Question: in the forestside summer camp there are 50 children . 90 % of the children are boys and the rest are girls . the camp administrator decided to make the number of girls only 5 % of the total number of children in the camp . how many more boys must she bring to make that happen ?

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

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

<gadget id="calculator">50 * (1/10)</gadget>
<output>5</output>

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

<gadget id="calculator">5 / (1/20)</gadget>
<output>100</output>

<gadget id="calculator">100 - 50</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50 .
B. 45 .
C. 40 .
D. 30 .
E. 25 .

subtract(divide(multiply(50, subtract(const_1, divide(90, const_100))), divide(5, const_100)), 50)

Explanation: given there are 50 students in the forestside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .


Question: on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?

<gadget id="calculator">109 / 9</gadget>
<output>109/9 = around 12.111111</output>

<gadget id="calculator">floor(109/9)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 10
B. 12
C. 14
D. 16
E. 18

Explanation: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 b )"


Question: if 0.75 : x : : 10 : 8 , then x is equal to :

<gadget id="calculator">0.75 * 8</gadget>
<output>6</output>

<gadget id="calculator">6 / 10</gadget>
<output>3/5 = around 0.6</output>
<result>3/5 = around 0.6</result>

Choices:
A. 0.6
B. 0.8
C. 0.85
D. 0.5
E. none

Explanation: "( x * 10 ) = ( 0.75 * 8 ) x = 6 / 10 x = 0.6 answer = a"


Question: there are 2 sections a and b in a class , consisting of 36 and 44 students respectively . if the average weight of section a is 40 kg and that of section b is 35 kg , find the average of the whole class ?

<gadget id="calculator">36 * 40</gadget>
<output>1_440</output>

<gadget id="calculator">44 * 35</gadget>
<output>1_540</output>

<gadget id="calculator">1_440 + 1_540</gadget>
<output>2_980</output>

<gadget id="calculator">36 + 44</gadget>
<output>80</output>

<gadget id="calculator">2_980 / 80</gadget>
<output>149/4 = around 37.25</output>
<result>149/4 = around 37.25</result>

Choices:
A. 35.29 kg
B. 37.25 kg
C. 42.45 kg
D. 55.12 kg
E. 29.78 kg

divide(add(multiply(36, 40), multiply(44, 35)), add(36, 44))

Explanation: total weight of 36 + 44 students = 36 * 44 + 44 * 35 = 2980 average weight of the class is = 2980 / 80 = 37.25 kg answer is b


Question: a box contains 100 pairs of shoes ( 200 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

<gadget id="calculator">200 - 1</gadget>
<output>199</output>

<gadget id="calculator">1 / 199</gadget>
<output>1/199 = around 0.005025</output>
<result>1/199 = around 0.005025</result>

Choices:
A. 1 / 190
B. 1 / 20
C. 1 / 199
D. 1 / 10
E. 1 / 9

Explanation: "the problem with your solution is that we do n ' t choose 1 shoe from 200 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 199 ( as after taking one at random there are 199 shoes left and only one is the pair of the first one ) = 1 / 199 answer : c ."


Question: the nasdaq index has decreased by 70 % since year 2000 . how much should the index increase in order to gain the same value as in year 2000 ?

<gadget id="calculator">70 / 100</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">(7/10) / (3/10)</gadget>
<output>7/3 = around 2.333333</output>

<gadget id="calculator">(7/3) * 100</gadget>
<output>700/3 = around 233.333333</output>
<result>700/3 = around 233.333333</result>

Choices:
A. 400 %
B. 80 %
C. 233 %
D. 60 %
E. none of the above

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

Explanation: let x be the index in the year 2000 . after the decrease it becomes 0.3 x now for 0.3 x to reach 1 x it has to raise by 0.7 x . the increase needs to be 0.7 x / 0.3 x * 100 = 233.3 % answer c


Question: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 52 , what is the compound interest on the same sum at the rate and for the same time ?

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

<gadget id="calculator">(1/20) * 2</gadget>
<output>1/10 = around 0.1</output>

<gadget id="calculator">52 / (1/10)</gadget>
<output>520</output>

<gadget id="calculator">520 * 5</gadget>
<output>2_600</output>

<gadget id="calculator">2_600 / 100</gadget>
<output>26</output>

<gadget id="calculator">26 + 520</gadget>
<output>546</output>

<gadget id="calculator">546 * 5</gadget>
<output>2_730</output>

<gadget id="calculator">2_730 / 100</gadget>
<output>273/10 = around 27.3</output>

<gadget id="calculator">546 + (273/10)</gadget>
<output>5_733/10 = around 573.3</output>

<gadget id="calculator">(5_733/10) - 520</gadget>
<output>533/10 = around 53.3</output>
<result>533/10 = around 53.3</result>

Choices:
A. s . 53.30
B. s . 53.22
C. s . 51.219
D. s . 53.18
E. s . 51.10

subtract(add(add(divide(multiply(divide(52, multiply(divide(5, const_100), 2)), 5), const_100), divide(52, multiply(divide(5, const_100), 2))), divide(multiply(add(divide(multiply(divide(52, multiply(divide(5, const_100), 2)), 5), const_100), divide(52, multiply(divide(5, const_100), 2))), 5), const_100)), divide(52, multiply(divide(5, const_100), 2)))

Explanation: explanation : sum = ( 52 * 100 ) / ( 2 * 5 ) = rs . 520 amount = [ 520 * ( 1 + 5 / 100 ) 2 ] = rs . 573.3 c . i . = ( 573.3 - 520 ) = rs . 53.30 . answer : a


Question: 29 persons can repair a road in 16 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?

<gadget id="calculator">29 * 16</gadget>
<output>464</output>

<gadget id="calculator">464 * 5</gadget>
<output>2_320</output>

<gadget id="calculator">30 * 6</gadget>
<output>180</output>

<gadget id="calculator">2_320 / 180</gadget>
<output>116/9 = around 12.888889</output>
<result>116/9 = around 12.888889</result>

Choices:
A. 12.88
B. 3.88
C. 13.88
D. 15
E. 18.8

divide(multiply(multiply(29, 16), 5), multiply(30, 6))

Explanation: "let the required number of days be x more persons , less days ( indirect proportion ) more hours , less days ( indirect proportion ) hence we can write as ( persons ) 29 : 30 } : : x : 16 ( hours ) 5 : 6 29 * 5 * 16 = 30 * 6 * x x = 12.88 answer : a"


Question: the income tax in country x is 8 % of any income up to $ 5000 . for incomes over $ 5000 , an 8 % tax is imposed on the first $ 5000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ?

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

<gadget id="calculator">5_000 * (2/25)</gadget>
<output>400</output>

<gadget id="calculator">950 - 400</gadget>
<output>550</output>

<gadget id="calculator">5_000 + 550</gadget>
<output>5_550</output>

<gadget id="calculator">5_550 + 5_000</gadget>
<output>10_550</output>
<result>10_550</result>

Choices:
A. $ 10500
B. $ 11000
C. $ 13000
D. $ 13500
E. $ 14,000

Explanation: given : for incomes over $ 5,000 , an 8 % tax is imposed on the first $ 5,000 , and a 10 % tax is imposed on the portion of the total income in excess of $ 5000 . if perry paid $ 950 in income tax last month , then what was perry ' s income ? for first 5000 , 8 % tax then we get 400 $ as tax . now perry paid 950 $ tax . . . we need to check which option is going to yield 550 $ on the remaining amount . a . $ 10,500 - 5000 = 5500 , then we get 10 % tax , we get 550 $ . . . ( $ 10,500 - 5000 - here already for 5000 $ we have calculated the tax and we need to tally for the remaining amount ) 550 + 400 = 950 $ . . . hence this is the option . answer : option a .


Question: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 23.5 % . what would have been the percentage of profit earned if no discount was offered ?

<gadget id="calculator">100 + 23.5</gadget>
<output>123.5</output>

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

<gadget id="calculator">123.5 / 95</gadget>
<output>1.3</output>

<gadget id="calculator">100 * 1.3</gadget>
<output>130</output>
<result>130</result>

Choices:
A. 140
B. 120
C. 130
D. 110
E. 150

multiply(const_100, divide(add(const_100, 23.5), subtract(const_100, 5)))

Explanation: c 130 % let c . p . be $ 100 . then , s . p . = $ 123.50 let marked price be $ x . then , 95 / 100 x = 123.50 x = 12350 / 95 = $ 130 now , s . p . = $ 130 , c . p . = $ 100 profit % = 30 % .


Question: if n = 2 ^ 0.15 and n ^ b = 8 , b must equal

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

<gadget id="calculator">2 ** 0.15</gadget>
<output>1.109569</output>

<gadget id="calculator">log(1.109569)</gadget>
<output>0.103972</output>

<gadget id="calculator">log(8) / 0.103972</gadget>
<output>9.61797406994191*log(8) = around 20.000015</output>
<result>9.61797406994191*log(8) = around 20.000015</result>

Choices:
A. 3 / 80
B. 3 / 5
C. 20
D. 5 / 3
E. 80 / 3

Explanation: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 3 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 3 b = 20 answer : c"


Question: last year sandy saved 10 % of her annual salary . this year , she made 10 % more money than last year , and she saved 6 % of her salary . the amount saved this year was what percent of the amount she saved last year ?

<gadget id="calculator">6 / 100</gadget>
<output>3/50 = around 0.06</output>

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

<gadget id="calculator">(3/50) * 110</gadget>
<output>33/5 = around 6.6</output>

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

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

<gadget id="calculator">(33/5) / 10</gadget>
<output>33/50 = around 0.66</output>

<gadget id="calculator">(33/50) * 100</gadget>
<output>66</output>
<result>66</result>

Choices:
A. 66 %
B. 80 %
C. 112 %
D. 136 %
E. 148 %

multiply(divide(multiply(divide(6, const_100), add(const_100, 10)), divide(multiply(10, const_100), const_100)), const_100)

Explanation: "let last year ' s salary be x . last year , sandy save 0.1 x this year , sandy saved 0.06 * 1.1 x = 0.066 x 0.066 x / 0.1 x = 0.66 = 66 % the answer is a ."


