Question: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors a ?

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

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

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

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

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

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

Choices:
A. 2
B. 3
C. 5
D. 6
E. 8

add(divide(add(const_1, const_4), divide(divide(divide(60, const_2), const_2), const_3)), const_2)

Explanation: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have a = 2 * 3 * 5 * 7 = 840 thus , answer b"


Question: the payment per hour for a daily - wages employee is increased by 33.33 and the working time is reduced by 33.33 % . what is the percentage change in the employee ' s income ?

<gadget id="calculator">33.33 / 100</gadget>
<output>0.3333</output>

<gadget id="calculator">1 + 0.3333</gadget>
<output>1.3333</output>

<gadget id="calculator">1 - 0.3333</gadget>
<output>0.6667</output>

<gadget id="calculator">1.3333 * 0.6667</gadget>
<output>0.888911</output>
<result>0.888911</result>

Choices:
A. rs . 0.7889
B. rs . 0.8889
C. rs . 0.9889
D. rs . 1.8889
E. rs . 2.8889

multiply(add(const_1, divide(33.33, const_100)), subtract(const_1, divide(33.33, const_100)))

Explanation: if payment per hr is increased by 33.33 % , then 11.11 % decrease in income if earlier he is getting rs 1 hr per hr and working for 1 hr , income = rs 1 now he is getting rs 1.3333 per hr and working for 0.66667 hrs , income = rs . 0.8889 answer : b


Question: the sub - duplicate ratio of 16 : 64 is

<gadget id="calculator">16 ** (1/2)</gadget>
<output>4</output>

<gadget id="calculator">64 ** (1/2)</gadget>
<output>8</output>

<gadget id="calculator">4 / 8</gadget>
<output>1/2 = around 0.5</output>
<result>1/2 = around 0.5</result>

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

Explanation: "root ( 16 ) : root ( 64 ) = 4 : 8 = 2 : 4 answer : e"


Question: there are 38 students in a certain geometry class . if two thirds of the students are boys and 3 fourths of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?

<gadget id="calculator">38 * 2</gadget>
<output>76</output>

<gadget id="calculator">76 * 3</gadget>
<output>228</output>

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

<gadget id="calculator">228 / 12</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 6
B. 12
C. 19
D. 24
E. 27

divide(multiply(multiply(38, const_2), 3), multiply(3, const_4))

Explanation: 38 * 2 / 3 * 3 / 4 = 19 answer : c


Question: a boat crossed a lake from north to east at the speed of 7 km / h , entered a river and covered twice as much distance going upstream at 6 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?

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

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

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

Explanation: "one way of solving this is : speed of boat on still water ( lake ) = 7 kmph speed upstream = 6 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 7 + 1 = 8 kmph ans is e"


Question: a bullet train 120 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 4 kmph in the direction opposite to that in which the bullet train is going ?

<gadget id="calculator">50 + 4</gadget>
<output>54</output>

<gadget id="calculator">54 * 1_000</gadget>
<output>54_000</output>

<gadget id="calculator">54_000 / 3_600</gadget>
<output>15</output>

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

Choices:
A. 23 sec
B. 15 sec
C. 12 sec
D. 8 sec
E. 16 sec

divide(120, divide(multiply(add(50, 4), const_1000), const_3600))

Explanation: "d 8 sec speed of the bullet train relative to man = ( 50 + 4 ) kmph = 54 * 5 / 18 m / sec = 45 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 120 m at ( 45 / 3 ) m / sec = ( 120 * 3 / 45 ) sec = 8 sec"


Question: 70,76 , 74,85 , 90,105 , 105,130 , 130,130 the list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . if the standard deviation of the 10 running times is 22.4 , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times .

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

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

Explanation: how many of the 10 running times are more than one sd below the meanmeans how many data points from given 10 are less thanmean - 1 sd . we are given that sd = 22.4 , so we should find mean - - > mean = 100 - - > there are only 3 data points below 100 - 22.4 = 77.6 , namely 70 75 , and 74 . answer : c .


Question: if the cost price of 60 articles is equal to the selling price of 40 articles , then what is the percent profit ?

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

<gadget id="calculator">4_000 / 60</gadget>
<output>200/3 = around 66.666667</output>

<gadget id="calculator">100 - (200/3)</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">(100/3) / (200/3)</gadget>
<output>1/2 = around 0.5</output>

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

Choices:
A. 30 %
B. 40 %
C. 50 %
D. 60 %
E. 70 %

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

Explanation: "let x be the cost price of one article . let y be the selling price of one article . 40 y = 60 x y = 1.5 x the answer is c ."


Question: john is the owner of a company and for thanksgiving he wants to give a turkey to each employee to celebrate the holiday . each turkey cost him $ 25 . if he has 85 employees , how much would john need to spend ?

<gadget id="calculator">25 * 85</gadget>
<output>2_125</output>
<result>2_125</result>

Choices:
A. $ 2125
B. $ 1320
C. $ 2000
D. $ 1580
E. $ 2000.75

Explanation: answer is ( a ) . if john wants to give each of his employees a turkey to help celebrate the thanksgiving holiday and each one costs him $ 25 multiplied by the number of employees ( 85 ) , he would have to pay a total of $ 2125 .


Question: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 5 ?

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

Choices:
A. 1
B. 2
C. 4
D. 8
E. 5

Explanation: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is e"


Question: there are 28 balls which are red , blue or green . if 12 balls are green and the sum of red balls and green balls is less than 24 , at most how many red balls are there ?

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

Choices:
A. 10
B. 12
C. 11
D. 13
E. 14

Explanation: r + g + b = 28 g = 12 r + g < 24 = > r + 12 < 24 = > r < 12 = > at most 11 red balls answer : c


Question: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 480 . find the sum ?

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

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

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

<gadget id="calculator">480 / (3/25)</gadget>
<output>4_000</output>
<result>4_000</result>

Choices:
A. 7000
B. 7029
C. 4000
D. 2800
E. 2791

divide(480, divide(multiply(subtract(18, 12), const_2), const_100))

Explanation: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 480 = > 36 x / 100 - 24 x / 100 = 480 = > 12 x / 100 = 480 = > x = 4000 . answer : c"


Question: a train 200 m long can cross an electric pole in 20 sec and then find the speed of the train ?

