Question: what annual payment will discharge a debt of rs . 1125 due in 2 years at the rate of 5 % compound interest ?

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

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

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

<gadget id="calculator">(441/400) * 1_125</gadget>
<output>19_845/16 = around 1_240.3125</output>

<gadget id="calculator">(19_845/16) / 2</gadget>
<output>19_845/32 = around 620.15625</output>
<result>19_845/32 = around 620.15625</result>

Choices:
A. 993.2
B. 551.25
C. 534.33
D. 605.03
E. 646.33

divide(multiply(power(add(divide(5, const_100), const_1), 2), 1125), 2)

Explanation: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1125 820 x + 1125 * 441 x = 605.03 so , value of each installment = rs . 605.03 answer : option d"


Question: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 2 ¤ √ 2 =

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

<gadget id="calculator">(sqrt(2)) + (sqrt(2))</gadget>
<output>2*sqrt(2) = around 2.828427</output>

<gadget id="calculator">(2*sqrt(2)) ** 2</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 0
B. 8
C. 10
D. 15
E. 20

Explanation: "x = √ 2 and y also = √ 2 applying the function ( √ 2 + √ 2 ) ^ 2 - ( √ 2 - √ 2 ) ^ 2 = ( 2 √ 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 2 and y = √ 2 you get the answer 8 . answer b"


Question: jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 4 hours . how long would it take taimour to paint the fence alone ?

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

Choices:
A. 6 hours
B. 8 hours
C. 12 hours
D. 24 hours
E. 32 hours

Explanation: i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 4 = > 1 / 12 working alone taimour can do the job in 1 = 1 / 12 * hours = > 12 answer c


Question: find √ ? / 20 = 4 ?

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

<gadget id="calculator">80 ** 2</gadget>
<output>6_400</output>
<result>6_400</result>

Choices:
A. 76
B. 6400
C. 304
D. 1296
E. none

Explanation: "answer let √ n / 20 = 4 then √ n = 20 x 4 = 80 ∴ n = 80 x 80 = 6400 . correct option : b"


Question: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 45 kmph , find the speed of the stream ?

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

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

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

Choices:
A. 12 kmph
B. 13 kmph
C. 14 kmph
D. 15 kmph
E. 16 kmph

subtract(45, divide(multiply(45, const_2), const_3))

Explanation: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 45 / 3 = 15 kmph answer : d"


Question: a box contains 14 pairs of shoes ( 28 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?

<gadget id="calculator">28 - 1</gadget>
<output>27</output>

<gadget id="calculator">1 / 27</gadget>
<output>1/27 = around 0.037037</output>
<result>1/27 = around 0.037037</result>

Choices:
A. 1 / 190
B. 1 / 20
C. 1 / 19
D. 1 / 27
E. 1 / 9

Explanation: "the problem with your solution is that we do n ' t choose 1 shoe from 28 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 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d"


Question: there are 1000 students in a school and among them 10 % of them attends chess class . 10 % of the students who are in the chess class are also enrolled for swimming . no other students are interested in swimming so how many will attend the swimming class if all enrolled attends ?

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

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

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

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

Choices:
A. 1
B. 10
C. 100
D. 50
E. 20

divide(multiply(divide(multiply(10, 1000), const_100), 10), const_100)

Explanation: "10 % of 1000 gives 100 . so 100 attends chess and 10 % of 100 gives 10 . so 10 enrolled for swimming answer : b"


Question: a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 20 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?

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

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

<gadget id="calculator">150 / (4/5)</gadget>
<output>375/2 = around 187.5</output>

<gadget id="calculator">(375/2) - 150</gadget>
<output>75/2 = around 37.5</output>

<gadget id="calculator">(75/2) * 100</gadget>
<output>3_750</output>

<gadget id="calculator">3_750 / 150</gadget>
<output>25</output>
<result>25</result>

Choices:
A. 45 %
B. 40 %
C. 35 %
D. 30 %
E. 25 %

divide(multiply(subtract(divide(150, subtract(const_1, divide(20, const_100))), 150), const_100), 150)

Explanation: anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 20 % of $ 150 but instead , 20 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 20 % of s = s s = 150 / 0.8 profit = 150 / 0.8 - 150 = which is calculated on cost price in % terms . so 37.5 / 150 * 100 = 25 % is profit . e


Question: a and b start walking towards each other at 4 pm at speed of 2 kmph and 3 kmph . they were initially 15 km apart . at what time do they meet ?

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

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

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

Choices:
A. 8 pm
B. 6 pm
C. 7 pm
D. 10 pm
E. 5 pm

Explanation: time of meeting = distance / relative speed = 15 / 3 + 2 = 15 / 5 = 3 hrs after 4 pm = 7 pm answer is c


Question: in a certain parallelogram the degree measure of one angle exceeds that of the other by 20 what is the degree measure of the smaller angle ?

<gadget id="calculator">3_600 / 10</gadget>
<output>360</output>

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

<gadget id="calculator">360 - 40</gadget>
<output>320</output>

<gadget id="calculator">320 / 4</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 75
B. 80
C. 85
D. 90
E. 95

divide(subtract(divide(const_3600, const_10), multiply(20, const_2)), const_4)

Explanation: "in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b ."


Question: 3 years ago , the average age of a , b and c was 27 years and that of b and c 5 years ago was 20 years . a ’ s present age is :

<gadget id="calculator">27 * 3</gadget>
<output>81</output>

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

<gadget id="calculator">81 + 9</gadget>
<output>90</output>

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

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

<gadget id="calculator">40 + 10</gadget>
<output>50</output>

<gadget id="calculator">90 - 50</gadget>
<output>40</output>
<result>40</result>

Choices:
A. 22
B. 88
C. 40
D. 87
E. 17

subtract(add(multiply(27, 3), multiply(3, 3)), add(multiply(20, const_2), multiply(5, const_2)))

Explanation: explanation : sum of the present ages of a , b and c = ( 27 × 3 + 3 × 3 ) years = 90 years . sum of the present ages of b and c = ( 20 × 2 + 5 × 2 ) years = 50 years . a ' s present age = 90 – 50 = 40 years . answer : c


Question: if the perimeter of a rectangular garden is 600 m , its length when its breadth is 120 m is ?

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

<gadget id="calculator">300 - 120</gadget>
<output>180</output>
<result>180</result>

Choices:
A. 286 m
B. 180 m
C. 200 m
D. 166 m
E. 187 m

Explanation: "2 ( l + 120 ) = 600 = > l = 180 m answer : b"


Question: the average of 5 consecutive even numbers a , b , c , d and e is 20 . what percent of e is d ?

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

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

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

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

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

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

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

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

<gadget id="calculator">16 + 2</gadget>
<output>18</output>

<gadget id="calculator">18 + 2</gadget>
<output>20</output>

<gadget id="calculator">20 + 2</gadget>
<output>22</output>

<gadget id="calculator">22 + 2</gadget>
<output>24</output>

<gadget id="calculator">22 / 24</gadget>
<output>11/12 = around 0.916667</output>

<gadget id="calculator">(11/12) * 100</gadget>
<output>275/3 = around 91.666667</output>
<result>275/3 = around 91.666667</result>

Choices:
A. 90.1
B. 91.7
C. 97.1
D. 101.1
E. 107.1

multiply(divide(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), add(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), const_2)), const_100)

Explanation: explanation : in such a case the middle number ( c ) is the average ∴ c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b


Question: the length of rectangle is thrice its breadth and its perimeter is 72 m , find the area of the rectangle ?

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

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

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

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

<gadget id="calculator">9 * 3</gadget>
<output>27</output>

<gadget id="calculator">27 * 9</gadget>
<output>243</output>
<result>243</result>

Choices:
A. 432
B. 212
C. 243
D. 992
E. 212

multiply(multiply(divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))))

Explanation: "2 ( 3 x + x ) = 72 l = 27 b = 9 lb = 27 * 9 = 243 answer : c"


Question: there are 5 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .

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

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

Choices:
A. 19
B. 20
C. 30
D. 32
E. 25

Explanation: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 5 and for second = 4 so total methods = 5 * 4 = 20 answer : b"


Question: if m is a positive integer and m ^ 2 is divisible by 36 , then the largest positive integer that must divide m is ?

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

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

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

Choices:
A. 3
B. 6
C. 8
D. 12
E. 16

multiply(const_3, divide(divide(36, const_3), const_3))

Explanation: "m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 12 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? d"


Question: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price per f glass on the second day ?

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

<gadget id="calculator">2 * 0.6</gadget>
<output>1.2</output>

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

<gadget id="calculator">1.2 / 3</gadget>
<output>0.4</output>
<result>0.4</result>

Choices:
A. $ 015
B. $ 0.20
C. $ 0.30
D. $ 0.40
E. $ 0.45

divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))

Explanation: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."


Question: in what time will a train 110 m long cross an electric pole , it its speed be 128 km / hr ?

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

<gadget id="calculator">128 * (5/18)</gadget>
<output>320/9 = around 35.555556</output>

<gadget id="calculator">110 / (320/9)</gadget>
<output>99/32 = around 3.09375</output>
<result>99/32 = around 3.09375</result>

Choices:
A. 2.5 sec
B. 2.9 sec
C. 3.1 sec
D. 8.7 sec
E. 8.5 sec

Explanation: "speed = 128 * 5 / 18 = 36 m / sec time taken = 110 / 36 = 3.1 sec . answer : c"


Question: two trains 160 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?

