Question: a certain high school has 500 students . of these students , 30 are taking music , 10 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?

<gadget id="calculator">30 + 10</gadget>
<output>40</output>

<gadget id="calculator">40 - 10</gadget>
<output>30</output>

<gadget id="calculator">500 - 30</gadget>
<output>470</output>
<result>470</result>

Choices:
A. 430
B. 440
C. 450
D. 460
E. 470

subtract(500, subtract(add(30, 10), 10))

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 10 z = 10 so , we have 30 students taking music , 10 taking art and 10 taking both music and art . 20 student taking just music 0 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 500 - 30 = 470 . e"


Question: in what time will a train 100 metres long cross an electric pole , if its speed be 144 km / hr ?

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

<gadget id="calculator">144 * (5/18)</gadget>
<output>40</output>

<gadget id="calculator">100 / 40</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 2.5 sec
B. 4.25 sec
C. 5 sec
D. 12.5 sec
E. none

Explanation: solution speed = ( 144 x 5 / 18 ) m / sec = 40 m / sec time taken = ( 100 / 40 ) sec = 2.5 sec . answer a


Question: a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 70 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?

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

<gadget id="calculator">1 + (7/10)</gadget>
<output>17/10 = around 1.7</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">(17/10) - (7/5)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) / (7/5)</gadget>
<output>3/14 = around 0.214286</output>

<gadget id="calculator">(3/14) * 100</gadget>
<output>150/7 = around 21.428571</output>
<result>150/7 = around 21.428571</result>

Choices:
A. 50 %
B. 40 %
C. 35 %
D. 32 %
E. 21 %

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

Explanation: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 170 , so from 2003 to 2005 it increased by ( 170 - 140 ) / 140 = 30 / 140 = ~ 21 % . answer : e ."


Question: a start walking from a place at a uniform speed of 4 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .

<gadget id="calculator">60 + 48</gadget>
<output>108</output>

<gadget id="calculator">108 / 60</gadget>
<output>9/5 = around 1.8</output>

<gadget id="calculator">1 / (9/5)</gadget>
<output>5/9 = around 0.555556</output>

<gadget id="calculator">(5/9) + 4</gadget>
<output>41/9 = around 4.555556</output>
<result>41/9 = around 4.555556</result>

Choices:
A. 4.7 kmph
B. 4.6 kmph
C. 4 kmph
D. 7 kmph
E. 5.3 kmph

add(divide(1, divide(add(const_60, 48), const_60)), 4)

Explanation: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 4 + 5 / 9 = 4.55 answer b"


Question: what is the smallest integer k for which 64 ^ k > 4 ^ 20 ?

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

<gadget id="calculator">floor(20/3)</gadget>
<output>6</output>

<gadget id="calculator">6 + 1</gadget>
<output>7</output>
<result>7</result>

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

Explanation: "64 ^ k > 4 ^ 20 4 ^ ( 3 k ) > 4 ^ 20 3 k > 20 k = 7 the answer is d ."


Question: a cistern 8 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :

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

<gadget id="calculator">(1/4) + 1</gadget>
<output>5/4 = around 1.25</output>

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

<gadget id="calculator">(5/4) * 8</gadget>
<output>10</output>

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

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

<gadget id="calculator">4 * 8</gadget>
<output>32</output>

<gadget id="calculator">30 + 32</gadget>
<output>62</output>
<result>62</result>

Choices:
A. 62 m 2
B. 50 m 2
C. 53.5 m 2
D. 55 m 2
E. 57 m 2

add(multiply(const_2, add(multiply(add(divide(25, const_100), 1), 4), multiply(add(divide(25, const_100), 1), 8))), multiply(4, 8))

Explanation: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 8 x 1.25 ) + 8 x 4 ] m 2 = 62 m 2 . answer : option a"


Question: if 2994 ã · 14.5 = 179 , then 29.94 ã · 1.45 = ?

<gadget id="calculator">14.5 / 1.45</gadget>
<output>10</output>

<gadget id="calculator">179 / 10</gadget>
<output>179/10 = around 17.9</output>
<result>179/10 = around 17.9</result>

Choices:
A. 17.1
B. 17.3
C. 17.5
D. 17.7
E. 17.9

Explanation: 29.94 / 1.45 = 299.4 / 14.5 = ( 2994 / 14.5 ) x 1 / 10 ) [ here , substitute 179 in the place of 2994 / 14.5 ] = 179 / 10 = 17.9 answer is e .


Question: ( √ 27 + √ 243 ) / √ 75 = ?

<gadget id="calculator">27 ** (1/2)</gadget>
<output>3*sqrt(3) = around 5.196152</output>

<gadget id="calculator">243 ** (1/2)</gadget>
<output>9*sqrt(3) = around 15.588457</output>

<gadget id="calculator">(3*sqrt(3)) + (9*sqrt(3))</gadget>
<output>12*sqrt(3) = around 20.78461</output>

<gadget id="calculator">75 ** (1/2)</gadget>
<output>5*sqrt(3) = around 8.660254</output>

<gadget id="calculator">(12*sqrt(3)) / (5*sqrt(3))</gadget>
<output>12/5 = around 2.4</output>
<result>12/5 = around 2.4</result>

Choices:
A. 2 √ 2
B. 2 √ 3
C. 3 √ 2
D. 3 √ 3
E. 12 / 5

Explanation: "( √ 27 + √ 243 ) / √ 75 = ( 3 √ 3 + 9 √ 3 ) / 5 √ 3 = 12 √ 3 / 5 √ 3 = 12 / 5 . hence , the correct answer is e"


Question: a set s = { x , - 8 , - 7 , - 6 , 6 , 8 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?

<gadget id="calculator">9 + 8</gadget>
<output>17</output>

<gadget id="calculator">17 + 6</gadget>
<output>23</output>

<gadget id="calculator">23 - 6</gadget>
<output>17</output>

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

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

Choices:
A. 1
B. 0
C. 2
D. - 1
E. can not be determined

subtract(subtract(subtract(add(add(9, 8), 6), 6), 7), 8)

Explanation: median of the set = ( - 6 + 6 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 23 - 21 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer c


Question: in a certain pond , 50 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 8 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?

<gadget id="calculator">8 / 50</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">50 / (4/25)</gadget>
<output>625/2 = around 312.5</output>
<result>625/2 = around 312.5</result>

Choices:
A. 400
B. 625
C. 1,250
D. 2,500
E. 312

Explanation: "total fish = x percentage of second catch = ( 8 / 50 ) * 100 = 16 % so , x * 16 % = 50 x = 312 ans . e"


Question: what is the sum of the digits of integer k , if k = ( 10 ^ 45 - 46 )

<gadget id="calculator">10 - 1</gadget>
<output>9</output>

<gadget id="calculator">45 - 2</gadget>
<output>43</output>

<gadget id="calculator">9 * 43</gadget>
<output>387</output>

<gadget id="calculator">387 + 10</gadget>
<output>397</output>
<result>397</result>

Choices:
A. 356
B. 366
C. 363
D. 396
E. 408

add(multiply(subtract(10, const_1), subtract(45, const_2)), 10)

Explanation: "there are 46 digits in 10 ^ 45 when we subtract 46 from it , there will be 45 digits left . 10 ^ 45 can be written as 9999999 . . . . ( 45 times ) + 1 so , 10 ^ 45 - 46 = 9999999 . . . . ( 45 times ) + 1 - 46 = 9999999 . . . . ( 45 times ) - 45 consider the last 2 digits , 99 - 45 = 54 the last 2 digits will be 54 . and our number would be 99999 . . . . . . 99954 with 2 less 9 s after subtraction . number of 9 s left are 43 and the last two digits are 54 the sum of the digits will be ( 43 * 9 ) + 5 + 4 = 396 answer : - d"


Question: if 5 a = 3125 , then the value of 5 ( a - 3 ) is :

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

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

Choices:
A. 25
B. 125
C. 625
D. 1625
E. none of these

Explanation: solution 5 a = 3125 ⇔ 5 a = 5 a ⇔ a = 5 . ∴ 5 ( a - 3 ) = 5 ( 5 - 3 ) = 52 = 25 . answer a


Question: in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 130 marks , the no of questions he attempts correctly is :

<gadget id="calculator">130 + 60</gadget>
<output>190</output>

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

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

Choices:
A. 33
B. 38
C. 99
D. 27
E. 71

Explanation: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 130 = > 5 x = 190 = > x = 38 answer : b"


Question: a is half good a work man as b and together they finish a job in 20 days . in how many days working alone b finish the job ?

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

<gadget id="calculator">20 * (3/2)</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 98 days
B. 30 days
C. 17 days
D. 18 days
E. 19 days

Explanation: "wc = 1 : 2 2 x + x = 1 / 20 = > x = 1 / 60 2 x = 1 / 60 = > 30 days answer : b"


Question: what is the value of n if the sum of the consecutive odd intergers y from 1 to n equals 169 ?

<gadget id="calculator">169 ** (1/2)</gadget>
<output>13</output>

<gadget id="calculator">13 * 2</gadget>
<output>26</output>

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

<gadget id="calculator">26 - 2</gadget>
<output>24</output>

<gadget id="calculator">24 + 1</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 47
B. 25
C. 37
D. 33
E. 29

add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1)

Explanation: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."


Question: if log 4 x + log 4 ( 1 / 6 ) = 1 / 2 then the value of x is ?

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

<gadget id="calculator">4 ** (1/2)</gadget>
<output>2</output>

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

Choices:
A. 18
B. 24
C. 16
D. 12
E. 10

Explanation: log 4 x + log 4 ( 1 / 6 ) = 1 / 2 = > log 4 [ x x 1 / 6 ] = 1 / 2 = > log 4 [ x / 6 ] = 1 / 2 = > 41 / 2 = x / 6 = > 2 = x / 6 therefore , x = 12 answer : d


Question: what quantity of water should taken out to concentrate 27 liters of 40 % acidic liquid to 60 % acidic liquid ?