<gadget id="calculator">200 / 1_000</gadget>
<output>1/5 = around 0.2</output>

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

<gadget id="calculator">(1/5) / (1/180)</gadget>
<output>36</output>
<result>36</result>

Choices:
A. 987
B. 271
C. 72
D. 27
E. 36

divide(divide(200, const_1000), divide(20, const_3600))

Explanation: "length = speed * time speed = l / t s = 200 / 20 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"


Question: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ?

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

<gadget id="calculator">binomial(5, 3)</gadget>
<output>10</output>

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

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

<gadget id="calculator">20 + 5</gadget>
<output>25</output>

<gadget id="calculator">binomial(5, 5)</gadget>
<output>1</output>

<gadget id="calculator">25 + 1</gadget>
<output>26</output>

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

<gadget id="calculator">26 / 32</gadget>
<output>13/16 = around 0.8125</output>
<result>13/16 = around 0.8125</result>

Choices:
A. 1 / 16
B. 5 / 16
C. 2 / 5
D. 13 / 16
E. 27 / 32

divide(add(add(add(choose(5, const_2), choose(5, const_3)), choose(5, const_4)), choose(5, 5)), power(const_2, 5))

Explanation: fair coin is tossed 5 times . hence total number of outcomes = 2 ^ 5 = 32 . problem asks for probability of getting atleast heads twice . hence if we calculate probability of getting heads exactly once and probability of not getting heads at all and subract it from the total probability of the event which is 1 ( as total probability of certain event will be always 1 ) we can get the probability of getting atleast heads twice . probability of getting exactly one head and no heads = ( number of possible outcomes [ htttt , thttt , tthtt , tttht , tttth , ttttt ] = 6 ) / ( total possible outcomes = 32 ) = > 6 / 32 = 3 / 16 hence probability of getting atleast heads twice = 1 - ( 3 / 16 ) = 13 / 16 = > choice [ d ]


Question: what is 3 / 4 of 4 / 5 of 2 / 3 ?

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

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

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

<gadget id="calculator">(4/5) * (2/3)</gadget>
<output>8/15 = around 0.533333</output>

<gadget id="calculator">(3/4) * (8/15)</gadget>
<output>2/5 = around 0.4</output>
<result>2/5 = around 0.4</result>

Choices:
A. 1 / 4
B. 2 / 5
C. 9 / 16
D. 5 / 8
E. 16 / 9

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

Explanation: "3 / 4 * 4 / 5 * 2 / 3 = 2 / 5 answer : b"


Question: if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction ?

<gadget id="calculator">2 / 15</gadget>
<output>2/15 = around 0.133333</output>

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

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

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

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">(6/5) / (3/4)</gadget>
<output>8/5 = around 1.6</output>

<gadget id="calculator">(2/15) / (8/5)</gadget>
<output>1/12 = around 0.083333</output>
<result>1/12 = around 0.083333</result>

Choices:
A. 1 / 12
B. 1 / 16
C. 1 / 19
D. 1 / 14
E. 1 / 13

divide(divide(2, 15), divide(divide(add(20, const_100), const_100), divide(subtract(const_100, 25), const_100)))

Explanation: "x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a"


Question: when w is divided by 13 , the reminder is 0 . if w is 3 more than it value and when divided by 11 its remainder is 0 . what is the value of w ?

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

Choices:
A. 13
B. 52
C. 39
D. 26
E. 35

Explanation: w is divided by 13 so that is multiple of 14 as 13 , 26,39 . . . w + 3 is divided by 11 the remainder is 0 so it is divisible by 11 . consider from option let us take the number is 13 it is divisible by 14 but 13 + 3 is not divisible by 11 so it is not answers so let us take 2 nd option 52 which is divisible by 13 and 52 + 3 = 55 is divisible by 11 so ans is b


Question: a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .

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

<gadget id="calculator">400 * (3/4)</gadget>
<output>300</output>

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

<gadget id="calculator">400 * (1/2)</gadget>
<output>200</output>

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

<gadget id="calculator">400 * (5/8)</gadget>
<output>250</output>

<gadget id="calculator">200 + 250</gadget>
<output>450</output>

<gadget id="calculator">300 + 450</gadget>
<output>750</output>

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

<gadget id="calculator">400 * (1/8)</gadget>
<output>50</output>

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

<gadget id="calculator">750 - 100</gadget>
<output>650</output>

<gadget id="calculator">650 - 400</gadget>
<output>250</output>
<result>250</result>

Choices:
A. 300
B. 200
C. 250
D. 150
E. 160

subtract(subtract(add(multiply(400, divide(3, 4)), add(multiply(400, divide(1, 2)), multiply(400, divide(5, 8)))), multiply(2, multiply(400, divide(1, 8)))), 400)

Explanation: basically , this question is asking you to figure out how many students are being double - counted . a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 50 ) . 750 = 400 + x + 100 x = 250 c


Question: a is two years older than b who is twice as old as c . if the total of the ages of a , b nd c be 27 , then how old is b ?

<gadget id="calculator">27 - 2</gadget>
<output>25</output>

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

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

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

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

divide(multiply(subtract(27, const_2), const_2), add(const_4, const_1))

Explanation: "solution let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ∴ ( 2 x + 2 ) + 2 x + x = 27 ⇔ 5 x = 25 ⇔ x = 5 . hence , b ' s age = 2 x = 10 years . answer d"


Question: last year elaine spent 20 % of her annual earnings on rent . this year she earned 35 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?