<gadget id="calculator">160 + 160</gadget>
<output>320</output>

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

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

<gadget id="calculator">100 * (5/18)</gadget>
<output>250/9 = around 27.777778</output>

<gadget id="calculator">320 / (250/9)</gadget>
<output>288/25 = around 11.52</output>
<result>288/25 = around 11.52</result>

Choices:
A. 10.52 sec
B. 18.8 sec
C. 14.52 sec
D. 10.8 sec
E. 11.52 sec

Explanation: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 160 + 160 = 320 m . required time = 320 * 9 / 250 = 288 / 25 = 11.52 sec . answer : e"


Question: two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?

<gadget id="calculator">200 + 150</gadget>
<output>350</output>

<gadget id="calculator">350 / 1_000</gadget>
<output>7/20 = around 0.35</output>

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

<gadget id="calculator">(7/20) / 8</gadget>
<output>7/160 = around 0.04375</output>

<gadget id="calculator">3_600 * (7/160)</gadget>
<output>315/2 = around 157.5</output>
<result>315/2 = around 157.5</result>

Choices:
A. 72 sec
B. 132 sec
C. 157.5 sec
D. 252 sec
E. none

multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(48, 40)))

Explanation: "solution relative speed = ( 48 - 40 ) kmph = 8 kmph = ( 8 x 5 / 18 ) m / sec = ( 40 / 18 ) m / sec time taken = ( 350 x 18 / 40 ) sec = 157.5 sec . answer c"


Question: a trader cheats both his supplier and customer by using faulty weights . when he buys from the supplier , he takes 10 % more than the indicated weight . when he sells to his customer , he gives the customer a weight such that 10 % of that is added to the weight , the weight claimed by the trader is obtained . if he charges the cost price of the weight that he claims , find his profit percentage .

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

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

<gadget id="calculator">(11/10) * 110</gadget>
<output>121</output>

<gadget id="calculator">121 - 100</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 20 %
B. 21 %
C. 21.33 %
D. 22.109 %
E. 23 %

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

Explanation: "lets say the indicated weight is x for $ 10 but the trader actually get 1.1 x for $ 10 now he tells to the customer that its 1.1 ( 1.1 x ) = 1.21 x and charges the price accordingly i . e . 1.21 x * 10 / x = 12.1 so profit % = ( 12.1 - 10 ) / 10 = 0.21 = 21 % answer : b"


Question: if the wheel is 14 cm then the number of revolutions to cover a distance of 2288 cm is ?

<gadget id="calculator">3 * 100</gadget>
<output>300</output>

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

<gadget id="calculator">300 + 10</gadget>
<output>310</output>

<gadget id="calculator">310 + 4</gadget>
<output>314</output>

<gadget id="calculator">314 / 100</gadget>
<output>157/50 = around 3.14</output>

<gadget id="calculator">2 * (157/50)</gadget>
<output>157/25 = around 6.28</output>

<gadget id="calculator">(157/25) * 14</gadget>
<output>2_198/25 = around 87.92</output>

<gadget id="calculator">2_288 / (2_198/25)</gadget>
<output>28_600/1_099 = around 26.023658</output>
<result>28_600/1_099 = around 26.023658</result>

Choices:
A. 26
B. 28
C. 17
D. 12
E. 88

divide(2288, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))

Explanation: "2 * 22 / 7 * 14 * x = 2288 = > x = 26 answer : a"


Question: in the seaside 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 * 50</gadget>
<output>4_500</output>

<gadget id="calculator">4_500 / 100</gadget>
<output>45</output>

<gadget id="calculator">50 - 45</gadget>
<output>5</output>

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

<gadget id="calculator">500 / 5</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(subtract(50, divide(multiply(90, 50), const_100)), const_100), 5), 50)

Explanation: given there are 50 students in the seaside 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: the average price of 3 items of furniture is rs . 15000 . if their prices are in the ratio 2 : 4 : 8 , the price of the cheapest item is ?

<gadget id="calculator">3 * 15_000</gadget>
<output>45_000</output>

<gadget id="calculator">45_000 / 8</gadget>
<output>5_625</output>
<result>5_625</result>

Choices:
A. 2379
B. 2889
C. 5625
D. 9000
E. 28311

Explanation: let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c


Question: in a group of 15 people , 8 read english , 7 read french while 3 of them read none of these two . how many of them read french and english both ?

<gadget id="calculator">8 + 7</gadget>
<output>15</output>

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

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

Choices:
A. 2
B. 3
C. 4
D. 7
E. 5

Explanation: in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f ∩ e } ) + e ] = 15 - 3 ( or ) f + e + ( f ∩ e ) = 12 . . . . . . ( 1 ) also , f + ( f ∩ e ) = 7 ; e + ( f ∩ e ) = 8 . by adding , f + e + 2 ( f ∩ e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f ∩ e ) = 3 . ∴ 3 of them read both french and english . answer : b


Question: if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?

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

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

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

Choices:
A. 50 km
B. 16 km
C. 18 km
D. 29 km
E. 19 km

multiply(10, divide(20, subtract(14, 10)))

Explanation: "let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 14 4 x - 200 = > x = 50 km . answer : a"


Question: sum of 36 odd numbers is ?

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

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

<gadget id="calculator">72 * 18</gadget>
<output>1_296</output>
<result>1_296</result>

Choices:
A. 1294
B. 1295
C. 1296
D. 1297
E. 1298

multiply(multiply(36, const_2), divide(36, const_2))

Explanation: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 36 odd numbers = 36 ^ 2 = 1296 answer : c"


Question: 15 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?

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

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

Choices:
A. 190
B. 200
C. 210
D. 220
E. 225

Explanation: "though 2 * ( 15 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 14 , so he ' ll play 28 matches . similarly , second guy has to play with the rest of 13 as his 2 games with the first guy are already played . so he plays 26 matches . this continues like this and the total matches are 28 + 26 + 24 . . . + 2 28 + 26 + . . . + 2 = 2 ( 14 + 13 + . . . + 1 ) = 2 ( ( 14 * 15 ) / 2 ) = 14 * 15 = 210 . answer : c"


Question: the height of the wall is 6 times its width and length of the wall is 8 times its height . if the volume of the wall be 36000 cu . m . its width is

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

<gadget id="calculator">48 * 6</gadget>
<output>288</output>

<gadget id="calculator">36_000 / 288</gadget>
<output>125</output>

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

<gadget id="calculator">125 ** (1/3)</gadget>
<output>5</output>
<result>5</result>

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

power(divide(36000, multiply(multiply(6, 8), 6)), divide(const_1, const_3))

Explanation: "explanation : let width = x then , height = 6 x and length = 48 x 48 x ã — 6 x ã — x = 36000 x = 5 answer : b"


Question: one - third of 600 is what percent of 120 ?

<gadget id="calculator">600 / 3</gadget>
<output>200</output>

<gadget id="calculator">200 / 120</gadget>
<output>5/3 = around 1.666667</output>

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

Choices:
A. 313.2
B. 30.1
C. 12.24
D. none of these
E. 166.6

multiply(const_100, divide(divide(600, const_3), 120))

Explanation: answer let one - third of 600 is n % of 120 . ∵ 600 / 3 = ( n x 120 ) / 100 ∴ n = ( 200 x 100 ) / 120 = 166.6 correct option : e


Question: how many diagonals does a 58 - sided convex polygon have ?

Choices:
A. 870
B. 1125
C. 1595
D. 2560
E. 3190

divide(factorial(58), multiply(factorial(subtract(58, const_2)), factorial(const_2)))

Explanation: "a 58 - sided convex polygon has 58 vertices . if we examine a single vertex , we can see that we can connect it with 55 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be ( 58 ) ( 55 ) = 3190 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3190 by 2 to get 1595 . the answer is c ."


Question: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 545 pounds after processing , how many pounds did it weigh before processing ?

<gadget id="calculator">545 * 100</gadget>
<output>54_500</output>

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

<gadget id="calculator">54_500 / 65</gadget>
<output>10_900/13 = around 838.461538</output>
<result>10_900/13 = around 838.461538</result>

Choices:
A. 191
B. 355
C. 737
D. 838
E. 1,560

divide(multiply(545, const_100), subtract(const_100, 35))

Explanation: let weight of side of beef before processing = x ( 65 / 100 ) * x = 545 = > x = ( 545 * 100 ) / 65 = 838 answer d


Question: miller street begins at baker street and runs directly east for 4.5 kilometers until it ends when it meets turner street . miller street is intersected every 250 meters by a perpendicular street , and each of those streets other than baker street and turner street is given a number beginning at 1 st street ( one block east of baker street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of turner street . what is the highest - numbered street that intersects miller street ?

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

<gadget id="calculator">4.5 / (1/4)</gadget>
<output>18</output>

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

Choices:
A. 15 th
B. 16 th
C. 17 th
D. 18 th
E. 19 th

subtract(divide(4.5, divide(250, const_1000)), 1)

Explanation: 4.5 km / 250 m = 18 . however , the street at the 4.5 - km mark is not 18 th street ; it is turner street . therefore , the highest numbered street is 17 th street . the answer is c .


