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 500000 ?

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

<gadget id="calculator">500_000 / 10_000</gadget>
<output>50</output>

<gadget id="calculator">50 * 4</gadget>
<output>200</output>
<result>200</result>

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

multiply(divide(500000, multiply(const_1000, const_10)), const_4)

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: the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?

<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 110
B. 122
C. 120
D. 125
E. 145

Explanation: "explanation : average of new numbers = 25 * 5 = 125 answer : option d"


Question: a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?

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

<gadget id="calculator">(2/5) + 1</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">90 / (7/5)</gadget>
<output>450/7 = around 64.285714</output>

<gadget id="calculator">90 - (450/7)</gadget>
<output>180/7 = around 25.714286</output>
<result>180/7 = around 25.714286</result>

Choices:
A. 25
B. 20
C. 47
D. 36
E. 30

subtract(90, divide(90, add(divide(2, 5), const_1)))

Explanation: "1 : 2 / 5 = 5 : 2 2 / 7 * 90 = 25 answer : a"


Question: a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is :

<gadget id="calculator">25 * 100</gadget>
<output>2_500</output>

<gadget id="calculator">16 * 100</gadget>
<output>1_600</output>

<gadget id="calculator">2_500 * 1_600</gadget>
<output>4_000_000</output>

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

<gadget id="calculator">4_000_000 / 200</gadget>
<output>20_000</output>
<result>20_000</result>

Choices:
A. 16000
B. 18000
C. 20000
D. 22000
E. none of these

divide(multiply(multiply(25, const_100), multiply(16, const_100)), multiply(20, 10))

Explanation: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 option c"


Question: find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?

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

<gadget id="calculator">10 + 2</gadget>
<output>12</output>

<gadget id="calculator">12 / 5</gadget>
<output>12/5 = around 2.4</output>

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

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) + 1</gadget>
<output>28/25 = around 1.12</output>

<gadget id="calculator">1_008 / (28/25)</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 900
B. 2217
C. 2889
D. 2777
E. 2991

divide(1008, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1))

Explanation: "1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a"


Question: if a sum of money doubles itself in 20 years at simple interest , the ratepercent per annum is

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

<gadget id="calculator">2 / (1/5)</gadget>
<output>10</output>

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

Choices:
A. 12
B. 12.5
C. 13
D. 5
E. 14

divide(divide(const_2, divide(20, const_100)), const_2)

Explanation: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 20 ) = 5 option d"


Question: at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?

<gadget id="calculator">100 + 20</gadget>
<output>120</output>

<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>

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

<gadget id="calculator">(6/5) * (1/2)</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">1 - (3/5)</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 7.5</gadget>
<output>3</output>
<result>3</result>

Choices:
A. $ 1.40
B. $ 3
C. $ 3.40
D. $ 4.40
E. $ 5.40

multiply(subtract(const_1, multiply(divide(add(const_100, 20), const_100), divide(const_1, const_2))), 7.50)

Explanation: "manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b"


Question: a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit

<gadget id="calculator">100 - 5</gadget>
<output>95</output>

<gadget id="calculator">95 / 100</gadget>
<output>19/20 = around 0.95</output>

<gadget id="calculator">1_140 / (19/20)</gadget>
<output>1_200</output>

<gadget id="calculator">100 + 5</gadget>
<output>105</output>

<gadget id="calculator">105 / 100</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">1_200 * (21/20)</gadget>
<output>1_260</output>
<result>1_260</result>

Choices:
A. rs . 1200
B. rs . 1230
C. rs . 1260
D. rs . 1290
E. none of these

multiply(divide(1140, divide(subtract(const_100, 5), const_100)), divide(add(const_100, 5), const_100))

Explanation: "explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 95 / 1140 = 105 / x ) = > x = 1260 option c"


Question: a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a signal post ?

<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">400 / (50/3)</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 28 seconds
B. 30 seconds
C. 40 seconds
D. 24 seconds
E. 18 seconds

Explanation: speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 meter time = distance / speed = 400 * ( 9 / 150 ) = 24 seconds answer : d


Question: how long does a train 105 m long running at the speed of 68 km / hr takes to cross a bridge 90 m length ?

<gadget id="calculator">105 + 90</gadget>
<output>195</output>

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

<gadget id="calculator">68 * (5/18)</gadget>
<output>170/9 = around 18.888889</output>

<gadget id="calculator">195 / (170/9)</gadget>
<output>351/34 = around 10.323529</output>
<result>351/34 = around 10.323529</result>

Choices:
A. 13.9 sec
B. 10.7 sec
C. 17.9 sec
D. 61.9 sec
E. 47.98 sec

Explanation: "speed = 68 * 5 / 18 = 19 m / sec total distance covered = 105 + 90 = 205 m . required time = 205 / 19 = 10.7 sec . answer : b"


Question: there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .

<gadget id="calculator">151 * 7</gadget>
<output>1_057</output>

<gadget id="calculator">6 * 152</gadget>
<output>912</output>

<gadget id="calculator">1_057 - 912</gadget>
<output>145</output>
<result>145</result>

Choices:
A. 145
B. 168
C. 189
D. 190
E. 200

subtract(multiply(151, 7), multiply(6, 152))

Explanation: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a"


Question: ms . lopez deposits $ 150 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?

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

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

<gadget id="calculator">1 + (1/10)</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(11/10) ** 2</gadget>
<output>121/100 = around 1.21</output>

<gadget id="calculator">150 * (121/100)</gadget>
<output>363/2 = around 181.5</output>
<result>363/2 = around 181.5</result>

Choices:
A. $ 118.00
B. $ 120.00
C. $ 181.15
D. $ 122.00
E. $ 140.00

multiply(150, power(add(const_1, divide(divide(20, const_100), const_2)), const_2))

Explanation: "using formula - a = p ( 1 + r / n ) ^ nt given p = 150 n = 2 t = 1 r = 0.2 substituting value in formula a = 150 ( 1 + 0.2 / 2 ) ^ 2 a = 181.15 $ = c"


Question: how much is 70 % of 40 is greater than 4 / 5 of 25 ?

<gadget id="calculator">70 / 100</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">40 * (7/10)</gadget>
<output>28</output>

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

<gadget id="calculator">(4/5) * 25</gadget>
<output>20</output>

<gadget id="calculator">28 - 20</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 22
B. 67
C. 88
D. 12
E. 8

subtract(multiply(40, divide(70, const_100)), multiply(divide(4, 5), 25))

Explanation: "( 70 / 100 ) * 40 – ( 4 / 5 ) * 25 = 8 answer : e"


Question: one man adds 3 liters of water to 12 liters of milk and another 4 liters of water to 10 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?

<gadget id="calculator">3 + 12</gadget>
<output>15</output>

<gadget id="calculator">12 / 15</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">4 + 10</gadget>
<output>14</output>

<gadget id="calculator">10 / 14</gadget>
<output>5/7 = around 0.714286</output>

<gadget id="calculator">(4/5) / (5/7)</gadget>
<output>28/25 = around 1.12</output>
<result>28/25 = around 1.12</result>

Choices:
A. 11 : 21
B. 15 : 33
C. 28 : 25
D. 3 : 2
E. 31 : 33

Explanation: "strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 12 / 15 strength of the milk 2 nd mixture = 10 / 14 the ratio of their strengths = 12 / 15 : 10 / 14 = 28 : 25 answer is c"


Question: 27 is a perfect cube . when x is added to the prime factor of 27 , the result is a prime number . what is x ?

<gadget id="calculator">27 - 3</gadget>
<output>24</output>

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

Choices:
A. 1
B. 3
C. 5
D. 8
E. 11

Explanation: 27 is 3 * 3 * 3 then a 3 + 1 = 4 b 3 + 3 = 6 c 3 + 5 = 8 d 3 + 8 = 11 e 3 + 11 = 14 here d is the only addition that gives a prime number .


Question: a part - time employee ’ s hourly wage was increased by 10 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?

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

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

<gadget id="calculator">110 / 100</gadget>
<output>11/10 = around 1.1</output>

<gadget id="calculator">(1/10) / (11/10)</gadget>
<output>1/11 = around 0.090909</output>

<gadget id="calculator">(1/11) * 100</gadget>
<output>100/11 = around 9.090909</output>
<result>100/11 = around 9.090909</result>

Choices:
A. 9 %
B. 15 %
C. 25 %
D. 50 %
E. 100 %

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

Explanation: "let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 10 % wage increase , the employee makes $ 1.10 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.10 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.10 to get : new # of hours = 100 / 1.10 ≈ 90 hours so , the number of hours decreases from 100 hours to ( approximately ) 90 hours . this represents a 10 % decrease ( approximately ) . answer choice a is the closest answer ."


Question: the price of stock decreased by 5 % last year and rose by 10 % this year . what is the net percentage change in the price of the stock ?

<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">5 / 100</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">1 - (1/20)</gadget>
<output>19/20 = around 0.95</output>

<gadget id="calculator">(11/10) * (19/20)</gadget>
<output>209/200 = around 1.045</output>

<gadget id="calculator">(209/200) - 1</gadget>
<output>9/200 = around 0.045</output>

<gadget id="calculator">(9/200) * 100</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. 0.2 %
B. 0.8 %
C. 1.2 %
D. 1.6 %
E. 4.5 %

multiply(subtract(multiply(add(divide(10, const_100), const_1), subtract(const_1, divide(5, const_100))), const_1), const_100)

Explanation: "( 100 % - 5 % ) * ( 100 % + 10 % ) = 0.95 * 1.10 = 1.045 = 104.5 % . the net percentage change in the price of the stock is ( + ) 4.5 % the answer is e"


Question: the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 7 seconds than it was moving after 5 seconds ?