<gadget id="calculator">27 * 40</gadget>
<output>1_080</output>

<gadget id="calculator">1_080 / 60</gadget>
<output>18</output>

<gadget id="calculator">27 - 18</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 5 liters
B. 10 liters
C. 15 liters
D. 9 liters
E. 6 liters

subtract(27, divide(multiply(27, 40), 60))

Explanation: "required answer is = 27 ( 60 - 40 ) / 60 = 9 liters answer is d"


Question: marts income is 30 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income

<gadget id="calculator">100 + 30</gadget>
<output>130</output>

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

<gadget id="calculator">100 / 60</gadget>
<output>5/3 = around 1.666667</output>

<gadget id="calculator">(5/3) * 100</gadget>
<output>500/3 = around 166.666667</output>

<gadget id="calculator">130 / (500/3)</gadget>
<output>39/50 = around 0.78</output>

<gadget id="calculator">(39/50) * 100</gadget>
<output>78</output>
<result>78</result>

Choices:
A. 124 %
B. 120 %
C. 78 %
D. 80 %
E. 64 %

multiply(divide(add(const_100, 30), multiply(divide(const_100, subtract(const_100, 40)), const_100)), const_100)

Explanation: "m = ( 130 / 100 ) t t = ( 60 / 100 ) j = > m = ( 78 / 100 ) j answer c ."


Question: there is a 5 - digit number . the fifth digit is one fourth of the third digit and one half of the fourth digit . third digit is one half of the first digit . second digit is 5 more than the fifth digit . what is that 5 - digit number ?

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

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

<gadget id="calculator">8 * 10_000</gadget>
<output>80_000</output>

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

<gadget id="calculator">80_000 + 5_000</gadget>
<output>85_000</output>

<gadget id="calculator">4 * 100</gadget>
<output>400</output>

<gadget id="calculator">85_000 + 400</gadget>
<output>85_400</output>

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

<gadget id="calculator">85_400 + 20</gadget>
<output>85_420</output>

<gadget id="calculator">85_420 + 1</gadget>
<output>85_421</output>
<result>85_421</result>

Choices:
A. 86421
B. 86424
C. 89421
D. 96421
E. 76421

add(add(add(add(multiply(multiply(const_4, const_2), multiply(const_1000, const_10)), multiply(5, const_1000)), multiply(const_4, const_100)), multiply(const_2, const_10)), const_1)

Explanation: we can prove it as follows suppose number is pqrst , now t = ( 1 / 4 ) r = ( 1 / 2 ) s . . . . . . ( 1 ) , r = ( 1 / 2 ) p . . . . . ( 2 ) , q = t + 5 . . . . ( 3 ) now from ( 1 ) 4 t = r = 2 s = k ( suppose ) . . . . ( 4 ) from ( 2 ) 2 r = p . . . ( 5 ) now ( 4 ) * 2 then we get 8 t = 2 r = 4 s = k ( again some integer ) . . . . ( 6 ) from ( 5 ) and ( 6 ) 8 t = 2 r = 4 s = p = k . . . . . . . . . ( 7 ) now we have to choose the value of k 1 ) if choose k = 0 then it is worthless number will be 00000 ( not a answer ) 2 ) for k = 1 to 7 and for k = 9 digits will be in fractions 3 ) for k = 8 we get p = 8 , s = 2 , r = 4 , t = 1 and q = 6 and number is pqrst = 86421 answer : a


Question: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 840 . find the sum ?

<gadget id="calculator">18 - 12</gadget>
<output>6</output>

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

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

<gadget id="calculator">840 / (3/25)</gadget>
<output>7_000</output>
<result>7_000</result>

Choices:
A. 7000
B. 2787
C. 2799
D. 2699
E. 2790

divide(840, divide(multiply(subtract(18, 12), const_2), const_100))

Explanation: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 840 = > 36 x / 100 - 24 x / 100 = 840 = > 12 x / 100 = 840 = > x = 7000 . answer : a"


Question: for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.15 – 6.15 * ?

<gadget id="calculator">floor(6.15)</gadget>
<output>6</output>

<gadget id="calculator">6.15 - 6</gadget>
<output>0.15</output>
<result>0.15</result>

Choices:
A. 1.5
B. 0.15
C. 6.25
D. 0.25
E. 6.0

Explanation: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.15 * = 6 ( the greatest positive even integer less than or equal to 6.15 is 6 ) . hence , 6.15 – 6.15 * = 6.15 - 6 = 0.15 answer : b ."


Question: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.15 , what is the value of y ?

<gadget id="calculator">floor(96.15)</gadget>
<output>96</output>

<gadget id="calculator">96.15 - 96</gadget>
<output>0.15</output>

<gadget id="calculator">9 / 0.15</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 96
B. 60
C. 48
D. 25
E. 12

Explanation: "guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 96.15 and remainder is 9 so . 15 x y = 9 hence y = 60 ans b"


Question: the cost of the paint is rs . 40.00 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 10 feet each side

<gadget id="calculator">6 * (10 ** 2)</gadget>
<output>600</output>

<gadget id="calculator">600 / 20</gadget>
<output>30</output>

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

Choices:
A. rs . 1200
B. rs . 672
C. rs . 546
D. rs . 876
E. none of these

Explanation: "explanation : surface area of a cube = 6 x 10 ^ 2 = 600 s q . ft quantity of paint required = ( 600 / 20 ) = 30 kg cost of painting = 40 x 30 = rs . 1200 answer : a"


Question: what is the perimeter of a rectangular field whose diagonal is 10 m and length is 3 m ?

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

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

<gadget id="calculator">100 - 9</gadget>
<output>91</output>

<gadget id="calculator">91 ** (1/2)</gadget>
<output>sqrt(91) = around 9.539392</output>

<gadget id="calculator">(sqrt(91)) + 3</gadget>
<output>3 + sqrt(91) = around 12.539392</output>

<gadget id="calculator">(3 + sqrt(91)) + (3 + sqrt(91))</gadget>
<output>6 + 2*sqrt(91) = around 25.078784</output>

<gadget id="calculator">(6 + 2*sqrt(91)) / 3</gadget>
<output>2 + 2*sqrt(91)/3 = around 8.359595</output>
<result>2 + 2*sqrt(91)/3 = around 8.359595</result>

Choices:
A. 12 m
B. 5 m
C. 10 m
D. 8 m
E. 6 m

divide(add(add(sqrt(subtract(power(10, const_2), power(3, const_2))), 3), add(sqrt(subtract(power(10, const_2), power(3, const_2))), 3)), const_3)

Explanation: sol : breadth of the rectangular plot is = 10 ^ 2 - 3 ^ 2 = 1 m therefore , perimeter of the rectangular plot = 2 ( 3 + 1 ) = 8 m d ) 8 m


Question: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?

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

<gadget id="calculator">10 - 3</gadget>
<output>7</output>

<gadget id="calculator">1 / 7</gadget>
<output>1/7 = around 0.142857</output>
<result>1/7 = around 0.142857</result>

Choices:
A. 2 : 9
B. 2 : 7
C. 1 : 7
D. 1 : 4
E. 1 : 3

Explanation: 2 % is 1 % - point below 3 % and 10 % is 7 % - points above 3 % . the ratio of a : b should be 1 : 7 . the answer is c .


Question: a 120.00001 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?

<gadget id="calculator">120 + 80</gadget>
<output>200</output>

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

<gadget id="calculator">200 * (5/18)</gadget>
<output>500/9 = around 55.555556</output>

<gadget id="calculator">(500/9) * 9</gadget>
<output>500</output>

<gadget id="calculator">500 - 120.00001</gadget>
<output>379.99999</output>
<result>379.99999</result>

Choices:
A. 220 meter
B. 225 meter
C. 380 meter
D. 435 meter
E. none of these

Explanation: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 120 / 9 = 500 / 9 = > x + 120 = 500 = > x = 380 so the length of the train is 380 meters option c"


Question: the ratio between the length and the breadth of a rectangular plot is 7 : 5 . if the perimeter of the plot is 288 metres , what is its area ?

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

<gadget id="calculator">1 + (7/5)</gadget>
<output>12/5 = around 2.4</output>

<gadget id="calculator">2 * (12/5)</gadget>
<output>24/5 = around 4.8</output>

<gadget id="calculator">288 / (24/5)</gadget>
<output>60</output>

<gadget id="calculator">7 * 60</gadget>
<output>420</output>

<gadget id="calculator">420 / 5</gadget>
<output>84</output>

<gadget id="calculator">84 * 60</gadget>
<output>5_040</output>
<result>5_040</result>

Choices:
A. 1320 sq . metres
B. 3260 sq . metres
C. 4280 sq . metres
D. 5040 sq . metres
E. none of these

rectangle_area(divide(multiply(7, divide(288, multiply(const_2, add(const_1, divide(7, 5))))), 5), divide(288, multiply(const_2, add(const_1, divide(7, 5)))))

Explanation: let the length and breadth be 7 x and 5 x respectively . then , p = 2 ( 7 x + 5 x ) = 288 â ‡ ’ x = 12 area = 7 ã — 12 ã — 5 ã — 12 = 5040 sq . m . answer d


Question: during the first two weeks of january , the total rainfall in springdale was 20 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?

<gadget id="calculator">1 + 1.5</gadget>
<output>2.5</output>

<gadget id="calculator">1.5 / 2.5</gadget>
<output>0.6</output>

<gadget id="calculator">20 * 0.6</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 5 inches
B. 6 inches
C. 9 inches
D. 10 inches
E. 12 inches

multiply(20, divide(1.5, add(const_1, 1.5)))

Explanation: "total rainfall in 2 weeks = 20 inches . assume the rainfall in second week = 1.5 x rainfall in first week = x total rainfall = 2.5 x = 20 inches x = 8 and 1.5 x = 12 rainfall during second week = 12 inches option e"


Question: the set s consists of 5 numbers : { 1 , 2,3 , 4,5 } . if all possible subsets including the null set are created and one subset is chosen at random , what is the probability that the subset has 3 or 4 as its largest number ?

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

<gadget id="calculator">2 ** 5</gadget>
<output>32</output>

<gadget id="calculator">12 / 32</gadget>
<output>3/8 = around 0.375</output>
<result>3/8 = around 0.375</result>

Choices:
A. 3 / 4
B. 3 / 8
C. 3 / 16
D. 5 / 16
E. 3 / 32

divide(multiply(4, 3), power(const_2, 5))

Explanation: the set s has 2 ^ 5 = 32 subsets . the number 5 is in half of these subsets . of the remaining 16 subsets , 4 is an element in 8 of them . thus 4 is the largest number in 8 subsets of s . of the remaining 8 subsets , 3 is an element in 4 of them . thus 3 is the largest number in 4 subsets of s . the probability that 3 or 4 is the largest number is 12 / 32 = 3 / 8 . the answer is c .


Question: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 4 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?

