget id="calculator">48 * 4</gadget>
<output>192</output>

<gadget id="calculator">46 * 4</gadget>
<output>184</output>

<gadget id="calculator">192 - 184</gadget>
<output>8</output>

<gadget id="calculator">42 - 8</gadget>
<output>34</output>
<result>34</result>

Choices:
A. 34
B. 55
C. 66
D. 81
E. 21

subtract(42, subtract(multiply(48, const_4), multiply(46, const_4)))

Explanation: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 – 150 = 34 . answer : a"


Question: a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?

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

<gadget id="calculator">8 / (1/5)</gadget>
<output>40</output>

<gadget id="calculator">40 - 1</gadget>
<output>39</output>

<gadget id="calculator">39 * 0.4</gadget>
<output>15.6</output>

<gadget id="calculator">2.1 + 15.6</gadget>
<output>17.7</output>
<result>17.7</result>

Choices:
A. 15.6
B. 16.0
C. 17.7
D. 18.7
E. 19.1

add(2.10, multiply(subtract(divide(8, divide(1, 5)), 1), 0.40))

Explanation: "a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c ."


Question: two cyclist start from the same places in opposite directions . one is going towards north at 30 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?

<gadget id="calculator">30 + 40</gadget>
<output>70</output>

<gadget id="calculator">50 / 70</gadget>
<output>5/7 = around 0.714286</output>
<result>5/7 = around 0.714286</result>

Choices:
A. 1.32 hr
B. 0.714 hrs
C. 3.231 hrs
D. 0.515 hrs
E. 6.214 hrs

Explanation: "to be ( 30 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 70 * 50 = 0.714 hrs answer is b"


Question: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?

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

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">16 + 9</gadget>
<output>25</output>

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">25 / 5</gadget>
<output>5</output>

<gadget id="calculator">4 * 5</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 12
B. 18
C. 24
D. 20
E. 40

multiply(4, divide(25, sqrt(add(power(4, const_2), power(3, const_2)))))

Explanation: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d"


Question: the average of 5 consecutive odd numbers a , b , c , d and e is 13 . what percent of b is c ?

<gadget id="calculator">5 * 13</gadget>
<output>65</output>

<gadget id="calculator">65 / 5</gadget>
<output>13</output>

<gadget id="calculator">13 + 2</gadget>
<output>15</output>

<gadget id="calculator">15 + 2</gadget>
<output>17</output>

<gadget id="calculator">17 / 15</gadget>
<output>17/15 = around 1.133333</output>

<gadget id="calculator">(17/15) * 100</gadget>
<output>340/3 = around 113.333333</output>
<result>340/3 = around 113.333333</result>

Choices:
A. 98.2
B. 102.8
C. 108.2
D. 118.2
E. 122.8

multiply(divide(add(add(divide(multiply(5, 13), 5), const_2), const_2), add(divide(multiply(5, 13), 5), const_2)), const_100)

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 13 and b = 11 required percentage = 13 / 11 x 100 = 118.2 answer : option d


Question: a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?

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

<gadget id="calculator">10 ** 4</gadget>
<output>10_000</output>

<gadget id="calculator">10_000 / 2</gadget>
<output>5_000</output>
<result>5_000</result>

Choices:
A. 4000
B. 4500
C. 5055
D. 5000
E. 2500

divide(power(const_10, divide(8, const_2)), const_2)

Explanation: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d"


Question: a person borrows rs . 7000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .