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

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

<gadget id="calculator">49 + 14</gadget>
<output>63</output>

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

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

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

<gadget id="calculator">63 - 35</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 4
B. 28
C. 15
D. 48
E. 63

subtract(add(power(7, 2), multiply(7, 2)), add(power(5, 2), multiply(5, 2)))

Explanation: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 z ( 7 ) = 7 ^ 2 + 2 * 7 = 63 therefore z ( 7 ) - z ( 3 ) = 63 - 35 = 28 km / hr option b"


Question: a soccer team played 280 games and won 65 percent of them . how many games did it win ?

<gadget id="calculator">65 * 280</gadget>
<output>18_200</output>

<gadget id="calculator">18_200 / 100</gadget>
<output>182</output>
<result>182</result>

Choices:
A. 182
B. 100
C. 104
D. 150
E. 124

Explanation: "65 % of 280 = x 0.65 * 280 = x 182 = x answer : a"


Question: the difference between two numbers is 2395 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is

<gadget id="calculator">2_395 - 15</gadget>
<output>2_380</output>

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

<gadget id="calculator">2_380 / 5</gadget>
<output>476</output>
<result>476</result>

Choices:
A. 120
B. 239
C. 476
D. 523
E. 526

divide(subtract(2395, 15), subtract(6, const_1))

Explanation: let the smaller number be x . then , larger number = ( 2395 + x ) therefore 2395 + x = ( 6 x + 15 ) ‹ = › 5 x = 2380 ‹ = › x = 476 . answer : c


Question: right triangle xyzs the base of the prism in the figure above . if xy = xz = â ˆ š 9 and the height of the prism is 6 , what is the volume of the prism ?

<gadget id="calculator">9 ** (1/2)</gadget>
<output>3</output>

<gadget id="calculator">(3 * 3) / 2</gadget>
<output>9/2 = around 4.5</output>

<gadget id="calculator">(9/2) * 6</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 3
B. 27
C. 13
D. 12
E. 15

Explanation: volume of prism = area of base * height = 1 / 2 * ( square root of 9 ) * ( square root of 9 ) * 6 = 27 answer : b


Question: on dividing 22 by a number , the quotient is 7 and the remainder is 1 . find the divisor .

<gadget id="calculator">22 / 7</gadget>
<output>22/7 = around 3.142857</output>

<gadget id="calculator">floor(22/7)</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 1
B. 2
C. 3
D. 6
E. 7

Explanation: "d = ( d - r ) / q = ( 22 - 1 ) / 7 = 21 / 7 = 3 c"


Question: the smallest number which when diminished by 5 , is divisible by 12 , 16 , 18 , 21 and 28 is

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

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

<gadget id="calculator">9 * 16</gadget>
<output>144</output>

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

<gadget id="calculator">144 * 7</gadget>
<output>1_008</output>

<gadget id="calculator">1_008 + 5</gadget>
<output>1_013</output>
<result>1_013</result>

Choices:
A. 1008
B. 1013
C. 1022
D. 1032
E. 1043

add(multiply(multiply(power(const_3, const_2.0), power(const_2.0, const_4)), add(const_3, const_4)), 5)

Explanation: "required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 5 = 1008 + 5 = 1013 answer : b"


Question: the ratio between x and y is 7 / 5 ; x is multiplied by y and y is multiplied by x , what is the ratio between the new values of x and y ?

<gadget id="calculator">7 * 5</gadget>
<output>35</output>

<gadget id="calculator">5 * 7</gadget>
<output>35</output>

<gadget id="calculator">35 / 35</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 7 / 5
B. 5 / 7
C. 1
D. 49 / 25
E. it can not be determined

Explanation: ratio = 7 k / 5 k = 7 / 5 , 14 / 10 , etc . x is multiplied by y and y is multiplied by x - - > ( 7 k * 9 k ) / ( 9 k * 7 k ) = 1 answer : c


Question: when x is multiplied by 3 , the result is 14 more than the result of subtracting x from 26 . what is the value of x ?

<gadget id="calculator">26 + 14</gadget>
<output>40</output>

<gadget id="calculator">3 + 1</gadget>
<output>4</output>

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

Choices:
A. 10
B. - 2
C. 11
D. 13
E. 22

divide(add(26, 14), add(const_3, const_1))

Explanation: the equation that can be formed is : 3 x - 14 = 26 - x or , 4 x = 40 or , x = 10 . a answer .


Question: raman , lakshmi and muthu enter into partnership . raman invests some money at the beginning , lakshmi invests double the amount after 6 months , and muthu invests thrice the amount after 8 months . if the annual gain be rs . 36000 . lakshmi ' s share is ?

<gadget id="calculator">2 / 6</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 36_000</gadget>
<output>12_000</output>
<result>12_000</result>

Choices:
A. 12000
B. 14000
C. 8000
D. 5000
E. 3000

Explanation: x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 36000 = 12000 answer : a


Question: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 10 per square m ?

<gadget id="calculator">20 * 15</gadget>
<output>300</output>

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

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

<gadget id="calculator">20 * 5</gadget>
<output>100</output>

<gadget id="calculator">100 * 2</gadget>
<output>200</output>

<gadget id="calculator">200 * 10</gadget>
<output>2_000</output>

<gadget id="calculator">6_000 + 2_000</gadget>
<output>8_000</output>

<gadget id="calculator">15 * 5</gadget>
<output>75</output>

<gadget id="calculator">75 * 2</gadget>
<output>150</output>

<gadget id="calculator">150 * 10</gadget>
<output>1_500</output>

<gadget id="calculator">8_000 + 1_500</gadget>
<output>9_500</output>
<result>9_500</result>

Choices:
A. s . 9500
B. s . 50000
C. s . 57000
D. s . 60000
E. s . 62000

add(add(multiply(multiply(multiply(20, 15), const_2), 10), multiply(multiply(multiply(20, 5), const_2), 10)), multiply(multiply(multiply(15, 5), const_2), 10))

Explanation: length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 10 * 950 = rs . 9500 a


Question: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 18 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 50 of the scientists attended that workshop , how many of them were nobel prize laureates ?

<gadget id="calculator">50 - 31</gadget>
<output>19</output>

<gadget id="calculator">19 - 3</gadget>
<output>16</output>

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

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

<gadget id="calculator">11 + 18</gadget>
<output>29</output>
<result>29</result>

Choices:
A. 11
B. 18
C. 24
D. 29
E. d ) 36

add(add(3, divide(subtract(subtract(50, 31), 3), const_2)), 18)

Explanation: "lets solve by creating equation . . w = 31 . . total = 50 . . not w = 50 - 31 = 19 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 19 or x = 8 . . so who won nobel but not wolf = x + 3 = 11 . . but people who won both w and n = 13 . . so total who won n = 11 + 18 = 29 . . d"


Question: if 4 men can colour 48 m long cloth in 2 days , then 2 men can colour 36 m long cloth in

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

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

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

<gadget id="calculator">36 / 12</gadget>
<output>3</output>
<result>3</result>

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

divide(36, multiply(divide(48, multiply(4, 2)), 2))

Explanation: "the length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 men = 36 / 6 × 2 = 3 day . c"


Question: a library has an average of 540 visitors on sundays and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :

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

<gadget id="calculator">30 / 7</gadget>
<output>30/7 = around 4.285714</output>

<gadget id="calculator">floor(30/7)</gadget>
<output>4</output>

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

<gadget id="calculator">5 * 540</gadget>
<output>2_700</output>

<gadget id="calculator">30 - 5</gadget>
<output>25</output>

<gadget id="calculator">25 * 240</gadget>
<output>6_000</output>

<gadget id="calculator">2_700 + 6_000</gadget>
<output>8_700</output>

<gadget id="calculator">8_700 / 30</gadget>
<output>290</output>
<result>290</result>

Choices:
A. 300
B. 276
C. 290
D. 285
E. none

divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 540), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 240)), 30)

Explanation: "since the month begins with sunday , to there will be five sundays in the month average required = ( 540 x 5 + 240 x 25 ) / 30 ) = 290 answer : option c"


Question: when sold at a 70 % discount , a sweater nets the merchant a 40 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?

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

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

<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">30 / (7/5)</gadget>
<output>150/7 = around 21.428571</output>

<gadget id="calculator">100 - (150/7)</gadget>
<output>550/7 = around 78.571429</output>
<result>550/7 = around 78.571429</result>

Choices:
A. 20 %
B. 40 %
C. 50 %
D. 60 %
E. 78.58 %

subtract(const_100, divide(subtract(const_100, 70), add(const_1, divide(40, const_100))))

Explanation: "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 70 % of 100 = 30 . . profit = 40 % . . therefore the wholesale purchase cost = x . . . . 1.4 x = 30 or x = 21.42 . . . marked price was 100 so . . . so answer is 78.58 % . . e"


Question: on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 13 : 7 . after the transaction , how many more horses than cows would the farm own ?

<gadget id="calculator">15 * 13</gadget>
<output>195</output>

<gadget id="calculator">15 * 7</gadget>
<output>105</output>

<gadget id="calculator">195 + 105</gadget>
<output>300</output>

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

<gadget id="calculator">28 - 13</gadget>
<output>15</output>

<gadget id="calculator">300 / 15</gadget>
<output>20</output>

<gadget id="calculator">4 * 20</gadget>
<output>80</output>

<gadget id="calculator">80 - 15</gadget>
<output>65</output>

<gadget id="calculator">20 + 15</gadget>
<output>35</output>

<gadget id="calculator">65 - 35</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 30
B. 60
C. 75
D. 90
E. 105

subtract(subtract(multiply(4, divide(add(multiply(15, 13), multiply(15, 7)), subtract(multiply(4, 7), 13))), 15), add(divide(add(multiply(15, 13), multiply(15, 7)), subtract(multiply(4, 7), 13)), 15))

Explanation: "originally , there were 4 k horses and k cows . 7 ( 4 k - 15 ) = 13 ( k + 15 ) 28 k - 13 k = 195 + 105 15 k = 300 k = 20 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 30 the answer is a ."