Question: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40000 , what is the value at the end of 2 years ?

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(3/4) ** 2</gadget>
<output>9/16 = around 0.5625</output>

<gadget id="calculator">40_000 * (9/16)</gadget>
<output>22_500</output>
<result>22_500</result>

Choices:
A. 3277
B. 2977
C. 22500
D. 6077
E. 17112

Explanation: explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c


Question: 5 years ago , paula was 3 times as old as karl . in 6 years , paula will be twice as old as karl . what is the sum of their ages now ?

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

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

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

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

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

<gadget id="calculator">6 + 10</gadget>
<output>16</output>

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

<gadget id="calculator">48 - 10</gadget>
<output>38</output>

<gadget id="calculator">38 + 16</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 42
B. 46
C. 50
D. 54
E. 58

add(subtract(multiply(add(negate(subtract(6, multiply(6, const_2))), subtract(multiply(5, 3), 5)), const_3), subtract(multiply(5, 3), 5)), add(negate(subtract(6, multiply(6, const_2))), subtract(multiply(5, 3), 5)))

Explanation: p - 5 = 3 ( k - 5 ) and so p = 3 k - 10 p + 6 = 2 ( k + 6 ) ( 3 k - 10 ) + 6 = 2 k + 12 k = 16 p = 38 p + k = 54 the answer is d .


Question: one fourth of a solution that was 8 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?

<gadget id="calculator">16 / 100</gadget>
<output>4/25 = around 0.16</output>

<gadget id="calculator">100 * (4/25)</gadget>
<output>16</output>

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

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

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

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

<gadget id="calculator">75 * (2/25)</gadget>
<output>6</output>

<gadget id="calculator">16 - 6</gadget>
<output>10</output>

<gadget id="calculator">10 / 25</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 100</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 74 %
B. 52 %
C. 40 %
D. 18 %
E. 8.5 %

multiply(divide(subtract(multiply(const_100, divide(16, const_100)), multiply(subtract(const_100, multiply(divide(const_1, const_4), const_100)), divide(8, const_100))), multiply(divide(const_1, const_4), const_100)), const_100)

Explanation: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.08 + 1 / 4 * x = 1 * 0.16 - - > x = 0.4 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.08 + 25 * x = 100 * 0.16 - - > x = 0.4 . answer : c ."


Question: a and b invests rs . 2000 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?

<gadget id="calculator">2_000 * 6</gadget>
<output>12_000</output>

<gadget id="calculator">2_000 * 2</gadget>
<output>4_000</output>

<gadget id="calculator">4_000 * 6</gadget>
<output>24_000</output>

<gadget id="calculator">12_000 + 24_000</gadget>
<output>36_000</output>

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

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

<gadget id="calculator">36_000 / 48_000</gadget>
<output>3/4 = around 0.75</output>
<result>3/4 = around 0.75</result>

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

divide(add(multiply(2000, 6), multiply(multiply(2000, const_2), 6)), multiply(4000, add(6, 6)))

Explanation: "( 2 * 6 + 4 * 6 ) : ( 4 * 12 ) 36 : 48 = > 3 : 4 answer : b"


Question: two trains of equal lengths take 8 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?

<gadget id="calculator">120 * 2</gadget>
<output>240</output>

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

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

<gadget id="calculator">8 + 15</gadget>
<output>23</output>

<gadget id="calculator">240 / 23</gadget>
<output>240/23 = around 10.434783</output>
<result>240/23 = around 10.434783</result>

Choices:
A. 22
B. 12
C. 77
D. 10
E. 21

divide(multiply(120, const_2), add(speed(120, 15), speed(120, 8)))

Explanation: "speed of the first train = 120 / 8 = 15 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 15 + 8 = 23 m / sec . required time = ( 120 + 120 ) / 23 = 10 sec . answer : d"


Question: a certain list consists of 21 different numbers . if n is in the list and n is 5 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?

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

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

<gadget id="calculator">5 + 21</gadget>
<output>26</output>

<gadget id="calculator">26 / 4</gadget>
<output>13/2 = around 6.5</output>

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

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

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

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

Choices:
A. 1 / 20
B. 1 / 6
C. 1 / 5
D. 4 / 21
E. 5 / 21

divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, const_4.0), 21), const_4.0), const_2), 5), const_3))

Explanation: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 5 * x hence , a 1 + a 2 + . . + a 20 + n = 25 x so , the fraction asked = 5 x / 25 x = 1 / 5 answer c"


Question: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 27 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">27 / 2</gadget>
<output>27/2 = around 13.5</output>
<result>27/2 = around 13.5</result>

Choices:
A. 13.5 minutes
B. 27 minutes
C. 35 minutes
D. 54 minutes
E. 81 minutes

Explanation: "danny ' s time is 27 minutes . the time to reach halfway is 13.5 minutes . steve ' s time is 54 minutes . the time to reach halfway is 27 minutes . the time difference is 27 - 13.5 = 13.5 minutes the answer is a ."


Question: a number exceeds by 40 from its 3 / 8 part . then the number is ?

<gadget id="calculator">40 * 8</gadget>
<output>320</output>

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

<gadget id="calculator">320 / 5</gadget>
<output>64</output>
<result>64</result>

Choices:
A. 32
B. 24
C. 64
D. 40
E. 45

Explanation: "x – 3 / 8 x = 40 x = 64 answer : c"


Question: amar takes as much time in running 22 meters as a car takes in covering 58 meters . what will be the distance covered by amar during the time the car covers 2.6 km ?

<gadget id="calculator">2.6 * 1_000</gadget>
<output>2_600</output>

<gadget id="calculator">22 * 2_600</gadget>
<output>57_200</output>

<gadget id="calculator">57_200 / 58</gadget>
<output>28_600/29 = around 986.206897</output>
<result>28_600/29 = around 986.206897</result>

Choices:
A. 700 m
B. 978 m
C. 970 m
D. 986 m
E. 640 m

divide(multiply(22, multiply(2.6, const_1000)), 58)

Explanation: "distance covered by amar = 22 / 58 ( 2.6 km ) = 11 / 29 ( 2600 ) = 986 m answer : d"


Question: a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?

<gadget id="calculator">88 / 100</gadget>
<output>22/25 = around 0.88</output>

<gadget id="calculator">340 * (22/25)</gadget>
<output>1_496/5 = around 299.2</output>

<gadget id="calculator">340 - (1_496/5)</gadget>
<output>204/5 = around 40.8</output>

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

<gadget id="calculator">340 * (1/20)</gadget>
<output>17</output>

<gadget id="calculator">(204/5) - 17</gadget>
<output>119/5 = around 23.8</output>

<gadget id="calculator">(119/5) + 3.2</gadget>
<output>27</output>

<gadget id="calculator">340 + 3.2</gadget>
<output>343.2</output>

<gadget id="calculator">343.2 + 10</gadget>
<output>353.2</output>

<gadget id="calculator">353.2 + 6.8</gadget>
<output>360</output>

<gadget id="calculator">27 / 360</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">(3/40) * 100</gadget>
<output>15/2 = around 7.5</output>
<result>15/2 = around 7.5</result>

Choices:
A. 6 % .
B. 7.5 % .
C. 9.2 % .
D. 10.5 % .
E. 11 % .

multiply(divide(add(subtract(subtract(340, multiply(340, divide(88, const_100))), multiply(340, divide(5, const_100))), 3.2), add(add(add(340, 3.2), 10), 6.8)), const_100)

Explanation: "denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 88 - . 05 ) + 3.2 340 ( 0.07 ) + 3.2 23.8 + 3.2 27 ratio : 27 / 360 = 3 / 40 answer : b"


Question: when the perimeter of a regular polygon is divided by 5 , the length of a side is 25 . what is the name of the polygon ? what is the perimeter ?

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

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

Choices:
A. 125
B. 126
C. 127
D. 128
E. 129

Explanation: regular polygon . a polygon with equal sides and equal sides . divided by 5 to get the length of a side . it is the pentagon since it has 5 sides . so p = 5 × s to get the perimeter , just multiply a side by 5 . since 25 × 5 = 125 , the perimeter is 125 . answer a


Question: a vessel of capacity 60 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?

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

<gadget id="calculator">60 - 9</gadget>
<output>51</output>

<gadget id="calculator">51 / 60</gadget>
<output>17/20 = around 0.85</output>

<gadget id="calculator">(17/20) * 9</gadget>
<output>153/20 = around 7.65</output>

<gadget id="calculator">51 - (153/20)</gadget>
<output>867/20 = around 43.35</output>
<result>867/20 = around 43.35</result>

Choices:
A. 23.89
B. 72.9
C. 38.3
D. 43.35
E. 79.3

subtract(subtract(60, multiply(const_3, const_3)), multiply(divide(subtract(60, multiply(const_3, const_3)), 60), multiply(const_3, const_3)))

Explanation: explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 60 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 60 - 9 ) / 60 ] ^ 2 ( 60 ) = 43.35 litres . answer : option d


Question: an empty wooden vessel weighs 8 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .

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

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

<gadget id="calculator">8 - 1</gadget>
<output>7</output>

<gadget id="calculator">3 / 7</gadget>
<output>3/7 = around 0.428571</output>
<result>3/7 = around 0.428571</result>

Choices:
A. 3 / 7
B. 5 / 9
C. 1 / 24
D. 4 / 9
E. 2 / 5

divide(subtract(divide(8, const_2), const_1), subtract(8, const_1))

Explanation: "an empty wooden vessel weighs 8 % of its total weight when filled with paint : vessel = 0.08 ( vessel + paint ) ; 8 v = v + p ( so the weight of completely filled vessel is 8 v ) p = 7 v ( so the weight of the paint when the vessels is completely filled is 7 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 8 v ; p ' = 3 v ( so the weight of the paint when the vessels is partially filled is 3 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 3 v / 7 v = 3 / 7 . answer : a ."