Question: the pressure someone experiences as he or she dives deeper and deeper in the ocean increases linearly . on the surface , the pressure is close to 15 pounds per square inch . 33 feet below the surface , the pressure is 30 pounds . if 25000 pounds per sq inch can crush your bones , what depth is extremely dangerous for humans ?

<gadget id="calculator">25_000 - 15</gadget>
<output>24_985</output>

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

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

<gadget id="calculator">33 * 12</gadget>
<output>396</output>

<gadget id="calculator">15 / 396</gadget>
<output>5/132 = around 0.037879</output>

<gadget id="calculator">24_985 / (5/132)</gadget>
<output>659_604</output>

<gadget id="calculator">659_604 / 12</gadget>
<output>54_967</output>
<result>54_967</result>

Choices:
A. 55522 feet
B. 45522 feet
C. 35522 feet
D. 25522 feet
E. none

divide(divide(subtract(25000, 15), divide(subtract(30, 15), multiply(33, multiply(const_4, const_3)))), multiply(const_4, const_3))

Explanation: solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 × 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a


Question: in a class total 34 students , 16 are have a brother , 15 are have sisters , 9 students do n ' t have either brothers or sisters . find the number of students having both brother and sisters .

<gadget id="calculator">16 + 15</gadget>
<output>31</output>

<gadget id="calculator">34 - 9</gadget>
<output>25</output>

<gadget id="calculator">31 - 25</gadget>
<output>6</output>
<result>6</result>

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

Explanation: total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c


Question: find the area of a parallelogram with base 26 cm and height 12 cm ?

<gadget id="calculator">26 * 12</gadget>
<output>312</output>
<result>312</result>

Choices:
A. 281
B. 284
C. 288
D. 255
E. 312

Explanation: "area of a parallelogram = base * height = 26 * 12 = 312 cm 2 answer : e"


Question: a can do a piece of work in 90 days & y can do it in 80 days . they began working together but a leaves after some days and then b completed the remaining work in 46 days . the number of days after which a left the work was ?

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

<gadget id="calculator">(1/80) * 46</gadget>
<output>23/40 = around 0.575</output>

<gadget id="calculator">1 - (23/40)</gadget>
<output>17/40 = around 0.425</output>

<gadget id="calculator">1 / 90</gadget>
<output>1/90 = around 0.011111</output>

<gadget id="calculator">(1/80) + (1/90)</gadget>
<output>17/720 = around 0.023611</output>

<gadget id="calculator">(17/40) / (17/720)</gadget>
<output>18</output>

<gadget id="calculator">18 - 2</gadget>
<output>16</output>
<result>16</result>

Choices:
A. 12 days
B. 18 days
C. 16 days
D. 19 days
E. 21 days

subtract(divide(subtract(const_1, multiply(divide(const_1, 80), 46)), add(divide(const_1, 80), divide(const_1, 90))), const_2)

Explanation: a and b did the work for some days . after that , b completed the remaining work in 46 days . in 46 days , word done by b = 1 80 x 46 = 23 45 remaining work = 1 – 23 / 45 = 17 / 45 remaining work is done by both a and b together = 17 / 45 x 90 x 80 / 90 + 80 = 16 days c


Question: by selling 10 pencils for a rupee a man loses 25 % . how many for a rupee should he sell in order to gain 25 % ?

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

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

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

<gadget id="calculator">125 * (1/75)</gadget>
<output>5/3 = around 1.666667</output>

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

<gadget id="calculator">(3/5) * 10</gadget>
<output>6</output>
<result>6</result>

Choices:
A. 6
B. 9
C. 10
D. 89
E. 81

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

Explanation: "75 % - - - 10 125 % - - - ? 75 / 125 * 10 = 6 answer : a"


Question: 1 / 0.05 is equal to

<gadget id="calculator">1 / 0.05</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 25.5
B. 2.5
C. 25
D. 20
E. none of these

Explanation: "explanation : 1 / 0.05 = ( 1 * 100 ) / 5 = 100 / 5 = 20 option d"


Question: amit and ananthu can do a work in 15 days and 60 days respectively . amit started the work and left after 3 days . ananthu took over and completed the work . in how many days was the total work completed ?

<gadget id="calculator">1 / 15</gadget>
<output>1/15 = around 0.066667</output>

<gadget id="calculator">(1/15) * 3</gadget>
<output>1/5 = around 0.2</output>

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

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

<gadget id="calculator">(4/5) / (1/60)</gadget>
<output>48</output>

<gadget id="calculator">48 + 3</gadget>
<output>51</output>
<result>51</result>

Choices:
A. 38 days
B. 40 days
C. 43 days
D. 45 days
E. 51 days

add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(60)), 3)

Explanation: "amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 60 ananthu can do work in = 4 / 5 * 60 = 48 days so total days = 48 + 3 = 51 days answer : e"


Question: a and b together can do a work in 7 days . if a alone can do it in 56 days . in how many days can b alone do it ?

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

<gadget id="calculator">1 / 56</gadget>
<output>1/56 = around 0.017857</output>

<gadget id="calculator">(1/7) - (1/56)</gadget>
<output>1/8 = around 0.125</output>

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

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

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

<gadget id="calculator">8 + (2/5)</gadget>
<output>42/5 = around 8.4</output>
<result>42/5 = around 8.4</result>

Choices:
A. 11
B. 8
C. 21
D. 20
E. 25

add(inverse(subtract(divide(const_1, 7), divide(const_1, 56))), divide(const_2, add(const_2, const_3)))

Explanation: "b 8 1 / 7 â € “ 1 / 56 = 1 / 8 = > 8"


Question: a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 180 kilometers ?

<gadget id="calculator">180 / 20</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 8.5 gallons
B. 9 gallons
C. 6.5 gallons
D. 5.5 gallons
E. 6 gallons

Explanation: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 180 kilometers ? 180 / 20 = 9 * 1 gallon = 9 gallons correct answer b"


Question: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 680 sq . feet , how many feet of fencing will be required ?

<gadget id="calculator">680 / 20</gadget>
<output>34</output>

<gadget id="calculator">34 * 2</gadget>
<output>68</output>

<gadget id="calculator">68 + 20</gadget>
<output>88</output>
<result>88</result>

Choices:
A. 34
B. 40
C. 68
D. 88
E. 98

add(multiply(divide(680, 20), const_2), 20)

Explanation: "explanation : we have : l = 20 ft and lb = 680 sq . ft . so , b = 34 ft . length of fencing = ( l + 2 b ) = ( 20 + 68 ) ft = 88 ft . answer : d"


Question: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 9 technicians is rs . 18000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :

<gadget id="calculator">18_000 - 8_000</gadget>
<output>10_000</output>

<gadget id="calculator">9 * 10_000</gadget>
<output>90_000</output>

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

<gadget id="calculator">90_000 / 2_000</gadget>
<output>45</output>

<gadget id="calculator">9 + 45</gadget>
<output>54</output>
<result>54</result>

Choices:
A. 22
B. 54
C. 88
D. 37
E. 29

Explanation: "explanation : lot the total number of workers be v then , 8 ooov = ( 18000 * 9 ) + 6000 ( v - 9 ) < = > 2000 v = 108000 < = > v = 54 answer : b ) 54"


Question: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?

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

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

<gadget id="calculator">125 / 95</gadget>
<output>25/19 = around 1.315789</output>

<gadget id="calculator">100 * (25/19)</gadget>
<output>2_500/19 = around 131.578947</output>
<result>2_500/19 = around 131.578947</result>

Choices:
A. 131.6
B. 120
C. 130
D. 110
E. 150

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

Explanation: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 95 / 100 x = 125 x = 12500 / 95 = $ 131.6 now , s . p . = $ 131.6 , c . p . = $ 100 profit % = 31.6 % . a"


Question: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 10 of money ?

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

<gadget id="calculator">10 / 20</gadget>
<output>1/2 = around 0.5</output>

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

<gadget id="calculator">50 * 20</gadget>
<output>1_000</output>
<result>1_000</result>

Choices:
A. 1500
B. 1992
C. 9921
D. 1000
E. 2789

multiply(multiply(divide(10, multiply(10, 2)), const_100), multiply(10, 2))

Explanation: "p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d"


Question: a room is 7 meters 68 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .

<gadget id="calculator">7 * 100</gadget>
<output>700</output>

<gadget id="calculator">700 + 68</gadget>
<output>768</output>

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

<gadget id="calculator">400 + 32</gadget>
<output>432</output>

<gadget id="calculator">768 * 432</gadget>
<output>331_776</output>

<gadget id="calculator">gcd(768, 432)</gadget>
<output>48</output>

<gadget id="calculator">48 * 48</gadget>
<output>2_304</output>

<gadget id="calculator">331_776 / 2_304</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 107
B. 144
C. 175
D. 165
E. 130

divide(multiply(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32))))

Explanation: "let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b"


Question: there is enough provisions for 600 men in an army camp for 25 days . if there were 300 men less , how long will the provision last ?

<gadget id="calculator">600 * 25</gadget>
<output>15_000</output>

<gadget id="calculator">15_000 / 300</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 35 days
B. 40 days
C. 45 days
D. 50 days
E. 55 days

Explanation: "exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 300 * d 2 d 2 = 600 * 25 / 300 = 50 days . answer : d"


Question: two cars start from the opposite places of a main road , 140 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?