Question: the total age of a and b is 12 years more than the total age of b and c . c is how many year younger than a

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

Choices:
A. 11
B. 12
C. 13
D. 14
E. 15

Explanation: "explanation : given that a + b = 12 + b + c = > a – c = 12 + b – b = 12 = > c is younger than a by 12 years answer : option b"


Question: if the diameter of circle r is 40 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?

<gadget id="calculator">pi * (40 ** 2)</gadget>
<output>1600*pi = around 5_026.548246</output>

<gadget id="calculator">(1600*pi) * 100</gadget>
<output>160000*pi = around 502_654.824574</output>

<gadget id="calculator">pi * (100 ** 2)</gadget>
<output>10000*pi = around 31_415.926536</output>

<gadget id="calculator">(160000*pi) / (10000*pi)</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 16 %
B. 18 %
C. 20 %
D. 22 %
E. 24 %

Explanation: "let diameter of circle r , dr = 40 and diameter of circle s , ds = 100 radius of circle r , rr = 20 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 20 / 50 ) ^ 2 = ( 4 / 10 ) ^ 2 = 16 % answer : a"


Question: if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is ?

<gadget id="calculator">72 / 2</gadget>
<output>36</output>

<gadget id="calculator">36 ** (1/2)</gadget>
<output>6</output>

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

Choices:
A. 6
B. 12
C. 24
D. 36
E. 48

Explanation: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer v that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"


Question: mary can do a piece of work in 26 days . rosy is 30 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?

<gadget id="calculator">30 / 100</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">1 + (3/10)</gadget>
<output>13/10 = around 1.3</output>

<gadget id="calculator">26 / (13/10)</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 22
B. 20
C. 24
D. 26
E. 30

divide(26, add(const_1, divide(30, const_100)))

Explanation: "ratio of times taken by mary and rosy = 130 : 100 = 13 : 10 suppose rosy takes x days to do the work . 13 : 10 : : 26 : x = > x = 20 days . hence , rosy takes 20 days to complete the work . answer : b"


Question: a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 56 marks . the maximum marks are ?

<gadget id="calculator">175 + 56</gadget>
<output>231</output>

<gadget id="calculator">33 / 100</gadget>
<output>33/100 = around 0.33</output>

<gadget id="calculator">231 / (33/100)</gadget>
<output>700</output>
<result>700</result>

Choices:
A. 450
B. 300
C. 500
D. 610
E. 700

divide(add(175, 56), divide(33, const_100))

Explanation: "let the maximum marks be x then , 33 % of x = 175 + 56 33 x / 100 = 231 x = 700 answer is e"


Question: if s and t are both odd prime numbers ands < t , then how many different positive integer factors does 2 sthave ?

<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

Explanation: s and t are both odd prime numbers - it means either s or t is not 2 and since prime numbers have only two factors - 1 and the number itself s and t each will have ( 1 + 1 ) = 2 factors hence 2 st will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer


Question: the maximum number of student amoung them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :

<gadget id="calculator">gcd(1_001, 910)</gadget>
<output>91</output>
<result>91</result>

Choices:
A. 91
B. 910
C. 1001
D. 1911
E. none of these

Explanation: "solution required number of student = h . c . f of 1001 and 910 = 91 . answer a"


Question: a class of 20 students took a science test . 10 students had an average ( arithmetic mean ) score of 80 . the other students had an average score of 60 . what is the average score of the whole class ?

<gadget id="calculator">10 * 80</gadget>
<output>800</output>

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

<gadget id="calculator">10 * 60</gadget>
<output>600</output>

<gadget id="calculator">800 + 600</gadget>
<output>1_400</output>

<gadget id="calculator">1_400 / 20</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 70
B. 60
C. 55
D. 65
E. 85

divide(add(multiply(10, 80), multiply(subtract(20, 10), 60)), 20)

Explanation: hear , 10 students had average score of 80 , so , 80 x 10 = 800 and 10 students had average score of 60 , so , 60 x 10 = 600 total no of student are 20 ( 800 + 600 ) / 20 = 70 correct ans is a


Question: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?

<gadget id="calculator">900 / 2</gadget>
<output>450</output>

<gadget id="calculator">450 ** 2</gadget>
<output>202_500</output>

<gadget id="calculator">922.5 - 900</gadget>
<output>22.5</output>

<gadget id="calculator">202_500 / 22.5</gadget>
<output>9_000</output>
<result>9_000</result>

Choices:
A. 9000
B. 6000
C. 5000
D. 4000
E. 3000

divide(power(divide(900, const_2), const_2), subtract(922.5, 900))

Explanation: simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer


Question: teas worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs 153 per kg , the price of the third variety per kg will be ?

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

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

<gadget id="calculator">153 * 4</gadget>
<output>612</output>

<gadget id="calculator">126 + 135</gadget>
<output>261</output>

<gadget id="calculator">612 - 261</gadget>
<output>351</output>

<gadget id="calculator">351 / 2</gadget>
<output>351/2 = around 175.5</output>
<result>351/2 = around 175.5</result>

Choices:
A. rs . 147.50
B. rs . 785.50
C. rs . 175.50
D. rs . 258.50
E. none of these

divide(subtract(multiply(153, add(add(1, 1), 2)), add(126, 135)), 2)

Explanation: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 153 ) / \ x − 153 22.50 = > x − ( 153 / 22.50 ) = 1 . = > x − 153 = 22.50 . = > x = 175.50 rs . answer : c"


Question: in what time will a railway train 50 m long moving at the rate of 36 kmph pass a telegraph post on its way ?

<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">50 / 10</gadget>
<output>5</output>
<result>5</result>

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

Explanation: "t = 50 / 36 * 18 / 5 = 5 sec answer : a"


Question: the marks obtained by vijay and amith are in the ratio 8 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?

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

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

<gadget id="calculator">24 / 10</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>

Choices:
A. 12 : 5
B. 12 : 1
C. 6 : 5
D. 12 : 2
E. 6 : 3

Explanation: 8 : 5 3 : 2 - - - - - - - 24 : 15 : 10 24 : 10 12 : 5 answer : a


Question: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 22 overs to reach the target of 282 runs ?

<gadget id="calculator">10 * 3.2</gadget>
<output>32</output>

<gadget id="calculator">282 - 32</gadget>
<output>250</output>

<gadget id="calculator">250 / 22</gadget>
<output>125/11 = around 11.363636</output>
<result>125/11 = around 11.363636</result>

Choices:
A. 6.25
B. 11.36
C. 7.4
D. 5
E. 6

divide(subtract(282, multiply(10, 3.2)), 22)

Explanation: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 22 run rate needed = 250 / 22 = 11.36 answer : option b"


Question: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 9 will be equal to :

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

<gadget id="calculator">1 * 9</gadget>
<output>9</output>

<gadget id="calculator">9 ** 2</gadget>
<output>81</output>

<gadget id="calculator">9 / 81</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 3
B. 6
C. 1 / 9
D. 1 / 3
E. 9

divide(multiply(1, power(3, const_2)), power(9, const_2))

Explanation: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 9 ^ 2 = 1 / 9 answer : c"


Question: a train running at the speed of 90 km / hr crosses a pole in 5 seconds . find the length of the train .

<gadget id="calculator">90 * 1_000</gadget>
<output>90_000</output>

<gadget id="calculator">90_000 / 3_600</gadget>
<output>25</output>

<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 150 meter
B. 145 meter
C. 140 meter
D. 125 meter
E. none of these

multiply(divide(multiply(90, const_1000), const_3600), 5)

Explanation: "explanation : speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time = 25 * 5 = 125 meter option d"


Question: find the mean proportional between 64 & 81 ?

<gadget id="calculator">64 + 81</gadget>
<output>145</output>

<gadget id="calculator">145 / 2</gadget>
<output>145/2 = around 72.5</output>
<result>145/2 = around 72.5</result>

Choices:
A. 59
B. 61
C. 63
D. 72
E. 67

Explanation: "formula = √ a × b a = 64 and b = 81 √ 64 × 81 = 8 × 9 = 72 d"


Question: if ( a + b ) = 12 , ( b + c ) = 9 and ( c + d ) = 3 , what is the value of ( a + d ) ?

<gadget id="calculator">12 + 3</gadget>
<output>15</output>

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

Choices:
A. 16 .
B. 8 .
C. 7 .
D. 6 .
E. - 2 .

Explanation: "given a + b = 12 = > a = 12 - b - - > eq 1 b + c = 9 c + d = 3 = > d = 3 - c - - > eq 2 then eqs 1 + 2 = > a + d = 12 - b + 3 - c = > 15 - ( b + c ) = > 15 - 9 = 6 . option d . . ."


Question: what is the perimeter of an isosceles right angled triangle . the area of the isosceles right angled triangle is 50 .