<gadget id="calculator">7_000 * 6</gadget>
<output>42_000</output>

<gadget id="calculator">42_000 * 2</gadget>
<output>84_000</output>

<gadget id="calculator">84_000 / 100</gadget>
<output>840</output>

<gadget id="calculator">7_000 * 4</gadget>
<output>28_000</output>

<gadget id="calculator">28_000 * 2</gadget>
<output>56_000</output>

<gadget id="calculator">56_000 / 100</gadget>
<output>560</output>

<gadget id="calculator">840 - 560</gadget>
<output>280</output>

<gadget id="calculator">280 / 2</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 100 rs
B. 150 rs
C. 140 rs
D. 180 rs
E. 200 rs

divide(subtract(divide(multiply(multiply(7000, 6), 2), const_100), divide(multiply(multiply(7000, 4), 2), const_100)), 2)

Explanation: "gain in 2 years = [ ( 7000 * 6 * 2 ) / 100 ] - [ ( 7000 * 4 * 2 ) / 100 ] 840 - 560 = 280 gain in 1 year = ( 280 / 2 ) = 140 rs answer : c"


Question: what is the difference between the local value of 1 and 2 in the number 2124 ?

<gadget id="calculator">1 * 100</gadget>
<output>100</output>

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">100 - 20</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 70
B. 75
C. 20
D. 80
E. 60

subtract(multiply(1, const_100), multiply(2, const_10))

Explanation: explanation : 100 â € “ 20 = 80 answer : d


Question: in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is

<gadget id="calculator">2 * 10</gadget>
<output>20</output>

<gadget id="calculator">20 + 10</gadget>
<output>30</output>

<gadget id="calculator">30 + 7</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 37
B. 38
C. 39
D. 40
E. 41

Explanation: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a"


Question: you buy a piece of land with an area of â ˆ š 1600 , how long is one side of the land plot ?

<gadget id="calculator">1_600 ** (1/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 28
B. 40
C. 30
D. 31
E. 32

Explanation: "try filling the numbers into the answer y x y = find the closest to 900 . answer b"


Question: a can do a work in 15 days b in 14 days and c in 16 days . if they work on it together then in how many days required to complete the work ?

<gadget id="calculator">15 * 14</gadget>
<output>210</output>

<gadget id="calculator">210 * 16</gadget>
<output>3_360</output>

<gadget id="calculator">15 + 14</gadget>
<output>29</output>

<gadget id="calculator">29 + 16</gadget>
<output>45</output>

<gadget id="calculator">45 * 15</gadget>
<output>675</output>

<gadget id="calculator">3_360 / 675</gadget>
<output>224/45 = around 4.977778</output>
<result>224/45 = around 4.977778</result>

Choices:
A. 3360 / 210
B. 3360 / 21
C. 3360 / 674
D. 3360 / 240
E. 3360 / 224

divide(multiply(multiply(15, 14), 16), multiply(add(add(15, 14), 16), 15))

Explanation: person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 15 ) ( 14 ) ( 16 ) rate - ( 224 ) ( 240 ) ( 210 ) ( 674 ) work - ( 3360 ) ( 3360 ) ( 3360 ) ( 3360 ) therefore a + b + c requires ( 3360 / 674 ) days to complete entire work = 3360 / 674 answer is c


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

<gadget id="calculator">9 / 10</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) ** 2</gadget>
<output>81/100 = around 0.81</output>

<gadget id="calculator">10 / 9</gadget>
<output>10/9 = around 1.111111</output>

<gadget id="calculator">(81/100) * (10/9)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) * 100</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 75 %
B. 90 %
C. 100 %
D. 120 %
E. 125 %

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

Explanation: "the radius of tank a is 9 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 81 / ( 4 * pi ^ 2 ) = 405 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 9 * pi * 100 / ( 4 * pi ^ 2 ) = 450 / ( 2 * pi ) tank a / tank b = 405 / 450 = 9 / 10 = 90 % the answer is b ."


Question: a cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?

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

<gadget id="calculator">1 / 12</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">(1/6) - (1/12)</gadget>
<output>1/12 = around 0.083333</output>

<gadget id="calculator">1 / (1/12)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 5.2 hrs
B. 2.9 hrs
C. 12 hrs
D. 7.2 hrs
E. 1.4 hrs

divide(const_1, subtract(divide(const_1, 6), divide(const_1, 12)))

Explanation: "net part filled in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : c"


Question: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 40 percent ryegrass , what percent of the weight of this mixture is x ?