<gadget id="calculator">140 - 35</gadget>
<output>105</output>

<gadget id="calculator">25 + 25</gadget>
<output>50</output>

<gadget id="calculator">105 - 50</gadget>
<output>55</output>
<result>55</result>

Choices:
A. 65
B. 38
C. 20
D. 55
E. 21

subtract(subtract(140, 35), add(25, 25))

Explanation: answer : d ) 55 km


Question: 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = ?

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

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

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

<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>

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

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

divide(1, add(1, divide(1, add(1, divide(1, 1)))))

Explanation: explanation : 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ 1 } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 } ] = 1 ÷ [ 1 + 1 ÷ 2 ] = 1 ÷ [ 1 + ( 1 / 2 ) ] = 1 ÷ 3 / 2 = 1 × 3 / 2 = 1 × 2 / 3 = 2 / 3 answer : option c


Question: john had a stock of 1000 books in his bookshop . he sold 75 on monday , 50 on tuesday , 64 on wednesday , 78 on thursday and 135 on friday . what percentage of the books were not sold ?

<gadget id="calculator">75 + 50</gadget>
<output>125</output>

<gadget id="calculator">64 + 78</gadget>
<output>142</output>

<gadget id="calculator">125 + 142</gadget>
<output>267</output>

<gadget id="calculator">267 + 135</gadget>
<output>402</output>

<gadget id="calculator">1_000 - 402</gadget>
<output>598</output>

<gadget id="calculator">598 / 1_000</gadget>
<output>299/500 = around 0.598</output>

<gadget id="calculator">(299/500) * 100</gadget>
<output>299/5 = around 59.8</output>
<result>299/5 = around 59.8</result>

Choices:
A. 59.8 %
B. 23.8 %
C. 66.5 %
D. 34.9 %
E. 43.5 %

Explanation: "let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1000 - n = 1000 - 402 = 598 percentage books not sold / total number of books = 598 / 1000 = 59.8 = 59.8 % correct answer a"


Question: a line that passes through ( – 1 , – 4 ) and ( 2 , k ) has a slope = k . what is the value of k ?

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

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

Explanation: "slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !"


Question: p , q and r have $ 8000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?

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

<gadget id="calculator">8_000 * 4</gadget>
<output>32_000</output>

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

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

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

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

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

<gadget id="calculator">32_000 / 10</gadget>
<output>3_200</output>
<result>3_200</result>

Choices:
A. 2400
B. 2403
C. 3200
D. 2539
E. 1930

divide(multiply(8000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))

Explanation: "c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 ."


Question: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes bil can make using this recipe ?

<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">15 / (5/2)</gadget>
<output>6</output>

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

<gadget id="calculator">(3/4) + 2</gadget>
<output>11/4 = around 2.75</output>

<gadget id="calculator">16 / (11/4)</gadget>
<output>64/11 = around 5.818182</output>

<gadget id="calculator">floor(64/11)</gadget>
<output>5</output>

<gadget id="calculator">min(6, 5)</gadget>
<output>5</output>

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

<gadget id="calculator">(1/3) + 1</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">8 / (4/3)</gadget>
<output>6</output>

<gadget id="calculator">min(5, 6)</gadget>
<output>5</output>
<result>5</result>

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

min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1)))

Explanation: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"


Question: of the 3,600 employees of company x , 16 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?

<gadget id="calculator">16 / 25</gadget>
<output>16/25 = around 0.64</output>

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

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

<gadget id="calculator">(16/25) * (3/4)</gadget>
<output>12/25 = around 0.48</output>

<gadget id="calculator">1 - (16/25)</gadget>
<output>9/25 = around 0.36</output>

<gadget id="calculator">(12/25) + (9/25)</gadget>
<output>21/25 = around 0.84</output>

<gadget id="calculator">(12/25) / (21/25)</gadget>
<output>4/7 = around 0.571429</output>

<gadget id="calculator">(4/7) * 100</gadget>
<output>400/7 = around 57.142857</output>
<result>400/7 = around 57.142857</result>

Choices:
A. 57 %
B. 22.2 %
C. 20 %
D. 12.5 %
E. 11.1 %

multiply(divide(multiply(divide(16, 25), subtract(1, divide(1, 4))), add(multiply(divide(16, 25), subtract(1, divide(1, 4))), subtract(1, divide(16, 25)))), const_100)

Explanation: "let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %"


Question: the difference between two numbers is 1365 . when the larger number is divided by the smaller one , the quotient is 6 and the remainder is 15 . the smaller number is

<gadget id="calculator">1_365 - 15</gadget>
<output>1_350</output>

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

<gadget id="calculator">1_350 / 5</gadget>
<output>270</output>
<result>270</result>

Choices:
A. 240
B. 250
C. 260
D. 270
E. none

divide(subtract(1365, 15), subtract(6, const_1))

Explanation: "solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 ‹ = › 5 x = 1350 . ‹ = › x = 270 . answer d"


Question: the sum of present age of abe and the age before 7 years is 33 . find the present age of abe . what will be his age after 7 years ?

<gadget id="calculator">33 + 7</gadget>
<output>40</output>

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

<gadget id="calculator">20 + 7</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 25
B. 26
C. 27
D. 28
E. 29

Explanation: "present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c"


Question: a train running at a speed of 60 kmph crosses a pole in 18 seconds . what is the length of the train ?

<gadget id="calculator">60 * 1_000</gadget>
<output>60_000</output>

<gadget id="calculator">60_000 / 3_600</gadget>
<output>50/3 = around 16.666667</output>

<gadget id="calculator">(50/3) * 18</gadget>
<output>300</output>
<result>300</result>

Choices:
A. 120 m
B. 300 m
C. 190 m
D. 150 m
E. 160 m

multiply(divide(multiply(60, const_1000), const_3600), 18)

Explanation: 60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b


Question: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number w of people surveyed by the company ?

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

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

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

<gadget id="calculator">120 / 2</gadget>
<output>60</output>

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

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

Choices:
A. 46
B. 80
C. w . 90
D. w . 100
E. 200

add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))

Explanation: "100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."


Question: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of t ?

<gadget id="calculator">39 - 15</gadget>
<output>24</output>

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

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

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

Choices:
A. 7
B. 8
C. 9
D. 10
E. 11

subtract(divide(subtract(39, 15), add(2, 1)), 1)

Explanation: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )"


Question: the average earning of a person for the first 4 days of a week is rs 18 and for the last 4 days is rs 22 . if he earns rs 20 on the fourth day , his average earning for the whole week is ?

<gadget id="calculator">4 * 18</gadget>
<output>72</output>

<gadget id="calculator">4 * 22</gadget>
<output>88</output>

<gadget id="calculator">72 + 88</gadget>
<output>160</output>

<gadget id="calculator">160 - 20</gadget>
<output>140</output>

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

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

Choices:
A. rs 18.95
B. rs 16
C. rs 20
D. rs 25.71
E. none of these

divide(subtract(add(multiply(4, 18), multiply(4, 22)), 20), add(const_4, const_3))

Explanation: total earning for the week = rs ( 4 × 18 + 4 × 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c


Question: mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?

<gadget id="calculator">50 / 100</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">1 + (1/2)</gadget>
<output>3/2 = around 1.5</output>

<gadget id="calculator">12 / (3/2)</gadget>
<output>8</output>
<result>8</result>

Choices:
A. 7
B. 8
C. 9
D. 11
E. 10

divide(12, add(const_1, divide(50, const_100)))

Explanation: ratio of times taken by mary and rosy = 150 : 100 = 3 : 2 suppose rosy takes x days to do the work . 3 : 2 : : 12 : x = > x = 8 days . hence , rosy takes 8 days to complete the work . answer : b


Question: points a , b , and , c have xy - coordinates ( 20 ) , ( 812 ) , and ( 140 ) , respectively . points x , y , and z have xy - coordinates ( 60 ) , ( 84 ) , and ( 100 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?

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

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

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

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

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

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

<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>
<result>1/9 = around 0.111111</result>

Choices:
A. 1 / 9
B. 1 / 8
C. 1 / 6
D. 1 / 5
E. 1 / 3

divide(divide(multiply(const_4, const_4), const_2), multiply(subtract(20, multiply(const_4, const_2)), divide(subtract(20, multiply(const_4, const_2)), const_2)))

Explanation: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a


Question: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 174 , how many hours overtime did he work ?

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

<gadget id="calculator">174 - 120</gadget>
<output>54</output>

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

<gadget id="calculator">54 / 6</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 8
B. 5
C. 9
D. 6
E. 10

divide(subtract(174, multiply(3, 40)), multiply(3, const_2))

Explanation: "at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 174 - $ 120 = $ 54 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 54 / $ 6 = 9 ans is c"


Question: the price of rice falls by 25 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?

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

<gadget id="calculator">75 / 20</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">100 / (15/4)</gadget>
<output>80/3 = around 26.666667</output>
<result>80/3 = around 26.666667</result>

Choices:
A. 5 kg
B. 15 kg
C. 26.67 kg
D. 30 kg
E. none

divide(const_100, divide(subtract(const_100, 25), 20))

Explanation: solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 20 % , new price for 20 kg rice , = ( 100 - 25 % of 100 ) = 75 new price of rice = 75 / 20 = rs . 3.75 per kg . rice can bought now at = 100 / 3.75 = 26.67 kg . answer : option c


Question: john purchased 1370 large bottles at $ 1.99 per bottle and 690 small bottles at $ 1.50 per bottle . what was the approximate average price paid per bottle ?