Question: in a government institute 20 nos . staffs are employed . in a festival season their boss give festival allowance to all . he says his accountant to calculate for 30 days @ 100 . also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash . he had given rs . 65000 / - to the accountant . how much amount will taken from petty cash ?

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

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

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

<gadget id="calculator">65_000 / 65</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 1000
B. 3000
C. 3500
D. 2500
E. 2250

divide(65000, subtract(100, add(20, divide(30, const_2))))

Explanation: for 20 staffs : 300 * 100 * 20 = 60000 for driver and cleaning staff : 300 * 100 * 2 = 6000 from petty cash : 1000 answer is a


Question: if $ 5,000 is invested in an account that earns 4 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?

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

Choices:
A. $ 4
B. $ 8
C. $ 12
D. $ 16
E. $ 432

Explanation: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.04 / 2 ) ^ 2 = 5404 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 4 / 100 ) = 5400 difference = 5404 - 5400 = 4 $ a"


Question: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?

<gadget id="calculator">1_500 / 5</gadget>
<output>300</output>

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

<gadget id="calculator">300 * 4</gadget>
<output>1_200</output>
<result>1_200</result>

Choices:
A. rs 1200
B. rs 1500
C. rs 1600
D. rs 1900
E. rs 1700

multiply(divide(1500, 5), subtract(7, 3))

Explanation: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 7 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2100 . hence , ( r - p ) = ( 2100 - 900 ) = 1200 answer : a"


Question: if a sum of money doubles itself in 25 years at simple interest , the ratepercent per annum is

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

<gadget id="calculator">2 / (1/4)</gadget>
<output>8</output>

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

Choices:
A. 12
B. 12.5
C. 13
D. 13.5
E. 4

divide(divide(const_2, divide(25, const_100)), const_2)

Explanation: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 25 ) = 4 option e"


Question: a company produces 50000 bottles of water everyday . if a case can hold 25 bottles of water . how many cases are required by the company to hold its one day production

<gadget id="calculator">50_000 / 25</gadget>
<output>2_000</output>
<result>2_000</result>

Choices:
A. 2000
B. 4500
C. 5000
D. 8000
E. 9000

Explanation: "number of bottles that can be held in a case = 25 number of cases required to hold 50000 bottles = 50000 / 25 = 2000 cases . so the answer is a = 2000"


Question: a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 25 gallons of gasoline ?

<gadget id="calculator">12.2 * 25</gadget>
<output>305</output>
<result>305</result>

Choices:
A. 190
B. 284.6
C. 300
D. 305
E. 312

Explanation: "to maximize the distance that suv could be driven on 25 gallons of gasoline , we need consider only highway driving . max distance = 25 * 12.2 = 305 answer d"


Question: 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 120 only . men â € ™ s wages are ?

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

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

Choices:
A. 6 rs
B. 2 rs
C. 4 rs
D. 9 rs
E. 8 rs

Explanation: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 120 rs . 5 m + 5 m + 5 m - - - - - 120 rs . 15 m - - - - - - 120 rs . = > 1 m = 8 rs . answer : e"


Question: a and b are two partially filled buckets of water . if 5 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?

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

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

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

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

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

<gadget id="calculator">2 + (1/2)</gadget>
<output>5/2 = around 2.5</output>

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

Choices:
A. 11
B. 52 / 5
C. 17
D. 21
E. 23

divide(multiply(add(add(5, const_3), const_2), divide(5, const_2)), add(const_2, divide(const_1, const_2)))

Explanation: "let a contains a , b contains b liters so , ( a - 5 ) / ( b + 5 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 4 ) / ( a + 4 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 52 / 5 ans : ( b )"


Question: a company pays 12.5 % dividend to its investors . if an investor buys rs . 60 shares and gets 25 % on investment , at what price did the investor buy the shares ?

<gadget id="calculator">12.5 * 60</gadget>
<output>750</output>

<gadget id="calculator">750 / 100</gadget>
<output>15/2 = around 7.5</output>

<gadget id="calculator">(15/2) * 100</gadget>
<output>750</output>

<gadget id="calculator">750 / 25</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 25
B. 66
C. 30
D. 19
E. 01

divide(multiply(divide(multiply(12.5, 60), const_100), const_100), 25)

Explanation: explanation : dividend on 1 share = ( 12.5 * 60 ) / 100 = rs . 7.5 rs . 25 is income on an investment of rs . 100 rs . 7.5 is income on an investment of rs . ( 7.5 * 100 ) / 25 = rs . 30 answer : c


Question: what is the 10 digit to the right of the decimal point , in the decimal expansion of ( 1 / 2 ) ^ 10 ?

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

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

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

Explanation: step 1 convert fraction to decimal with two decimal places 1 / 2 = 0.50 then convert to scientific number = 5 * 10 ^ - 1 step 2 multiply 5 ^ 10 by 10 ^ - 10 step 3 5 has the sequence 5 , 25 , 125 answer is e


Question: find the curved surface area , if the radius of a cone is 35 m and slant height is 30 m ?

<gadget id="calculator">35 * 30</gadget>
<output>1_050</output>

<gadget id="calculator">pi * 1_050</gadget>
<output>1050*pi = around 3_298.672286</output>
<result>1050*pi = around 3_298.672286</result>

Choices:
A. 1100
B. 2200
C. 3300
D. 4400
E. 5500

Explanation: "cone curved surface area = ï € rl 22 / 7 ã — 35 ã — 30 = 110 ã — 30 = 3300 m ( power 2 ) answer is c ."


Question: a man have 8 t - shirt and some pant . he can dress in 72 ways . then tell me the no . of pant that man have .

<gadget id="calculator">72 / 8</gadget>
<output>9</output>
<result>9</result>

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

Explanation: let he have x pant . by fundamental principle total no . of ways in which he can dress = 8 x 8 x = 72 x = 9 pants answer b


Question: on average , machine a will produce a completed item once every 4 minutes , and machine b will produce a completed item once every 5 minutes . the number of items machine a produces in a 24 - hour period is approximately what percent greater than the number of items machine b would produce in that same period ?

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

<gadget id="calculator">15 * 24</gadget>
<output>360</output>

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

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

<gadget id="calculator">360 / 288</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">(5/4) * 100</gadget>
<output>125</output>

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

Choices:
A. 25 %
B. 15 %
C. 45 %
D. 33 %
E. 55 %

subtract(multiply(divide(multiply(divide(const_60, 4), 24), multiply(divide(const_60, 5), 24)), const_100), const_100)

Explanation: machine a : 1 item in 4 minutes - - > 1 / 4 items in 1 minute ; machine b : 1 item in 5 minutes - - > 1 / 5 items in 1 minute . in the same time period , machine a produces ( 1 / 4 - 1 / 5 ) / ( 1 / 5 ) * 100 = ~ 25 % more items than machine b . answer : a .


Question: what is the divisor ? the dividend is 76 , the remainder is 8 , the quotient is 4

<gadget id="calculator">76 - 8</gadget>
<output>68</output>

<gadget id="calculator">68 / 4</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 32
B. 48
C. 67
D. 17
E. 26

Explanation: divisor = dividend - remainder divided by the quotient divisor = 76 - 8 divided by 4 divisor = 68 / 4 divisor = 17


Question: at what rate percent per annum will a sum of money double in 6 years .

<gadget id="calculator">100 / 6</gadget>
<output>50/3 = around 16.666667</output>
<result>50/3 = around 16.666667</result>

Choices:
A. 12.5 %
B. 13.5 %
C. 11.5 %
D. 14.5 %
E. 16.6 %

Explanation: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 6 ) ] % = 16.6 % per annum . answer : e"


Question: if 8 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?

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

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(9/10) - (3/4)</gadget>
<output>3/20 = around 0.15</output>

<gadget id="calculator">8 / (3/20)</gadget>
<output>160/3 = around 53.333333</output>

<gadget id="calculator">(160/3) * (3/4)</gadget>
<output>40</output>

<gadget id="calculator">40 + 8</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 20
B. 24
C. 36
D. 48
E. 60

add(multiply(divide(8, subtract(divide(9, 10), divide(3, 4))), divide(3, 4)), 8)

Explanation: "let the capacity of the tank = c ( 3 / 4 ) c + 8 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 8 = > ( 3 / 20 ) c = 8 = > c = ( 8 * 20 ) / 3 = 53.33 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 8 = 39.99 + 8 = 47.99 = 48 answer d"


Question: a certain company ’ s profit in 1996 was 15 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?

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

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

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

<gadget id="calculator">1 + (3/20)</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">(6/5) * (23/20)</gadget>
<output>69/50 = around 1.38</output>

<gadget id="calculator">(69/50) - 1</gadget>
<output>19/50 = around 0.38</output>

<gadget id="calculator">(19/50) * 100</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 5 %
B. 18 %
C. 33 %
D. 35 %
E. 38 %

multiply(subtract(multiply(add(divide(20, const_100), const_1), add(const_1, divide(15, const_100))), const_1), const_100)

Explanation: "soln : - profit in 1995 - 100 profit in 1996 - 115 % increase profit in 1997 in comparison to 1995 = 15 + 115 * 20 % = 38 % answer : e"


Question: i chose a number and divide it by 2 . then i subtracted 100 from the result and got 4 . what was the number i chose ?

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

<gadget id="calculator">104 * 2</gadget>
<output>208</output>
<result>208</result>

Choices:
A. 200
B. 208
C. 400
D. 500
E. 100

Explanation: "let x be the number i chose , then x / 2 − 100 = 4 x / 2 = 104 x = 208 answer is b ."


Question: the perimeter of an isosceles right triangle is 12 + 12 sq rt 2 . what is the length of the hypotenuse of the triangle ?