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

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

<gadget id="calculator">200 * (3/4)</gadget>
<output>150</output>

<gadget id="calculator">150 * (3/4)</gadget>
<output>225/2 = around 112.5</output>

<gadget id="calculator">(225/2) * (3/4)</gadget>
<output>675/8 = around 84.375</output>
<result>675/8 = around 84.375</result>

Choices:
A. 40
B. 46
C. 52
D. 62
E. 85

multiply(multiply(multiply(200, subtract(1, divide(1, 4))), subtract(1, divide(1, 4))), subtract(1, divide(1, 4)))

Explanation: "the probability of survival for each of the first 3 months of life is 1 - 1 / 4 = 3 / 4 , so of 200 newborn 200 * 3 / 4 * 3 / 4 * 3 / 4 = ~ 85 is expected to survive . answer : e ."


Question: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 390 kilograms of pears that day , how many kilograms did he sell in the afternoon ?

<gadget id="calculator">390 / 3</gadget>
<output>130</output>

<gadget id="calculator">130 * 2</gadget>
<output>260</output>
<result>260</result>

Choices:
A. 120
B. 180
C. 260
D. 280
E. 320

Explanation: "3 x = 390 x = 130 therefore , the salesman sold 130 kg in the morning and 2 ⋅ 130 = 260 kg in the afternoon . so answer is c ."


Question: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability q that this product will be a multiple of 45 ?

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

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

Choices:
A. 1 / 32
B. 1 / 28
C. 1 / 24
D. 1 / 16
E. 1 / 14

Explanation: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability q = 1 / 24 . answer c ."


Question: a certain high school has 500 students . of these students , 20 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?

<gadget id="calculator">20 + 20</gadget>
<output>40</output>

<gadget id="calculator">40 - 10</gadget>
<output>30</output>

<gadget id="calculator">500 - 30</gadget>
<output>470</output>
<result>470</result>

Choices:
A. 430
B. 440
C. 450
D. 460
E. 470

subtract(500, subtract(add(20, 20), 10))

Explanation: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 20 y = 20 z = 10 so , we have 20 students taking music , 20 taking art and 10 taking both music and art . that 10 person has been counted twice though ( once in the music ' group ' and once in the art ' group ' ) , so what we really have is . . . 10 student taking just music 10 student taking just art 10 student taking both music and art total = 30 students we ' re asked for the total number of students who are taking neither course . that is 5000 - 30 = 470 . e"


Question: a courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof . what could be the weight in grams of a package for which the charge is $ 2.15 ?

<gadget id="calculator">65 / 100</gadget>
<output>13/20 = around 0.65</output>

<gadget id="calculator">2.15 - (13/20)</gadget>
<output>1.5</output>

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

<gadget id="calculator">(1/10) / 100</gadget>
<output>1/1_000 = around 0.001</output>

<gadget id="calculator">(1/1_000) * 250</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">1.5 + (1/4)</gadget>
<output>1.75</output>

<gadget id="calculator">1.75 / (1/1_000)</gadget>
<output>1_750</output>
<result>1_750</result>

Choices:
A. 980
B. 1120
C. 1260
D. 1420
E. 1670

divide(add(subtract(2.15, divide(65, 100)), multiply(divide(divide(10, 100), 100), 250)), divide(divide(10, 100), 100))

Explanation: "the charge is 65 cents for the first 250 grams . this leaves a charge of $ 2.15 - $ 0.65 = $ 1.50 the charge for the next 1400 grams is $ 1.40 which leaves a charge of $ 0.10 the weight is somewhere between 1650 and 1750 . the answer is e ."


Question: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 1 year the amount to be paid is ?

<gadget id="calculator">100 + 4</gadget>
<output>104</output>

<gadget id="calculator">104 / 100</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) * (26/25)</gadget>
<output>676/625 = around 1.0816</output>

<gadget id="calculator">7_500 * (676/625)</gadget>
<output>8_112</output>
<result>8_112</result>

Choices:
A. 3377
B. 2688
C. 2688
D. 7800
E. 1268

multiply(7500, multiply(divide(add(const_100, 4), const_100), divide(add(const_100, 4), const_100)))

Explanation: "a = 7500 ( 26 / 25 ) ^ 1 = 7800 answer : d"


Question: a car gets 24 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?

<gadget id="calculator">24 / 75</gadget>
<output>8/25 = around 0.32</output>

<gadget id="calculator">(8/25) * 100</gadget>
<output>32</output>

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

<gadget id="calculator">24 * 12</gadget>
<output>288</output>

<gadget id="calculator">384 - 288</gadget>
<output>96</output>
<result>96</result>

Choices:
A. 96
B. 100
C. 104
D. 108
E. 112

subtract(multiply(multiply(divide(24, 75), const_100), 12), multiply(24, 12))

Explanation: "originally , the distance the car could go on a full tank was 12 * 24 = 288 miles . after it has been modified , the car can go 24 / 0.75 = 32 miles per gallon . on a full tank , the car can go 32 * 12 = 384 miles , thus 96 miles more . the answer is a ."


Question: the h . c . f . of two numbers is 15 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :

<gadget id="calculator">15 * 15</gadget>
<output>225</output>
<result>225</result>

Choices:
A. 225
B. 300
C. 299
D. 322
E. 345

Explanation: "the numbers are ( 15 x 11 ) and ( 15 x 15 ) . larger number = ( 15 x 15 ) = 225 . answer : a"


Question: a metallic sheet is of rectangular shape with dimensions 46 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is :

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

<gadget id="calculator">46 - 16</gadget>
<output>30</output>

<gadget id="calculator">36 - 16</gadget>
<output>20</output>

<gadget id="calculator">30 * 20 * 8</gadget>
<output>4_800</output>
<result>4_800</result>

Choices:
A. 4830
B. 5120
C. 6420
D. 4800
E. 8960

volume_rectangular_prism(subtract(46, multiply(8, const_2)), subtract(36, multiply(8, const_2)), 8)

Explanation: "l = ( 46 - 16 ) m = 30 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . volume of the box = ( 30 x 20 x 8 ) m 3 = 4800 m 3 . answer : option d"


Question: in an election between two candidates , one got 60 % of the total valid votes , 30 % of the votes were invalid . if the total number of votes was 9000 , the number of valid votes that the other candidate got , was :

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

<gadget id="calculator">1 - (3/10)</gadget>
<output>7/10 = around 0.7</output>

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

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

<gadget id="calculator">(7/10) * (2/5)</gadget>
<output>7/25 = around 0.28</output>

<gadget id="calculator">(7/25) * 9_000</gadget>
<output>2_520</output>
<result>2_520</result>

Choices:
A. 2500
B. 2520
C. 3000
D. 3100
E. none of these

multiply(multiply(subtract(const_1, divide(30, const_100)), subtract(const_1, divide(60, const_100))), 9000)

Explanation: "explanation : number of valid votes = 70 % of 9000 = 6300 . valid votes polled by other candidates = 40 % of 6300 ( 40 / 1006300 ) = 2520 . harsh mishra a year ago 0 upvotes answer : b"


Question: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 20 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?

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

<gadget id="calculator">10 / 80</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * 100</gadget>
<output>25/2 = around 12.5</output>
<result>25/2 = around 12.5</result>

Choices:
A. 10.5 %
B. 12.5 %
C. 15 %
D. 22 %
E. 30 %

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

Explanation: suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 20 % of y exceeded the speed limit but did n ' t received the ticket , i . e . y / 5 . it means 4 y / 5 received the ticket . hence , 4 y / 5 = x / 10 or y / x = 1 / 8 or y / x * 100 = 1 / 8 * 100 = 12.5 % answer : b


Question: x and y are two towns . ganesh covers the distance from x to y at an average speed of 60 km / hr . however , he covers the distance from y to x at an average speed of 30 km / hr . his average speed during the whole journey in km / hr . is :

<gadget id="calculator">60 - 10</gadget>
<output>50</output>

<gadget id="calculator">50 + 100</gadget>
<output>150</output>

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

<gadget id="calculator">150 / 60</gadget>
<output>5/2 = around 2.5</output>

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

<gadget id="calculator">(5/2) + 5</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">300 / (15/2)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 34
B. 43
C. 40
D. 38
E. 29

divide(add(add(subtract(60, const_10), const_100), add(subtract(60, const_10), const_100)), add(divide(add(subtract(60, const_10), const_100), 60), divide(add(subtract(60, const_10), const_100), 30)))

Explanation: "solution : average speed = 2 xy / x + y = 2 * 60 * 30 / 60 + 30 = 40 answer : c"


Question: a drink vendor has 20 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?

<gadget id="calculator">gcd(20, 144)</gadget>
<output>4</output>

<gadget id="calculator">gcd(4, 368)</gadget>
<output>4</output>

<gadget id="calculator">368 / 4</gadget>
<output>92</output>

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

<gadget id="calculator">144 / 4</gadget>
<output>36</output>

<gadget id="calculator">5 + 36</gadget>
<output>41</output>

<gadget id="calculator">92 + 41</gadget>
<output>133</output>
<result>133</result>

Choices:
A. 135
B. 137
C. 142
D. 130
E. 133

Explanation: "the number of liters in each can = hcf of 20 , 144 and 368 = 4 liters . number of cans of maaza = 20 / 4 = 5 number of cans of pepsi = 144 / 4 = 36 number of cans of sprite = 368 / 4 = 92 the total number of cans required = 5 + 36 + 92 = 133 cans . answer : e"


Question: jonathan can type a 40 page document in 40 minutes , susan can type it in 30 minutes , and jack can type it in 24 minutes . working together , how much time will it take them to type the same document ?

<gadget id="calculator">40 / 24</gadget>
<output>5/3 = around 1.666667</output>

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

<gadget id="calculator">40 / 30</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">1 + (4/3)</gadget>
<output>7/3 = around 2.333333</output>

<gadget id="calculator">(5/3) + (7/3)</gadget>
<output>4</output>

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

Choices:
A. 5 minutes
B. 10 minutes
C. 15 minutes
D. 18 minutes
E. 20 minutes

Explanation: "you may set up common equation like this : job / a + job / b + job / c = job / x memorize this universal formula , you will need it definitely for gmat . and find x from this equation in this specific case , the equation will look like this : 40 / 40 + 40 / 30 + 40 / 24 = 40 / x if you solve this equation , you get the same answer b ( 10 )"


Question: find the least number must be subtracted from 62575 so that remaining number is divisible by 99 .