<gadget id="calculator">50 * 2</gadget>
<output>100</output>

<gadget id="calculator">100 ** (1/2)</gadget>
<output>10</output>

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

<gadget id="calculator">10 * (sqrt(2))</gadget>
<output>10*sqrt(2) = around 14.142136</output>

<gadget id="calculator">(10*sqrt(2)) + 10 + 10</gadget>
<output>10*sqrt(2) + 20 = around 34.142136</output>
<result>10*sqrt(2) + 20 = around 34.142136</result>

Choices:
A. 25
B. 36
C. 25
D. 30
E. 34.14

triangle_perimeter(multiply(sqrt(multiply(50, const_2)), sqrt(const_2)), sqrt(multiply(50, const_2)), sqrt(multiply(50, const_2)))

Explanation: an isosceles right angled triangle has both the base and height same . the area of an isosceles triangle = 1 / 2 * base * height since height = base 1 / 2 * height * height = 1 / 2 * height ^ 2 = 50 height ^ 2 = 100 height = 10 = base since we know the base and height . we will calculate the hypotenuse using pythagoras base ^ 2 + height ^ 2 = hypotenuse ^ 2 10 ^ 2 + 10 ^ 2 = hypotenuse ^ 2 hypotenuse ^ 2 = 200 hypotenuse = 14.14 perimeter of the triangle = 10 + 10 + 14.14 = 34.14 ans : e


Question: here 10 programmers , type 10 lines within 10 minutes then 60 lines can type within 60 minutes . how many programmers are needed ?

<gadget id="calculator">60 / 10</gadget>
<output>6</output>

<gadget id="calculator">6 * 10</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 16
B. 10
C. 6
D. 60
E. 50

Explanation: 10 10 programmer 10 line 10 mins . 10 programmer 20 line 20 mins . . . . . 10 programmer 60 line 60 mins . answer : d


Question: in a store , the total price for 25 shirts is $ 400 and the total price for 75 sweaters is $ 1500 . by how much does the average ( arithmetic mean ) price of a sweater exceed that of a shirt in this store ?

<gadget id="calculator">1_500 / 75</gadget>
<output>20</output>

<gadget id="calculator">400 / 25</gadget>
<output>16</output>

<gadget id="calculator">20 - 16</gadget>
<output>4</output>
<result>4</result>

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

subtract(divide(1500, 75), divide(400, 25))

Explanation: the average price of a shirt is : $ 400 / 25 = $ 16 . the average price of a sweater is : $ 1500 / 75 = $ 20 . the difference in price is : $ 20 - $ 16 = $ 4 . the answer is d .


Question: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 6 hours . how long would it take taimour to paint the fence alone ?

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

Choices:
A. 6 hours
B. 8 hours
C. 18 hours
D. 24 hours
E. 32 hours

Explanation: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 6 = > 1 / 18 working alone taimour can do the job in 1 = 1 / 18 * hours = > 18 answer c"


Question: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 800 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 820 . what is the value of x ?

<gadget id="calculator">800 / 2</gadget>
<output>400</output>

<gadget id="calculator">400 ** 2</gadget>
<output>160_000</output>

<gadget id="calculator">820 - 800</gadget>
<output>20</output>

<gadget id="calculator">160_000 / 20</gadget>
<output>8_000</output>
<result>8_000</result>

Choices:
A. 8000
B. 6000
C. 5000
D. 4000
E. 3000

divide(power(divide(800, const_2), const_2), subtract(820, 800))

Explanation: "simple way to solve this question is to use options . from si , we know that x * y = 40,000 . now , put the value of x = 8000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 8000 + 5 % of 8000 = 8400 . 2 nd year , amount = 8400 + 5 % of 8400 = 8820 . we can see after 2 years interest = 8820 - 8000 = 820 . hence , it satisfies the question . hence a is the correct answer"


Question: i had 30 donuts when i left home this morning but only 9 when i came back home . what percentage of the donuts are missing ?

<gadget id="calculator">30 * 2</gadget>
<output>60</output>

<gadget id="calculator">60 + 10</gadget>
<output>70</output>
<result>70</result>

Choices:
A. 70
B. 65
C. 55
D. 75
E. 60

Explanation: 30 - 9 = 21 21 / 30 or 7 / 10 7 / 10 = 70 / 100 = 70 % answer is a


Question: a semicircle has a radius of 10 . what is the approximate perimeter of the semicircle ?

<gadget id="calculator">2 * pi * 10</gadget>
<output>20*pi = around 62.831853</output>

<gadget id="calculator">(20*pi) / 2</gadget>
<output>10*pi = around 31.415927</output>

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

<gadget id="calculator">(10*pi) + 20</gadget>
<output>20 + 10*pi = around 51.415927</output>
<result>20 + 10*pi = around 51.415927</result>

Choices:
A. 27
B. 33
C. 39
D. 45
E. 51

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

Explanation: "the perimeter of a circle is 2 * pi * r . the perimeter of a semicircle is 2 * pi * r / 2 + 2 r = pi * r + 2 r the perimeter is pi * 10 + 2 * 10 which is about 51 . the answer is e ."


Question: find the average of the first 19 natural numbers ?

<gadget id="calculator">19 + 1</gadget>
<output>20</output>

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

<gadget id="calculator">10 * 19</gadget>
<output>190</output>

<gadget id="calculator">190 / 19</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 8
B. 9
C. 10
D. 11
E. 12

divide(multiply(divide(add(19, const_1), const_2), 19), 19)

Explanation: average of the first ' n ' natural numbers = ( n + 1 ) / 2 we get ( 19 + 1 ) / 2 = 10 answer : c


Question: if the remainder is 11 when positive integer n is divided by 18 , what is the remainder when n is divided by 9 ?

<gadget id="calculator">18 / 9</gadget>
<output>2</output>
<result>2</result>

Choices:
A. 0
B. 2
C. 1
D. 3
E. 4

Explanation: "assume x is quotient here , n = 18 x + 11 - - - - - - - - - - ( 1 ) and n = 9 x + ? we can also write equation ( 1 ) as : n = ( 18 x + 9 ) + 2 . ie 9 ( 2 x + 1 ) + 2 ie the first term is perfectly divisible by 6 . so , the remainder left is 2 . so , answer ( b ) is right choice ."


Question: if n = 16 × 10 ^ ( - p ) and − 4 < p < 4 , how many different integer values of p will make n a perfect square ?

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

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

Choices:
A. 0
B. 2
C. 3
D. 5
E. 7

Explanation: i think the answer should be c . thoose are p - values that satisfy given restriction : - 2 , 0 , 2 ( note , a fraction can be also a perfect square ) - - > 16 * 100 , 16 * 1 , 16 / 100


Question: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 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 + 9</gadget>
<output>39</output>
<result>39</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 + 9 = > 2 b - b - 9 = 30 b = 39 so the present age of b is 39 years answer : c"


Question: on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays interest on a yearly basis , what must the interest rate be for james to have y dollars at the end of the year ?

<gadget id="calculator">2.5 * 4</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 22.04 %
B. 16.12 %
C. 8 %
D. 18.25 %
E. 10.5 %

Explanation: per quarter , interest = 2.5 % so for a year , interest = 10 % due to quarter cumulation , effective yield ( ytm ) would be slight higher than 10 % answer = 10.5 % = answer : e


Question: two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?

<gadget id="calculator">120 + 120</gadget>
<output>240</output>

<gadget id="calculator">120 / 15</gadget>
<output>8</output>

<gadget id="calculator">120 / 10</gadget>
<output>12</output>

<gadget id="calculator">8 + 12</gadget>
<output>20</output>

<gadget id="calculator">240 / 20</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 12
B. 14
C. 16
D. 20
E. 18

Explanation: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 15 ] m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = m / sec = 20 m / sec . ∴ required time = ( 120 + 120 ) / 20 secc = 12 sec . answer a"


Question: in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 82 per kg ?

<gadget id="calculator">96 - 82</gadget>
<output>14</output>

<gadget id="calculator">96 - 68</gadget>
<output>28</output>

<gadget id="calculator">14 / 28</gadget>
<output>1/2 = around 0.5</output>

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

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

Choices:
A. 5 : 8
B. 4 : 7
C. 3 : 7
D. 1 : 1
E. 9 : 8

divide(divide(subtract(96, 82), subtract(96, 68)), subtract(const_1, divide(subtract(96, 82), subtract(96, 68))))

Explanation: "( 96 - 82 ) / ( 82 - 68 ) = 14 / 14 = 1 / 1 answer : d"


Question: an article with cost price of 240 is sold at 20 % profit . what is the selling price ?

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

<gadget id="calculator">240 * (1/5)</gadget>
<output>48</output>

<gadget id="calculator">240 + 48</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 288
B. 200
C. 204
D. 207
E. 210

add(240, multiply(240, divide(20, const_100)))

Explanation: "sp = 1.20 * 240 = 288 answer : a"


Question: a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability r that the first ball picked up is odd numbered ?

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

Choices:
A. 0
B. 1 / 3
C. 1 / 2
D. 2 / 3
E. 1

Explanation: "answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability r is 2 / 3 . d"


Question: a store reported total sales of $ 460 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?

<gadget id="calculator">460 - 320</gadget>
<output>140</output>

<gadget id="calculator">140 / 320</gadget>
<output>7/16 = around 0.4375</output>

<gadget id="calculator">(7/16) * 100</gadget>
<output>175/4 = around 43.75</output>
<result>175/4 = around 43.75</result>

Choices:
A. 2 %
B. 17 %
C. 44 %
D. 65 %
E. 83 %

multiply(divide(subtract(460, 320), 320), const_100)

Explanation: "new value – old value ) / old value x 100 we are given : february sales this year = 460 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 460 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 460 – 320 ) / 320 ] x 100 ≈ 44 % . the answer is c ."


Question: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 55 ° c , what is the temperature of the pot of water in ° f ?