<gadget id="calculator">1_370 * 1.99</gadget>
<output>2_726.3</output>

<gadget id="calculator">690 * 1.5</gadget>
<output>1_035</output>

<gadget id="calculator">2_726.3 + 1_035</gadget>
<output>3_761.3</output>

<gadget id="calculator">1_370 + 690</gadget>
<output>2_060</output>

<gadget id="calculator">3_761.3 / 2_060</gadget>
<output>1.825874</output>
<result>1.825874</result>

Choices:
A. $ 1.63
B. $ 1.64
C. $ 1.68
D. $ 1.72
E. $ 1.83

Explanation: "( 1370 * 1.99 + 690 * 1.50 ) / ( 1370 + 690 ) = ~ 1.83 - option ( e )"


Question: find the ratio in which rice at rs . 7.30 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg

<gadget id="calculator">6.3 - 5.7</gadget>
<output>0.6</output>

<gadget id="calculator">7.3 - 6.3</gadget>
<output>1</output>

<gadget id="calculator">0.6 / 1</gadget>
<output>0.6</output>
<result>0.6</result>

Choices:
A. 2 : 0
B. 2 : 3
C. 3 : 5
D. 2 : 2
E. 2 : 8

Explanation: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 100 = 3 : 5 answer : c"


Question: 3 different containers contain 50 litres , 100 litres and 150 litres of mixture of milk and water respectively . what is the biggest measure can measure all the different quantities exactly ?

<gadget id="calculator">gcd(50, 100)</gadget>
<output>50</output>

<gadget id="calculator">gcd(50, 150)</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 120 litres
B. 57 litres
C. 60 litres
D. 50 litres
E. 100 litres

Explanation: m 1 = 50 litres m 2 = 100 litres m 3 = 150 litres required measurement = h . c . f . of m 1 , m 2 , m 3 = 50 litres answer is d


Question: 2034 - ( 1002 / 20.04 ) = ?

<gadget id="calculator">1_002 / 20.04</gadget>
<output>50</output>

<gadget id="calculator">2_034 - 50</gadget>
<output>1_984</output>
<result>1_984</result>

Choices:
A. 2984
B. 2983
C. 2982
D. 2981
E. 1984

Explanation: 2034 - 50 = 1984 answer : e


Question: x , y , and z are all unique numbers . if x is chosen randomly from the set { 10 , 11 } and y and z are chosen randomly from the set { 20 , 21 , 22 , 23 } , what is the probability that x and y are prime and z is not ?

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

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

<gadget id="calculator">(1/2) * (1/4)</gadget>
<output>1/8 = around 0.125</output>
<result>1/8 = around 0.125</result>

Choices:
A. 1 / 5
B. 3 / 20
C. 1 / 8
D. 3 / 10
E. 1 / 10

multiply(divide(const_1, const_2), divide(const_1, const_4))

Explanation: p ( x is prime ) = 1 / 2 p ( y is prime ) = 1 / 4 if y is prime , then z is not prime since y and z are unique . then the probability is 1 / 2 * 1 / 4 = 1 / 8 the answer is c .


Question: marty ' s pizza shop guarantees that their pizzas all have at least 75 % of the surface area covered with toppings , with a crust of uniform width surrounding them . if you order their best seller – a circular pizza with a diameter of 16 inches – what is the maximum width you can expect to see for the crust ?

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

<gadget id="calculator">pi * (8 ** 2)</gadget>
<output>64*pi = around 201.06193</output>

<gadget id="calculator">(64*pi) * 75</gadget>
<output>4800*pi = around 15_079.644737</output>

<gadget id="calculator">(4800*pi) / 100</gadget>
<output>48*pi = around 150.796447</output>

<gadget id="calculator">(48*pi) / pi</gadget>
<output>48</output>

<gadget id="calculator">48 ** (1/2)</gadget>
<output>4*sqrt(3) = around 6.928203</output>

<gadget id="calculator">(4*sqrt(3)) * 2</gadget>
<output>8*sqrt(3) = around 13.856406</output>

<gadget id="calculator">16 - (8*sqrt(3))</gadget>
<output>16 - 8*sqrt(3) = around 2.143594</output>

<gadget id="calculator">(16 - 8*sqrt(3)) / 2</gadget>
<output>8 - 4*sqrt(3) = around 1.071797</output>
<result>8 - 4*sqrt(3) = around 1.071797</result>

Choices:
A. 0.8 inches
B. 1.1 inches
C. 1.6 inches
D. 2.0 inches
E. 2.5 inches

divide(subtract(16, multiply(sqrt(divide(divide(multiply(circle_area(divide(16, const_2)), 75), const_100), const_pi)), const_2)), const_2)

Explanation: total area = 8 * 8 * pi radius = 64 pi surface = . 75 * 64 * pi = 48 pi radius of surface = 4 sqrt ( 3 ) ~ 6.8 radius width = 8 - 6.8 = 1.2 answer : b


Question: compute all real solutions to 16 x + 4 x + 1 - 96 = 0

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

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

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

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

divide(subtract(4, 1), subtract(subtract(4, 1), 1))

Explanation: if we substitute y = 4 x , we have y 2 + 4 y - 96 = 0 , so y = - 4 or y = 8 . the first does not map to a real solution , while the second maps to x = 3 / 2 correct answer a


Question: virginia , adrienne , and dennis have taught history for a combined total of 87 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?

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

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

<gadget id="calculator">87 - 27</gadget>
<output>60</output>

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

<gadget id="calculator">20 + 18</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 23
B. 32
C. 38
D. 41
E. 44

add(divide(subtract(87, add(add(9, 9), 9)), const_3), add(9, 9))

Explanation: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 87 = > 3 d = 87 + 27 = 114 = > d = 38 answer c"


Question: the edges of a cuboid are 4 cm , 5 cm and 7 cm . find the volume of the cuboid ?

<gadget id="calculator">4 * 5 * 7</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 140
B. 278
C. 378
D. 368
E. 367

Explanation: "4 * 5 * 7 = 120 answer : a"


Question: what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?

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

<gadget id="calculator">1_000 / 35</gadget>
<output>200/7 = around 28.571429</output>

<gadget id="calculator">50 + (200/7)</gadget>
<output>550/7 = around 78.571429</output>

<gadget id="calculator">20 * 35</gadget>
<output>700</output>

<gadget id="calculator">1_000 / 700</gadget>
<output>10/7 = around 1.428571</output>

<gadget id="calculator">(550/7) - (10/7)</gadget>
<output>540/7 = around 77.142857</output>

<gadget id="calculator">1_000 - (540/7)</gadget>
<output>6_460/7 = around 922.857143</output>
<result>6_460/7 = around 922.857143</result>

Choices:
A. 567
B. 850
C. 560
D. 923
E. 240

subtract(1000, subtract(add(divide(1000, 20), divide(1000, 35)), divide(1000, multiply(20, 35))))

Explanation: "in 1000 consecutive numbers , number of multiples of 20 = 1000 / 20 = 50 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 20 * 35 i . e . 700 = 1000 / 700 = 1 number of integers from 1 to 1000 that are divisible by neither 20 nor by 35 = 1000 - ( 50 + 28 - 1 ) { using the concept of sets here ) = 923 answer is d"


Question: the population of a town is 10000 . it decreases annually at the rate of 20 % p . a . what will be its population after 2 years ?

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

<gadget id="calculator">10_000 * (1/5)</gadget>
<output>2_000</output>

<gadget id="calculator">10_000 - 2_000</gadget>
<output>8_000</output>

<gadget id="calculator">8_000 * (1/5)</gadget>
<output>1_600</output>

<gadget id="calculator">8_000 - 1_600</gadget>
<output>6_400</output>
<result>6_400</result>

Choices:
A. 6400
B. 4500
C. 5120
D. 5230
E. 5366

subtract(subtract(10000, multiply(10000, divide(20, const_100))), multiply(subtract(10000, multiply(10000, divide(20, const_100))), divide(20, const_100)))

Explanation: "10000 × 80 / 100 × 80 / 100 = 6400 answer : a"


Question: in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 4 , 1 ) , ( 1 , 1 ) , ( 1 , - 3 ) and ( - 4 , - 3 ) ?

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

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

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

Choices:
A. 16
B. 20
C. 24
D. 25
E. 30

Explanation: "length of side 1 = 4 + 1 = 5 length of side 2 = 3 + 1 = 4 area of rectangle = 5 * 4 = 20 b is the answer"


Question: each person in a group of 110 investors has investments in either equities or securities or both . exactly 25 of the investors in equities have investments in securities , and exactly 40 of the investors in securities have investments in equities . how many have investments in equities ?