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

<gadget id="calculator">12 * (sqrt(2))</gadget>
<output>12*sqrt(2) = around 16.970563</output>

<gadget id="calculator">(12*sqrt(2)) / 2</gadget>
<output>6*sqrt(2) = around 8.485281</output>
<result>6*sqrt(2) = around 8.485281</result>

Choices:
A. 5
B. 6
C. 7
D. 8.485
E. 8

Explanation: side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 12 + 12 sqrt 2 or , a . ( 2 + sqrt 2 ) = 12 ( 1 + sqrt 2 ) , a = 12 * ( 1 + sqrt 2 ) / 2 + sqrt 2 = 12 * 2.414 / 3.414 = then hypotenuse = 8.485 d


Question: a certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?

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

<gadget id="calculator">10 / 50</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 100</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 25 %
B. 33 1 / 3 %
C. 50 %
D. 66 2 / 3 %
E. 20 %

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

Explanation: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 50 / 50 ∗ 100 = 20 answer : e ."


Question: given that 268 * 74 = 19832 , find the values of 2.68 * 0.74 .

<gadget id="calculator">2.68 * 0.74</gadget>
<output>1.9832</output>
<result>1.9832</result>

Choices:
A. 1.9328
B. 1.9832
C. 1.9823
D. 1.9382
E. none of them

Explanation: sum of decimal places = ( 2 + 2 ) = 4 2.68 * 0.74 = 1.9832 . answer is b .


Question: the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________

<gadget id="calculator">0.25 + 0.4</gadget>
<output>0.65</output>

<gadget id="calculator">0.65 - 0.15</gadget>
<output>0.5</output>

<gadget id="calculator">1 - 0.5</gadget>
<output>0.5</output>
<result>0.5</result>

Choices:
A. 0.45
B. 0.4
C. 0.5
D. 0.05
E. 0.6

subtract(const_1, subtract(add(0.25, 0.40), 0.15))

Explanation: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 15 = . 50 but the probability of neither a nor b = 1 - . 50 = 0.50 answer : c"


Question: if henry were to add 9 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?

<gadget id="calculator">7 / 8</gadget>
<output>7/8 = around 0.875</output>

<gadget id="calculator">3 / 4</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(7/8) - (3/4)</gadget>
<output>1/8 = around 0.125</output>

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

<gadget id="calculator">9 * 8</gadget>
<output>72</output>
<result>72</result>

Choices:
A. 25
B. 40
C. 64
D. 72
E. 96

multiply(9, divide(const_1, subtract(divide(7, 8), divide(3, 4))))

Explanation: "7 / 8 x - 3 / 4 x = 9 galls 1 / 8 * x = 9 gallons x = 72 gallons answer d"


Question: bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many w hours does it currently take anne to clean the house on her own ?

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

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

<gadget id="calculator">(1/3) - (1/4)</gadget>
<output>1/12 = around 0.083333</output>

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

Choices:
A. 6
B. 7
C. 8
D. 12
E. 14

inverse(subtract(divide(const_1, 3), divide(const_1, 4)))

Explanation: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is w equal to 1 / 3 ( as the work is completed in w = 3 hours ) solving these 2 equations we can find b as 12 so , d"


Question: the price of a book is increased from $ 300 to $ 330 . what is the % of increase in its price ?

<gadget id="calculator">330 - 300</gadget>
<output>30</output>

<gadget id="calculator">30 / 300</gadget>
<output>1/10 = around 0.1</output>

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

Choices:
A. 10 %
B. 20 %
C. 30 %
D. 35 %
E. 45 %

multiply(divide(subtract(330, 300), 300), const_100)

Explanation: explanation : change in the price = rs 330 – rs 300 = rs 30 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 30 / 300 ) * 100 = 10 % a


Question: a sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest . what is the rate of interest ?

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

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

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

<gadget id="calculator">(1/4) + (1/4)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">9 + (1/2)</gadget>
<output>19/2 = around 9.5</output>

<gadget id="calculator">1 / (19/2)</gadget>
<output>2/19 = around 0.105263</output>

<gadget id="calculator">(2/19) * 100</gadget>
<output>200/19 = around 10.526316</output>
<result>200/19 = around 10.526316</result>

Choices:
A. 12 %
B. 11 %
C. 16 %
D. 15 %
E. 18 %

multiply(divide(divide(const_3, 3), add(multiply(const_3, 3), add(const_0_25, const_0_25))), const_100)

Explanation: "b 11 % s . i . = ( 19800 - 14800 ) = 5000 . rate = ( 100 x 5000 ) / ( 14800 x 3 ) % = 11 %"


Question: from the sale of sleeping bags , a retailer made a gross profit of 16 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?

<gadget id="calculator">28 * 100</gadget>
<output>2_800</output>

<gadget id="calculator">100 + 16</gadget>
<output>116</output>

<gadget id="calculator">2_800 / 116</gadget>
<output>700/29 = around 24.137931</output>
<result>700/29 = around 24.137931</result>

Choices:
A. 3.0
B. 3.36
C. 24.13
D. 25.0
E. 31.36

divide(multiply(28, const_100), add(const_100, 16))

Explanation: "cost price * 1.16 = selling price - - > cost price * 1.16 = $ 28 - - > cost price = $ 24.13 . answer : c ."


Question: a number is doubled and 5 is added . if the resultant is trebled , it becomes 129 . what is that number ?

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

<gadget id="calculator">129 - 15</gadget>
<output>114</output>

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

<gadget id="calculator">114 / 6</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 12
B. 29
C. 27
D. 19
E. 99

divide(subtract(129, multiply(const_3, 5)), multiply(const_3, const_2))

Explanation: explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 129 6 x + 15 = 129 6 x = 114 x = 19 answer : d


Question: the average temperature for tuesday , wednesday and thursday was 42 ° c . the average temperature for wednesday , thursday and friday was 44 ° c . if the temperature on friday be 43 ° c , what was the temperature on tuesday ?

<gadget id="calculator">42 * 3</gadget>
<output>126</output>

<gadget id="calculator">44 * 3</gadget>
<output>132</output>

<gadget id="calculator">132 - 43</gadget>
<output>89</output>

<gadget id="calculator">126 - 89</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 39 ° c
B. 44 ° c
C. 37 ° c
D. 42 ° c
E. none of these

subtract(multiply(42, const_3), subtract(multiply(44, const_3), 43))

Explanation: "explanation : t + w + t = 42 × 3 = 126 ° c w + t + f = 44 × 3 = 132 ° c also , temperature on friday = 43 ° c temperature on tuesday = 126 + 43 - 132 = 37 ° c answer : option c"


Question: if a , b , and c are positive real numbers such that a ( b + c ) = 152 , b ( c + a ) = 162 , and c ( a + b ) = 170 , then abc is

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

<gadget id="calculator">170 + 162</gadget>
<output>332</output>

<gadget id="calculator">152 + 332</gadget>
<output>484</output>

<gadget id="calculator">170 + 484</gadget>
<output>654</output>

<gadget id="calculator">4 + 654</gadget>
<output>658</output>

<gadget id="calculator">20 + 658</gadget>
<output>678</output>

<gadget id="calculator">678 + 20</gadget>
<output>698</output>
<result>698</result>

Choices:
A. 672
B. 688
C. 704
D. 720
E. 750

Explanation: ab + bc = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) bc + ba = 162 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) ac + ab = 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : ac + cb = 162 + 8 ac + cb = bc + ba + 8 ac = ba + 8 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 ac = 160 ac = 80 abc has to be multiple of 80 , only 720 fits in answer = d


Question: s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is

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

<gadget id="calculator">49 * 2</gadget>
<output>98</output>

<gadget id="calculator">56 + 98</gadget>
<output>154</output>
<result>154</result>

Choices:
A. 198
B. 154
C. 199
D. 102
E. 105

add(56, multiply(subtract(50, const_1), 2))

Explanation: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is first term = 56 ; total terms = 50 ; difference = 2 56 + ( 49 ) 2 = 154 ans b"


Question: the total number of digit used in numbering the pages of a book having 366 pages , is :

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

<gadget id="calculator">10 * 9</gadget>
<output>90</output>

<gadget id="calculator">2 * 90</gadget>
<output>180</output>

<gadget id="calculator">9 + 180</gadget>
<output>189</output>

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">366 - 99</gadget>
<output>267</output>

<gadget id="calculator">3 * 267</gadget>
<output>801</output>

<gadget id="calculator">189 + 801</gadget>
<output>990</output>
<result>990</result>

Choices:
A. 732
B. 990
C. 1098
D. 1305
E. none of these

add(add(subtract(const_10, const_1), multiply(const_2, multiply(const_10, subtract(const_10, const_1)))), multiply(const_3, subtract(366, subtract(const_100, const_1))))

Explanation: solution total number of digits = ( no . of digits in 1 - digits page nos . + no . of digits in 2 - digits page nos . + no . of digits i 3 - digits page nos . ) = ( 1 * 9 + 2 * 90 + 3 * 267 ) = ( 9 + 180 + 801 ) = 990 . answer b


Question: running at the same constant rate , 6 identical machines can produce a total of 240 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?

<gadget id="calculator">240 / 6</gadget>
<output>40</output>

<gadget id="calculator">40 * 4</gadget>
<output>160</output>

<gadget id="calculator">160 * 10</gadget>
<output>1_600</output>
<result>1_600</result>

Choices:
A. 648
B. 1,800
C. 1,600
D. 10,800
E. 64,800

multiply(multiply(divide(240, 6), 4), 10)

Explanation: "6 machines produce 240 bottles per minute ; 1 machine produces 240 / 6 = 40 bottles per minute ; 10 machines produce 40 * 10 = 400 bottles per minute ; in 4 minutes 10 machines produce 400 * 4 = 1,600 bottles . answer : c ."


Question: there are 5 boxes in a cargo . the weight of the 1 st box is 200 kg , the weight of the 2 nd box is 20 % higher than the third box , whose weight is 25 % higher than the 1 st box weight . the 4 th box which weighs 350 kg is 30 % lighter than the 5 th box . find the difference in average weight of the 4 heaviest boxes and the 4 lightest boxes .