<gadget id="calculator">40 - 25</gadget>
<output>15</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(2/5) - (1/4)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">15 / (3/20)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100 %
B. 33.33 %
C. 40 %
D. 50 %
E. 66.66 %

divide(subtract(40, 25), subtract(divide(40, const_100), divide(25, const_100)))

Explanation: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 40 % 0.4 x + ( m - x ) 0.25 = 0.4 m 0.15 x = 0.15 m x = 1 m x = 100 % of m a"


Question: the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?

<gadget id="calculator">12 - 1</gadget>
<output>11</output>

<gadget id="calculator">110 / 11</gadget>
<output>10</output>

<gadget id="calculator">10 + 1</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 11
B. 12
C. 13
D. 15
E. 18

Explanation: ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a


Question: each month a retailer sells 100 identical items . on each item he makes a profit of $ 60 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?

<gadget id="calculator">100 * 60</gadget>
<output>6_000</output>

<gadget id="calculator">6_000 / 10</gadget>
<output>600</output>

<gadget id="calculator">600 + 60</gadget>
<output>660</output>

<gadget id="calculator">660 * 5</gadget>
<output>3_300</output>

<gadget id="calculator">3_300 / 100</gadget>
<output>33</output>

<gadget id="calculator">60 - 33</gadget>
<output>27</output>

<gadget id="calculator">6_000 / 27</gadget>
<output>2_000/9 = around 222.222222</output>
<result>2_000/9 = around 222.222222</result>

Choices:
A. 191
B. 213
C. 221
D. 223
E. 226

divide(multiply(100, 60), subtract(60, divide(multiply(add(divide(multiply(100, 60), 10), 60), 5), 100)))

Explanation: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 60 sell price = $ 600 + $ 60 thus , the sell price is $ 660 for each item . selling all 100 items gives the retailer . . . 100 ( $ 60 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 660 ) = $ 33 discount $ 627 = $ 600 + $ 27 now , the retailer makes a profit of just $ 27 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 27 ( x ) = $ 2,000 x = 2,000 / 27 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"


Question: a and b go around a circular track of length 200 m on a cycle at speeds of 36 kmph and 72 kmph . after how much time will they meet for the first time at the starting point ?

<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">36 * (5/18)</gadget>
<output>10</output>

<gadget id="calculator">20 - 10</gadget>
<output>10</output>

<gadget id="calculator">200 / 10</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 120 sec
B. 198 sec
C. 178 sec
D. 20 sec
E. 276 sec

divide(200, subtract(multiply(72, const_0_2778), multiply(36, const_0_2778)))

Explanation: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 200 / ( 36 * 5 / 18 ) , 200 / ( 72 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : d"


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

<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>

Choices:
A. 3
B. 4
C. 6
D. 8
E. 12

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

Explanation: since 2 xy prime r 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 .


Question: a man can row 8 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?

<gadget id="calculator">8 + 3</gadget>
<output>11</output>

<gadget id="calculator">8 - 3</gadget>
<output>5</output>

<gadget id="calculator">11 * 5</gadget>
<output>55</output>

<gadget id="calculator">11 + 5</gadget>
<output>16</output>

<gadget id="calculator">55 / 16</gadget>
<output>55/16 = around 3.4375</output>

<gadget id="calculator">(55/16) * 2</gadget>
<output>55/8 = around 6.875</output>
<result>55/8 = around 6.875</result>

Choices:
A. 5.75
B. 5.7
C. 5.76
D. 5.74
E. 6.8

multiply(divide(multiply(add(8, 3), subtract(8, 3)), add(add(8, 3), subtract(8, 3))), const_2)

Explanation: "m = 8 s = 3 ds = 11 us = 5 x / 11 + x / 5 = 1 x = 3.4 d = 3.4 * 2 = 6.8 answer : e"


Question: the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?