<gadget id="calculator">62_575 / 99</gadget>
<output>62_575/99 = around 632.070707</output>

<gadget id="calculator">floor(62_575/99)</gadget>
<output>632</output>

<gadget id="calculator">632 * 99</gadget>
<output>62_568</output>

<gadget id="calculator">62_575 - 62_568</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 93
B. 7
C. 54
D. 9
E. 6

subtract(62575, multiply(floor(divide(62575, 99)), 99))

Explanation: on dividing 62571 by 99 we get the remainder 7 , so 7 should be subtracted . answer is b


Question: a man is 12 years older than his brother . in two years , his age will be twice the age of his brother . the present age of his brother is :

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

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

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

Choices:
A. 10
B. 21
C. 22
D. 23
E. 24

subtract(add(12, const_2), multiply(const_2, const_2))

Explanation: let the brother ' s present age be x years . then , man ' s present age = ( x + 12 ) years . ( x + 12 ) + 2 = 2 ( x + 2 ) x + 14 = 2 x + 4 x = 10 . answer : a


Question: a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 280 pounds of the mixture ?

<gadget id="calculator">5 * 280</gadget>
<output>1_400</output>

<gadget id="calculator">5 + 2</gadget>
<output>7</output>

<gadget id="calculator">1_400 / 7</gadget>
<output>200</output>
<result>200</result>

Choices:
A. 200
B. 84
C. 40
D. 28
E. 20

Explanation: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 280 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 280 = 200 pounds answer ( a )"


Question: how many 4 - digit numbers that do not contain the digits 2 , 3 , 4 , 5 , 6 , or 7 are there ?

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

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

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

Choices:
A. 168
B. 176
C. 184
D. 192
E. 200

multiply(multiply(multiply(3, 4), 4), 4)

Explanation: the 1 st digit can be filled up by the numbers : { 1 , 8,9 } = 3 ways the 2 nd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 3 rd digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the 4 th digit can be filled up by the numbers : { 0,1 , 8,9 } = 4 ways the total number of such four - digit numbers is 3 * 4 * 4 * 4 = 192 the answer is d .


Question: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?

<gadget id="calculator">8 * 100</gadget>
<output>800</output>

<gadget id="calculator">6 * 100</gadget>
<output>600</output>

<gadget id="calculator">800 * 600</gadget>
<output>480_000</output>

<gadget id="calculator">480_000 * 22.5</gadget>
<output>10_800_000</output>

<gadget id="calculator">25 * 11.25</gadget>
<output>281.25</output>

<gadget id="calculator">281.25 * 6</gadget>
<output>1_687.5</output>

<gadget id="calculator">10_800_000 / 1_687.5</gadget>
<output>6_400</output>
<result>6_400</result>

Choices:
A. 5600
B. 6000
C. 6400
D. 7200
E. none

divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))

Explanation: "solution number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 / 25 x 11.25 x 6 ) = 6400 . answer c"


Question: the average weight of 6 person ' s increases by 1.8 kg when a new person comes in place of one of them weighing 69 kg . what might be the weight of the new person ?

<gadget id="calculator">6 * 1.8</gadget>
<output>10.8</output>

<gadget id="calculator">10.8 + 69</gadget>
<output>79.8</output>
<result>79.8</result>

Choices:
A. 73 kg
B. 79.8 kg
C. 86 kg
D. data inadequate
E. none of these

Explanation: "total weight increased = ( 6 x 1.8 ) kg = 10.8 kg . weight of new person = ( 69 + 10.8 ) kg = 79.8 kg . answer : option b"


Question: a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 7200 interest . the principal amount borrowed by him was .

<gadget id="calculator">7_200 * 100</gadget>
<output>720_000</output>

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

<gadget id="calculator">720_000 / 36</gadget>
<output>20_000</output>
<result>20_000</result>

Choices:
A. rs 14000
B. rs 15000
C. rs 16000
D. rs 20000
E. none of these

divide(multiply(7200, const_100), multiply(12, 3))

Explanation: "explanation : s . i . = p â ˆ — r â ˆ — t / 100 = > p = s . i . â ˆ — 100 / r â ˆ — t = > p = 7200 â ˆ — 100 / 12 â ˆ — 3 = rs 20000 option d"


Question: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1986 on her 30 nd birthday first be eligible to retire under this provision ?

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

<gadget id="calculator">40 / 2</gadget>
<output>20</output>

<gadget id="calculator">1_986 + 20</gadget>
<output>2_006</output>
<result>2_006</result>

Choices:
A. 2003
B. 2004
C. 2005
D. 2006
E. 2007

add(1986, divide(subtract(70, 30), const_2))

Explanation: "she must gain at least 70 points , now she has 30 and every year gives her two more points : one for age and one for additional year of employment , so 30 + 2 * ( # of years ) = 70 - - > ( # of years ) = 20 - - > 1986 + 20 = 2006 . answer : d ."


Question: i had rs . 10000 with me . out of this , money i lent some money to a for 2 years at 15 % simple interest . i lent the remaining money to b for an equal number of years at 18 % simple interest . after 2 years , i found that a had given me rs . 360 more as interest as compared to ( b ) the amount of money which i had lent to b must have been

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

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

<gadget id="calculator">10_000 * (3/10)</gadget>
<output>3_000</output>

<gadget id="calculator">3_000 - 360</gadget>
<output>2_640</output>

<gadget id="calculator">2 * 18</gadget>
<output>36</output>

<gadget id="calculator">36 / 100</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(3/10) + (9/25)</gadget>
<output>33/50 = around 0.66</output>

<gadget id="calculator">2_640 / (33/50)</gadget>
<output>4_000</output>
<result>4_000</result>

Choices:
A. 2000
B. 3000
C. 4000
D. 5000
E. 6000

divide(subtract(multiply(10000, divide(multiply(2, 15), const_100)), 360), add(divide(multiply(2, 15), const_100), divide(multiply(2, 18), const_100)))

Explanation: explanation : total amount = rs . 10000 let money lent a = rs . x and money lent to b = rs . ( 10000 x ) x = rs . 6000 . so the amount of money lent to b = rs . 4000 answer : c


Question: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 785 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?

<gadget id="calculator">785 / 4</gadget>
<output>785/4 = around 196.25</output>
<result>785/4 = around 196.25</result>

Choices:
A. 191
B. 197
C. 193
D. 212
E. 213

Explanation: "total movies submitted are 785 . as per question we need to take 1 / 4 of 785 to be considered for top 10 movies = 196.25 approximate the value we 197 . imo option b is the correct answer . . ."


Question: the number 0.5 is how much greater than 1 / 3 ?

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

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

Choices:
A. 1 / 6
B. 2 / 10
C. 1 / 50
D. 1 / 500
E. 2 / 500

Explanation: "let x be the difference then . 5 - 1 / 3 = x 5 / 10 - 1 / 3 = x x = 1 / 6 ans a"


Question: the concentration of spirit in 3 different vessels a , b and c are 45 % , 30 % and 10 % respectively . if 4 litres from vessel a , 5 litres from vessel b and 6 litres from vessel c are mixed , find the concentration of spirit in the resultant solution .

<gadget id="calculator">4 * 45</gadget>
<output>180</output>

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

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

<gadget id="calculator">150 / 100</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">(9/5) + (3/2)</gadget>
<output>33/10 = around 3.3</output>

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

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

<gadget id="calculator">(33/10) + (3/5)</gadget>
<output>39/10 = around 3.9</output>

<gadget id="calculator">(39/10) * 100</gadget>
<output>390</output>

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

<gadget id="calculator">390 / 15</gadget>
<output>26</output>
<result>26</result>

Choices:
A. 26 %
B. 33 %
C. 34 %
D. 35 %
E. 24 %

divide(multiply(add(add(divide(multiply(4, 45), const_100), divide(multiply(30, 5), const_100)), divide(multiply(10, 6), const_100)), const_100), add(10, 5))

Explanation: quantity of spirit in new solution = ( 4 * 45 / 100 ) + ( 5 * 30 / 100 ) + ( 6 * 10 / 100 ) = 1.8 + 1.5 + 0.6 = 3.9 liters so % concentration of spirit = 100 * 3.9 / ( 4 + 5 + 6 ) = 26 % answer : a


Question: there are 2 sections a and b in a class , consisting of 50 and 70 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?

<gadget id="calculator">50 * 50</gadget>
<output>2_500</output>

<gadget id="calculator">70 * 70</gadget>
<output>4_900</output>

<gadget id="calculator">2_500 + 4_900</gadget>
<output>7_400</output>

<gadget id="calculator">50 + 70</gadget>
<output>120</output>

<gadget id="calculator">7_400 / 120</gadget>
<output>185/3 = around 61.666667</output>
<result>185/3 = around 61.666667</result>

Choices:
A. 50.78 kg
B. 49.32 kg
C. 61.67 kg
D. 69.15 kg
E. 70.89 kg

divide(add(multiply(50, 50), multiply(70, 70)), add(50, 70))

Explanation: "total weight of 50 + 70 students = 50 * 50 + 70 * 70 = 7400 average weight of the class is = 7400 / 120 = 61.67 kg answer is c"


Question: if x ^ 2 – 3 x = 18 , then one possible value of x – 4 =

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

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

Choices:
A. - 9
B. - 5
C. - 3
D. - 1
E. 2

Explanation: x ^ 2 – 3 x = 18 i . e . x ^ 2 – 3 x - 18 = 0 i . e . x ^ 2 – 6 x + 3 x - 18 = 0 i . e . ( x - 6 ) ( x + 3 ) = 0 i . e . x = 6 or - 3 i . e . x - 4 = 6 - 4 or - 3 - 4 i . e . x - 4 = 2 or - 7 answer : option e


Question: if 4 x + y = 8 and 3 x - 4 y = 5 , then what is the value of 7 x - 3 y ?

<gadget id="calculator">8 + 5</gadget>
<output>13</output>

<gadget id="calculator">13 + 10</gadget>
<output>23</output>
<result>23</result>

Choices:
A. 23
B. 3
C. 15
D. 52 / 7
E. 60 / 7

Explanation: 4 x + y = 8 . . . equation 1 3 x - 4 y = 5 . . . equation 2 adding both the equations 7 x - 3 y = 23 correct answer option a


Question: working alone , a can complete a certain kind of job in 3 hours . a and d , working together at their respective rates , can complete one of these jobs in 2 hours . in how many hours can d , working alone , complete one of these jobs ?