<gadget id="calculator">350 - 25</gadget>
<output>325</output>

<gadget id="calculator">325 - 25</gadget>
<output>300</output>

<gadget id="calculator">300 / 4</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 22
B. 75
C. 25
D. 70
E. 11

divide(subtract(subtract(350, 25), 25), 4)

Explanation: weight of 1 st box = 200 weight of 3 rd box = ( 125 / 100 ) * 200 = 250 weight of 2 nd box = ( 120 / 100 ) * 250 = 300 weight of 4 th box = 350 weight of 5 th box = ( 10 / 7 ) * 350 = 500 average of 4 highest weighted boxes = ( 500 + 350 + 300 + 250 ) / 4 = 350 average of 4 lightest boxes = ( 350 + 300 + 250 + 200 ) / 4 = 275 therefore difference = 350 - 275 = 75 answer : b


Question: veena ranks 73 rd from the top in a class of 198 . what is her rank from the bottom if 22 students have failed the examination ?

<gadget id="calculator">198 - 22</gadget>
<output>176</output>

<gadget id="calculator">73 - 1</gadget>
<output>72</output>

<gadget id="calculator">176 - 72</gadget>
<output>104</output>

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

Choices:
A. 88
B. 104
C. 110
D. 90
E. 93

subtract(subtract(subtract(198, 22), subtract(73, const_1)), const_4)

Explanation: "total student = 198 failed = 22 paasd student = 198 - 22 = 176 from bottom her rank is = 176 - 73 + 1 = 104 answer : b"


Question: by selling 20 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ?

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

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

<gadget id="calculator">1 / 70</gadget>
<output>1/70 = around 0.014286</output>

<gadget id="calculator">130 * (1/70)</gadget>
<output>13/7 = around 1.857143</output>

<gadget id="calculator">1 / (13/7)</gadget>
<output>7/13 = around 0.538462</output>

<gadget id="calculator">(7/13) * 20</gadget>
<output>140/13 = around 10.769231</output>
<result>140/13 = around 10.769231</result>

Choices:
A. 8.56
B. 10.75
C. 14.5
D. 16.5
E. 11.4

multiply(divide(const_1, multiply(add(const_100, 30), divide(const_1, subtract(const_100, 30)))), 20)

Explanation: "70 % - - - 20 130 % - - - ? 70 / 130 * 20 = 10.75 answer : b"


Question: a man buys 60 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?

<gadget id="calculator">100 - 1</gadget>
<output>99</output>

<gadget id="calculator">60 * 99</gadget>
<output>5_940</output>

<gadget id="calculator">46 * 100</gadget>
<output>4_600</output>

<gadget id="calculator">5_940 - 4_600</gadget>
<output>1_340</output>

<gadget id="calculator">1_340 / 4_600</gadget>
<output>67/230 = around 0.291304</output>

<gadget id="calculator">100 * (67/230)</gadget>
<output>670/23 = around 29.130435</output>
<result>670/23 = around 29.130435</result>

Choices:
A. 7.6 %
B. 7.7 %
C. 29.13 %
D. 33.6 %
E. 37.82 %

multiply(const_100, divide(subtract(multiply(60, subtract(const_100, 1)), multiply(46, const_100)), multiply(46, const_100)))

Explanation: explanation : let marked price be re . 1 each c . p . of 60 pens = rs . 46 s . p . of 60 pens = 99 % of rs . 60 = rs . 59.4 profit % = ( profit / c . p . ) x 100 profit % = ( 13.4 / 46 ) x 100 = 29.13 % answer : c


Question: a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .

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

<gadget id="calculator">125 / 100</gadget>
<output>5/4 = around 1.25</output>

<gadget id="calculator">225 / (5/4)</gadget>
<output>180</output>

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

<gadget id="calculator">180 / (5/4)</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 237
B. 126
C. 971
D. 611
E. 144

divide(divide(225, divide(add(const_100, 25), const_100)), divide(add(25, const_100), const_100))

Explanation: "explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 25 % profit = 125 x ( 1 + 25 / 100 ) = 156.25 cp sp 100 - - - 156.25 x - - - 225 cp = 225 x 100 / 156.25 = 144 answer : e"


Question: what is the area of a regular hexagon with sides 1 in . long ?

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

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

<gadget id="calculator">4 / pi</gadget>
<output>4/pi = around 1.27324</output>

<gadget id="calculator">(4/pi) / 2</gadget>
<output>2/pi = around 0.63662</output>

<gadget id="calculator">(2/pi) * (2/pi)</gadget>
<output>4/pi**2 = around 0.405285</output>

<gadget id="calculator">(4/pi**2) * pi</gadget>
<output>4/pi = around 1.27324</output>

<gadget id="calculator">(4/pi) * 2</gadget>
<output>8/pi = around 2.546479</output>
<result>8/pi = around 2.546479</result>

Choices:
A. 1.59 square inch
B. 2.59 square inch
C. 3.59 square inch
D. 4.59 square inch
E. 2.69 square inch

multiply(multiply(multiply(divide(divide(multiply(sqrt(1), const_4), const_pi), const_2), divide(divide(multiply(sqrt(1), const_4), const_pi), const_2)), const_pi), const_2)

Explanation: "a regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch . area of each triangle = ( root 3 / 4 ) * side ^ 2 = ( root 3 / 4 ) area of 6 triangles = 6 * ( root 3 / 4 ) = 1.5 root 3 = 2.59 square inch answer : b"


Question: ratio between rahul and deepak is 4 : 2 , after 10 years rahul age will be 26 years . what is deepak present age

<gadget id="calculator">26 - 10</gadget>
<output>16</output>

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

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

Choices:
A. 14
B. 15
C. 12
D. 22
E. 8

divide(multiply(subtract(26, 10), 2), 4)

Explanation: "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 answer : option e"


Question: what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 5 years ?

<gadget id="calculator">100 * 160</gadget>
<output>16_000</output>

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

<gadget id="calculator">16_000 / 4_000</gadget>
<output>4</output>
<result>4</result>

Choices:
A. 5 %
B. 7 %
C. 9 %
D. 2 %
E. 4 %

divide(multiply(const_100, 160), multiply(800, 5))

Explanation: "160 = ( 800 * 5 * r ) / 100 r = 4 % answer : e"


Question: a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 3 new workers . how many different ways can she assign the new workers ?

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

<gadget id="calculator">factorial(4)</gadget>
<output>24</output>

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

<gadget id="calculator">factorial(12)</gadget>
<output>479_001_600</output>

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

<gadget id="calculator">factorial(9)</gadget>
<output>362_880</output>

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

<gadget id="calculator">362_880 * 6</gadget>
<output>2_177_280</output>

<gadget id="calculator">479_001_600 / 2_177_280</gadget>
<output>220</output>

<gadget id="calculator">12 * 220</gadget>
<output>2_640</output>
<result>2_640</result>

Choices:
A. 2430
B. 2640
C. 3300
D. 4860
E. 5400

multiply(divide(factorial(divide(12, 3)), const_2), divide(factorial(12), multiply(factorial(subtract(12, 3)), factorial(3))))

Explanation: "whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12 c 3 = 220 ways . now 3 out of 12 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 3 out of 12 ) * arranging those teams in shifts = 220 * 24 = 2640 ans : b"


Question: a and b invests rs . 5000 and rs . 6000 in a business . after 6 months , a withdraws two - fifth of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?

<gadget id="calculator">5_000 * 4</gadget>
<output>20_000</output>

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

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

<gadget id="calculator">2_000 * 12</gadget>
<output>24_000</output>

<gadget id="calculator">20_000 + 24_000</gadget>
<output>44_000</output>

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

<gadget id="calculator">6_000 * 6</gadget>
<output>36_000</output>

<gadget id="calculator">6_000 - 2_000</gadget>
<output>4_000</output>

<gadget id="calculator">4_000 * 6</gadget>
<output>24_000</output>

<gadget id="calculator">36_000 + 24_000</gadget>
<output>60_000</output>

<gadget id="calculator">44_000 / 60_000</gadget>
<output>11/15 = around 0.733333</output>
<result>11/15 = around 0.733333</result>

Choices:
A. 3 : 5
B. 7 : 8
C. 5 : 6
D. 3 : 4
E. 7 : 9

divide(add(multiply(5000, const_4.0), multiply(divide(6000, const_3), multiply(2, 6))), add(multiply(6000, multiply(2, const_3)), multiply(subtract(6000, divide(6000, const_3)), multiply(2, const_3))))

Explanation: "a : b ( 5000 * 6 ) + ( 3000 * 6 ) : ( 6000 * 8 ) + ( 4000 * 4 ) 48000 : 64000 3 : 4 answer : d"


Question: in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 150 more than the correct answer . find the number .

<gadget id="calculator">150 * 16</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 * 6</gadget>
<output>14_400</output>

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

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

<gadget id="calculator">80 - 30</gadget>
<output>50</output>

<gadget id="calculator">14_400 / 50</gadget>
<output>288</output>
<result>288</result>

Choices:
A. 125
B. 288
C. 384
D. 400
E. 500

divide(multiply(multiply(150, 16), 6), subtract(multiply(5, 16), multiply(5, 6)))

Explanation: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 150 25 * x / 48 = 150 x = 288 answer b"


Question: a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 880 as his share . find the share of a .

<gadget id="calculator">11_000 * 8</gadget>
<output>88_000</output>

<gadget id="calculator">88_000 / 100</gadget>
<output>880</output>

<gadget id="calculator">880 / 880</gadget>
<output>1</output>

<gadget id="calculator">7_000 * 1</gadget>
<output>7_000</output>

<gadget id="calculator">7_000 * 8</gadget>
<output>56_000</output>

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

Choices:
A. $ 320
B. $ 440
C. $ 560
D. $ 670
E. $ 780

divide(multiply(multiply(7000, divide(880, divide(multiply(11000, 8), const_100))), 8), const_100)

Explanation: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 880 = $ 560 the answer is c ."