<gadget id="calculator">212 - 32</gadget>
<output>180</output>

<gadget id="calculator">180 / 100</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">(9/5) * 55</gadget>
<output>99</output>

<gadget id="calculator">99 + 32</gadget>
<output>131</output>
<result>131</result>

Choices:
A. 116 ° f
B. 125 ° f
C. 131 ° f
D. 138 ° f
E. 145 ° f

add(multiply(divide(subtract(212, 32), 100), 55), 32)

Explanation: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 55 ) / 5 + 32 = 131 ° f the answer is c ."


Question: what distance will be covered by a bus moving at 126 kmph in 10 seconds ?

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

<gadget id="calculator">126 * (5/18)</gadget>
<output>35</output>

<gadget id="calculator">35 * 10</gadget>
<output>350</output>
<result>350</result>

Choices:
A. 287
B. 600
C. 350
D. 276
E. 207

Explanation: "126 kmph = 126 * 5 / 18 = 35 mps d = speed * time = 35 * 10 = 350 m . answer : c"


Question: the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is

<gadget id="calculator">10 + 7</gadget>
<output>17</output>

<gadget id="calculator">2 * 17</gadget>
<output>34</output>

<gadget id="calculator">34 * 5</gadget>
<output>170</output>

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

<gadget id="calculator">2 * 1.5</gadget>
<output>3</output>

<gadget id="calculator">6 + 3</gadget>
<output>9</output>

<gadget id="calculator">9 + 3</gadget>
<output>12</output>

<gadget id="calculator">170 - 12</gadget>
<output>158</output>

<gadget id="calculator">158 * 3</gadget>
<output>474</output>
<result>474</result>

Choices:
A. 2488
B. 378
C. 739
D. 474
E. 291

multiply(subtract(multiply(multiply(2, add(10, 7)), 5), add(add(multiply(2, 3), multiply(2, 1.5)), multiply(2, 1.5))), 3)

Explanation: explanation : area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d


Question: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) is :

<gadget id="calculator">5.3 * 1</gadget>
<output>5.3</output>

<gadget id="calculator">-6.7</gadget>
<output>-6.7</output>

<gadget id="calculator">(-6.7) * 1</gadget>
<output>-6.7</output>

<gadget id="calculator">5.3 + (-6.7)</gadget>
<output>-1.4</output>

<gadget id="calculator">-7.3</gadget>
<output>-7.3</output>

<gadget id="calculator">(-1.4) + (-7.3)</gadget>
<output>-8.7</output>

<gadget id="calculator">6.6 * 1</gadget>
<output>6.6</output>

<gadget id="calculator">(-8.7) + 6.6</gadget>
<output>-2.1</output>
<result>-2.1</result>

Choices:
A. - 4
B. - 2
C. 0
D. 2
E. 4

add(add(add(multiply(5.3, const_1), multiply(negate(6.7), const_1)), negate(7.3)), multiply(6.6, const_1))

Explanation: o ( 5.3 ) + e ( – 6.7 ) + o ( – 7.3 ) + e ( 6.6 ) = 7 + ( - 6 ) + ( - 9 ) + 6 = - 2 the answer is b .


Question: a quadratic function f ( x ) attains a maximum of 3 at x = 1 . the value of the function at x = 0 is 1 . what is the value of f ( x ) at x = 10 ?

<gadget id="calculator">10 ** 2</gadget>
<output>100</output>

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

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

<gadget id="calculator">100 * (-2)</gadget>
<output>-200</output>

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

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

<gadget id="calculator">(-200) + 40</gadget>
<output>-160</output>

<gadget id="calculator">(-160) + 1</gadget>
<output>-159</output>
<result>-159</result>

Choices:
A. - 119
B. - 159
C. - 110
D. - 180
E. - 105

add(add(multiply(power(10, const_2), negate(subtract(3, 1))), multiply(subtract(subtract(3, 1), negate(subtract(3, 1))), 10)), 1)

Explanation: explanation : let , the quadratic equation be ax 2 + bx + c . so , f ( x ) = ax 2 + bx + c at x = 0 , the value of function is 1 . x = 0 , f ( x ) = 1 ax 2 + bx + c = a * 0 + b * 0 + c = c c = 1 . at x = 1 , f ( x ) = 3 x = 1 , f ( x ) = 3 a * 1 + b * 1 + c = 3 since c = 1 , a + b = 2 . also , we know that f ( x ) is maximum when x = 1 . if f ( x ) is maximum , ( dx / dt ) ( f ( x ) ) = 0 differentiating f ( x ) , we have d / dt ( ax 2 + bx + c ) = 2 ax + b at x = 1 , 2 ax + b = 0 . 2 a + b = 0 . b = - 2 a . substituting we have a + b = 2 , or a + - 2 a = 2 . a = - 2 . so , b = 4 . so the equation is - 2 x 2 + 4 x + 1 . at x = 10 , the value is - 2 * 100 + 4 * 10 + 1 i . e - 159 . answer : b


Question: in a certain company , a third of the workers do not have a retirement plan . 40 % 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 120 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">40 / 100</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">(1/3) - (2/15)</gadget>
<output>1/5 = around 0.2</output>

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

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

<gadget id="calculator">(1/5) + (4/15)</gadget>
<output>7/15 = around 0.466667</output>

<gadget id="calculator">120 / (7/15)</gadget>
<output>1_800/7 = around 257.142857</output>

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

<gadget id="calculator">(2/15) + (2/5)</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">(1_800/7) * (8/15)</gadget>
<output>960/7 = around 137.142857</output>
<result>960/7 = around 137.142857</result>

Choices:
A. 80
B. 95
C. 105
D. 120
E. 137

multiply(divide(120, add(subtract(divide(const_1, const_3), multiply(divide(const_1, const_3), divide(40, const_100))), multiply(subtract(const_1, divide(const_1, const_3)), divide(40, const_100)))), add(multiply(divide(const_1, const_3), divide(40, 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 120 = 0,4 * 2 / 3 * x + 0,6 * 1 / 3 * x 120 = 14 / 30 x x = 257 257 - 120 = 137 answer e"


Question: the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 72.0 billion , a year ago . by what percent did the revenue fall ?

<gadget id="calculator">72 - 48</gadget>
<output>24</output>

<gadget id="calculator">24 / 72</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(1/3) * 100</gadget>
<output>100/3 = around 33.333333</output>
<result>100/3 = around 33.333333</result>

Choices:
A. 20.8
B. 30.4
C. 31.8
D. 32.5
E. 33.3

multiply(divide(subtract(72.0, 48.0), 72.0), const_100)

Explanation: "$ 72 - $ 48 = 24 $ ( 24 / 72 ) * 100 = 33.33 % answer : e"


Question: a trader bought a car at 10 % discount on its original price . he sold it at a 80 % increase on the price he bought it . what percent of profit did he make on the original price ?

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

<gadget id="calculator">100 + 80</gadget>
<output>180</output>

<gadget id="calculator">90 * 180</gadget>
<output>16_200</output>

<gadget id="calculator">16_200 / 100</gadget>
<output>162</output>

<gadget id="calculator">162 / 100</gadget>
<output>81/50 = around 1.62</output>

<gadget id="calculator">(81/50) - 1</gadget>
<output>31/50 = around 0.62</output>

<gadget id="calculator">(31/50) * 100</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 17 %
B. 62 %
C. 12 %
D. 19 %
E. 22 %

multiply(subtract(divide(divide(multiply(subtract(const_100, 10), add(const_100, 80)), const_100), const_100), const_1), const_100)

Explanation: "original price = 100 cp = 90 s = 90 * ( 180 / 100 ) = 162 100 - 162 = 62 % answer : b"


Question: a man buys a cycle for rs . 2800 and sells it at a loss of 25 % . what is the selling price of the cycle ?

<gadget id="calculator">100 - 25</gadget>
<output>75</output>

<gadget id="calculator">75 * 2_800</gadget>
<output>210_000</output>

<gadget id="calculator">210_000 / 100</gadget>
<output>2_100</output>
<result>2_100</result>

Choices:
A. s . 2090
B. s . 2160
C. s . 2100
D. s . 2202
E. s . 2092

divide(multiply(subtract(const_100, 25), 2800), const_100)

Explanation: "s . p . = 75 % of rs . 2800 = rs . 75 x 2800 / 100 = rs . 1190 answer : option c"


Question: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 25 percent of a , and m equals b decreased by 40 percent of b , what is the value of m / x ?

<gadget id="calculator">100 - 40</gadget>
<output>60</output>

<gadget id="calculator">100 + 25</gadget>
<output>125</output>

<gadget id="calculator">60 / 125</gadget>
<output>12/25 = around 0.48</output>

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

<gadget id="calculator">(12/25) * (5/4)</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>

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

multiply(divide(subtract(const_100, 40), add(const_100, 25)), divide(5, 4))

Explanation: a / b = 4 / 5 m / x = ( 3 / 5 ) * 5 / ( 5 / 4 ) * 4 = 3 / 5 the answer is e .


Question: the area of a triangle is with base 10 m and height 5 m ?

<gadget id="calculator">(10 * 5) / 2</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 11
B. 25
C. 787
D. 122
E. 12

Explanation: "1 / 2 * 10 * 5 = 25 m 2 answer : b"


Question: how many diagonals does a polygon with 13 sides have , if one of its vertices does not connect to any diagonal ?

<gadget id="calculator">13 - 1</gadget>
<output>12</output>

<gadget id="calculator">12 - 3</gadget>
<output>9</output>

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

<gadget id="calculator">108 / 2</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 65
B. 62
C. 58
D. 54
E. 60

divide(multiply(subtract(13, const_1), subtract(subtract(13, const_1), const_3)), const_2)

Explanation: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 13 - 1 then 12 * ( 12 - 3 ) / 2 = 54 correct option : d"


Question: a car averages 30 miles per hour for the first 5 hours of a trip and averages 42 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 38 miles per hour , how many hours long is the trip ?