<gadget id="calculator">36 * 1_000</gadget>
<output>36_000</output>

<gadget id="calculator">60 / 1</gadget>
<output>60</output>

<gadget id="calculator">36_000 / 60</gadget>
<output>600</output>

<gadget id="calculator">600 / 2</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 752
B. 799
C. 300
D. 750
E. 712

divide(divide(multiply(36, const_1000), divide(const_60, const_1)), const_2)

Explanation: "speed = [ 36 * 5 / 18 ] m / sec = 10 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 10 ã ¨ x = 10 * 60 / 2 = 300 answer : c"


Question: the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?

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

Choices:
A. 11
B. 15
C. 12
D. 19
E. 20

Explanation: "d 19 ( x + y ) â € “ ( y + z ) = 19 x â € “ z = 19"


Question: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

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

<gadget id="calculator">16 / (2/3)</gadget>
<output>24</output>

<gadget id="calculator">24 / (2/3)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 30
B. 33
C. 36
D. 39
E. 42

divide(divide(16, subtract(const_1, divide(const_1, 3))), subtract(const_1, divide(const_1, 3)))

Explanation: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c ."


Question: a group of men decided to do a work in 55 days , but 15 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?

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

<gadget id="calculator">60 - 55</gadget>
<output>5</output>

<gadget id="calculator">900 / 5</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 180
B. 150
C. 140
D. 100
E. 25

divide(multiply(15, 60), subtract(60, 55))

Explanation: "original number of men = 15 * 60 / ( 60 - 55 ) = 180 answer is a"


Question: a train 250 m long , running with a speed of 50 km / hr will pass a tree in ?

<gadget id="calculator">50 * 1_000</gadget>
<output>50_000</output>

<gadget id="calculator">250 / 50_000</gadget>
<output>1/200 = around 0.005</output>

<gadget id="calculator">(1/200) * 3_600</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 18 sec
B. 20 sec
C. 25 sec
D. 30 sec
E. 1 min

multiply(divide(250, multiply(50, const_1000)), const_3600)

Explanation: "speed = 50 * 5 / 18 = 125 / 9 m / sec time taken = 250 * 9 / 125 = 18 sec answer : a"


Question: country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(3/20) * 30_000</gadget>
<output>4_500</output>

<gadget id="calculator">5_500 - 4_500</gadget>
<output>1_000</output>

<gadget id="calculator">25 / 100</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/4) - (3/20)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">1_000 / (1/10)</gadget>
<output>10_000</output>
<result>10_000</result>

Choices:
A. $ 10000
B. $ 11000
C. $ 12000
D. $ 10500
E. $ 11500

divide(subtract(5500, multiply(divide(15, const_100), 30000)), subtract(divide(25, const_100), divide(15, const_100)))

Explanation: let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a


Question: in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?

<gadget id="calculator">230 + 423</gadget>
<output>653</output>
<result>653</result>

Choices:
A. 515 .
B. 545 .
C. 618 .
D. 649 .
E. 666 .

Explanation: "answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 ."


Question: the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">48 + 6</gadget>
<output>54</output>

<gadget id="calculator">54 + 1</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 46
B. 47
C. 48
D. 55
E. 50

Explanation: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d ."


Question: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?

<gadget id="calculator">0.06 * 9</gadget>
<output>0.54</output>

<gadget id="calculator">0.6 - 0.54</gadget>
<output>0.06</output>

<gadget id="calculator">0.08 - 0.06</gadget>
<output>0.02</output>

<gadget id="calculator">0.06 / 0.02</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 3
B. 9
C. 15
D. 21
E. 30

divide(subtract(0.60, multiply(0.06, 9)), subtract(0.08, 0.06))

Explanation: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a ."


Question: zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 9 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 9 questions did zachary answer correctly ?