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

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

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

<gadget id="calculator">1 / (1/6)</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 2
B. 4
C. 6
D. 8
E. 10

Explanation: let total time taken by d to complete the job = d total time taken by a to complete the job = 3 work done by a in an hour 1 / a = 1 / 3 working together a and d can complete the job in 2 hours 1 / a + 1 / d = 1 / 2 = > 1 / d = 1 / 2 - 1 / a = 1 / 2 - 1 / 3 = 1 / 6 = > d = 6 hours answer c


Question: a class of boys stands in a single line , one boy is 19 th in order from both the ends , how many boys are there in the class ?

<gadget id="calculator">19 * 2</gadget>
<output>38</output>

<gadget id="calculator">38 - 1</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 37
B. 38
C. 27
D. 29
E. 11

Explanation: explanation : number of boys in the class = ( 18 + 1 + 18 ) = 37 answer : a ) 37


Question: what number must be added to 6 , 16 and 8 to get an average of 13 ?

<gadget id="calculator">13 * 4</gadget>
<output>52</output>

<gadget id="calculator">6 + 16</gadget>
<output>22</output>

<gadget id="calculator">8 + 22</gadget>
<output>30</output>

<gadget id="calculator">52 - 30</gadget>
<output>22</output>
<result>22</result>

Choices:
A. 23
B. 22
C. 44
D. 33
E. 55

subtract(multiply(13, const_4), add(8, add(6, 16)))

Explanation: b 22


Question: the average age of 30 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .

<gadget id="calculator">30 * 15</gadget>
<output>450</output>

<gadget id="calculator">450 + 16</gadget>
<output>466</output>

<gadget id="calculator">466 + 30</gadget>
<output>496</output>

<gadget id="calculator">496 - 450</gadget>
<output>46</output>
<result>46</result>

Choices:
A. 46
B. 55
C. 43
D. 39
E. 54

subtract(add(add(multiply(30, 15), 16), 30), multiply(30, 15))

Explanation: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 30 ) = 46 years answer : a"


Question: if x = the product of 7 distinct prime numbers , how many factors does x have besides 1 and itself ?

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

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

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

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

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

<gadget id="calculator">32 * 2</gadget>
<output>64</output>

<gadget id="calculator">64 * 2</gadget>
<output>128</output>
<result>128</result>

Choices:
A. 108
B. 114
C. 120
D. 126
E. 132

multiply(multiply(multiply(multiply(multiply(multiply(add(1, 1), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1)), add(1, 1))

Explanation: since x has 7 distinct prime factors , x has a total of 2 ^ 7 = 128 factors . besides 1 and itself , x has 126 factors . the answer is d .


Question: how many integers n are prime numbers in the range 200 < n < 220 ?

<gadget id="calculator">200 / 200</gadget>
<output>1</output>
<result>1</result>

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

Explanation: to test a number n on whether it is a prime number , take square root ( n ) . consider as it is if it is a natural number . otherwise , increase the sq . root to the next natural no . then divide given no . by all prime numbers below the sq . root obtained . if the no . is divisible by any of the prime numbers , then it is not a prime number ; else it is . square root of 200 or 220 is less than 15 so , lets check if any number between 200 and 220 is not divisible by prime numbers 2 , 35 , 711 ( < 15 ) . that ' s it . out : 201 , 202 , 203 , 204 , 205 , 206 , 207 , 208 , 209 , 210 , 212 , 213 , 214 , 215 , 216 , 217 , 218 , 219 only 211 is a prime number in the given range correct option : a


Question: a sum of $ 800 amounts to $ 920 in 3 years at simple interest . if the interest rate is increased by 3 % it would amount to how much ?

<gadget id="calculator">920 - 800</gadget>
<output>120</output>

<gadget id="calculator">120 / 3</gadget>
<output>40</output>

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

<gadget id="calculator">4_000 / 800</gadget>
<output>5</output>

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

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">800 * (2/25)</gadget>
<output>64</output>

<gadget id="calculator">64 * 3</gadget>
<output>192</output>

<gadget id="calculator">800 + 192</gadget>
<output>992</output>
<result>992</result>

Choices:
A. $ 506
B. $ 774
C. $ 992
D. $ 854
E. $ 1021

add(800, multiply(multiply(800, divide(add(divide(multiply(divide(subtract(920, 800), 3), const_100), 800), 3), const_100)), 3))

Explanation: s . i = 920 - 800 = 120 p = $ 800 t = 3 years r = 100 * 120 / 800 * 3 = 5 % new rate = 5 + 3 = 8 % new s . i . = 800 * 8 * 3 / 100 = $ 192 new amount = 800 + 192 = $ 992 answer is c


Question: a copy machine , working at a constant rate , makes 35 copies per minute . a second copy machine , working at a constant rate , makes 65 copies per minute . working together at their respective rates , how many copies do the two machines make in half an hour ?

<gadget id="calculator">35 + 65</gadget>
<output>100</output>

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

<gadget id="calculator">6_000 / 2</gadget>
<output>3_000</output>
<result>3_000</result>

Choices:
A. 3,000
B. 2,700
C. 4,500
D. 5,400
E. 324,000

divide(multiply(add(35, 65), const_60), const_2)

Explanation: "together the two machines make 35 + 65 = 100 copies per minute . so , in half an hour they will make 100 * 30 = 3,000 copies . answer : a ."


Question: 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 4554 , how much was it in the beginning ?

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

<gadget id="calculator">90 / 100</gadget>
<output>9/10 = around 0.9</output>

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

<gadget id="calculator">80 / 100</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(9/10) * (4/5)</gadget>
<output>18/25 = around 0.72</output>

<gadget id="calculator">4_554 / (18/25)</gadget>
<output>6_325</output>

<gadget id="calculator">floor(6_325)</gadget>
<output>6_325</output>
<result>6_325</result>

Choices:
A. 7349
B. 6300
C. 6325
D. 6939
E. 2989

floor(divide(4554, multiply(divide(subtract(const_100, 10), const_100), divide(subtract(const_100, 20), const_100))))

Explanation: "x * ( 90 / 100 ) * ( 80 / 100 ) = 4554 x = 6325 answer : c"


Question: cost is expressed by the formula tb ^ 4 . if b is doubled , the new cost w is what percent of the original cost ?

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

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

Choices:
A. w = 200
B. w = 600
C. w = 800
D. w = 1600
E. w = 50

Explanation: "original cost w , c 1 = t 1 * b 1 ^ 4 new cost c 2 = t 2 * b 2 ^ 4 . . . . only b is doubled so t 2 = t 1 and b 2 = 2 b 1 c 2 = t 2 * ( 2 b 1 ) ^ 4 = 16 ( t 1 * b 1 ^ 4 ) = 16 c 1 16 times c 1 = > 1600 % of c 1 ans d = 1600"


Question: if a car went the first third of the distance at 80 kmh , the second third at 30 kmh , and the last third at 48 kmh , what was the average speed of the car for the entire trip ?

<gadget id="calculator">1 / 80</gadget>
<output>1/80 = around 0.0125</output>

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

<gadget id="calculator">(1/80) + (1/30)</gadget>
<output>11/240 = around 0.045833</output>

<gadget id="calculator">1 / 48</gadget>
<output>1/48 = around 0.020833</output>

<gadget id="calculator">(11/240) + (1/48)</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">3 / (1/15)</gadget>
<output>45</output>
<result>45</result>

Choices:
A. 36 kmh
B. 40 kmh
C. 42 kmh
D. 45 kmh
E. 50 kmh

divide(const_3, add(add(divide(const_1, 80), divide(const_1, 30)), divide(const_1, 48)))

Explanation: assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 30 and 48 ) so : 240 = 80 * t 1 = 3 hrs 240 = 30 * t 2 = 8 hrs 240 = 48 * t 3 = 5 hrs t = t 1 + t 2 + t 3 = 16 hrs d = rt ( 240 * 3 ) = r * 16 r = 45 answer : d


Question: a cement mixture is composed of 3 elements . by weight , 1 / 2 of the mixture is sand , 1 / 5 of the mixture is water , and the remaining 15 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?

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

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

<gadget id="calculator">(1/2) + (1/5)</gadget>
<output>7/10 = around 0.7</output>

<gadget id="calculator">1 - (7/10)</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">15 / (3/10)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 30
B. 40
C. 50
D. 60
E. 80

divide(15, subtract(1, add(divide(1, 2), divide(1, 5))))

Explanation: "let the total weight be x . sand content = ( 1 / 2 ) x water content = ( 1 / 5 ) x gravel = x - ( 1 / 2 ) x - ( 1 / 5 ) x = ( 3 / 10 ) x = 15 x = 50 then answer will be c = 50"


Question: reema took a loan of rs 900 with simple interest for as many years as the rate of interest . if she paid rs . 729 as interest at the end of the loan period , what was the rate of interest .

<gadget id="calculator">900 / 100</gadget>
<output>9</output>

<gadget id="calculator">729 / 9</gadget>
<output>81</output>

<gadget id="calculator">81 ** (1/2)</gadget>
<output>9</output>
<result>9</result>

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

Explanation: "explanation : let rate = r % then time = r years . = > 900 ∗ r ∗ r / 100 = 729 = > r 2 = 81 = > r = 9 % option e"


Question: a student committee on academic integrity has 132 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?

<gadget id="calculator">4 * 132</gadget>
<output>528</output>

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

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

<gadget id="calculator">528 + 1</gadget>
<output>529</output>

<gadget id="calculator">529 ** (1/2)</gadget>
<output>23</output>

<gadget id="calculator">1 + 23</gadget>
<output>24</output>

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

Choices:
A. 7
B. 8
C. 9
D. 10
E. 12

divide(add(const_1, sqrt(add(multiply(const_4, 132), power(negate(const_1), const_2)))), const_2)

Explanation: "xc 1 * ( x - 1 ) c 1 = 132 x ^ 2 - x - 132 = 0 ( x - 12 ) ( x + 11 ) = 0 x = 12 , - 11 - 11 ca n ' t possible . hence 12 should be the answer e"


Question: a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?

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

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

<gadget id="calculator">(1/3) - (1/5)</gadget>
<output>2/15 = around 0.133333</output>

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

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

<gadget id="calculator">(1/5) - (1/8)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(2/15) / (3/40)</gadget>
<output>16/9 = around 1.777778</output>
<result>16/9 = around 1.777778</result>

Choices:
A. 1 : 4
B. 16 : 9
C. 2 : 3
D. 1 : 2
E. 2 : 5

divide(subtract(divide(const_1, 3), divide(const_1, 5)), subtract(divide(const_1, 5), divide(const_1, multiply(const_2, const_4))))

Explanation: the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 5 = 2 / 15 = 4 / 30 dollars . the selling price of a mango from the second stack = 1 / 8 dollars - - > the loss from one mango = 1 / 5 - 1 / 8 = 3 / 40 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 4 / 30 * 40 / 3 = 16 / 9 b


Question: if an investor puts $ 800 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?