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

<gadget id="calculator">(7/20) + 1</gadget>
<output>27/20 = around 1.35</output>

<gadget id="calculator">(27/20) * 30</gadget>
<output>81/2 = around 40.5</output>

<gadget id="calculator">(81/2) / 20</gadget>
<output>81/40 = around 2.025</output>

<gadget id="calculator">(81/40) * 100</gadget>
<output>405/2 = around 202.5</output>
<result>405/2 = around 202.5</result>

Choices:
A. 202.5
B. 194.5
C. 197.5
D. 182.5
E. 177.5

multiply(divide(multiply(add(divide(35, const_100), const_1), 30), 20), const_100)

Explanation: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 15 % more , or $ 135 . she would ' ve spent 30 % of this on rent , or $ 40.5 do $ 40.5 / $ 20 this will give you 202.5 % a is the correct answer ."


Question: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 21 as commission , the cloth sold through him on that day is worth

<gadget id="calculator">2.5 / 100</gadget>
<output>0.025</output>

<gadget id="calculator">21 / 0.025</gadget>
<output>840</output>
<result>840</result>

Choices:
A. 333
B. 500
C. 840
D. 299
E. 132

Explanation: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 21 < = > ( 25 / 10 * 1 / 100 * x ) = 21 < = > x = 840 . answer : c"


Question: the average temperature for tuesday , wednesday and thursday was 32 ° c . the average temperature for wednesday , thursday and friday was 34 ° c . if the temperature on friday be 44 ° c , what was the temperature on tuesday ?

<gadget id="calculator">32 * 3</gadget>
<output>96</output>

<gadget id="calculator">34 * 3</gadget>
<output>102</output>

<gadget id="calculator">102 - 44</gadget>
<output>58</output>

<gadget id="calculator">96 - 58</gadget>
<output>38</output>
<result>38</result>

Choices:
A. 39 ° c
B. 44 ° c
C. 38 ° c
D. 42 ° c
E. none of these

subtract(multiply(32, const_3), subtract(multiply(34, const_3), 44))

Explanation: "explanation : t + w + t = 32 × 3 = 96 ° c w + t + f = 34 × 3 = 102 ° c also , temperature on friday = 44 ° c temperature on tuesday = 96 + 44 - 102 = 38 ° c answer : option c"


Question: a cyclist bikes x distance at 10 miles per hour and returns over the same path at 9 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?

<gadget id="calculator">10 + 9</gadget>
<output>19</output>

<gadget id="calculator">19 / 2</gadget>
<output>19/2 = around 9.5</output>
<result>19/2 = around 9.5</result>

Choices:
A. 8.1
B. 8.3
C. 8.6
D. 8.9
E. 9.5

Explanation: "distance = d 1 = x miles speed = s 1 = 10 miles per hour time = t 1 = distance / speed = x / 10 2 . going from b to a distance = d 2 = x miles speed = s 2 = 9 miles per hour time = t 2 = distance / speed = x / 9 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 9 = x ( 1 / 10 + 1 / 9 ) = x ( 4 + 5 ) / 40 = 19 x / 90 speed = 2 x / ( 19 x / 90 ) = ( 2 x * 90 ) / 9 x = 180 x / 19 x = 180 / 19 = 9.5 answer : e"


Question: the diagonal of a cube is 8 √ 3 . find its volume and surface area .

<gadget id="calculator">3 ** (1/2)</gadget>
<output>sqrt(3) = around 1.732051</output>

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

<gadget id="calculator">(8*sqrt(3)) / (sqrt(3))</gadget>
<output>8</output>

<gadget id="calculator">6 * (8 ** 2)</gadget>
<output>384</output>
<result>384</result>

Choices:
A. 354
B. 384
C. 324
D. 344
E. 364

Explanation: √ 3 . a = 8 √ 3 = > a = 8 volume = a ( power ) 3 = > ( 8 × 8 × 8 ) cm ( power ) 3 = > 512 cm ( power ) 3 surface area = > 6 a ( power ) 2 = > ( 6 × 8 × 8 ) cm ( power ) 2 = > 384 cm ( power ) 2 answer is b .


Question: a group of boy scouts and girls scouts is going on a rafting trip . 70 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .

<gadget id="calculator">60 * 75</gadget>
<output>4_500</output>

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

<gadget id="calculator">70 - 45</gadget>
<output>25</output>

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

<gadget id="calculator">25 / 40</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. 50 %
B. 60 %
C. 63 %
D. 66 %
E. 70 %

multiply(divide(subtract(70, divide(multiply(60, 75), const_100)), subtract(const_100, 60)), const_100)

Explanation: 60 % were boy scouts so 40 % ( 100 - 60 = 40 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 60 % of the total going ) + ( ? % of 40 % of the total going ) = 70 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 60 * 1,000 + x * . 40 * 1,000 = . 70 * 1,000 450 + x * 400 = 700 400 x = 250 x = 250 / 400 x = . 625 converting this to a percent , we have 62.5 % . rounding , we have 63 % . c


Question: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 216 ° of the circle , what percentage of megatek employees are in manufacturing ?

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

<gadget id="calculator">216 / 360</gadget>
<output>3/5 = around 0.6</output>

<gadget id="calculator">(3/5) * 100</gadget>
<output>60</output>
<result>60</result>

Choices:
A. 20 %
B. 25 %
C. 30 %
D. 35 %
E. 60 %

multiply(divide(216, divide(const_3600, const_10)), const_100)

Explanation: "answer : e 216 ° divided by 360 ° equals 0.6 , therefore the sector is equal to 60 % of the total"


Question: in a school of 850 boys , 34 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

<gadget id="calculator">34 + 28</gadget>
<output>62</output>

<gadget id="calculator">62 + 10</gadget>
<output>72</output>

<gadget id="calculator">100 - 72</gadget>
<output>28</output>

<gadget id="calculator">850 * 28</gadget>
<output>23_800</output>

<gadget id="calculator">23_800 / 100</gadget>
<output>238</output>
<result>238</result>

Choices:
A. 125
B. 627
C. 153
D. 238
E. 159

divide(multiply(850, subtract(const_100, add(add(34, 28), 10))), const_100)

Explanation: "34 + 28 + 10 = 72 % 100 – 72 = 28 % 850 * 28 / 100 = 238 answer : d"


Question: 2 ^ 46655 mod 9 = ?