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

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

<gadget id="calculator">(2/5) / (1/4)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(8/5) * (1/4)</gadget>
<output>2/5 = around 0.4</output>

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

<gadget id="calculator">(2/5) + (3/5)</gadget>
<output>1</output>

<gadget id="calculator">(8/5) - (2/5)</gadget>
<output>6/5 = around 1.2</output>

<gadget id="calculator">1 + (6/5)</gadget>
<output>11/5 = around 2.2</output>

<gadget id="calculator">110 / (11/5)</gadget>
<output>50</output>

<gadget id="calculator">50 * (8/5)</gadget>
<output>80</output>
<result>80</result>

Choices:
A. 65
B. 80
C. 120
D. 180
E. 190

multiply(divide(110, add(add(multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)), subtract(const_1, multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100)))), subtract(divide(divide(40, const_100), divide(25, const_100)), multiply(divide(divide(40, const_100), divide(25, const_100)), divide(25, const_100))))), divide(divide(40, const_100), divide(25, const_100)))

Explanation: explanation : the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let x , y , and z denote the number of people in the respective categories . since the total number of investors is 110 , we have : - = > x + y + z = 110 - - - - - - - - - - - - - ( 1 ) . also , the number of people with investments in equities is x + z and the number of people with investments in securities is y + z . since exactly 25 % of the investors in equities have investments in securities , we have the equation = > ( 25 / 100 ) × ( x + z ) = z . = > ( 25 / 100 ) × x = 75 z / 100 . = > x = 3 z . - - - - - - - - - - - - - - ( 2 ) since exactly 40 % of the investors in securities have investments in equities , we have the equation = > ( 40 / 100 ) × ( y + z ) = z . = > ( y + z ) = 5 z / 2 . = > y = 3 z / 2 . - - - - - - - - - - - - - - - - - ( 3 ) substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) gives : - = > 3 z + ( 3 z / 2 ) + z = 110 . = > 11 z / 2 = 110 . = > z = 110 × 2 / 11 = 20 . hence , the number of people with investments in equities is : = > x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 . answer : b


Question: a certain number of two digits is 3 times the sum of its digits and if 45 be added to it , the degits are reversed . the number is .

<gadget id="calculator">45 - 10</gadget>
<output>35</output>

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

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

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

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

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

<gadget id="calculator">20 + 7</gadget>
<output>27</output>
<result>27</result>

Choices:
A. 23
B. 27
C. 32
D. 72
E. 46

add(multiply(subtract(divide(subtract(45, const_10), subtract(subtract(const_10, 3), const_2)), subtract(subtract(const_10, 3), const_2)), const_10), divide(subtract(45, const_10), subtract(subtract(const_10, 3), const_2)))

Explanation: let the ten ' s digit be x and unit ' s digit be y . then 10 x + y = 3 ( x + y ) = = > 7 x - 2 y = 0 = = > 7 x - 2 y = 0 - - - - > ( i ) 10 + y + 45 = 10 y + x = = > y - x = 5 = = = > - 2 x + 2 y = 10 - - - - - - ( ii ) by adding ( i ) and ( ii ) we get 5 x = 10 so x = 2 and y = 7 so the required number is 27 . so the correct option is b ) 27 .


Question: tom , working alone , can paint a room in 16 hours . peter and john , working independently , can paint the same room in 8 hours and 4 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?

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

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

<gadget id="calculator">4 / 9</gadget>
<output>4/9 = around 0.444444</output>
<result>4/9 = around 0.444444</result>

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

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

Explanation: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 16 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 8 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 4 * t part of the job : 1 / 16 * ( t + 4 ) + 1 / 8 * ( t + 2 ) + 1 / 4 * t = 1 - - > multiply by 16 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 16 - - > t = 10 / 7 ; hence peter has done 1 / 8 * ( 10 / 7 + 2 ) = 1 / 8 * 24 / 7 = 3 / 7 answer : e"


Question: an angry arjun carried some arrows for fighting with bheeshm . with half the arrows , he cut down the arrows thrown by bheeshm on him and with 6 other arrows he killed the chariot driver of bheeshm . with one arrow each he knocked down respectively the chariot , the flag and the bow of bheeshm . finally , with one more than 4 times the square root of arrows he laid bheeshm unconscious on an arrow bed . find the total number of arrows arjun had .

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

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

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

Explanation: x / 2 + 6 + 3 + 1 + 4 sqrt ( x ) = x x / 2 + 10 + 4 sqrt ( x ) = x 4 sqrt ( x ) = x / 2 - 10 squaring on both sides 16 x = x ² / 4 + 100 - 10 x simplifying x ² - 104 x + 400 = 0 x = 100 , 4 x = 4 is not possible therefore x = 100 answer : b


Question: find the distance covered by a man walking for 10 min at a speed of 6 km / hr ?

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

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

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

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

Choices:
A. 1 km
B. 2 km
C. 3 km
D. 1.5 km
E. 4 km

divide(multiply(10, divide(multiply(6, const_1000), const_60)), const_1000)

Explanation: "distance = 6 * 10 / 60 = 1 km answer is a"


Question: in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 15 , what is the greatest possible value of b x a ?

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

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

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

Choices:
A. 0
B. 15
C. 25
D. 30
E. 35

multiply(add(const_3, const_4), add(const_2, const_3))

Explanation: "i also was confused when i was looking forabove number : d as far as i understood , 15 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 15 x 1 ( a = 1 , b = 5 respectively we have = 5 ) . to ensure , let ' s check ( avoid even multiples of 2,4 , 6,8 etc ( we will have 0 in units thus making our result 0 ) 15 x 3 = 45 ( a = 4 b = 5 respectively . hey ! that ' s 20 . but we do n ' t have this number in answer choices , move on ) . 15 x 5 = 75 ( a = 7 , b = 5 respectively . increasing trend , we have 35 now ) 15 x 7 = 105 ( a = 0 , b = 5 . have 0 now . can create a pattern ) imo e ."


Question: let s be the set of all positive integers that , when divided by 8 , have a remainder of 5 . what is the 79 th number in this set ?

<gadget id="calculator">79 - 1</gadget>
<output>78</output>

<gadget id="calculator">78 * 8</gadget>
<output>624</output>

<gadget id="calculator">624 + 5</gadget>
<output>629</output>
<result>629</result>

Choices:
A. 605
B. 608
C. 613
D. 616
E. 629

add(multiply(subtract(79, const_1), 8), 5)

Explanation: "the set s = { 5 , 13 , 21 , 29 , . . . . . . . . . . . . . . . . . . . . . } 1 st number = 8 * 0 + 5 = 5 2 nd number = 8 * 1 + 5 = 13 3 rd number = 8 * 2 + 5 = 21 79 th number = 8 * ( 79 - 1 ) + 5 = 629 answer = e"


Question: the area of a sector of a circle of radius 4 cm formed by an arc of length 4.5 cm is ?

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

<gadget id="calculator">4 * 4.5</gadget>
<output>18</output>

<gadget id="calculator">(1/2) * 18</gadget>
<output>9</output>
<result>9</result>

Choices:
A. 8.78
B. 8.67
C. 8.75
D. 8.98
E. 9

multiply(divide(const_1, const_2), multiply(4, 4.5))

Explanation: "( 4 * 4.5 ) / 2 = 9 answer : e"


Question: the speed at which a man can row a boat in still water is 21 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 90 metres ?

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

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

<gadget id="calculator">26 * (5/18)</gadget>
<output>65/9 = around 7.222222</output>

<gadget id="calculator">90 / (65/9)</gadget>
<output>162/13 = around 12.461538</output>
<result>162/13 = around 12.461538</result>

Choices:
A. 23.46
B. 27.46
C. 28.46
D. 12.46
E. 25.46

divide(90, multiply(add(21, 5), const_0_2778))

Explanation: speed of the boat downstream = 21 + 5 = 26 kmph = 26 * 5 / 18 = 7.22 m / s hence time taken to cover 90 m = 90 / 7.22 = 12.46 seconds . answer : d


Question: if a man lost 4 % by selling oranges at the rate of 48 a rupee at how many a rupee must he sell them to gain 44 % ?

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

<gadget id="calculator">96 * 48</gadget>
<output>4_608</output>

<gadget id="calculator">100 + 44</gadget>
<output>144</output>

<gadget id="calculator">4_608 / 144</gadget>
<output>32</output>
<result>32</result>

Choices:
A. 1
B. 8
C. 9
D. 4
E. 32

divide(multiply(subtract(const_100, 4), 48), add(const_100, 44))

Explanation: "96 % - - - - 48 144 % - - - - ? 96 / 144 * 48 = 32 answer : e"


Question: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 28 metre of cloth ?

<gadget id="calculator">28 / 0.128</gadget>
<output>218.75</output>
<result>218.75</result>

Choices:
A. 175 seconds
B. 219 seconds
C. 155 seconds
D. 115 seconds
E. 115 seconds

Explanation: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 28 : x = > x = { \ color { blue } \ frac { 28 \ times 1 } { 0.128 } } = > x = 218.75 so time will be approx 219 seconds answer : b"


Question: the radius of a circular wheel is 1.75 m , how many revolutions will it make in traveling 1 km ?