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

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

<gadget id="calculator">1 + (1/20)</gadget>
<output>21/20 = around 1.05</output>

<gadget id="calculator">(21/20) ** 2</gadget>
<output>441/400 = around 1.1025</output>

<gadget id="calculator">800 * (441/400)</gadget>
<output>882</output>
<result>882</result>

Choices:
A. $ 878
B. $ 880
C. $ 882
D. $ 884
E. $ 886

multiply(800, power(add(const_1, divide(divide(10, const_2), const_100)), const_2))

Explanation: "1.05 * 1.05 * 800 = $ 882 the answer is c ."


Question: in an election between two candidates , one got 55 % of the total valid votes . 20 % of the votes were invalid . if the total number of votes was 7500 , what was the number of valid votes that the other candidate got ?

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

<gadget id="calculator">1 - (1/5)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">55 / 100</gadget>
<output>11/20 = around 0.55</output>

<gadget id="calculator">1 - (11/20)</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">(4/5) * (9/20)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(9/25) * 7_500</gadget>
<output>2_700</output>
<result>2_700</result>

Choices:
A. 2800
B. 2700
C. 2100
D. 2500
E. 3000

multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(55, const_100))), 7500)

Explanation: "total no of votes = 7500 20 % invalid = > 80 % valid tot valid votes = 7500 * 80 / 100 = > valid for 2 nd candidate got 7500 * 80 / 100 * 45 / 100 = 2700 answer b"


Question: indu gave bindu rs . 625 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?

<gadget id="calculator">4 / 100</gadget>
<output>1/25 = around 0.04</output>

<gadget id="calculator">1 + (1/25)</gadget>
<output>26/25 = around 1.04</output>

<gadget id="calculator">(26/25) ** 2</gadget>
<output>676/625 = around 1.0816</output>

<gadget id="calculator">625 * (676/625)</gadget>
<output>676</output>

<gadget id="calculator">676 - 625</gadget>
<output>51</output>

<gadget id="calculator">625 * (1/25)</gadget>
<output>25</output>

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

<gadget id="calculator">51 - 50</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 1
B. 2
C. 7
D. 4
E. 9

subtract(subtract(multiply(625, power(add(const_1, divide(4, const_100)), 2)), 625), multiply(multiply(625, divide(4, const_100)), 2))

Explanation: "625 = d ( 100 / 4 ) 2 d = 1 answer : a"


Question: a 1400 m long train crosses a tree in 100 sec , how much time will it take to pass a platform 700 m long ?

<gadget id="calculator">1_400 + 700</gadget>
<output>2_100</output>

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

<gadget id="calculator">2_100 / 14</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 288
B. 190
C. 150
D. 188
E. 12

Explanation: "l = s * t s = 1400 / 100 s = 14 m / sec . total length ( d ) = 2100 m t = d / s t = 2100 / 14 t = 150 sec answer : c"


Question: during the last 4 years , a large truck company purchased diesel at rates of $ 1.2 , $ 1.3 , $ 1.8 and $ 2.1 per gallon . what was the mean cost of diesel over the 4 - year period if the company spends the same amount of dollars on diesel each year ?

<gadget id="calculator">1.2 + 1.3</gadget>
<output>2.5</output>

<gadget id="calculator">1.8 + 2.1</gadget>
<output>3.9</output>

<gadget id="calculator">2.5 + 3.9</gadget>
<output>6.4</output>

<gadget id="calculator">6.4 / 4</gadget>
<output>1.6</output>

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

<gadget id="calculator">8 / 100</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">1.6 - (2/25)</gadget>
<output>1.52</output>
<result>1.52</result>

Choices:
A. $ 2.5
B. $ 2.55
C. $ 1.52
D. $ 3.25
E. $ 3.0

Explanation: finding the harmonic mean here . hm = 4 / ( 1 / 12 + 1 / 13 + 1 / 18 + 1 / 21 ) = 15.18 c


Question: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 5200 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?

<gadget id="calculator">5_000 + 1_500</gadget>
<output>6_500</output>

<gadget id="calculator">6_500 + 4_500</gadget>
<output>11_000</output>

<gadget id="calculator">11_000 + 2_500</gadget>
<output>13_500</output>

<gadget id="calculator">13_500 + 2_000</gadget>
<output>15_500</output>

<gadget id="calculator">15_500 + 5_200</gadget>
<output>20_700</output>

<gadget id="calculator">20_700 * 100</gadget>
<output>2_070_000</output>

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

<gadget id="calculator">2_070_000 / 90</gadget>
<output>23_000</output>

<gadget id="calculator">23_000 - 20_700</gadget>
<output>2_300</output>
<result>2_300</result>

Choices:
A. 2160
B. 2350
C. 2000
D. 2300
E. none of these

Explanation: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 5200 = 20700 exp in % = 100 - 10 = 90 % , 20700 = 90 % saving = 10 % = 20700 x 10 / 90 = rs . 2300 answer : d"


Question: shekar scored 76 , 65 , 82 , 47 and 85 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?

<gadget id="calculator">76 + 65</gadget>
<output>141</output>

<gadget id="calculator">141 + 82</gadget>
<output>223</output>

<gadget id="calculator">223 + 47</gadget>
<output>270</output>

<gadget id="calculator">270 + 85</gadget>
<output>355</output>

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

<gadget id="calculator">355 / 5</gadget>
<output>71</output>
<result>71</result>

Choices:
A. 71
B. 69
C. 75
D. 85
E. 90

Explanation: "explanation : average = ( 76 + 65 + 82 + 47 + 85 ) / 5 = 355 / 5 = 71 hence average = 71 answer : a"


Question: how many multiples of 4 are there between 12 and 104 , inclusive ?

<gadget id="calculator">104 - 12</gadget>
<output>92</output>

<gadget id="calculator">92 / 4</gadget>
<output>23</output>

<gadget id="calculator">23 + 1</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 21
B. 22
C. 23
D. 24
E. 25

add(divide(subtract(104, 12), 4), const_1)

Explanation: "the multiples of 4 are from 4 * 3 up to 4 * 26 . 26 - 3 + 1 = 24 . the answer is d ."


Question: how many kg of rice at rs . 6.60 per kg . be mixed with 56 kg of rice at rs . 9.60 per kg to get a mixture worth rs . 8.20 per kg

<gadget id="calculator">9.6 * 56</gadget>
<output>537.6</output>

<gadget id="calculator">56 * 8.2</gadget>
<output>459.2</output>

<gadget id="calculator">537.6 - 459.2</gadget>
<output>78.4</output>

<gadget id="calculator">8.2 - 6.6</gadget>
<output>1.6</output>

<gadget id="calculator">78.4 / 1.6</gadget>
<output>49</output>
<result>49</result>

Choices:
A. 56 kg
B. 52 kg
C. 44 kg
D. 49 kg
E. none of these

divide(subtract(multiply(9.6, 56), multiply(56, 8.2)), subtract(8.2, 6.6))

Explanation: explanation : by the rule of alligation , we have cost of 1 kg of 1 st kind rice cost of 1 kg of 2 nd kind rice 6.6 9.6 price of 1 kg of the mixture 8.2 9.6 - 8.2 = 1.4 8.2 - 6.6 = 1.6 quantity of 1 st kind rice : quantity of 2 nd kind rice = 1.4 : 1.6 = 7 : 8 quantity of 1 st kind rice : 56 = 7 : 8 = > quantity of 1 st kind rice = 56 × 78 = 49 answer : option d


Question: a box measuring 36 inches long by 45 inches wide by 18 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?

<gadget id="calculator">36 * 45</gadget>
<output>1_620</output>

<gadget id="calculator">1_620 * 18</gadget>
<output>29_160</output>

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

<gadget id="calculator">9 ** 3</gadget>
<output>729</output>

<gadget id="calculator">29_160 / 729</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 32
B. 34
C. 38
D. 40
E. 42

divide(multiply(multiply(36, 45), 18), volume_cube(divide(18, const_2)))

Explanation: "least number of cubes will be required when the cubes that could fit in are biggest . 9 is the biggest number that could divide all three , 36 , 45 and 18 . thus side of cube must be 9 , and total number of cubes = 36 / 9 * 45 / 9 * 18 / 9 = 40 ans d ."


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

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

<gadget id="calculator">(4/5) ** 2</gadget>
<output>16/25 = around 0.64</output>

<gadget id="calculator">10 / 8</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(16/25) * (5/4)</gadget>
<output>4/5 = around 0.8</output>

<gadget id="calculator">(4/5) * 100</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 90 %
B. 50 %
C. 60 %
D. 70 %
E. 80 %

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

Explanation: "circumference of a = 2 ( pie ) r = 8 so r = 4 / pie volume = pie ( 4 / pie ) ^ 2 * 10 = 160 / pie circumference of b = 2 ( pie ) r = 10 so r = 5 / pie volume = pie ( 5 / pie ) ^ 2 * 8 = 200 / pie so ratio of capacities = 160 / 200 = 0.8 so capacity of a will be 80 % of the capacity of b answer : e"


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 $ 6.50 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) * 6.5</gadget>
<output>2.6</output>
<result>2.6</result>

Choices:
A. $ 2.6
B. $ 2.40
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))), 6.5)

Explanation: manager wages per hour = $ 6.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 6.50 ) = = > $ 3.25 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.25 = ( 20 * ( $ 3.25 ) ) / 100 - - > ( $ 65 ) / 100 - - > $ 0.65 therefore , chef wages per hour = $ 3.25 + $ 0.65 = = > $ 3.9 difference of wages between manager and chef = $ 6.50 - $ 3.9 = = > $ 2.6 answer : a


Question: the cost of paint is 60 per kilograme . a kilogram paint covers 20 square feet . how much will it cost to paint the outside of a cube having each side 10 feet ?