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

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

<gadget id="calculator">32 % 9</gadget>
<output>5</output>
<result>5</result>

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

reminder(power(2, add(const_2, const_3)), 9)

Explanation: by remainder theorem remainder = { [ ( 2 ^ 3 ) ^ 1551 * 2 ^ 2 ] / 9 } = [ { ( - 1 ) ^ 1551 * 4 } / 9 ] = 5 answer : b


Question: a cube has five of its faces painted half red and half white . the other face is completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?

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

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

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

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

<gadget id="calculator">(5/2) + 1</gadget>
<output>7/2 = around 3.5</output>

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

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

Choices:
A. 6 : 11
B. 2 : 5
C. 3 : 4
D. 5 : 7
E. 2 : 3

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

Explanation: let x be the area of each face of the cube . the area painted red is 5 ( x / 2 ) = 5 x / 2 the area painted white is 5 ( x / 2 ) + x = 7 x / 2 x the ratio of red to white is 5 x / 2 : 7 x / 2 which is 5 : 7 . the answer is d .


Question: the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :

<gadget id="calculator">25 * 14</gadget>
<output>350</output>
<result>350</result>

Choices:
A. 276
B. 299
C. 322
D. 345
E. 350

Explanation: "clearly , the numbers are ( 25 x 13 ) and ( 25 x 14 ) . larger number = ( 25 x 14 ) = 350 . answer : option e"


Question: increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?

<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">(1/4) + 1</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. 31.25
B. 37.5
C. 50.0
D. 52.5
E. 62.5

multiply(subtract(multiply(add(divide(30, const_100), const_1), add(divide(25, const_100), const_1)), const_1), const_100)

Explanation: we ' re told that the original price of an item is increased by 25 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 25 % = 100 + . 25 ( 100 ) = 125 + 30 % = 125 + . 30 ( 125 ) = 125 + 37.5 = 162.5 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 62.5 / 100 = 62.50 % final answer : e


Question: the population of a bacteria colony doubles every day . if it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?

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

<gadget id="calculator">2 ** 11</gadget>
<output>2_048</output>

<gadget id="calculator">2_048 - 1</gadget>
<output>2_047</output>
<result>2_047</result>

Choices:
A. 512
B. 768
C. 1024
D. 2048
E. 4096

subtract(power(2, add(10, const_1)), const_1)

Explanation: "2 ^ 10 ( 2 ) = 2 ^ 11 = 2048 the answer is d ."


Question: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,200 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?

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

<gadget id="calculator">16 * 1_000</gadget>
<output>16_000</output>

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

<gadget id="calculator">16_000 + 200</gadget>
<output>16_200</output>

<gadget id="calculator">80 + 2</gadget>
<output>82</output>

<gadget id="calculator">82 * 150</gadget>
<output>12_300</output>

<gadget id="calculator">16_200 + 12_300</gadget>
<output>28_500</output>

<gadget id="calculator">28_500 / 150</gadget>
<output>190</output>
<result>190</result>

Choices:
A. $ 28
B. $ 82
C. $ 110
D. $ 190
E. $ 192

divide(add(add(multiply(multiply(const_4, const_4), const_1000), multiply(2, const_100)), multiply(add(80, 2), 150)), 150)

Explanation: "this question can be solved easily using a equation model . 150 * p = 16200 ( fixed cost ) + 150 * 80 + 150 * 2 . = 16200 + 12000 + 300 = 28500 p = $ 190 . d"


Question: in a sports club with 42 members , 20 play badminton and 23 play tennis and 6 do not play either . how many members play both badminton and tennis ?

<gadget id="calculator">20 + 23</gadget>
<output>43</output>

<gadget id="calculator">43 + 6</gadget>
<output>49</output>

<gadget id="calculator">49 - 42</gadget>
<output>7</output>
<result>7</result>

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

Explanation: "20 + 23 = 43 but where as total number is 42 - 6 = 36 therefore answer is 43 - 36 = 7 hence answer is d"


Question: a tempo , while travelling at 70 kmph , uses 30 % more petrol than it uses while travelling at 50 kmph for travelling a certain distance . using one litre of petrol , it can travel 19.5 km at 50 kmph . how far can the tempo travel on 10 litres of petrol at a speed of 70 kmph ?

<gadget id="calculator">10 * 19.5</gadget>
<output>195</output>

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

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

<gadget id="calculator">195 / (13/10)</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 150 kms
B. 160 kms
C. 170 kms
D. 180 kms
E. 190 kms

divide(multiply(10, 19.5), add(const_1, divide(30, const_100)))

Explanation: @ 50 kmph , one km distance uses 1 / 19.5 ltr petrol . @ 70 kmph , one km dist . uses 1.3 / 19.5 ltr petrol distance travelled with 10 ltrs @ 70 kmph = 10 * 19.5 / 1.3 = 150 kms . answer : a


Question: in an examination it is necessary for a candidate to get 45 % of the maximum marks to pass . a candidate who gets 180 marks , fails by 45 marks . find the maximum marks .

<gadget id="calculator">180 + 45</gadget>
<output>225</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

<gadget id="calculator">225 / (9/20)</gadget>
<output>500</output>
<result>500</result>

Choices:
A. 450
B. 600
C. 500
D. 550
E. 650

divide(add(180, 45), divide(45, const_100))

Explanation: let max . mark = x pass mark = 45 x / 100 180 = 45 x / 100 - 45 x = 180 * 100 - 4500 / 45 = 500 answer : c


Question: in a box of 9 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?

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

<gadget id="calculator">6 / 9</gadget>
<output>2/3 = around 0.666667</output>

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

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

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

<gadget id="calculator">(2/3) * (5/8)</gadget>
<output>5/12 = around 0.416667</output>
<result>5/12 = around 0.416667</result>

Choices:
A. 3 / 10
B. 4 / 11
C. 5 / 12
D. 6 / 13
E. 7 / 15

multiply(divide(subtract(9, 3), 9), divide(subtract(subtract(9, 3), const_1), subtract(9, const_1)))

Explanation: p ( neither pen is defective ) = 6 / 9 * 5 / 8 = 5 / 12 the answer is c .


Question: find a two digit number , given that the sum of the digits is 9 and the difference of the digits is 3 . ?