<gadget id="calculator">9 - 2</gadget>
<output>7</output>

<gadget id="calculator">2 * 7</gadget>
<output>14</output>

<gadget id="calculator">3 * 2</gadget>
<output>6</output>

<gadget id="calculator">14 - 6</gadget>
<output>8</output>

<gadget id="calculator">8 + 31</gadget>
<output>39</output>

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

<gadget id="calculator">39 / 5</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>

Choices:
A. 6
B. 7
C. 8
D. 9
E. 10

divide(add(subtract(multiply(2, subtract(9, 2)), multiply(3, 2)), 31), add(3, 2))

Explanation: "i got two equations : 3 x - 2 y = 25 x + y = 9 3 x - 2 ( 9 - x ) = 25 3 x - 18 + 2 x = 25 5 x = 43 x = 8.6 or between 8 and 9 . ( ans c )"


Question: if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?

<gadget id="calculator">60 * 5</gadget>
<output>300</output>

<gadget id="calculator">300 - 10</gadget>
<output>290</output>

<gadget id="calculator">290 / 5</gadget>
<output>58</output>

<gadget id="calculator">58 + 10</gadget>
<output>68</output>
<result>68</result>

Choices:
A. 50
B. 52
C. 49
D. 68
E. 74

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

Explanation: "sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d"


Question: in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 160 of the workers of that company are men , how many of the workers are women ?

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">20 / 100</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/3) * (1/5)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/3) - (1/15)</gadget>
<output>4/15 = around 0.266667</output>

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

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/3) * (2/5)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">(4/15) + (4/15)</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">160 / (8/15)</gadget>
<output>300</output>

<gadget id="calculator">(2/3) - (4/15)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(1/15) + (2/5)</gadget>
<output>7/15 = around 0.466667</output>

<gadget id="calculator">300 * (7/15)</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 80
B. 95
C. 105
D. 120
E. 140

multiply(divide(160, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(20, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(20, const_100)), subtract(subtract(const_1, divide(const_1, const_3)), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))))

Explanation: "set up equation : x = total number of workers 160 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 160 = 16 / 30 x x = 300 300 - 160 = 140 answer e"


Question: sum of 53 odd numbers is ?

<gadget id="calculator">53 * 2</gadget>
<output>106</output>

<gadget id="calculator">53 / 2</gadget>
<output>53/2 = around 26.5</output>

<gadget id="calculator">106 * (53/2)</gadget>
<output>2_809</output>
<result>2_809</result>

Choices:
A. 2709
B. 2809
C. 2909
D. 3009
E. 3109

multiply(multiply(53, const_2), divide(53, const_2))

Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b"


Question: find the value of 5 + 2 â € ¢ ( 8 â € “ 3 )

<gadget id="calculator">8 - 3</gadget>
<output>5</output>

<gadget id="calculator">5 * 2</gadget>
<output>10</output>

<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 25
B. 13
C. 17
D. 24
E. 15

Explanation: 5 + 2 â € ¢ ( 8 â € “ 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e


Question: what least number should be added to 1057 , so that the sum is completely divisible by 23

<gadget id="calculator">1_057 % 23</gadget>
<output>22</output>

<gadget id="calculator">23 - 22</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 4
B. 1
C. 2
D. 3
E. 5

Explanation: "explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b"


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

<gadget id="calculator">20 * 10</gadget>
<output>200</output>

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

Choices:
A. 3323
B. 1000
C. 2877
D. 2992
E. 7111

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


Question: when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is

<gadget id="calculator">1 / 10</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">100 * 10</gadget>
<output>1_000</output>

<gadget id="calculator">4 + 4</gadget>
<output>8</output>

<gadget id="calculator">1_000 * 8</gadget>
<output>8_000</output>

<gadget id="calculator">(1/10) * 8_000</gadget>
<output>800</output>
<result>800</result>

Choices:
A. 50
B. 200
C. 380
D. 798
E. 400

multiply(inverse(10), multiply(multiply(const_100, const_10), add(const_4, const_4)))

Explanation: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d


Question: 35 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?