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

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

<gadget id="calculator">6 * 100</gadget>
<output>600</output>

<gadget id="calculator">600 / 20</gadget>
<output>30</output>

<gadget id="calculator">30 * 60</gadget>
<output>1_800</output>
<result>1_800</result>

Choices:
A. 3000
B. 900
C. 1800
D. 360
E. none of these

multiply(divide(multiply(multiply(const_2, const_3), power(10, const_2)), 20), 60)

Explanation: area of cube = 6 × ( side ) 2 = 6 × 10 × 10 = 600 square feet . cost to paint outside of the cube = 600 ⁄ 20 × 60 = 1800 answer c


Question: the original price of a suit is $ 160 . the price increased 25 % , and after this increase , the store published a 25 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 25 % off the increased price , how much did these consumers pay for the suit ?

<gadget id="calculator">160 * 25</gadget>
<output>4_000</output>

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

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

<gadget id="calculator">200 * 25</gadget>
<output>5_000</output>

<gadget id="calculator">5_000 / 100</gadget>
<output>50</output>

<gadget id="calculator">200 - 50</gadget>
<output>150</output>
<result>150</result>

Choices:
A. $ 140
B. $ 145
C. $ 150
D. $ 155
E. $ 160

subtract(add(160, divide(multiply(160, 25), const_100)), divide(multiply(add(160, divide(multiply(160, 25), const_100)), 25), const_100))

Explanation: 0.75 * ( 1.25 * 160 ) = $ 150 the answer is c .


Question: in a throw of dice what is the probability of getting number greater than 5

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

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

Choices:
A. 1 / 7
B. 1 / 6
C. 1 / 11
D. 1 / 13
E. 2 / 9

Explanation: "number greater than 5 is 6 , so only 1 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 1 / 6 b )"


Question: of 60 children , 30 are happy , 10 are sad , and 20 are neither happy nor sad . there are 19 boys and 41 girls . if there are 6 happy boys and 4 sad girls , how many boys are neither happy nor sad ?

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

<gadget id="calculator">19 - 6</gadget>
<output>13</output>

<gadget id="calculator">13 - 6</gadget>
<output>7</output>
<result>7</result>

Choices:
A. 2
B. 7
C. 6
D. 8
E. 10

subtract(subtract(19, subtract(10, 4)), 6)

Explanation: "venn diagrams are useful for multiple values of a single variable e . g . state of mind - happy / sad / neither . when you have two or more variables such as here where you have gender - boy / girl too , it becomes unwieldy . in this case , either use the table or logic . table method is shown above ; here is how you will use logic : there are 6 happy boys . there are 4 sad girls but total 10 sad children . so rest 6 sad children must be sad boys . we have 6 happy boys and 6 sad boys . total we have 19 boys . so 19 - 6 - 6 = 7 boys must be neither happy nor sad . answer ( b )"


Question: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 64 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )

<gadget id="calculator">64 * 2</gadget>
<output>128</output>

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

<gadget id="calculator">64 * (3/5)</gadget>
<output>192/5 = around 38.4</output>

<gadget id="calculator">128 - (192/5)</gadget>
<output>448/5 = around 89.6</output>

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

<gadget id="calculator">(448/5) / (8/5)</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 48
B. 52
C. 54
D. 58
E. 56

divide(subtract(multiply(64, 2), multiply(64, divide(60, const_100))), add(divide(60, const_100), 1))

Explanation: "let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 64 or 1 / 7 t + 1 t = 64 therefore t = 64 * 7 / 8 = 56 e"


Question: if the radius of a circle that centers at the origin is 5 , how many points q on the circle have integer coordinates ?

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

<gadget id="calculator">5 + 4</gadget>
<output>9</output>

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

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

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

Choices:
A. 4
B. 8
C. 12
D. 15
E. 20

subtract(subtract(multiply(5, 5), add(5, const_4)), power(const_2, const_2))

Explanation: "i understand this might not be required but i used the equation of a circle . since the origin is at 0 , x ^ 2 + y ^ 2 = 5 ^ 2 . x , y could be + / - ( 0,5 or 5,0 ) - 4 possibilities . x , y could be + / - ( 3,4 or 4,3 ) - 8 possibilities . ans : q = c"


Question: the ratio of the radius of two circles is 1 : 5 , and then the ratio of their areas is ?

<gadget id="calculator">pi * (1 ** 2)</gadget>
<output>pi = around 3.141593</output>

<gadget id="calculator">pi * (5 ** 2)</gadget>
<output>25*pi = around 78.539816</output>

<gadget id="calculator">pi / (25*pi)</gadget>
<output>1/25 = around 0.04</output>
<result>1/25 = around 0.04</result>

Choices:
A. 1 : 7
B. 2 : 9
C. 1 : 25
D. 3 : 7
E. 3 : 4

Explanation: "r 1 : r 2 = 1 : 5 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 1 : 25 answer : c"


Question: the average of 11 numbers is 60 . out of 11 numbers the average of first 6 no . is 98 , and last 6 numbers is 65 then find 6 th number ?

<gadget id="calculator">6 * 98</gadget>
<output>588</output>

<gadget id="calculator">6 * 65</gadget>
<output>390</output>

<gadget id="calculator">588 + 390</gadget>
<output>978</output>

<gadget id="calculator">11 * 60</gadget>
<output>660</output>

<gadget id="calculator">978 - 660</gadget>
<output>318</output>
<result>318</result>

Choices:
A. 318
B. 65
C. 58
D. 62
E. 48

subtract(add(multiply(6, 98), multiply(6, 65)), multiply(11, 60))

Explanation: 6 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 98 + 6 * 65 - 11 * 60 = 318 answer is a


Question: a man bought 40 shares of rs . 60 at 8 discount , the rate of dividend being 1212 % the rate of interest obtained is

<gadget id="calculator">40 * 60</gadget>
<output>2_400</output>

<gadget id="calculator">1_212 / 100</gadget>
<output>303/25 = around 12.12</output>

<gadget id="calculator">2_400 * (303/25)</gadget>
<output>29_088</output>

<gadget id="calculator">60 - 8</gadget>
<output>52</output>

<gadget id="calculator">40 * 52</gadget>
<output>2_080</output>

<gadget id="calculator">29_088 / 2_080</gadget>
<output>909/65 = around 13.984615</output>
<result>909/65 = around 13.984615</result>

Choices:
A. 13.64 %
B. 15.5 %
C. 14 %
D. 14.42 %
E. 14.95 %

divide(multiply(multiply(40, 60), divide(1212, const_100)), multiply(40, subtract(60, 8)))

Explanation: "explanation : face value of a share = rs . 60 he bought each share at rs . 60 - rs . 8 = rs . 52 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 60 × 25 / 2 × 100 = rs . 7.5 total dividend = ( 40 × 7.5 ) ie , he got a dividend of ( 40 × 7.5 ) for an investment of rs . ( 40 × 52 ) interest obtained = 40 × 7.5 × 100 / 40 × 52 = 14.42 % answer : option d"


Question: the area of a triangle is 615 m 2 . if one of its sides is 123 metre , find the length of the perpendicular dropped on that side from opposite vertex .

<gadget id="calculator">615 * 2</gadget>
<output>1_230</output>

<gadget id="calculator">1_230 / 123</gadget>
<output>10</output>
<result>10</result>

Choices:
A. 15 metres
B. 12 metres
C. 10 metres
D. 9 metres
E. none of these

Explanation: in a triangle , area = 1 ⁄ 2 × length of perpendicular × base or 615 = 1 ⁄ 2 × length of perpendicular × 123 ∴ length of perpendicular = 615 × 2 / 123 = 10 m answer c


Question: in an election between the two candidates , the candidates who gets 60 % of votes polled is wined by 280 votes majority . what is the total number of votes polled ?

<gadget id="calculator">100 * 280</gadget>
<output>28_000</output>

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

<gadget id="calculator">60 - 40</gadget>
<output>20</output>

<gadget id="calculator">28_000 / 20</gadget>
<output>1_400</output>
<result>1_400</result>

Choices:
A. 1400
B. 1500
C. 1600
D. 1700
E. 1800

divide(multiply(const_100, 280), subtract(60, subtract(const_100, 60)))

Explanation: note : majority ( 20 % ) = difference in votes polled to win ( 60 % ) & defeated candidates ( 40 % ) 20 % = 60 % - 40 % 20 % - - - - - > 280 ( 20 × 14 = 280 ) 100 % - - - - - > 1400 ( 100 × 14 = 1400 ) a


Question: what is the remainder if 7 ^ 12 is divided by 100 ?

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

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

<gadget id="calculator">50 - 49</gadget>
<output>1</output>
<result>1</result>

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

subtract(divide(100, const_2), multiply(7, 7))

Explanation: 7 ^ 16 can be written as ( 7 ^ 4 ) ^ 3 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 3 by 100 , the reminder is 1 ^ 3 = 1 answer : a


Question: calculate the average of all the numbers between 10 and 86 which are divisible by 9 .

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

<gadget id="calculator">floor(10/9)</gadget>
<output>1</output>

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

<gadget id="calculator">86 / 9</gadget>
<output>86/9 = around 9.555556</output>

<gadget id="calculator">floor(86/9)</gadget>
<output>9</output>

<gadget id="calculator">2 + 9</gadget>
<output>11</output>

<gadget id="calculator">11 / 2</gadget>
<output>11/2 = around 5.5</output>

<gadget id="calculator">(11/2) * 9</gadget>
<output>99/2 = around 49.5</output>
<result>99/2 = around 49.5</result>

Choices:
A. 49.5
B. 41.5
C. 45.5
D. 40.5
E. 47.5

multiply(divide(add(add(floor(divide(10, 9)), const_1), floor(divide(86, 9))), const_2), 9)

Explanation: "explanation : numbers divisible by 9 are 18,27 , 36,45 , 54,63 , 72,81 , average = ( 18 + 27 + 36 + 45 + 54 + 63 + 72 + 81 , ) / 8 = 396 / 8 = 49.5 answer : a"


Question: what is the length of a bridge ( in meters ) , which a train 156 meters long and travelling at 45 km / h can cross in 30 seconds ?

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

<gadget id="calculator">45 * (5/18)</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 30</gadget>
<output>375</output>

<gadget id="calculator">375 - 156</gadget>
<output>219</output>
<result>219</result>

Choices:
A. 203
B. 211
C. 219
D. 227
E. 235

subtract(multiply(multiply(45, const_0_2778), 30), 156)

Explanation: speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 156 = 219 meters the answer is c .


Question: the average of first 17 even numbers is ?

<gadget id="calculator">17 + 1</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 10
B. 11
C. 18
D. 20
E. 24

Explanation: "sum of 17 even numbers = 17 * 18 = 306 average = 306 / 17 = 18 answer : c"


Question: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 11 multiples of 14 , how many multiples of 7 are there in q ?