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

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

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

Choices:
A. 75
B. 63
C. 83
D. 94
E. 39

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

Explanation: using elimination method find which of the options fit the description of the number . . . from the option only 63 meets this description sum of digits - - - 6 + 3 = 9 difference of digits - - - 6 - 3 = 3 answer b .


Question: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 25 percent , what is the discount rate on pony jeans ?

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

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

<gadget id="calculator">(1/4) * 36</gadget>
<output>9</output>

<gadget id="calculator">9 - 9</gadget>
<output>0</output>

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

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

<gadget id="calculator">0 / 9</gadget>
<output>0</output>

<gadget id="calculator">(1/4) - 0</gadget>
<output>1/4 = around 0.25</output>

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

Choices:
A. 9 %
B. 10 %
C. 11 %
D. 12 %
E. 25 %

multiply(subtract(divide(25, const_100), divide(subtract(9, multiply(divide(25, const_100), multiply(18, 2))), subtract(multiply(15, 3), multiply(18, 2)))), const_100)

Explanation: "x discount on pony jeans , ( 0.25 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.25 - x ) + 2 * 18 x = 9 - - > x = 0.25 = 25 % answer : e ."


Question: if x is an integer and 2.13 × 10 ^ x is less than 2100 , what is the greatest possible value for x ?

<gadget id="calculator">2_100 / 2.13</gadget>
<output>985.915493</output>

<gadget id="calculator">log(985.915493)</gadget>
<output>6.893571</output>

<gadget id="calculator">log(10)</gadget>
<output>log(10) = around 2.302585</output>

<gadget id="calculator">6.893571 / log(10)</gadget>
<output>6.893571/log(10) = around 2.99384</output>

<gadget id="calculator">floor(6.893571/log(10))</gadget>
<output>2</output>
<result>2</result>

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

Explanation: "if x = 3 2.13 × 10 ^ 3 = 2130 > 2,100 so , x = 2 answer : a"


Question: if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is ?

<gadget id="calculator">360 - 340</gadget>
<output>20</output>

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

<gadget id="calculator">20 / (1/20)</gadget>
<output>400</output>
<result>400</result>

Choices:
A. 127
B. 688
C. 400
D. 121
E. 123

divide(subtract(360, 340), divide(5, const_100))

Explanation: "let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : c"


Question: 3 candidates in an election and received 6136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?

Choices:
A. 46 %
B. 49 %
C. 57 %
D. 59 %
E. 61 %

Explanation: "total number of votes polled = ( 6136 + 7636 + 11628 ) = 25400 so , required percentage = 11628 / 25400 * 100 = 46 % a"


Question: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and one - half of the females in the class ?

<gadget id="calculator">2 * 360</gadget>
<output>720</output>

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

<gadget id="calculator">720 / 5</gadget>
<output>144</output>
<result>144</result>

Choices:
A. 128
B. 136
C. 144
D. 152
E. 160

divide(multiply(2, const_360), add(2, 3))

Explanation: 1 / 4 * 2 / 5 + 1 / 2 * 3 / 5 = 2 / 20 + 6 / 20 = 2 / 5 the number of degrees is 2 / 5 * 360 = 144 degrees the answer is c .


Question: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 45 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?

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

<gadget id="calculator">(2/5) * 300</gadget>
<output>120</output>

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

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

<gadget id="calculator">300 * (3/5)</gadget>
<output>180</output>

<gadget id="calculator">(9/20) * 180</gadget>
<output>81</output>

<gadget id="calculator">120 - 81</gadget>
<output>39</output>

<gadget id="calculator">39 / 300</gadget>
<output>13/100 = around 0.13</output>

<gadget id="calculator">(13/100) * 100</gadget>
<output>13</output>
<result>13</result>

Choices:
A. 15
B. 25
C. 13
D. 45
E. 75

multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(45, 100), multiply(300, divide(60, 100)))), 300), 100)

Explanation: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 45 % = 81 responded as satisfied , so remaining satisfied are 120 - 81 = 39 so 39 is what percentage of 300 - 13 % so the answer should be c"


Question: solution a is 30 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?

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

<gadget id="calculator">50 * (4/5)</gadget>
<output>40</output>

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

<gadget id="calculator">50 * (1/2)</gadget>
<output>25</output>

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

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

<gadget id="calculator">(4/5) - (3/10)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">15 / (1/2)</gadget>
<output>30</output>

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

<gadget id="calculator">30 / 20</gadget>
<output>3/2 = around 1.5</output>
<result>3/2 = around 1.5</result>

Choices:
A. 6 : 4
B. 6 : 14
C. 4 : 4
D. 4 : 6
E. 3 : 2

divide(divide(subtract(multiply(50, divide(80, const_100)), multiply(50, divide(50, const_100))), subtract(divide(80, const_100), divide(30, const_100))), subtract(50, divide(subtract(multiply(50, divide(80, const_100)), multiply(50, divide(50, const_100))), subtract(divide(80, const_100), divide(30, const_100)))))

Explanation: "forget the volumes for the time being . you have to mix 30 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 30 ) = 3 / 2 so the volume of the two solutions will be equal . answer has to be 3 : 2 e"


Question: the monthly rent of a shop of dimension 18 feet × 22 feet is rs . 2244 . what is the annual rent per square foot of the shop ? ( a ) rs . 5 ( 2 / 3 )

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

<gadget id="calculator">18 * 22</gadget>
<output>396</output>

<gadget id="calculator">2_244 / 396</gadget>
<output>17/3 = around 5.666667</output>

<gadget id="calculator">12 * (17/3)</gadget>
<output>68</output>
<result>68</result>

Choices:
A. 43
B. 56
C. 68
D. 87
E. 92

multiply(add(const_10, const_2), divide(2244, rectangle_area(18, 22)))

Explanation: "sol . monthly rent per square feet = 2244 / ( 18 * 22 ) & annual rent per square feet = 12 * ( 2244 / ( 18 * 22 ) ) = 68 c"


Question: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 135 mangoes .