<gadget id="calculator">pi * 2</gadget>
<output>2*pi = around 6.283185</output>

<gadget id="calculator">(2*pi) * 1.75</gadget>
<output>3.5*pi = around 10.995574</output>

<gadget id="calculator">(3.5*pi) * 1_000</gadget>
<output>3500.0*pi = around 10_995.574288</output>

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

<gadget id="calculator">(3500.0*pi) / 11</gadget>
<output>318.181818181818*pi = around 999.597663</output>
<result>318.181818181818*pi = around 999.597663</result>

Choices:
A. 1000
B. 2788
C. 2677
D. 2899
E. 2771

divide(multiply(multiply(multiply(const_pi, const_2), 1.75), const_1000), add(1, const_10))

Explanation: 2 * 22 / 7 * 1.75 * x = 11000 x = 1000 answer : a


Question: a 340 - liter solution of kola is made from 88 % water , 5 % concentrated kola and the rest is made from sugar . if 4.2 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) + 4.2</gadget>
<output>28</output>

<gadget id="calculator">340 + 4.2</gadget>
<output>344.2</output>

<gadget id="calculator">344.2 + 10</gadget>
<output>354.2</output>

<gadget id="calculator">354.2 + 6.8</gadget>
<output>361</output>

<gadget id="calculator">28 / 361</gadget>
<output>28/361 = around 0.077562</output>

<gadget id="calculator">(28/361) * 100</gadget>
<output>2_800/361 = around 7.756233</output>
<result>2_800/361 = around 7.756233</result>

Choices:
A. 6 % .
B. 7.7 % .
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))), 4.2), add(add(add(340, 4.2), 10), 6.8)), const_100)

Explanation: "denominator : 340 + 10 + 4.2 + 6.8 = 361 numerator : 340 ( 1 - . 88 - . 05 ) + 4.2 340 ( 0.07 ) + 4.2 23.8 + 4.2 28 ratio : 28 / 361 = 0.077 answer : b"


Question: if the radius of a cylinder is doubled and so is the height , what is the new volume of the cylinder divided by the old one ?

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

<gadget id="calculator">pi * (2 ** 2) * 2</gadget>
<output>8*pi = around 25.132741</output>

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

<gadget id="calculator">(8*pi) / pi</gadget>
<output>8</output>
<result>8</result>

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

divide(volume_cylinder(multiply(const_1, const_2), multiply(const_1, const_2)), volume_cylinder(const_1, const_1))

Explanation: let the radius be r and the the height be h . new radius = 2 r and height = 2 h . area ( new ) : area ( old ) = pi ∗ ( 2 r ) ^ 2 ∗ 2 h / pi ∗ r ^ 2 ∗ h = 8 : 1 . hence the answer is a .


Question: oil is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 9 feet long , 8 feet wide , and 5 feet deep , approximately how many hours does it take to fill the tank ?

<gadget id="calculator">9 * 8 * 5</gadget>
<output>360</output>

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

Choices:
A. 60
B. 70
C. 80
D. 90
E. 100

divide(volume_rectangular_prism(9, 8, 5), 4)

Explanation: the volume the tank is : length * width * depth = 9 * 8 * 5 = 360 cubic feet . 360 cubic feet / 4 cubic feet per hour = 90 hours . it will take 90 hours to fill the tank . the answer is d .


Question: the speed of a boat in still water in 37 km / hr and the rate of current is 13 km / hr . the distance travelled downstream in 10 minutes is :

<gadget id="calculator">37 + 13</gadget>
<output>50</output>

<gadget id="calculator">10 / 60</gadget>
<output>1/6 = around 0.166667</output>

<gadget id="calculator">50 * (1/6)</gadget>
<output>25/3 = around 8.333333</output>
<result>25/3 = around 8.333333</result>

Choices:
A. 10.44 km
B. 10.6 km
C. 11.4 km
D. 11.22 km
E. 8.33 km

multiply(add(37, 13), divide(10, const_60))

Explanation: "explanation : speed downstream = ( 37 + 13 ) = 50 kmph time = 24 minutes = 10 / 60 hour = 1 / 6 hour distance travelled = time × speed = ( 1 / 6 ) × 50 = 8.33 km answer : option e"


Question: a train 600 m long can cross an electric pole in 20 sec and then find the speed of the train ?

<gadget id="calculator">600 / 1_000</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">20 / 3_600</gadget>
<output>1/180 = around 0.005556</output>

<gadget id="calculator">(3/5) / (1/180)</gadget>
<output>108</output>
<result>108</result>

Choices:
A. 76 kmph
B. 108 kmph
C. 72 kmph
D. 34 kmph
E. 91 kmph

divide(divide(600, const_1000), divide(20, const_3600))

Explanation: "length = speed * time speed = l / t s = 600 / 20 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : b"


Question: the average of 30 numbers is 25 . if each number is multiplied by 5 , find the new average ?

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

Choices:
A. 115
B. 125
C. 135
D. 145
E. 155

Explanation: "sum of the 30 numbers = 30 * 25 = 750 if each number is multiplied by 5 , the sum also gets multiplied by 5 and the average also gets multiplied by 5 . thus , the new average = 25 * 5 = 125 . answer : b"


Question: √ ( 21 ) ^ 2

<gadget id="calculator">21 ** 2</gadget>
<output>441</output>

<gadget id="calculator">441 ** (1/2)</gadget>
<output>21</output>
<result>21</result>

Choices:
A. 7
B. 14
C. 49
D. 21
E. none of these

Explanation: "explanation √ ( 21 ) ^ 2 = ? or , ? = 21 answer d"


Question: a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 798 find the share of a .

<gadget id="calculator">3_000 * 8</gadget>
<output>24_000</output>

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

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

<gadget id="calculator">2_000 * 4</gadget>
<output>8_000</output>

<gadget id="calculator">24_000 + 8_000</gadget>
<output>32_000</output>

<gadget id="calculator">4_000 * 8</gadget>
<output>32_000</output>

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

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

<gadget id="calculator">32_000 + 20_000</gadget>
<output>52_000</output>

<gadget id="calculator">32_000 + 52_000</gadget>
<output>84_000</output>

<gadget id="calculator">798 / 84_000</gadget>
<output>19/2_000 = around 0.0095</output>

<gadget id="calculator">(19/2_000) * 32_000</gadget>
<output>304</output>
<result>304</result>

Choices:
A. 240
B. 388
C. 379
D. 304
E. 122

multiply(divide(798, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))

Explanation: "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 798 = 304 answer : d"


Question: the speed of a boat in still water is 15 km / hr and the rate of the current is 3 km / hr . the distance travelled downstream in 12 minutes is

<gadget id="calculator">12 / 60</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">15 + 3</gadget>
<output>18</output>

<gadget id="calculator">(1/5) * 18</gadget>
<output>18/5 = around 3.6</output>
<result>18/5 = around 3.6</result>

Choices:
A. 1.2 km
B. 1.8 km
C. 2.4 km
D. 3.6 km
E. none

multiply(divide(12, const_60), add(15, 3))

Explanation: "speed downstream = ( 15 + 3 ) km / hr = 18 km / hr . distance travelled = ( 18 x 12 / 60 ) hours = 3.6 km . answer d"


Question: a certain animal in the zoo has consumed 39 pounds of food in 6 days . if it continues to eat at the same rate , in how many more days will its total consumption be 117 pounds ?

<gadget id="calculator">39 / 6</gadget>
<output>13/2 = around 6.5</output>

<gadget id="calculator">117 / (13/2)</gadget>
<output>18</output>

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

Choices:
A. 8
B. 7
C. 12
D. 9
E. none of the above

Explanation: ans is c : 39 pounds - - > 6 days 117 pounds - - > x days x = 117 * 6 / 39 = 18 the animal has already consumed food in 6 days so the the number of days for it ' s total consumption be 117 pounds is 18 - 6 = 12


Question: the length of a rectangular floor is more than its breadth by 200 % . if rs . 441 is required to paint the floor at the rate of rs . 3 / sq m , what would be the length of the floor ?

<gadget id="calculator">441 / 3</gadget>
<output>147</output>

<gadget id="calculator">147 / 3</gadget>
<output>49</output>

<gadget id="calculator">49 ** (1/2)</gadget>
<output>7</output>

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

Choices:
A. 12
B. 18
C. 20
D. 21
E. 24

multiply(sqrt(divide(divide(441, 3), const_3)), const_3)

Explanation: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 441 / 3 = 147 sq m l b = 147 i . e . , l * l / 3 = 147 l ^ 2 = 441 = > l = 21 . d"


Question: in a class of 42 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?

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

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

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

<gadget id="calculator">22 + 2</gadget>
<output>24</output>

<gadget id="calculator">42 - 24</gadget>
<output>18</output>

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

<gadget id="calculator">17 * 3</gadget>
<output>51</output>

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

<gadget id="calculator">12 + 20</gadget>
<output>32</output>

<gadget id="calculator">51 + 32</gadget>
<output>83</output>

<gadget id="calculator">84 - 83</gadget>
<output>1</output>
<result>1</result>

Choices:
A. 1
B. 5
C. 8
D. 13
E. 15

subtract(multiply(42, 2), add(multiply(subtract(subtract(42, add(add(multiply(12, 1), 10), 2)), 1), 3), add(multiply(12, 1), multiply(10, 2))))

Explanation: "total # of students = 42 avg # of books per student = 2 total # of books = 42 * 2 = 84 # of student borrowed at least 3 books = 42 - 2 - 12 - 10 = 18 # of books borrowed by above 18 students = 84 - ( 12 * 1 ) + ( 10 * 2 ) = 52 considering that 17 out of above 18 students borrowed only 3 books , # of books borrowed = 17 * 3 = 51 so maximum # of books borrowed by any single student = 52 - 51 = 1 option a"


Question: a set of consecutive positive integers beginning with 1 is written on the blackboard . a student came along and erased one number . the average of the remaining numbers is 35 * 7 / 17 . what was the number erased ?