<gadget id="calculator">100 - 35</gadget>
<output>65</output>

<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>

<gadget id="calculator">40 / 100</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">35 / 100</gadget>
<output>7/20 = around 0.35</output>

<gadget id="calculator">60 / 100</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(7/20) * (3/5)</gadget>
<output>21/100 = around 0.21</output>

<gadget id="calculator">(2/5) - (21/100)</gadget>
<output>19/100 = around 0.19</output>

<gadget id="calculator">(13/20) - (19/100)</gadget>
<output>23/50 = around 0.46</output>

<gadget id="calculator">(23/50) / (13/20)</gadget>
<output>46/65 = around 0.707692</output>

<gadget id="calculator">(46/65) * 100</gadget>
<output>920/13 = around 70.769231</output>
<result>920/13 = around 70.769231</result>

Choices:
A. 4 %
B. 10 %
C. 96 %
D. 90.12 %
E. 70.77 %

multiply(divide(subtract(divide(subtract(const_100, 35), const_100), subtract(divide(40, const_100), multiply(divide(35, const_100), divide(60, const_100)))), divide(subtract(const_100, 35), const_100)), const_100)

Explanation: no of employees = 100 ( say ) men = 35 women = 65 men speaking french = 0.6 * 35 = 21 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 21 = 19 and women not speaking french = 65 - 19 = 46 % of women speaking french = 46 / 65 * 100 = 70.77 % answer e


Question: a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 45 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?

<gadget id="calculator">120 / 2</gadget>
<output>60</output>

<gadget id="calculator">60 + 120</gadget>
<output>180</output>

<gadget id="calculator">180 / 45</gadget>
<output>4</output>

<gadget id="calculator">4 / 4</gadget>
<output>1</output>

<gadget id="calculator">1 * 60</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 40
B. 45
C. 50
D. 55
E. 60

multiply(divide(divide(add(divide(120, const_2), 120), 45), const_4), divide(120, const_2))

Explanation: "a - b = 120 miles b - c = 60 miles avg speed = 45 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 45 = 180 / 4 t t = 60 b - c = 60 mph answer e"


Question: dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?

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

<gadget id="calculator">(1/10) + 1</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">2 - (11/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">1 - (9/10)</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">(1/10) * 100</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 10 %
B. 15 %
C. 20 %
D. 25 %
E. 30 %

multiply(subtract(const_1, subtract(const_2, add(divide(10, const_100), const_1))), const_100)

Explanation: "1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a"


Question: robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?

<gadget id="calculator">7 - 5</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 4
B. 7
C. 9
D. 5
E. 2

Explanation: 7 - 5 = 2 . answer is e


Question: a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?

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

<gadget id="calculator">600 / 5</gadget>
<output>120</output>

<gadget id="calculator">120 * 3</gadget>
<output>360</output>

<gadget id="calculator">120 * 4</gadget>
<output>480</output>

<gadget id="calculator">360 * 480</gadget>
<output>172_800</output>
<result>172_800</result>

Choices:
A. 172,800
B. 19,600
C. 20,000
D. 20,400
E. 20,800

multiply(multiply(divide(600, add(const_2, const_3)), const_3), multiply(divide(600, add(const_2, const_3)), const_4))

Explanation: you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer .


Question: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor

<gadget id="calculator">109 / 9</gadget>
<output>109/9 = around 12.111111</output>

<gadget id="calculator">floor(109/9)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 14
C. 18
D. 22
E. 24

Explanation: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )"


Question: find compound interest on $ 10000 at 15 % per annum for 2 years 4 months , compounded annually .