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

<gadget id="calculator">1 - (1/10)</gadget>
<output>9/10 = around 0.9</output>

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

<gadget id="calculator">400 - 360</gadget>
<output>40</output>

<gadget id="calculator">40 / 12</gadget>
<output>10/3 = around 3.333333</output>

<gadget id="calculator">(10/3) * 135</gadget>
<output>450</output>
<result>450</result>

Choices:
A. 360
B. 380
C. 400
D. 450
E. 412

multiply(divide(subtract(divide(360, subtract(const_1, divide(const_1, const_10))), 360), 12), 135)

Explanation: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 135 mangoes = 135 * 3.33 = 450 . answer d


Question: a gambler has won 40 % of his 20 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?

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

<gadget id="calculator">20 * (3/5)</gadget>
<output>12</output>

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

<gadget id="calculator">20 * (2/5)</gadget>
<output>8</output>

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

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

<gadget id="calculator">(4/5) - (3/5)</gadget>
<output>1/5 = around 0.2</output>

<gadget id="calculator">4 / (1/5)</gadget>
<output>20</output>
<result>20</result>

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

divide(subtract(multiply(20, divide(60, const_100)), multiply(20, divide(40, const_100))), subtract(divide(80, const_100), divide(60, const_100)))

Explanation: "let x be the number of additional games the gambler needs to play . 0.4 ( 20 ) + 0.8 x = 0.6 ( x + 20 ) 0.2 x = 4 x = 20 the answer is a ."


Question: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?

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

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

<gadget id="calculator">6_000 * 10</gadget>
<output>60_000</output>

<gadget id="calculator">(4/5) * 60_000</gadget>
<output>48_000</output>

<gadget id="calculator">48_000 / 60</gadget>
<output>800</output>
<result>800</result>

Choices:
A. 1000
B. 1400
C. 1200
D. 800
E. 1000

divide(multiply(divide(80, const_100), multiply(multiply(60, 100), 10)), 60)

Explanation: "volume of pool = 60 * 100 * 10 cu . ft , 80 % full = 60 * 100 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 100 * 10 * 0.8 / 60 min = 800 min d"


Question: walking at 4 / 5 of her normal speed , a worker is 10 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is

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

Choices:
A. 30
B. 35
C. 40
D. 45
E. 50

Explanation: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 10 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 10 ) t / 5 = 8 t = 40 the answer is c ."


Question: find the length of the longest pole that can be placed in a room 12 m long , 8 m broad and 9 m high .

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

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

<gadget id="calculator">8 ** 2</gadget>
<output>64</output>

<gadget id="calculator">144 + 64</gadget>
<output>208</output>

<gadget id="calculator">81 + 208</gadget>
<output>289</output>

<gadget id="calculator">289 ** (1/2)</gadget>
<output>17</output>
<result>17</result>

Choices:
A. 10 m
B. 12 m
C. 17 m
D. 19 m
E. none

sqrt(add(power(9, const_2), add(power(12, const_2), power(8, const_2))))

Explanation: solution length of longest pole = length of the diagonal of the room = √ ( 12 ) 2 + 82 + 92 ‹ = › √ 289 = 17 m . answer c


Question: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is :

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

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

<gadget id="calculator">36 - 8</gadget>
<output>28</output>

<gadget id="calculator">40 * 28 * 4</gadget>
<output>4_480</output>
<result>4_480</result>

Choices:
A. 4480
B. 5120
C. 6420
D. 8960
E. 7960

volume_rectangular_prism(subtract(48, multiply(4, const_2)), subtract(36, multiply(4, const_2)), 4)

Explanation: "clearly , l = ( 48 - 8 ) m = 40 m , b = ( 36 - 8 ) m = 28 m , h = 8 m . volume of the box = ( 40 x 28 x 4 ) m 3 = 4480 m 3 . answer : option a"


Question: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 15 days , a finished the remaining work . in how many days a alone can finish the job ?

<gadget id="calculator">15 * 40</gadget>
<output>600</output>

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

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

Choices:
A. 10
B. 25
C. 60
D. 30
E. 20

divide(multiply(15, 40), subtract(40, 10))

Explanation: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 15 days whole work will be done by a in 15 * 4 / 3 = 20 days answer is e"


Question: if the radius of a cylinder is made 3 times and height is doubled , what is the new volume of the cylinder divided by the old one ?

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

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

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

Choices:
A. 18 .
B. 2 .
C. 6 .
D. 4 .
E. 10 .

add(multiply(3, const_4), multiply(const_3, const_2))

Explanation: let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 2 h ) v ' = 18 v a ) 18


Question: a train 110 m long is running with a speed of 82 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?

<gadget id="calculator">82 + 6</gadget>
<output>88</output>

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

<gadget id="calculator">88 * (5/18)</gadget>
<output>220/9 = around 24.444444</output>

<gadget id="calculator">110 / (220/9)</gadget>
<output>9/2 = around 4.5</output>
<result>9/2 = around 4.5</result>

Choices:
A. 7 sec
B. 6 sec
C. 8 sec
D. 4.5 sec
E. 2 sec

divide(110, multiply(add(82, 6), const_0_2778))

Explanation: "speed of train relative to man = 82 + 6 = 88 km / hr . = 88 * 5 / 18 = 24.44 m / sec . time taken to pass the men = 110 / 24.44 = 4.5 sec . answer : d"


Question: the average marks of a class of 35 students is 40 and that of another class of 45 students is 60 . find the average marks of all the students ?

<gadget id="calculator">35 * 40</gadget>
<output>1_400</output>

<gadget id="calculator">45 * 60</gadget>
<output>2_700</output>

<gadget id="calculator">1_400 + 2_700</gadget>
<output>4_100</output>

<gadget id="calculator">35 + 45</gadget>
<output>80</output>

<gadget id="calculator">4_100 / 80</gadget>
<output>205/4 = around 51.25</output>
<result>205/4 = around 51.25</result>

Choices:
A. 52.6
B. 52.4
C. 52.1
D. 51.2
E. 52.9

divide(add(multiply(35, 40), multiply(45, 60)), add(35, 45))

Explanation: "sum of the marks for the class of 35 students = 35 * 40 = 1400 sum of the marks for the class of 45 students = 45 * 60 = 2700 sum of the marks for the class of 80 students = 1400 + 2700 = 4100 average marks of all the students = 4100 / 80 = 51.2 . answer : d"


Question: abcd is a square where ab = √ 2016 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .