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

<gadget id="calculator">22 - 1</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 19
B. 20
C. 21
D. 22
E. 23

Explanation: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 11 + 10 = 21 . the answer is c ."


Question: the ratio between the presents of the a and b is 2 : 3 . if b is 5 years older than a , what will be the ratio of the ages of a and b after 5 years ?

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

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

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

<gadget id="calculator">15 + 5</gadget>
<output>20</output>

<gadget id="calculator">15 / 20</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

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

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

Explanation: "let a and b ages will be 2 x and 3 x 3 x - 2 x = 5 x = 5 required ratio = 2 x + 5 : 3 x + 5 = 15 : 20 = 3 : 4 answer is a"


Question: if x * y = xy – 2 ( x + y ) for all integers x and y , then 1 * ( – 3 ) =

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

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

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

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

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

<gadget id="calculator">4 + (-3)</gadget>
<output>1</output>
<result>1</result>

Choices:
A. – 16
B. – 11
C. – 4
D. 4
E. 1

add(negate(multiply(add(negate(3), 1), 2)), multiply(negate(3), 1))

Explanation: "1 * ( - 3 ) = 1 * ( - 3 ) - 2 ( 1 + ( - 3 ) ) = - 3 + 4 = 1 option ( e )"


Question: on increasing the price of t . v . sets by 40 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?

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

<gadget id="calculator">140 * 20</gadget>
<output>2_800</output>

<gadget id="calculator">2_800 / 100</gadget>
<output>28</output>

<gadget id="calculator">28 + 100</gadget>
<output>128</output>

<gadget id="calculator">140 - 128</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 4
B. 5
C. 56
D. 12
E. 7

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

Explanation: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 140 × 80 ) = rs . 11200 increase % = 1200 / 10000 × 100 = 12 % answer : d"


Question: a 10 % stock yields 8 % . the market value of the stock is :

<gadget id="calculator">100 / 8</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">(25/2) * 10</gadget>
<output>125</output>
<result>125</result>

Choices:
A. rs . 72
B. rs . 125
C. rs . 112.50
D. rs . 116.50
E. none of these

Explanation: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 10 , investment = rs . ( 100 / 8 x 10 ) = rs . 125 ∴ market value of rs . 100 stock = rs . 125 answer b"


Question: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 300 . find the sum ?

<gadget id="calculator">18 - 12</gadget>
<output>6</output>

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

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

<gadget id="calculator">300 / (3/25)</gadget>
<output>2_500</output>
<result>2_500</result>

Choices:
A. 7000
B. 2500
C. 2778
D. 2800
E. 2791

divide(300, divide(multiply(subtract(18, 12), const_2), const_100))

Explanation: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 300 = > 36 x / 100 - 24 x / 100 = 300 = > 12 x / 100 = 300 = > x = 2500 . answer : b"


Question: at a monthly meeting , 3 / 5 of the attendees were males and 7 / 8 of the male attendees arrived on time . if 4 / 5 of the female attendees arrived on time , what fraction of the attendees at the monthly meeting did not arrive on time ?

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

<gadget id="calculator">1 - (4/5)</gadget>
<output>1/5 = around 0.2</output>

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

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

<gadget id="calculator">(1/5) * (2/5)</gadget>
<output>2/25 = around 0.08</output>

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>

<gadget id="calculator">1 - (7/8)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/8) * (3/5)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(2/25) + (3/40)</gadget>
<output>31/200 = around 0.155</output>
<result>31/200 = around 0.155</result>

Choices:
A. 47 / 200
B. 31 / 200
C. 17 / 100
D. 11 / 100
E. 7 / 50

add(multiply(subtract(const_1, divide(4, 5)), subtract(const_1, divide(3, 5))), multiply(subtract(const_1, divide(7, 8)), divide(3, 5)))

Explanation: "males who did not arrive on time are 1 / 8 * 3 / 5 = 3 / 40 of the attendees . females who did not arrive on time are 1 / 5 * 2 / 5 = 2 / 25 of the attendees . the fraction of all attendees who did not arrive on time is 3 / 40 + 2 / 25 = 31 / 200 the answer is b ."


Question: how many quarters are equal to 4 dollars ?

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

Choices:
A. 16
B. 8
C. 12
D. 9
E. 7

Explanation: "4 * 4 = 16 quarters answer : a"


Question: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 33 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?

<gadget id="calculator">33 / 2</gadget>
<output>33/2 = around 16.5</output>
<result>33/2 = around 16.5</result>

Choices:
A. 16.5 minutes
B. 33 minutes
C. 49.5 minutes
D. 66 minutes
E. 99 minutes

Explanation: "danny ' s time is 33 minutes . the time to reach halfway is 16.5 minutes . steve ' s time is 66 minutes . the time to reach halfway is 33 minutes . the time difference is 33 - 16.5 = 16.5 minutes the answer is a ."


Question: a fair 2 sided coin is flipped 4 times . what is the probability that tails will be the result at least twice , but not more than 4 times ?

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

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">(1/16) * 4</gadget>
<output>1/4 = around 0.25</output>

<gadget id="calculator">(1/16) + (1/16)</gadget>
<output>1/8 = around 0.125</output>

<gadget id="calculator">(1/4) + (1/8)</gadget>
<output>3/8 = around 0.375</output>

<gadget id="calculator">1 - (3/8)</gadget>
<output>5/8 = around 0.625</output>
<result>5/8 = around 0.625</result>

Choices:
A. 1 / 8
B. 2 / 3
C. 5 / 8
D. 4 / 7
E. 3 / 7

subtract(const_1, add(multiply(inverse(power(2, 4)), 4), add(inverse(power(2, 4)), inverse(power(2, 4)))))

Explanation: "at least twice , but not more than 4 timesmeans exactly 2 times , 3 times , 4 times the probability of getting exactly k results out of n flips is nck / 2 ^ n 4 c 2 / 2 ^ 4 + 4 c 3 / 2 ^ 4 = 10 / 16 = 5 / 8 option : c"


Question: find the sum of divisors of 544 which are perfect squares .

<gadget id="calculator">544 / 2</gadget>
<output>272</output>

<gadget id="calculator">272 / 2</gadget>
<output>136</output>

<gadget id="calculator">136 / 2</gadget>
<output>68</output>

<gadget id="calculator">68 / 2</gadget>
<output>34</output>

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

<gadget id="calculator">544 / 17</gadget>
<output>32</output>

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

<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>

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

<gadget id="calculator">16 + 5</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 32
B. 64
C. 42
D. 21
E. none of these

add(divide(divide(544, divide(divide(divide(divide(divide(544, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(544, divide(divide(divide(divide(divide(544, const_2), const_2), const_2), const_2), const_2)), const_2))))

Explanation: "544 = 25 + 171 = ( 2 ) 0 + ( 2 ) 1 + ( 2 ) 2 + ( 2 ) 3 + ( 2 ) 4 + ( 2 ) 5 x ( 17 ) 0 + ( 17 ) 1 . here 20 = 1 = 11 a perfect square , 22 and 24 = 16 = 44 are perfect squares , hence , 1 + 4 + 16 = 21 . correct answer is : d"


Question: a glass was filled with 10 ounces of water , and 0.03 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?

<gadget id="calculator">0.03 * 20</gadget>
<output>0.6</output>

<gadget id="calculator">0.6 / 10</gadget>
<output>0.06</output>

<gadget id="calculator">0.06 * 100</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 0.006 %
B. 0.06 %
C. 0.6 %
D. 6 %
E. 60 %

multiply(divide(multiply(0.03, 20), 10), const_100)

Explanation: "we are given that 0.03 ounces of water evaporated each day . furthermore , we know that this process happened over a 20 - day period . to calculate the total amount of water that evaporated during this time frame we need to multiply 0.01 by 20 . this gives us : 0.03 x 20 = 0.6 ounces finally , we are asked for “ what percent ” of the original amount of water evaporated during this period . to determine this percentage , we have to make sure we translate the expression correctly . we can translate it to : ( amount evaporated / original amount ) x 100 % ( 0.6 / 10 ) x 100 % ( 6 / 100 ) x 100 % = 6 % answer d"


Question: a cistern is normally filled in 6 hours but takes two hours longer to fill because of a leak in its bottom . if the cistern is full , the leak will empty it in ?

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

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

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

<gadget id="calculator">(1/6) - (1/8)</gadget>
<output>1/24 = around 0.041667</output>

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

Choices:
A. 33
B. 88
C. 24
D. 99
E. 11

inverse(subtract(divide(const_1, 6), divide(const_1, add(6, const_2))))

Explanation: 1 / 6 - 1 / x = 1 / 8 x = 24 answer : c


Question: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 50 percent .

<gadget id="calculator">50 / 20</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">(5/2) * 60</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 145
B. 150
C. 175
D. 160
E. 130

Explanation: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 50 percent 150 min . answer : b


Question: the diagonals of a rhombus are 10 cm and 12 cm . find its area ?

<gadget id="calculator">(10 * 12) / 2</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 158
B. 60
C. 150
D. 123
E. 117

Explanation: "1 / 2 * 10 * 12 = 60 answer : b"


Question: a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm 3 , then the weight of the pipe is :

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

<gadget id="calculator">pi * (4 ** 2) * 21</gadget>
<output>336*pi = around 1_055.575132</output>

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

<gadget id="calculator">pi * (3 ** 2) * 21</gadget>
<output>189*pi = around 593.761012</output>

<gadget id="calculator">(336*pi) - (189*pi)</gadget>
<output>147*pi = around 461.81412</output>

<gadget id="calculator">(147*pi) * 8</gadget>
<output>1176*pi = around 3_694.512961</output>

<gadget id="calculator">(1176*pi) / 1_000</gadget>
<output>147*pi/125 = around 3.694513</output>
<result>147*pi/125 = around 3.694513</result>

Choices:
A. 3.6 kg
B. 3.696 kg
C. 36 kg
D. 36.9 kg
E. none

divide(multiply(subtract(volume_cylinder(divide(8, const_2), 21), volume_cylinder(subtract(divide(8, const_2), 1), 21)), 8), const_1000)

Explanation: "solution external radius = 4 cm , internal radius = 3 cm . volume of iron = ( 22 / 7 × ( 42 ) - ( 32 ) × 21 ) cm 3 = ( 22 / 7 × 7 × 1 × 21 ) cm 3 = 462 cm 3 . weight of iron = ( 462 x 8 ) gm = 3696 gm = 3.696 kg . answer b"