<gadget id="calculator">38 * 5</gadget>
<output>190</output>

<gadget id="calculator">30 * 5</gadget>
<output>150</output>

<gadget id="calculator">190 - 150</gadget>
<output>40</output>

<gadget id="calculator">42 - 38</gadget>
<output>4</output>

<gadget id="calculator">40 / 4</gadget>
<output>10</output>

<gadget id="calculator">10 + 5</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 13
B. 14
C. 15
D. 16
E. 17

add(divide(subtract(multiply(38, 5), multiply(30, 5)), subtract(42, 38)), 5)

Explanation: "let t be the total time of the trip . 30 * 5 + 42 ( t - 5 ) = 38 t 4 t = 210 - 150 t = 15 the answer is c ."


Question: in a certain country 1 / 5 of 8 = 4 . assuming the same proportion , what would be the value of 1 / 4 of 16 ?

<gadget id="calculator">5 / 8</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">(5/8) * 16</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 13
B. 12
C. 10
D. 16
E. 14

Explanation: c 10


Question: in what ratio must a grocer mix two varieties of pulses costing rs . 15 and rs . 20 per kg respectively so as to get a mixture worth rs . 16.50 per kg ?

<gadget id="calculator">20 - 16.5</gadget>
<output>3.5</output>

<gadget id="calculator">16.5 - 15</gadget>
<output>1.5</output>

<gadget id="calculator">3.5 / 1.5</gadget>
<output>2.333333</output>
<result>2.333333</result>

Choices:
A. 3 : 7
B. 5 : 7
C. 7 : 3
D. 7 : 5
E. none

divide(subtract(20, 16.5), subtract(16.5, 15))

Explanation: solution required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3 . answer c


Question: a can do a piece of work in 4 days . b can do it in 10 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?

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

<gadget id="calculator">40 / 4</gadget>
<output>10</output>

<gadget id="calculator">40 / 10</gadget>
<output>4</output>

<gadget id="calculator">10 + 4</gadget>
<output>14</output>

<gadget id="calculator">14 * 2</gadget>
<output>28</output>

<gadget id="calculator">40 - 28</gadget>
<output>12</output>

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

<gadget id="calculator">40 / 6</gadget>
<output>20/3 = around 6.666667</output>
<result>20/3 = around 6.666667</result>

Choices:
A. 22 days
B. 20 / 3 days
C. 67 days
D. 17 / 6 days
E. 18 days

divide(multiply(4, 10), divide(subtract(multiply(4, 10), multiply(add(divide(multiply(4, 10), 4), divide(multiply(4, 10), 10)), 2)), 2))

Explanation: "c = 1 / 2 - 1 / 4 - 1 / 10 = 3 / 20 = > 20 / 3 days answer : b"


Question: a and b invests rs . 1500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?

<gadget id="calculator">1_500 * 6</gadget>
<output>9_000</output>

<gadget id="calculator">1_500 * 2</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 * 6</gadget>
<output>18_000</output>

<gadget id="calculator">9_000 + 18_000</gadget>
<output>27_000</output>

<gadget id="calculator">6 + 6</gadget>
<output>12</output>

<gadget id="calculator">4_000 * 12</gadget>
<output>48_000</output>

<gadget id="calculator">27_000 / 48_000</gadget>
<output>9/16 = around 0.5625</output>
<result>9/16 = around 0.5625</result>

Choices:
A. 9 : 5
B. 9 : 8
C. 9 : 2
D. 9 : 9
E. 9 : 16

divide(add(multiply(1500, 6), multiply(multiply(1500, const_2), 6)), multiply(4000, add(6, 6)))

Explanation: "( 1.5 * 6 + 3 * 6 ) : ( 4 * 12 ) 27 : 48 = > 9 : 16 answer : e"


Question: the length of a rectangular garden is 2 feet longer than 3 times its width . if the perimeter of the garden is 100 feet , find the length of the garden .

<gadget id="calculator">100 - 4</gadget>
<output>96</output>

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

<gadget id="calculator">96 / 8</gadget>
<output>12</output>

<gadget id="calculator">12 * 3</gadget>
<output>36</output>

<gadget id="calculator">36 + 2</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 42
B. 38
C. 28
D. 57
E. 49

add(multiply(divide(subtract(100, const_4), multiply(2, const_4)), 3), 2)

Explanation: let l and w be the length and width of the garden . the statement ` ` the length of a rectangular garden is 2 feet longer than 3 times its width ' ' may be formulated by l = 2 + 3 w the formula for the perimeter is given by p = 2 l + 2 w substitute p and l in the above equation by 100 and 2 + 3 w respectively to obtain 100 = 2 ( 2 + 3 w ) + 2 w solve for w and l w = 12 and l = 2 + 3 w = 38 . check that the perimeter of the rectangular garden is 100 p = 2 l + 2 w = 76 + 24 = 100 correct answer b


Question: calculate 24 x 99

<gadget id="calculator">24 * 99</gadget>
<output>2_376</output>
<result>2_376</result>

Choices:
A. 2673
B. 2763
C. 2637
D. 2736
E. 2376

Explanation: "= 24 - 1 = 23 = ( decrement each digit of the number obtained from 9 ) here we got 23 . now = 9 - 2 = 7 and 9 - 3 = 6 . so we have 76 just write these numbers together . that is we have 23 and 76 . hence answer is 2376 answer is e ."


Question: a reduction of 40 % in the price of oil enables a house wife to obtain 8 kgs more for rs . 2400 , what is the reduced price for kg ?

<gadget id="calculator">2_400 * 40</gadget>
<output>96_000</output>

<gadget id="calculator">96_000 / 100</gadget>
<output>960</output>

<gadget id="calculator">960 / 8</gadget>
<output>120</output>
<result>120</result>

Choices:
A. rs . 120
B. rs . 125
C. rs . 130
D. rs . 135
E. rs . 140

divide(divide(multiply(2400, 40), const_100), 8)

Explanation: "explanation : 2400 * ( 40 / 100 ) = 960 - - - - 8 ? - - - - 1 = > rs . 120 answer : a"


Question: a trail mix company keeps costs down by employing the peanuts : cashews : almonds ratio of 10 : 4 : 1 in each bag of up to 75 total nuts . what is the maximum percentage by which the company could decrease its number of peanuts per bag and still have peanuts constitute more than half the total amount of nuts ?

<gadget id="calculator">10 + 4</gadget>
<output>14</output>

<gadget id="calculator">14 + 1</gadget>
<output>15</output>

<gadget id="calculator">75 / 15</gadget>
<output>5</output>

<gadget id="calculator">5 * 10</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 40 %
B. 48 %
C. 49 %
D. 50 %
E. 58 %

multiply(divide(75, add(add(10, 4), 1)), 10)

Explanation: peanuts = 50 cashews = 20 almonds = 5 we want to remove as many peanuts as possible while still having peanuts represent more than half of the mixture . . . the number of cashews and almonds will stay the same though , so we have 20 + 5 = 25 of those non - peanuts in total . if we had 25 peanuts and 25 non - peanuts , then that would be 50 % exactly . we want more than 50 % though , so we need to add in 1 more peanut . this gives us . . . peanuts = 26 cashews = 20 almonds = 5 the question asked for the decrease in the number of peanuts as a percentage . we started with 50 peanuts and removed 24 = 24 / 50 = 48 % ; answer : b


Question: we bought a total of 90 books at the store . math books cost $ 4 and history books cost $ 5 . the total price was $ 390 . how many math books did we buy ?

<gadget id="calculator">90 * 4</gadget>
<output>360</output>

<gadget id="calculator">390 - 360</gadget>
<output>30</output>

<gadget id="calculator">90 - 30</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 57
B. 60
C. 63
D. 66
E. 69

subtract(90, subtract(390, multiply(90, 4)))

Explanation: "m + h = 90 h = 90 - m 4 m + 5 h = 390 4 m + 5 * ( 90 - m ) = 390 m = 60 the answer is b ."


Question: a number when divided by 133 leaves 16 as a remainder . what will be the remainder if the number is divided by 50 ?

<gadget id="calculator">133 + 16</gadget>
<output>149</output>

<gadget id="calculator">149 % 50</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 51
B. 56
C. 49
D. 17
E. 7

Explanation: "133 + 16 = 149 dividing 149 evenly into whole numbers is 2 and leaves 49 remaining . the correct answer is c ."


Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 240 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?

<gadget id="calculator">240 / 3</gadget>
<output>80</output>

<gadget id="calculator">80 / 3</gadget>
<output>80/3 = around 26.666667</output>

<gadget id="calculator">(80/3) ** (1/2)</gadget>
<output>4*sqrt(15)/3 = around 5.163978</output>

<gadget id="calculator">(4*sqrt(15)/3) * 3</gadget>
<output>4*sqrt(15) = around 15.491933</output>
<result>4*sqrt(15) = around 15.491933</result>

Choices:
A. 65
B. 44
C. 18
D. 15.49
E. 14

multiply(sqrt(divide(divide(240, 3), const_3)), const_3)

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 240 / 3 = 80 sq m l b = 80 i . e . , l * l / 3 = 240 l 2 = 240 = > l = 15.49 answer : d"


Question: if the cost price of 50 articles is equal to the selling price of 40 articles , then the gain or loss percent is ?