<gadget id="calculator">7 / 17</gadget>
<output>7/17 = around 0.411765</output>

<gadget id="calculator">35 + (7/17)</gadget>
<output>602/17 = around 35.411765</output>

<gadget id="calculator">(602/17) * 2</gadget>
<output>1_204/17 = around 70.823529</output>

<gadget id="calculator">floor(1_204/17)</gadget>
<output>70</output>

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

<gadget id="calculator">70 - 1</gadget>
<output>69</output>

<gadget id="calculator">35 * 69</gadget>
<output>2_415</output>

<gadget id="calculator">69 - 1</gadget>
<output>68</output>

<gadget id="calculator">(602/17) * 68</gadget>
<output>2_408</output>

<gadget id="calculator">2_415 - 2_408</gadget>
<output>7</output>
<result>7</result>

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

subtract(multiply(divide(floor(multiply(add(35, divide(7, 17)), const_2)), const_2), subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1)), multiply(add(35, divide(7, 17)), subtract(subtract(floor(multiply(add(35, divide(7, 17)), const_2)), const_1), 1)))

Explanation: explanation : let the higher number be n and x be the number erased . then ( ( n ( n + 1 ) / 2 ) + x ) / ( n + 1 ) = 35 * 7 / 17 = 602 / 17 hence , n = 69 and x = 7 satisfy the above conditions . answer : a


Question: find the number which is nearest to 3105 and is exactly divisible by 21 ?

<gadget id="calculator">3_105 % 21</gadget>
<output>18</output>

<gadget id="calculator">21 - 18</gadget>
<output>3</output>

<gadget id="calculator">3_105 + 3</gadget>
<output>3_108</output>
<result>3_108</result>

Choices:
A. 3100
B. 2500
C. 2545
D. 5800
E. 3108

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


Question: the lengths of the diagonals of a rhombus are 20 and 48 meters . find the perimeter of the rhombus ?

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

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

Choices:
A. 150 merters
B. 125 meters
C. 96 meters
D. 104 meters
E. 152 meters

Explanation: below is shown a rhombus with the given diagonals . consider the right triangle boc and apply pythagora ' s theorem as follows bc 2 = 10 ^ 2 + 24 ^ 2 and evaluate bc bc = 26 meters . we now evaluate the perimeter p as follows : p = 4 * 26 = 104 meters . answer is d


Question: a courtyard is 21 meter long and 14 meter board is to be paved with bricks of dimensions 14 cm by 8 cm . the total number of bricks required is :

<gadget id="calculator">21 * 100</gadget>
<output>2_100</output>

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

<gadget id="calculator">2_100 * 1_400</gadget>
<output>2_940_000</output>

<gadget id="calculator">14 * 8</gadget>
<output>112</output>

<gadget id="calculator">2_940_000 / 112</gadget>
<output>26_250</output>
<result>26_250</result>

Choices:
A. 16000
B. 18000
C. 20000
D. 26250
E. none of these

divide(multiply(multiply(21, const_100), multiply(14, const_100)), multiply(14, 8))

Explanation: "explanation : number of bricks = courtyard area / 1 brick area = ( 2100 ã — 1400 / 14 ã — 8 ) = 26250 option d"


Question: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.3 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is ?

<gadget id="calculator">15.8 - 15.4</gadget>
<output>0.4</output>

<gadget id="calculator">16.3 - 15.8</gadget>
<output>0.5</output>

<gadget id="calculator">0.4 / 0.5</gadget>
<output>0.8</output>
<result>0.8</result>

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

Explanation: "let the ratio be k : 1 . then , k * 16.3 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.3 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.5 = 4 / 5 required ratio = 4 / 5 : 1 = 4 : 5 . answer : c"


Question: during the first two weeks of june , the total rainfall in springdale was 40 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall in inches during the second week of june ?

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

<gadget id="calculator">40 / 2.5</gadget>
<output>16</output>

<gadget id="calculator">16 * 1.5</gadget>
<output>24</output>
<result>24</result>

Choices:
A. 15
B. 18
C. 21
D. 24
E. 27

multiply(divide(40, add(const_1, 1.5)), 1.5)

Explanation: let x be the rainfall in the first week . then 1.5 x was the rainfall in the second week . 2.5 x = 40 x = 16 the rainfall during the second week was 1.5 * 16 = 24 inches the answer is d .


Question: the owner of a furniture shop charges his customer 18 % more than the cost price . if a customer paid rs . 6000 for a computer table , then what was the cost price of the computer table ?

<gadget id="calculator">18 / 100</gadget>
<output>9/50 = around 0.18</output>

<gadget id="calculator">1 + (9/50)</gadget>
<output>59/50 = around 1.18</output>

<gadget id="calculator">6_000 / (59/50)</gadget>
<output>300_000/59 = around 5_084.745763</output>
<result>300_000/59 = around 5_084.745763</result>

Choices:
A. rs . 6289
B. rs . 6298
C. rs . 6290
D. rs . 5084
E. rs . 6708

divide(6000, add(const_1, divide(18, const_100)))

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 6000 ( 100 / 118 ) = rs . 5084 . answer : d"


Question: find the simple interest on $ 10000 at 7 % per annum for 12 months ?

<gadget id="calculator">7 / 100</gadget>
<output>7/100 = around 0.07</output>

<gadget id="calculator">10_000 * (7/100)</gadget>
<output>700</output>
<result>700</result>

Choices:
A. $ 410
B. $ 500
C. $ 650
D. $ 700
E. $ 1000

Explanation: "p = $ 10000 r = 7 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 7 * 1 / 100 = $ 700 answer is d"


Question: two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days . the number of days required by 1 man to complete the work is

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

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

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

<gadget id="calculator">7 / 3</gadget>
<output>7/3 = around 2.333333</output>

<gadget id="calculator">(7/3) - 1</gadget>
<output>4/3 = around 1.333333</output>

<gadget id="calculator">20 / (4/3)</gadget>
<output>15</output>
<result>15</result>

Choices:
A. 60 days
B. 15 days
C. 6 days
D. 51 days
E. 50 days

divide(subtract(multiply(7, 4), add(4, 4)), subtract(divide(7, 3), 1))

Explanation: two men and 7 children complete a certain piece of work in 4 days or 8 men and 28 children complete a certain piece of work in 1 days 4 men and 4 children complete the same work in only 3 days . or 12 men and 12 children complete the same work in only 3 days . so 8 men + 28 children = 12 men + 12 children 1 man = 4 children 4 men and 4 children complete the same work in only 3 days or 4 men and 1 man ( in place of 4 children ) complete the same work in only 3 days or 5 men complete the same work in 3 days or 1 man will complete the same work in 5 * 3 = 15 days answer : b


Question: a particular store purchased a stock of turtleneck sweaters and marked up its cost by 20 % . during the new year season , it further marked up its prices by 25 % of the original retail price . in february , the store then offered a discount of 15 % . what was its profit on the items sold in february ?

<gadget id="calculator">100 - 15</gadget>
<output>85</output>

<gadget id="calculator">85 / 100</gadget>
<output>17/20 = around 0.85</output>

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

<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">120 * (5/4)</gadget>
<output>150</output>

<gadget id="calculator">(17/20) * 150</gadget>
<output>255/2 = around 127.5</output>

<gadget id="calculator">(255/2) - 100</gadget>
<output>55/2 = around 27.5</output>
<result>55/2 = around 27.5</result>

Choices:
A. 27.5 %
B. 30 %
C. 35 %
D. 37.5 %
E. 40 %

subtract(multiply(divide(subtract(const_100, 15), const_100), multiply(add(const_100, 20), divide(add(const_100, 25), const_100))), const_100)

Explanation: assume the total price = 100 x price after 20 % markup = 120 x price after 25 % further markup = 1.25 * 120 x = 150 x price after the discount = 0.85 * 150 x = 127.5 x hence total profit = 27.5 % option a


Question: the total surface area of a solid hemisphere of diameter 14 cm , is :

<gadget id="calculator">3 * pi</gadget>
<output>3*pi = around 9.424778</output>

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

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

<gadget id="calculator">(3*pi) * 49</gadget>
<output>147*pi = around 461.81412</output>
<result>147*pi = around 461.81412</result>

Choices:
A. 462 cm ²
B. 530 cm ²
C. 1345 cm ²
D. 1788 cm ²
E. none

multiply(multiply(const_3, const_pi), power(divide(14, const_2), const_2))

Explanation: sol . total surface area = 3 ∏ r ² = [ 3 * 22 / 7 * 7 * 7 ] cm ² = 462 cm ² answer a


Question: a certain company ’ s profit in 1996 was 25 percent greater than its profit in 1995 , and its profit in 1997 was 30 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">30 / 100</gadget>
<output>3/10 = around 0.3</output>

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

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

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

<gadget id="calculator">(13/10) * (5/4)</gadget>
<output>13/8 = around 1.625</output>

<gadget id="calculator">(13/8) - 1</gadget>
<output>5/8 = around 0.625</output>

<gadget id="calculator">(5/8) * 100</gadget>
<output>125/2 = around 62.5</output>
<result>125/2 = around 62.5</result>

Choices:
A. 5 %
B. 62.5 %
C. 33 %
D. 35 %
E. 38 %

multiply(subtract(multiply(add(divide(30, const_100), const_1), add(const_1, divide(25, const_100))), const_1), const_100)

Explanation: "profit in 1995 - 100 profit in 1996 - 125 % increae profit in 1997 in comparison to 1995 = 25 + 125 * 30 % = 62.5 correct option : b"