<gadget id="calculator">2_016 / 2</gadget>
<output>1_008</output>
<result>1_008</result>

Choices:
A. 3008
B. 2002
C. 1008
D. 2016
E. 3000

Explanation: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 2016 / 2 = 1008 . correct answer c


Question: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8600 for a computer table , then what was the cost price of the computer table ?

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

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

<gadget id="calculator">8_600 / (6/5)</gadget>
<output>21_500/3 = around 7_166.666667</output>
<result>21_500/3 = around 7_166.666667</result>

Choices:
A. rs . 6289
B. rs . 6298
C. rs . 6290
D. rs . 7166
E. rs . 7708

divide(8600, add(const_1, divide(20, const_100)))

Explanation: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8600 ( 100 / 120 ) = rs . 7166 . answer : d"


Question: what is the perimeter , in meters , of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?

<gadget id="calculator">16 * 12</gadget>
<output>192</output>

<gadget id="calculator">192 / 16</gadget>
<output>12</output>

<gadget id="calculator">2 * (12 + 16)</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 48
B. 56
C. 60
D. 56
E. 192

rectangle_perimeter(divide(rectangle_area(16, 12), 16), 16)

Explanation: "say length of garden is l meters . then ( l * 16 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 12 meters . perimeter of garden = 2 * ( 12 + 16 ) = 56 meter . answer is d"


Question: mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 19 of them answered question 1 correctly . if 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?

<gadget id="calculator">19 + 24</gadget>
<output>43</output>

<gadget id="calculator">43 + 5</gadget>
<output>48</output>

<gadget id="calculator">48 - 29</gadget>
<output>19</output>
<result>19</result>

Choices:
A. 3
B. 9
C. 11
D. 17
E. 19

Explanation: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 19 . number of students who answered both q 1 & q 2 correctly = 19 . answer : e"


Question: if m is a positive integer and m ^ 2 is divisible by 33 , then the largest positive integer that must divide m is ?

<gadget id="calculator">33 / 3</gadget>
<output>11</output>

<gadget id="calculator">11 / 3</gadget>
<output>11/3 = around 3.666667</output>

<gadget id="calculator">3 * (11/3)</gadget>
<output>11</output>
<result>11</result>

Choices:
A. 3
B. 6
C. 8
D. 11
E. 16

multiply(const_3, divide(divide(33, const_3), const_3))

Explanation: "m ^ 2 is divisible by 33 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 11 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 33 then answer should be 16 . is the question right ? or am i missing some thing ? d"


Question: from a total of 5 boys and 6 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?

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

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

<gadget id="calculator">15 * 10</gadget>
<output>150</output>
<result>150</result>

Choices:
A. 16
B. 24
C. 60
D. 120
E. 150

multiply(multiply(const_3, 5), multiply(5, 2))

Explanation: answer = e = 150 no of 4 person committees that can be formed = 5 c 2 * 6 c 2 = 150 answer e


Question: the simple interest on a sum of money will be rs . 1400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?

<gadget id="calculator">1_400 / 10</gadget>
<output>140</output>

<gadget id="calculator">140 * 5</gadget>
<output>700</output>

<gadget id="calculator">700 * 3</gadget>
<output>2_100</output>

<gadget id="calculator">2_100 + 700</gadget>
<output>2_800</output>
<result>2_800</result>

Choices:
A. 2800
B. 3799
C. 1200
D. 2693
E. 1732

add(multiply(multiply(divide(1400, 10), 5), const_3), multiply(divide(1400, 10), 5))

Explanation: "p - - - 10 - - - - 1400 p - - - 5 - - - - - 700 3 p - - - 5 - - - - - 2100 - - - - - - = > 2800 answer : a"


Question: two cars start at the same time from opposite ends of a highway that is 175 miles long . one car is riding at 25 mph and the second car is riding at 45 mph . how long after they begin will they meet ?

<gadget id="calculator">25 + 45</gadget>
<output>70</output>

<gadget id="calculator">175 / 70</gadget>
<output>5/2 = around 2.5</output>
<result>5/2 = around 2.5</result>

Choices:
A. 2
B. 2.5
C. 3
D. 3.5
E. 4

Explanation: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 45 + 25 = 70 mph total distance to be covered = 175 miles . time taken would be : 175 miles / 70 mph = 2.5 hours b is the answer ."


Question: in a school of 850 boys , 46 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?

<gadget id="calculator">46 + 28</gadget>
<output>74</output>

<gadget id="calculator">74 + 10</gadget>
<output>84</output>

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

<gadget id="calculator">850 * 16</gadget>
<output>13_600</output>

<gadget id="calculator">13_600 / 100</gadget>
<output>136</output>
<result>136</result>

Choices:
A. 136
B. 627
C. 153
D. 721
E. 159

divide(multiply(850, subtract(const_100, add(add(46, 28), 10))), const_100)

Explanation: "46 + 28 + 10 = 84 % 100 – 84 = 16 % 850 * 16 / 100 = 136 answer : a"


Question: 45 % of x is greater than 1 / 3 rd of x by 110 . what is x ?

<gadget id="calculator">45 / 100</gadget>
<output>9/20 = around 0.45</output>

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

<gadget id="calculator">(9/20) - (1/3)</gadget>
<output>7/60 = around 0.116667</output>

<gadget id="calculator">110 / (7/60)</gadget>
<output>6_600/7 = around 942.857143</output>
<result>6_600/7 = around 942.857143</result>

Choices:
A. 100
B. 200
C. 300
D. 350
E. 943

divide(110, subtract(divide(45, const_100), divide(1, 3)))

Explanation: "45 x / 100 - x / 3 = 110 7 x / 60 = 110 x = 943 answer : e"


Question: a / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 6 . what is the largest possible value of the expression ?