<gadget id="calculator">100 * 40</gadget>
<output>4_000</output>

<gadget id="calculator">4_000 / 50</gadget>
<output>80</output>

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

<gadget id="calculator">20 / 80</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 33 %
B. 29 %
C. 25 %
D. 55 %
E. 39 %

multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 40), 50)), divide(multiply(const_100, 40), 50)))

Explanation: "c 25 % given that , cost price of 50 article is equal to selling price of 40 articles . let cost price of one article = rs . 1 selling price of 40 articles = rs . 50 but cost price of 40 articles = rs . 40 therefore , the trader made profit . \ percentage of profit = 10 / 40 * 100 = 25 %"


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

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

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

Choices:
A. 2
B. - 2
C. 1
D. - 1
E. 5

Explanation: if we solve the question , we get x = 1 . option : c


Question: evaluate 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 = ?

<gadget id="calculator">100 + 1</gadget>
<output>101</output>

<gadget id="calculator">100 * 101</gadget>
<output>10_100</output>

<gadget id="calculator">10_100 / 2</gadget>
<output>5_050</output>
<result>5_050</result>

Choices:
A. 3043
B. 5050
C. 5176
D. 9356
E. 4890

divide(multiply(100, add(100, const_1)), const_2)

Explanation: b 5050 you must have noticed that 50 pairs of n ^ 2 – ( n - 1 ) ^ 2 exist . n ^ 2 – ( n - 1 ) ^ 2 = n + ( n – 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050


Question: the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is

<gadget id="calculator">10 * 3</gadget>
<output>30</output>

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

<gadget id="calculator">39.4 - 19.4</gadget>
<output>20</output>

<gadget id="calculator">20 / 1_000</gadget>
<output>1/50 = around 0.02</output>

<gadget id="calculator">(1/50) * 100</gadget>
<output>2</output>

<gadget id="calculator">70 / 2</gadget>
<output>35</output>
<result>35</result>

Choices:
A. 20
B. r = 25
C. r = 30
D. r = 35
E. 40

divide(subtract(const_100, multiply(const_10, const_3)), multiply(divide(subtract(39.4, 19.4), 1000), const_100))

Explanation: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."


Question: there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ?

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

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

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

Choices:
A. 12 .
B. 9 .
C. 8 .
D. 7 .
E. 6 .

Explanation: "7 = 3 blue balls + 12 / 3 answer : d"


Question: the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?

<gadget id="calculator">8 * 43.1</gadget>
<output>344.8</output>

<gadget id="calculator">344.8 - 158.4</gadget>
<output>186.4</output>

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

<gadget id="calculator">186.4 / 4</gadget>
<output>46.6</output>
<result>46.6</result>

Choices:
A. 12.8
B. 24.2
C. 46.6
D. 72.1
E. 96.8

divide(subtract(multiply(8, 43.1), 158.4), divide(8, const_2))

Explanation: arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer .


Question: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 45 kms . what was the total distance traveled in 12 hours ?

<gadget id="calculator">2 * 45</gadget>
<output>90</output>

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

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

<gadget id="calculator">90 + 22</gadget>
<output>112</output>

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

<gadget id="calculator">112 * 6</gadget>
<output>672</output>
<result>672</result>

Choices:
A. 252 kms
B. 152 kms
C. 672 kms
D. 752 kms
E. 152 kms

multiply(add(multiply(2, 45), multiply(subtract(12, const_1), 2)), divide(12, 2))

Explanation: explanation : total distance travelled in 12 hours = ( 45 + 47 + 49 + . . . . . upto 12 terms ) this is an a . p with first term , a = 45 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 45 + { 12 - 1 ) x 2 ] = 6 ( 112 ) = 672 kms . answer : c


Question: n denotes the number obtained when n is rounded to the nearest tenth . for example 4.31 = 4.3 0.089 - 1.135 =

<gadget id="calculator">0.089 - 1.135</gadget>
<output>-1.046</output>
<result>-1.046</result>

Choices:
A. 1.05
B. 1.04
C. - 1.05
D. - 1.0
E. - 0.1

Explanation: here let the first quantity be a = > a rounded to nearest tenths = > 0.1 similarly let the second quantity be b = > b rounded to nearest tenths = > 1.1 = > a - b = 0.1 - 1.1 = - 1 hence a - b = - 1 answer : d


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

<gadget id="calculator">14 - 2</gadget>
<output>12</output>

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

<gadget id="calculator">60 / 4</gadget>
<output>15</output>

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

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

Choices:
A. 12
B. 14
C. 15
D. 24
E. 36

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

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


Question: a certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?

<gadget id="calculator">45 - 30</gadget>
<output>15</output>

<gadget id="calculator">15 / 30</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) * 100</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 25 %
B. 33 1 / 3 %
C. 50 %
D. 66 2 / 3 %
E. 75 %

multiply(divide(subtract(45, 30), 30), const_100)

Explanation: general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 45 − 30 / 30 ∗ 100 = 50 answer : c .


Question: a bus trip of 660 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?

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

<gadget id="calculator">3_300 * 4</gadget>
<output>13_200</output>

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

<gadget id="calculator">13_200 + 25</gadget>
<output>13_225</output>

<gadget id="calculator">13_225 ** (1/2)</gadget>
<output>115</output>

<gadget id="calculator">115 - 5</gadget>
<output>110</output>

<gadget id="calculator">110 / 2</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 40
B. 45
C. 50
D. 55
E. 60

divide(subtract(sqrt(add(multiply(multiply(660, 5), const_4), power(5, const_2))), 5), const_2)

Explanation: "the time is the distance / speed . the time difference is 1 hour . 660 / v - 660 / ( v + 5 ) = 1 660 ( v + 5 ) - 660 v = ( v ) ( v + 5 ) 3300 = ( v ) ( v + 5 ) 55 * 60 = ( v ) ( v + 5 ) v = 55 mph the answer is d ."


Question: in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .

<gadget id="calculator">30 + 54</gadget>
<output>84</output>

<gadget id="calculator">100 - 84</gadget>
<output>16</output>

<gadget id="calculator">300 * 16</gadget>
<output>4_800</output>

<gadget id="calculator">4_800 / 100</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 33
B. 37
C. 54
D. 99
E. 48

divide(multiply(300, subtract(const_100, add(30, 54))), const_100)

Explanation: the number of students with first division = 30 % of 300 = 30 / 100 × 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 90 + 162 ) = 48 answer : e


Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men â € ™ s wages are ?

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

<gadget id="calculator">45 / 15</gadget>
<output>3</output>
<result>3</result>

Choices:
A. 6 rs
B. 7 rs
C. 8 rs
D. 4 rs
E. 3 rs

Explanation: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e"


Question: two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?

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

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

<gadget id="calculator">(1/6) * (1/6)</gadget>
<output>1/36 = around 0.027778</output>

<gadget id="calculator">(1/36) * 6</gadget>
<output>1/6 = around 0.166667</output>
<result>1/6 = around 0.166667</result>

Choices:
A. 3 / 8
B. 2 / 3
C. 1 / 2
D. 1 / 3
E. 1 / 6

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

Explanation: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible two dice are rolled , n ( s ) = 6 × 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6


Question: if x is 12 percent greater than 80 , then x =

<gadget id="calculator">12 / 100</gadget>
<output>3/25 = around 0.12</output>

<gadget id="calculator">(3/25) * 80</gadget>
<output>48/5 = around 9.6</output>

<gadget id="calculator">80 + (48/5)</gadget>
<output>448/5 = around 89.6</output>
<result>448/5 = around 89.6</result>

Choices:
A. 89.6
B. 91.0
C. 88.0
D. 70.9
E. 71.2

add(80, multiply(divide(12, const_100), 80))

Explanation: "12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a ."


Question: a and b complete a work in 6 days . a alone can do it in 8 days . if both together can do the work in how many days ?

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

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

<gadget id="calculator">(1/6) + (1/8)</gadget>
<output>7/24 = around 0.291667</output>

<gadget id="calculator">1 / (7/24)</gadget>
<output>24/7 = around 3.428571</output>
<result>24/7 = around 3.428571</result>

Choices:
A. 3.75 days
B. 3.43 days
C. 2.99 days
D. 2.98 days
E. 2.44 days

Explanation: "1 / 6 + 1 / 8 = 7 / 24 24 / 7 = 3.43 days answer : b"


Question: 130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?

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

<gadget id="calculator">130 / 5</gadget>
<output>26</output>

<gadget id="calculator">26 * 3</gadget>
<output>78</output>

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

<gadget id="calculator">160 / 7</gadget>
<output>160/7 = around 22.857143</output>

<gadget id="calculator">(160/7) * 3</gadget>
<output>480/7 = around 68.571429</output>

<gadget id="calculator">78 + (480/7)</gadget>
<output>1_026/7 = around 146.571429</output>
<result>1_026/7 = around 146.571429</result>

Choices:
A. 140.6 kg
B. 145.3 kg
C. 146.5 kg
D. 110.8 kg
E. 114 kg

add(multiply(divide(130, add(2, 3)), 3), multiply(divide(160, add(3, 4)), 3))

Explanation: "quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c"


Question: a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 5 days and b leaves after 3 days from the beginning . how long will work lost ?