Question: bill downloads the movierevenge of the avengersto his computer in 2.5 hours , using a download manager that downloads from 3 sources marked a , b and c . each source provides download at a constant rate , but the rates of different sources are not necessarily identical . if the movie was downloaded from sources a and c alone , it would take 4 hours to complete the download . the next day , source b is available , but the other sources are inactive . how long will it take to download the trailer of the movie , a file that is 10 times smaller , from source b alone ?

<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>44</output>

<gadget id="calculator">44 - 4</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 40 minutes
B. 15 minutes
C. 12 minutes
D. 10 minutes
E. 3 minutes

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

Explanation: let the movie size be 400 u . given , a + c = 4 hrs . a + c = 100 u / hr and a + b + c = 2.5 hrs or 400 / 2.5 = 160 u / hr b alone = 160 - 100 = 60 u / hr trailer = 40 times smaller or 400 / 10 = 40 u b will take 40 / 60 hrs or 40 minutes . ans a


Question: a bowl of fruit contains 14 apples and 21 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?

<gadget id="calculator">14 + 21</gadget>
<output>35</output>

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

<gadget id="calculator">35 * (7/10)</gadget>
<output>49/2 = around 24.5</output>

<gadget id="calculator">(49/2) - 14</gadget>
<output>21/2 = around 10.5</output>

<gadget id="calculator">(21/2) / (7/10)</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 3
B. 15
C. 14
D. 17
E. 20

divide(subtract(multiply(add(14, 21), divide(70, const_100)), 14), divide(70, const_100))

Explanation: "number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 21 - x ) = 35 - x 14 / ( 35 - x ) = 7 / 10 = > 20 = 35 - x = > x = 15 answer b"


Question: the present worth of rs . 2310 due 2 years hence , the rate of interest being 15 % per annum , is :

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

<gadget id="calculator">(3/20) + 1</gadget>
<output>23/20 = around 1.15</output>

<gadget id="calculator">(23/20) ** 2</gadget>
<output>529/400 = around 1.3225</output>

<gadget id="calculator">2_310 / (529/400)</gadget>
<output>924_000/529 = around 1_746.691871</output>
<result>924_000/529 = around 1_746.691871</result>

Choices:
A. 1689
B. 1680
C. 1682
D. 1681
E. 1686

divide(2310, power(add(divide(15, const_100), const_1), 2))

Explanation: "p . w . = rs . 100 x 2310 = rs . 1680 . 100 + 15 x 5 2 answer : b"


Question: after decreasing 24 % in the price of an article costs rs . 684 . find the actual cost of an article ?

<gadget id="calculator">24 / 100</gadget>
<output>6/25 = around 0.24</output>

<gadget id="calculator">1 - (6/25)</gadget>
<output>19/25 = around 0.76</output>

<gadget id="calculator">684 / (19/25)</gadget>
<output>900</output>
<result>900</result>

Choices:
A. 218
B. 777
C. 900
D. 2688
E. 1991

divide(684, subtract(const_1, divide(24, const_100)))

Explanation: "cp * ( 76 / 100 ) = 684 cp = 9 * 100 = > cp = 900 answer : c"


Question: a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat in still water and stream is

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

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

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

Choices:
A. 3 : 1
B. 1 : 3
C. 2 : 4
D. 4 : 2
E. none of these

divide(add(const_1, const_2), subtract(const_2, const_1))

Explanation: "explanation : let speed downstream = x kmph then speed upstream = 2 x kmph so ratio will be , ( 2 x + x ) / 2 : ( 2 x - x ) / 2 = > 3 x / 2 : x / 2 = > 3 : 1 option a"


Question: ritesh and co . generated revenue of rs . 1,600 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?

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

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

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

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

<gadget id="calculator">5 * 100</gadget>
<output>500</output>

<gadget id="calculator">2_000 + 500</gadget>
<output>2_500</output>

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

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

<gadget id="calculator">1_000 + 600</gadget>
<output>1_600</output>

<gadget id="calculator">12.5 / 100</gadget>
<output>0.125</output>

<gadget id="calculator">1_600 / 0.125</gadget>
<output>12_800</output>

<gadget id="calculator">2_500 / 12_800</gadget>
<output>25/128 = around 0.195312</output>

<gadget id="calculator">(25/128) * 100</gadget>
<output>625/32 = around 19.53125</output>
<result>625/32 = around 19.53125</result>

Choices:
A. 12.5 %
B. 19.53 %
C. 25 %
D. 50 %
E. none of these

multiply(divide(add(multiply(const_2, multiply(multiply(const_2, add(const_1, const_4)), const_100)), multiply(add(const_1, const_4), const_100)), divide(add(multiply(multiply(const_2, add(const_1, const_4)), const_100), multiply(add(const_2, const_4), const_100)), divide(12.5, const_100))), const_100)

Explanation: explanation : given , ritesh and co . generated revenue of rs . 1,600 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1600 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1600 . = > 12,800 . hence , the total revenue by end of 2007 is rs . 12,800 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 12800 ) × 100 . = > 19.53 % . answer : b


Question: the average ( arithmetic mean ) of the integers from 100 to 400 , inclusive , is how much greater than the average of the integers from 50 to 250 , inclusive ?

<gadget id="calculator">100 + 400</gadget>
<output>500</output>

<gadget id="calculator">500 / 2</gadget>
<output>250</output>

<gadget id="calculator">50 + 250</gadget>
<output>300</output>

<gadget id="calculator">300 / 2</gadget>
<output>150</output>

<gadget id="calculator">250 - 150</gadget>
<output>100</output>
<result>100</result>

Choices:
A. 100
B. 175
C. 200
D. 125
E. 300

subtract(divide(add(100, 400), const_2), divide(add(50, 250), const_2))

Explanation: for an ap the mean or average of series is average of first and last term . so , average of numbers between 100 to 400 , inclusive = ( 100 + 400 ) / 2 = 250 average of numbers between 50 to 250 , inclusive = ( 50 + 250 ) / 2 = 150 difference = 250 - 150 = 100 answer is a


Question: a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 11 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?

<gadget id="calculator">1_720 - 600</gadget>
<output>1_120</output>

<gadget id="calculator">1_120 * 11</gadget>
<output>12_320</output>

<gadget id="calculator">12_320 / 100</gadget>
<output>616/5 = around 123.2</output>
<result>616/5 = around 123.2</result>

Choices:
A. $ 54.00
B. $ 64.80
C. $ 90.00
D. $ 100.80
E. $ 123.20

divide(multiply(subtract(1720, 600), 11), const_100)

Explanation: "correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.11 ( $ 1120 ) = $ 123.20 . the correct answer is e ."


Question: how much is 60 % of 40 is greater than 4 / 5 of 30 ?

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

<gadget id="calculator">40 * (3/5)</gadget>
<output>24</output>

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

<gadget id="calculator">(4/5) * 30</gadget>
<output>24</output>

<gadget id="calculator">24 - 24</gadget>
<output>0</output>
<result>0</result>

Choices:
A. 8
B. 3
C. 7
D. 0
E. 1

subtract(multiply(40, divide(60, const_100)), multiply(divide(4, 5), 30))

Explanation: "( 60 / 100 ) * 40 â € “ ( 4 / 5 ) * 30 24 - 24 = 0 answer : d"


Question: find the greatest number which on dividing 6215 and 7373 , leaves a reminder of 23 and 29 respectively

<gadget id="calculator">6_215 - 23</gadget>
<output>6_192</output>

<gadget id="calculator">7_373 - 29</gadget>
<output>7_344</output>

<gadget id="calculator">gcd(6_192, 7_344)</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 125
B. 127
C. 129
D. 131
E. 144

Explanation: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 6215 - 23 ) and ( 7373 - 29 ) = hcf ( 6192 , 7344 ) = 144 option e"


Question: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 8 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?

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

<gadget id="calculator">40 / 60</gadget>
<output>2/3 = around 0.666667</output>

<gadget id="calculator">60 * (2/3)</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 20 km
B. 30 km
C. 40 km
D. 50 km
E. 60 km

multiply(60, divide(multiply(5, 8), 60))

Explanation: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 8 = 40 km imo , correct answer is ` ` c . ' '"


Question: the sum of ages of 5 children born at the intervals of 2 years each is 55 years . what is the age of the youngest child ?

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

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

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

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

Explanation: "let the ages of children be x , ( x + 2 ) , ( x + 4 ) , ( x + 6 ) and ( x + 8 ) years . then , x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) + ( x + 8 ) = 50 5 x = 55 - 20 = 35 x = 7 . age of the youngest child = x = 7 years . answer : b"


Question: two goods trains each 820 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?

<gadget id="calculator">45 + 30</gadget>
<output>75</output>
<result>75</result>

Choices:
A. 228
B. 27.32
C. 76.6
D. 78.72
E. 21

Explanation: relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 820 + 820 = 1640 m . required time = 1640 * 6 / 125 = 78.72 sec . answer : d


Question: 20 beavers , working together in a constant pace , can build a dam in 3 hours . how many hours c will it take 12 beavers that work at the same pace , to build the same dam ?

<gadget id="calculator">3 * 20</gadget>
<output>60</output>

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

Choices:
A. 2 .
B. 4 .
C. c = 5 .
D. c = 6 .
E. 8 .

Explanation: "c . 5 hrs if there were 10 beavers it qould have taken double c = 6 hrs . . so closest to that option is 5 ."


Question: indu gave bindu rs . 1875 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">1_875 * (676/625)</gadget>
<output>2_028</output>

<gadget id="calculator">2_028 - 1_875</gadget>
<output>153</output>

<gadget id="calculator">1_875 * (1/25)</gadget>
<output>75</output>

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

<gadget id="calculator">153 - 150</gadget>
<output>3</output>
<result>3</result>

Choices:
A. s . 10
B. s . 2
C. s . 5
D. s . 3
E. s . 4

subtract(subtract(multiply(1875, power(add(const_1, divide(4, const_100)), 2)), 1875), multiply(multiply(1875, divide(4, const_100)), 2))

Explanation: "1875 = d ( 100 / 4 ) 2 d = 3 answer : d"


Question: how many integers are between 7 and 57 / 4 , inclusive ?