<gadget id="calculator">15 / 100</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">10_000 * (3/20)</gadget>
<output>1_500</output>

<gadget id="calculator">10_000 + 1_500</gadget>
<output>11_500</output>

<gadget id="calculator">11_500 * (3/20)</gadget>
<output>1_725</output>

<gadget id="calculator">1_500 + 1_725</gadget>
<output>3_225</output>

<gadget id="calculator">11_500 + 1_725</gadget>
<output>13_225</output>

<gadget id="calculator">(3/20) / 3</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">13_225 * (1/20)</gadget>
<output>2_645/4 = around 661.25</output>

<gadget id="calculator">3_225 + (2_645/4)</gadget>
<output>15_545/4 = around 3_886.25</output>
<result>15_545/4 = around 3_886.25</result>

Choices:
A. 3886.25
B. 3286.25
C. 3186.25
D. 3386.25
E. 3586.25

add(add(multiply(10000, divide(15, const_100)), multiply(add(10000, multiply(10000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(10000, multiply(10000, divide(15, const_100))), multiply(add(10000, multiply(10000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))

Explanation: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 10000 x ( 1 +  ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 10000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 13886.25 . : . c . i . = rs . ( 13886.25 - 10000 ) = $ 3886.25 answer a ."


Question: having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john ’ s weekly allowance ?

<gadget id="calculator">3 / 5</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 / 3</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(1/3) * (2/5)</gadget>
<output>2/15 = around 0.133333</output>

<gadget id="calculator">(3/5) + (2/15)</gadget>
<output>11/15 = around 0.733333</output>

<gadget id="calculator">1 - (11/15)</gadget>
<output>4/15 = around 0.266667</output>

<gadget id="calculator">1.28 / (4/15)</gadget>
<output>4.8</output>
<result>4.8</result>

Choices:
A. $ 2.40
B. $ 3.00
C. $ 3.20
D. $ 3.60
E. $ 4.80

divide(1.28, subtract(const_1, add(divide(3, 5), multiply(divide(const_1, 3), subtract(const_1, divide(3, 5))))))

Explanation: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e"


Question: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 60 ps per meter is ?

<gadget id="calculator">3_750 * 2</gadget>
<output>7_500</output>

<gadget id="calculator">7_500 / 3</gadget>
<output>2_500</output>

<gadget id="calculator">2_500 ** (1/2)</gadget>
<output>50</output>

<gadget id="calculator">3_750 / 50</gadget>
<output>75</output>

<gadget id="calculator">2 * (50 + 75)</gadget>
<output>250</output>

<gadget id="calculator">60 * 250</gadget>
<output>15_000</output>

<gadget id="calculator">15_000 / 100</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 287
B. 369
C. 150
D. 279
E. 361

divide(multiply(60, rectangle_perimeter(sqrt(divide(multiply(3750, 2), 3)), divide(3750, sqrt(divide(multiply(3750, 2), 3))))), const_100)

Explanation: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.60 = rs . 150 answer : c"


Question: if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :

<gadget id="calculator">25 - 10</gadget>
<output>15</output>

<gadget id="calculator">20 / 15</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">10 * (4/3)</gadget>
<output>40/3 = around 13.333333</output>
<result>40/3 = around 13.333333</result>

Choices:
A. 50 km
B. 56 km
C. 13.3 km
D. 70 km
E. 80 km

multiply(10, divide(20, subtract(25, 10)))

Explanation: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c"


Question: a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/4) - (3/10)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">45 / (9/20)</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 36 liters
B. 40 liters
C. 45 liters
D. 54 liters
E. 100 liters

divide(45, subtract(divide(3, 4), divide(30, const_100)))

Explanation: "a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e ."


Question: find the smallest number that should be multiplied with 54000 to make it a perfect cube .

<gadget id="calculator">54_000 / 1_000</gadget>
<output>54</output>

<gadget id="calculator">54 / 3</gadget>
<output>18</output>

<gadget id="calculator">18 / 3</gadget>
<output>6</output>

<gadget id="calculator">6 / 3</gadget>
<output>2</output>

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

Choices:
A. 4
B. 5
C. 6
D. 3
E. 7

multiply(divide(divide(divide(divide(54000, const_1000), const_3), const_3), const_3), divide(divide(divide(divide(54000, const_1000), const_3), const_3), const_3))

Explanation: 54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a