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

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">1 / 20</gadget>
<output>1/20 = around 0.05</output>

<gadget id="calculator">(1/15) + (1/20)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">(-2) * (7/60)</gadget>
<output>-7/30 = around -0.233333</output>

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

<gadget id="calculator">(1/10) + (1/15)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/20) + (1/6)</gadget>
<output>13/60 = around 0.216667</output>

<gadget id="calculator">(13/60) * 5</gadget>
<output>13/12 = around 1.083333</output>

<gadget id="calculator">(-7/30) + (13/12)</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">1 - (17/20)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">(3/20) / (1/15)</gadget>
<output>9/4 = around 2.25</output>

<gadget id="calculator">(9/4) + 4</gadget>
<output>25/4 = around 6.25</output>
<result>25/4 = around 6.25</result>

Choices:
A. 2
B. 4
C. 5
D. 6
E. 7

add(divide(subtract(const_1, add(multiply(subtract(3, 5), add(inverse(15), inverse(20))), multiply(add(inverse(20), add(inverse(10), inverse(15))), 5))), inverse(15)), const_4.0)

Explanation: "5 / 10 + 3 / 15 + x / 20 = 1 x = 18 / 3 = 6 answer : d"


Question: at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?

<gadget id="calculator">40 * 3</gadget>
<output>120</output>

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

<gadget id="calculator">120 / (7/20)</gadget>
<output>2_400/7 = around 342.857143</output>
<result>2_400/7 = around 342.857143</result>

Choices:
A. 120
B. 300
C. 401.36
D. 350.15
E. 342.86

divide(multiply(40, 3), divide(35, const_100))

Explanation: "system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86"


Question: the length of the bridge , which a train 130 metres long and travelling at 54 km / hr can cross in 30 seconds , is :

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

<gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>

<gadget id="calculator">3_600 / 1</gadget>
<output>3_600</output>

<gadget id="calculator">54_000 / 3_600</gadget>
<output>15</output>

<gadget id="calculator">15 * 30</gadget>
<output>450</output>

<gadget id="calculator">450 - 130</gadget>
<output>320</output>
<result>320</result>

Choices:
A. 200 m
B. 225 m
C. 320 m
D. 250 m
E. 240 m

subtract(multiply(divide(multiply(54, speed(const_1000, const_1)), speed(const_3600, const_1)), 30), 130)

Explanation: "speed = [ 54 x 5 / 18 ] m / sec = [ 15 / 1 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) = 450 = > x = 450 - 130 = 320 m answer : c"


Question: the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than

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

Choices:
A. 14 years
B. 12 years
C. 56 years
D. 16 years
E. 55 years

Explanation: "given that a + b = 16 + b + c = > a â € “ c = 16 + b â € “ b = 16 = > c is younger than a by 16 years answer : d"


Question: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 ° is ?

<gadget id="calculator">30 * pi</gadget>
<output>30*pi = around 94.24778</output>

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

<gadget id="calculator">(30*pi) * 144</gadget>
<output>4320*pi = around 13_571.680264</output>

<gadget id="calculator">(4320*pi) / 360</gadget>
<output>12*pi = around 37.699112</output>
<result>12*pi = around 37.699112</result>

Choices:
A. 35 m 2
B. 36 m 2
C. 37 m 2
D. 38 m 2
E. 40 m 2

divide(multiply(multiply(30, const_pi), power(12, const_2)), const_360)

Explanation: 30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c


Question: find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

<gadget id="calculator">1_360 - 15</gadget>
<output>1_345</output>

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

<gadget id="calculator">1_345 / 5</gadget>
<output>269</output>

<gadget id="calculator">269 * 6</gadget>
<output>1_614</output>
<result>1_614</result>

Choices:
A. 1254
B. 1376
C. 1456
D. 1555
E. 1629

multiply(divide(subtract(1360, 15), subtract(6, const_1)), 6)

Explanation: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e"


Question: solve the equation 2 – x = 2 b – 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7

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

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

Choices:
A. 0
B. 1
C. 2
D. 3
E. 4

Explanation: solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 ≠ 0 , i . e . a ≠ 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b ≠ 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) ≠ 0 in this case the equation has no solution . if b = 7 and a ≠ 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b


Question: in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .

<gadget id="calculator">50 * 2</gadget>
<output>100</output>

<gadget id="calculator">45 * 4</gadget>
<output>180</output>

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

<gadget id="calculator">8 * 4</gadget>
<output>32</output>

<gadget id="calculator">280 + 32</gadget>
<output>312</output>

<gadget id="calculator">50 + 45</gadget>
<output>95</output>

<gadget id="calculator">95 + 8</gadget>
<output>103</output>

<gadget id="calculator">312 - 103</gadget>
<output>209</output>

<gadget id="calculator">224 - 209</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 25
B. 20
C. 15
D. 13
E. 14

subtract(224, subtract(add(add(multiply(50, const_2), multiply(45, const_4)), multiply(8, const_4)), add(add(50, 45), 8)))

Explanation: let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c .


Question: a motorcyclist goes from bombay to pune , a distance of 160 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?

<gadget id="calculator">160 / 32</gadget>
<output>5</output>

<gadget id="calculator">160 / 5</gadget>
<output>32</output>

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

<gadget id="calculator">160 / 2</gadget>
<output>80</output>

<gadget id="calculator">32 / 80</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

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

divide(divide(160, divide(160, 32)), divide(160, subtract(divide(160, 32), const_3)))

Explanation: "t = 160 / 32 = 5 h t = 5 - 3 = 2 time ratio = 5 : 2 = 5 : 2 speed ratio = 2 : 5 answer : b"


Question: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?

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

<gadget id="calculator">1 + (2/5)</gadget>
<output>7/5 = around 1.4</output>

<gadget id="calculator">(7/5) ** 2</gadget>
<output>49/25 = around 1.96</output>

<gadget id="calculator">(49/25) - 1</gadget>
<output>24/25 = around 0.96</output>

<gadget id="calculator">(24/25) * 100</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 95 %
B. 90 %
C. 85 %
D. 96 %
E. 25 %

multiply(subtract(power(add(const_1, divide(40, const_100)), const_2), const_1), const_100)

Explanation: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d"


Question: how many shots of 1 cm radius can be prepared from a sphere of 5 cm radius ?

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

<gadget id="calculator">25 * 5</gadget>
<output>125</output>
<result>125</result>

Choices:
A. 33
B. 88
C. 27
D. 125
E. 199

Explanation: 4 / 3 ï € * 5 * 5 * 5 = 4 / 3 ï € * 1 * 1 * 1 * x x = 125 answer : d


Question: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .

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

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

<gadget id="calculator">(9/10) * 150</gadget>
<output>135</output>

<gadget id="calculator">135 ** 2</gadget>
<output>18_225</output>

<gadget id="calculator">150 ** 2</gadget>
<output>22_500</output>

<gadget id="calculator">90 ** 2</gadget>
<output>8_100</output>

<gadget id="calculator">22_500 + 8_100</gadget>
<output>30_600</output>

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

<gadget id="calculator">30_600 ** (1/2)</gadget>
<output>30*sqrt(34) = around 174.928557</output>

<gadget id="calculator">(30*sqrt(34)) - 135</gadget>
<output>-135 + 30*sqrt(34) = around 39.928557</output>

<gadget id="calculator">(-135 + 30*sqrt(34)) ** 2</gadget>
<output>(-135 + 30*sqrt(34))**2 = around 1_594.289652</output>

<gadget id="calculator">18_225 + ((-135 + 30*sqrt(34))**2)</gadget>
<output>(-135 + 30*sqrt(34))**2 + 18225 = around 19_819.289652</output>

<gadget id="calculator">((-135 + 30*sqrt(34))**2 + 18225) ** (1/2)</gadget>
<output>sqrt((-135 + 30*sqrt(34))**2 + 18225) = around 140.780999</output>
<result>sqrt((-135 + 30*sqrt(34))**2 + 18225) = around 140.780999</result>

Choices:
A. 140
B. 141
C. 142
D. 143
E. 144

power(add(power(multiply(subtract(1, divide(1, 10)), 150), const_2), power(subtract(power(add(power(150, const_2), power(90, const_2)), divide(1, 2)), multiply(subtract(1, divide(1, 10)), 150)), const_2)), divide(1, 2))

Explanation: next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b


Question: a train 124 m long running at 68 kmph crosses a platform in 19 sec . what is the length of the platform ?

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

<gadget id="calculator">68 * (5/18)</gadget>
<output>170/9 = around 18.888889</output>

<gadget id="calculator">19 * (170/9)</gadget>
<output>3_230/9 = around 358.888889</output>

<gadget id="calculator">(3_230/9) - 124</gadget>
<output>2_114/9 = around 234.888889</output>
<result>2_114/9 = around 234.888889</result>

Choices:
A. 338
B. 234
C. 240
D. 881
E. 271

subtract(multiply(19, multiply(68, const_0_2778)), 124)

Explanation: "d = 68 * 5 / 18 = 19 = 358 – 124 = 234 answer : b"


Question: the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .

<gadget id="calculator">42 * 12</gadget>
<output>504</output>
<result>504</result>

Choices:
A. 462
B. 450
C. 480
D. 504
E. 555

Explanation: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d"


Question: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 468 per week . how much does she earn in dollars per hour ?

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

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

<gadget id="calculator">24 + 12</gadget>
<output>36</output>

<gadget id="calculator">468 / 36</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 2
B. 8
C. 9
D. 11
E. 13

divide(468, add(multiply(8, const_3), multiply(6, const_2)))

Explanation: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 468 . hourly wage = 468 / 36 = 13 answer : e"


Question: a trader bought a car at 20 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?

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

<gadget id="calculator">100 + 50</gadget>
<output>150</output>

<gadget id="calculator">80 * 150</gadget>
<output>12_000</output>

<gadget id="calculator">12_000 / 100</gadget>
<output>120</output>

<gadget id="calculator">120 / 100</gadget>
<output>6/5 = around 1.2</output>

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

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 17 %
B. 72 %
C. 20 %
D. 82 %
E. 16 %

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

Explanation: "original price = 100 cp = 80 s = 80 * ( 150 / 100 ) = 120 100 - 120 = 20 % answer : c"