<gadget id="calculator">57 / 4</gadget>
<output>57/4 = around 14.25</output>

<gadget id="calculator">(57/4) - 7</gadget>
<output>29/4 = around 7.25</output>

<gadget id="calculator">(29/4) + 1</gadget>
<output>33/4 = around 8.25</output>
<result>33/4 = around 8.25</result>

Choices:
A. 4
B. 5
C. 7
D. 8
E. 10

add(subtract(divide(57, 4), 7), const_1)

Explanation: "57 / 4 = 14 . xx we are not concerned about the exact value of 57 / 4 as we just need the integers . since the values are small , we can write down the integers . the different integers between 7 and 57 / 4 would be 7 , 8 , 9 , 10 , 11 , 12 , 13,14 total number of integers = 8 option d"


Question: 3 / 5 * [ ( 2 / 3 + 3 / 8 ) / 2 ] - 1 / 16 =

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

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

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

<gadget id="calculator">(2/3) + (3/8)</gadget>
<output>25/24 = around 1.041667</output>

<gadget id="calculator">(25/24) / 2</gadget>
<output>25/48 = around 0.520833</output>

<gadget id="calculator">(3/5) * (25/48)</gadget>
<output>5/16 = around 0.3125</output>

<gadget id="calculator">1 / 16</gadget>
<output>1/16 = around 0.0625</output>

<gadget id="calculator">(5/16) - (1/16)</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

Choices:
A. 1 / 4
B. 19 / 16
C. 15 / 16
D. 9 / 13
E. 0

subtract(multiply(divide(3, 5), divide(add(divide(2, 3), divide(3, 8)), 2)), divide(1, 16))

Explanation: we need to simplify the expression using pemdas . parentheses exponents multiplication anddivision addition andsubtraction the calculation of an equation or expression must be carried out in the following order : 1 ) operations within parentheses ( or absolute value bars or radicals ) 2 ) exponents 3 ) multiplication and division from left to right 4 ) addition and subtraction from left to right the answer is a .


Question: each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 93 % water by weight . what is the new weight of the cucumbers , in pounds ?

<gadget id="calculator">100 - 99</gadget>
<output>1</output>

<gadget id="calculator">100 - 93</gadget>
<output>7</output>

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

<gadget id="calculator">(1/7) * 100</gadget>
<output>100/7 = around 14.285714</output>
<result>100/7 = around 14.285714</result>

Choices:
A. 2
B. 15
C. 92
D. 96
E. 98

multiply(divide(subtract(100, 99), subtract(100, 93)), 100)

Explanation: "out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 93 % water and 7 % of non - water , so now 1 pound of non - water composes 7 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.07 = 15 pounds . answer : b ."


Question: the cost of the paint is rs . 50 per kg . if 1 kg of paint covers 20 sq . ft , how much will it cost to paint outside of a cube having 20 feet each side

<gadget id="calculator">6 * (20 ** 2)</gadget>
<output>2_400</output>

<gadget id="calculator">2_400 / 20</gadget>
<output>120</output>

<gadget id="calculator">120 * 50</gadget>
<output>6_000</output>
<result>6_000</result>

Choices:
A. rs . 962
B. rs . 6000
C. rs . 546
D. rs . 876
E. none of these

Explanation: "explanation : surface area of a cube = 6 x 20 ^ 2 = 2400 sq . ft quantity of paint required = ( 2400 / 20 ) = 120 kg cost of painting = 50 x 120 = rs . 6000 answer : b"


Question: a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 160 meter length ?

<gadget id="calculator">360 + 160</gadget>
<output>520</output>

<gadget id="calculator">45 * 1_000</gadget>
<output>45_000</output>

<gadget id="calculator">45_000 / 3_600</gadget>
<output>25/2 = around 12.5</output>

<gadget id="calculator">520 / (25/2)</gadget>
<output>208/5 = around 41.6</output>
<result>208/5 = around 41.6</result>

Choices:
A. 11 seconds
B. 41.6 seconds
C. 40 seconds
D. 88 seconds
E. 19 seconds

divide(add(360, 160), divide(multiply(45, const_1000), const_3600))

Explanation: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 160 = 520 meter time = distance / speed = 520 * ( 2 / 25 ) = 41.6 seconds answer : b"


Question: the ratio of three numbers is 1 : 2 : 3 and the sum of their squares is 2016 . the sum of the numbers is ?

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

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

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

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

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

<gadget id="calculator">2_016 / 14</gadget>
<output>144</output>

<gadget id="calculator">144 ** (1/2)</gadget>
<output>12</output>
<result>12</result>

Choices:
A. 10
B. 12
C. 15
D. 14
E. 9

sqrt(divide(2016, add(power(3, 2), add(power(1, 2), power(2, 2)))))

Explanation: "let the numbers be x , 2 x , 3 x then , x ^ 2 + 4 x ^ 2 + 9 x ^ 2 = 2016 14 x ^ 2 = 2016 x ^ 2 = 144 x = 12 answer is b"


Question: a certain airline ' s fleet consisted of 90 type a planes at the beginning of 1980 . at the end of each year , starting with 1980 , the airline retired 3 of the type a planes and acquired 4 new type b plans . how many years did it take before the number of type a planes left in the airline ' s fleet was less than 50 percent of the fleet ?

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

<gadget id="calculator">90 / 7</gadget>
<output>90/7 = around 12.857143</output>
<result>90/7 = around 12.857143</result>

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

Explanation: "let x be the number of years . 4 x > 90 - 3 x 7 x > 90 x > 12 + 6 / 7 the answer is c ."


Question: john makes $ 60 a week from his job . he earns a raise andnow makes $ 78 a week . what is the % increase ?

<gadget id="calculator">78 - 60</gadget>
<output>18</output>

<gadget id="calculator">18 / 60</gadget>
<output>3/10 = around 0.3</output>

<gadget id="calculator">(3/10) * 100</gadget>
<output>30</output>
<result>30</result>

Choices:
A. 16.12 %
B. 16.66 %
C. 30 %
D. 17.66 %
E. 18.1 %

multiply(divide(subtract(78, 60), 60), const_100)

Explanation: "increase = ( 18 / 60 ) * 100 = ( 3 / 10 ) * 100 = 30 % . c"


Question: a jogger running at 9 km / hr along side a railway track is 250 m ahead of the engine of a 120 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?

<gadget id="calculator">250 + 120</gadget>
<output>370</output>

<gadget id="calculator">45 - 9</gadget>
<output>36</output>

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

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

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

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

<gadget id="calculator">370 / 10</gadget>
<output>37</output>
<result>37</result>

Choices:
A. 37 sec
B. 89 sec
C. 36 sec
D. 87 sec
E. 45 sec

divide(add(250, 120), multiply(subtract(45, 9), divide(divide(const_10, const_2), divide(subtract(45, 9), const_2))))

Explanation: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 250 + 120 = 370 m . time taken = 370 / 10 = 37 sec . answer : a"


Question: two pipes a and b can separately fill a cistern in 60 minutes and 75 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 50 minutes . in how much time , the third pipe alone can empty the cistern ?

<gadget id="calculator">1 / 60</gadget>
<output>1/60 = around 0.016667</output>

<gadget id="calculator">1 / 75</gadget>
<output>1/75 = around 0.013333</output>

<gadget id="calculator">(1/60) + (1/75)</gadget>
<output>3/100 = around 0.03</output>

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

<gadget id="calculator">(3/100) - (1/50)</gadget>
<output>1/100 = around 0.01</output>

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

Choices:
A. 90 min
B. 100 min
C. 110 min
D. 120 min
E. 130 min

Explanation: "1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 third pipe can empty in 100 minutes answer : b"


Question: of the 20,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?

<gadget id="calculator">2 / 7</gadget>
<output>2/7 = around 0.285714</output>

<gadget id="calculator">(2/7) / 2</gadget>
<output>1/7 = around 0.142857</output>

<gadget id="calculator">1 - (2/7)</gadget>
<output>5/7 = around 0.714286</output>

<gadget id="calculator">(1/7) + (5/7)</gadget>
<output>6/7 = around 0.857143</output>

<gadget id="calculator">(1/7) / (6/7)</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">(1/6) * 100</gadget>
<output>50/3 = around 16.666667</output>

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

Choices:
A. 14.3 %
B. 16.67 %
C. 33 %
D. 28.6 %
E. 49.67 %

multiply(multiply(divide(divide(divide(2, 7), const_2), add(divide(divide(2, 7), const_2), subtract(const_1, divide(2, 7)))), const_100), const_3)

Explanation: the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 49.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . e


Question: if jimmy drinks 8 ounces of water each time for 8 times a day . how much gallons of water he would have to prepare ahead to drink for 5 days ? ( 1 ounce = 0.0078125 gallon )

<gadget id="calculator">8 * 8</gadget>
<output>64</output>

<gadget id="calculator">64 * 0.007812</gadget>
<output>0.499968</output>

<gadget id="calculator">0.499968 * 5</gadget>
<output>2.49984</output>
<result>2.49984</result>

Choices:
A. 1
B. 1.5
C. 2
D. 2.5
E. 3

multiply(multiply(multiply(8, 8), 0.0078125), 5)

Explanation: 8 ounces * 8 times / day = 64 ounces of water = 64 * 0.0078125 = 0.5 gallon . 5 days need 0.5 * 5 = 2.5 gallons . correct option : 2.5 answer : d


Question: 100 people are attending a newspaper conference . 45 of them are writers and more than 36 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?

<gadget id="calculator">36 + 1</gadget>
<output>37</output>

<gadget id="calculator">37 + 45</gadget>
<output>82</output>

<gadget id="calculator">100 - 82</gadget>
<output>18</output>
<result>18</result>

Choices:
A. 26
B. 24
C. 18
D. 20
E. 22

subtract(100, add(add(36, const_1), 45))

Explanation: "{ total } = { writers } + { editors } - { both } + { neither } . { total } = 100 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 100 = 45 + { editors } - x + 2 x - - > x = 55 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 37 , thus x = { both } = 55 - 37 = 18 . answer : c ."


Question: two trains , a and b , started simultaneously from opposite ends of a 120 - mile route and traveled toward each other on parallel tracks . train a , traveling at a constant rate , completed the 120 - mile trip in 6 hours ; train b , traveling at a constant rate , completed the 120 - mile trip in 4 hours . how many miles had train a traveled when it met train b ?

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

<gadget id="calculator">4 / 10</gadget>
<output>2/5 = around 0.4</output>

<gadget id="calculator">(2/5) * 120</gadget>
<output>48</output>
<result>48</result>

Choices:
A. 28
B. 36
C. 48
D. 50
E. 54

Explanation: "as the ratio of the rates of a and b is 4 to 6 then the distance covered at the time of the meeting ( so after traveling the same time interval ) would also be in that ratio , which means that x would cover 4 / ( 4 + 6 ) = 4 / 10 of 120 miles : 120 * 4 / 10 = 48 miles . answer : c ."


Question: if a speaks the truth 55 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time

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

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

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

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

<gadget id="calculator">(11/20) * (3/5)</gadget>
<output>33/100 = around 0.33</output>
<result>33/100 = around 0.33</result>

Choices:
A. 0.29
B. 0.33
C. 0.41
D. 0.482
E. 0.411

multiply(divide(55, multiply(multiply(const_4, const_5), const_5)), divide(60, multiply(multiply(const_4, const_5), const_5)))

Explanation: "explanation : probability that a speaks truth is 55 / 100 = 0.55 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.55 × 0.6 = 0.33 answer : b"


Question: the closest approximation of ( 69.28 × 0.004 ) / 0.03 is

<gadget id="calculator">0.004 / 0.03</gadget>
<output>0.133333</output>

<gadget id="calculator">0.133333 * 69.28</gadget>
<output>9.23731</output>
<result>9.23731</result>

Choices:
A. 0.092
B. 0.92
C. 9.2
D. 92
E. 920

Explanation: "( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . answer : c"


Question: to complete a work a and b takes 8 days , b and c takes 12 days , a , b and c takes 6 days . how much time a and c will take

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

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

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

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

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

Choices:
A. 24 days
B. 16 days
C. 12 days
D. 8 days
E. none of these

divide(multiply(8, 6), add(subtract(8, 6), subtract(8, const_4)))

Explanation: explanation : a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + b + c 1 day work = 1 / 6 we can get a work by ( a + b + c ) - ( b + c ) and c by ( a + b + c ) - ( a + b ) so a 1 day work = 1 / 6 − 1 / 12 = 1 / 12 similarly c 1 day work = 1 / 6 − 1 / 8 = 4 − 3 / 24 = 1 / 24 so a and c 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 so a and c can together do this work in 8 days option d


Question: maxwell leaves his home and walks toward brad ' s house . one hour later , brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 34 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h . what is the total time it takes maxwell before he meets up with brad ?

<gadget id="calculator">34 + 6</gadget>
<output>40</output>

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

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

Choices:
A. 3
B. 4
C. 5
D. 6
E. 8

Explanation: "total distance = 34 kms maxwell speed = 4 kms / hr maxwell travelled for 1 hour before brad started , therefore maxwell traveled for 4 kms in 1 hour . time taken = total distance / relative speed total distance after brad started = 30 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken to meet brad after brad started = 30 / 10 = 3 hrs distance traveled by maxwell = maxwell ' s speed * time taken = 4 * 3 = 12 + 4 = 16 kms . . . therefore total time taken by maxwell to meet brad = distance travelled by maxwell / maxwell ' s speed = 16 / 4 = 4 hrs . . . answer b"


Question: the salary of a person was reduced by 25 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?

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

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

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

<gadget id="calculator">25 / 75</gadget>
<output>1/3 = around 0.333333</output>

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

Choices:
A. 10 %
B. 33.33 %
C. 20 %
D. 25 %
E. 50 %

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

Explanation: "let the original salary be $ 100 new salary = $ 75 increase on 75 = 25 increase on 100 = [ ( 25 / 75 ) 100 ] % = 33.33 % answer is b"


Question: if ( x + 1 ) ( x + 3 ) = x ^ 2 + x , what is a possible value of x ?

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

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

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

Explanation: rearranging the given expression : ( x + 1 ) ( x + 3 ) = x ^ 2 + x i . e . x ^ 2 + 4 x + 3 = x ^ 2 + x i . e . 3 x = - 3 i . e . x = - 3 / 3 = - 1 answer : option e had it been a difficult expression to solve further , then we could have used options to check which one satisfies the expression after solving it as further as possible .


Question: as a treat for her two children , a mother runs to the freezer in which she has 3 cherry ice pops , 4 orange ice pops , and 4 lemon ice pops . she chooses two at random to bring outside to the children , but realizes as she runs out the door that she can not bring them different flavors without one being jealous of the other and getting even more upset . what is the probability that she has to return to the freezer to make sure that they each receive the same flavor ?

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

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

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

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

<gadget id="calculator">45 + 10</gadget>
<output>55</output>

<gadget id="calculator">15 / 55</gadget>
<output>3/11 = around 0.272727</output>

<gadget id="calculator">1 - (3/11)</gadget>
<output>8/11 = around 0.727273</output>
<result>8/11 = around 0.727273</result>

Choices:
A. 3 / 5
B. 5 / 7
C. 8 / 11
D. 11 / 15
E. 13 / 20

subtract(const_1, divide(add(add(3, multiply(const_2, 3)), multiply(const_2, 3)), add(multiply(add(add(3, multiply(const_2, 3)), multiply(const_2, 3)), 3), const_10)))

Explanation: p ( 2 cherry ) = 3 / 11 * 2 / 10 = 6 / 110 p ( 2 orange ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 lemon ) = 4 / 11 * 3 / 10 = 12 / 110 p ( 2 of the same flavor ) = 30 / 110 p ( 2 different flavors ) = 1 - 30 / 110 = 80 / 110 = 8 / 11 the answer is c .


Question: a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 10 metres apart , how many poles will be needed ?

<gadget id="calculator">2 * (90 + 50)</gadget>
<output>280</output>

<gadget id="calculator">280 / 10</gadget>
<output>28</output>
<result>28</result>

Choices:
A. 28
B. 56
C. 57
D. 58
E. none of these

Explanation: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 10 ] = 28 m answer a"


Question: if in a race of 80 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :

<gadget id="calculator">25 - 20</gadget>
<output>5</output>

<gadget id="calculator">5 / 25</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">(1/5) * 80</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 16 m
B. 18 m
C. 15 m
D. 14 m
E. 11 m

multiply(divide(subtract(25, 20), 25), 80)

Explanation: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 80 * 5 ) / 25 = 16 m hence , a beats b by 16 m . answer : a"


Question: when two dice are rolled , what is the probability that the sum of the two numbers is 6 ?

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

<gadget id="calculator">6 * 6</gadget>
<output>36</output>

<gadget id="calculator">5 / 36</gadget>
<output>5/36 = around 0.138889</output>
<result>5/36 = around 0.138889</result>

Choices:
A. 1 / 9
B. 5 / 36
C. 1 / 3
D. 2 / 36
E. none of the above

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

Explanation: we have 5 outcomes that satisfy the question : 1 - 5 2 - 4 3 - 3 4 - 2 5 - 1 the probability is ( 1 / 6 * 1 / 6 ) * 5 = 5 / 36 . i think the answer is b


Question: two trains start from a & b and travel towards each other at speed of 50 kmph and 60 kmph resp . at the time of the meeting the second train has traveled 100 km more than the first . the distance between them .

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

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

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

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

<gadget id="calculator">500 + 600</gadget>
<output>1_100</output>
<result>1_100</result>

Choices:
A. 800 km
B. 900 km
C. 1000 km
D. 1100 km
E. 1200 km

add(multiply(50, divide(100, subtract(60, 50))), multiply(60, divide(100, subtract(60, 50))))

Explanation: let the distance traveled by the first train be x km then distance covered by the second train is x + 100 km x / 50 = x + 100 / 60 x = 500 so the distance between a & b is x + x + 100 = 1100 km answer is d .


Question: a dog takes 5 leaps for every 7 leaps of a hare . if one leap of the dog is equal to 3 leaps of the hare , the ratio of the speed of the dog to that of the hare is :

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

<gadget id="calculator">15 / 7</gadget>
<output>15/7 = around 2.142857</output>
<result>15/7 = around 2.142857</result>

Choices:
A. 16 : 7
B. 15 : 7
C. 20 : 7
D. 7 : 15
E. 14 : 7

Explanation: explanation : dog : hare = ( 5 * 3 ) leaps of hare : 7 leaps of hare = 15 : 7 answer : b


Question: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value a of z - x ?

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

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

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

Explanation: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] a = z - x = x + 9 - x = 9 ans : d"


Question: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 140 m long ?

<gadget id="calculator">140 / 1_000</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">360 / 1_000</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(7/50) + (9/25)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">(1/2) / 45</gadget>
<output>1/90 = around 0.011111</output>

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

Choices:
A. 38 sec
B. 35 sec
C. 44 sec
D. 40 sec
E. 48 sec

multiply(divide(add(divide(140, const_1000), divide(360, const_1000)), 45), const_3600)

Explanation: "train length = 360 m platform length = 140 m time = ? length = speed * time total length = 360 + 140 = 500 m speed = 45 km / hr = 45 * ( 5 / 18 ) ( m / sec ) = 12.5 m / sec time = length / speed = 500 / 12.5 = 40 sec answer : d"