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

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

Choices:
A. 2 / 18
B. 6 / 3
C. 30 / 2
D. 18 / 2
E. 6 / 18

Explanation: a / ( b / c ) = ( a * c ) / b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 6 * 3 ) / 2 = 18 / 2 answer d


Question: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent . overall he make a .

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

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

<gadget id="calculator">15_000 * (19/20)</gadget>
<output>14_250</output>

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

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

<gadget id="calculator">8_000 * (11/10)</gadget>
<output>8_800</output>

<gadget id="calculator">14_250 + 8_800</gadget>
<output>23_050</output>

<gadget id="calculator">15_000 + 8_000</gadget>
<output>23_000</output>

<gadget id="calculator">23_050 - 23_000</gadget>
<output>50</output>
<result>50</result>

Choices:
A. 50
B. 288
C. 27
D. 200
E. 881

subtract(add(multiply(15000, subtract(const_1, divide(5, const_100))), multiply(8000, add(const_1, divide(10, const_100)))), add(15000, 8000))

Explanation: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . answer : a"


Question: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .

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

<gadget id="calculator">87 - 51</gadget>
<output>36</output>

<gadget id="calculator">36 + 3</gadget>
<output>39</output>
<result>39</result>

Choices:
A. 39
B. 88
C. 26
D. 87
E. 11

Explanation: "explanation : consider the avg for first 16 innings is x . then total runs scored till 16 innings is 16 x . total runs after 17 innings = 16 x + 87 . thus , 16 x + 8717 = x + 316 x + 8717 = x + 3 ⇒ x = 36 so his average after 17 innings = 39 . answer : a"


Question: the area of a square is equal to five times the area of a rectangle of dimensions 32 cm * 10 cm . what is the perimeter of the square ?

<gadget id="calculator">32 * 10</gadget>
<output>320</output>

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

<gadget id="calculator">320 * 5</gadget>
<output>1_600</output>

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

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

Choices:
A. 289 cm
B. 160 cm
C. 829 cm
D. 288 cm
E. 289 cm

multiply(sqrt(multiply(rectangle_area(32, 10), divide(const_10, const_2))), const_4)

Explanation: area of the square = s * s = 5 ( 32 * 10 ) = 1600 = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b


Question: working alone , mary can pave a driveway in 4 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?

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

<gadget id="calculator">33.33 / 100</gadget>
<output>0.3333</output>

<gadget id="calculator">0.3333 + 1</gadget>
<output>1.3333</output>

<gadget id="calculator">(1/4) * 1.3333</gadget>
<output>0.333325</output>

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

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

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

<gadget id="calculator">0.333325 + (1/6)</gadget>
<output>0.499992</output>

<gadget id="calculator">1 / 0.499992</gadget>
<output>2.000032</output>
<result>2.000032</result>

Choices:
A. 2 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 7 hours

inverse(add(multiply(divide(const_1, 4), add(divide(33.33, const_100), const_1)), multiply(divide(const_1, 3), divide(50, const_100))))

Explanation: initial working rates : mary = 1 / 4 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 4 + ( 1 / 3 * 1 / 4 ) = 1 / 3 per hour hillary = 1 / 3 - ( 1 / 2 * 1 / 3 ) = 1 / 6 per hour together they work 1 / 3 + 1 / 6 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a .


Question: if y is a positive number and 1 / 2 the square root of x is the cube root of y , then y =

<gadget id="calculator">2 ** 3</gadget>
<output>8</output>

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

Choices:
A. 64
B. 32
C. 16
D. 4
E. 1

multiply(power(2, const_3), power(2, const_3))

Explanation: 1 / 2 the square root of x is cube root of y . if y = 64 . . then 1 / 2 the square root of y = 4 and cube of y is 64 . option a .


Question: the perimeter of a semi circle is 180 cm then the radius is ?

<gadget id="calculator">2 + pi</gadget>
<output>2 + pi = around 5.141593</output>

<gadget id="calculator">180 / (2 + pi)</gadget>
<output>180/(2 + pi) = around 35.008608</output>
<result>180/(2 + pi) = around 35.008608</result>

Choices:
A. 22
B. 28
C. 35
D. 37
E. 13

Explanation: "36 / 7 r = 180 = > r = 35 answer : c"


Question: the sum of the ages of 4 children born at the intervals of 1 years each is 12 years . what is the age of the youngest child ?

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

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

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

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

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

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

Choices:
A. 2.5
B. 1.5
C. 1
D. 3.5
E. 4.5

divide(subtract(divide(12, divide(4, const_2)), multiply(subtract(4, const_1), 1)), const_2)

Explanation: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 we know that the sum of their ages is 12 so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 12 therefore the youngest child is 1.5 years old answer : b"


Question: what is the decimal equivalent of ( 1 / 2 ) ^ 2 ?

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

<gadget id="calculator">(1/2) ** 2</gadget>
<output>1/4 = around 0.25</output>
<result>1/4 = around 0.25</result>

Choices:
A. 0.0016
B. 0.0625
C. 0.16
D. 0.25
E. 0.5

Explanation: "( 1 / 2 ) ² = ( 1 / 2 ) ( 1 / 2 ) = 1 / 4 approach # 1 : use long division to divide 4 into 1 to get 1 / 4 = 0.25 d"


Question: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 3 ] = ?

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

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

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

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

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

Choices:
A. [ 22 ]
B. [ 44 ]
C. [ 45 ]
D. [ 28 ]
E. [ 10 ]

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

Explanation: [ 6 ] * [ 3 ] = ( 6 / 2 + 1 ) ( 3 * 2 + 1 ) = [ 28 ] . ans - d


Question: the sum of all the integers a such that - 26 < a < 24 is

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

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

<gadget id="calculator">(-25) + 1</gadget>
<output>-24</output>

<gadget id="calculator">(-25) + (-24)</gadget>
<output>-49</output>
<result>-49</result>

Choices:
A. 0
B. - 2
C. - 25
D. - 49
E. - 51

add(add(negate(26), const_1), add(add(negate(26), const_1), const_1))

Explanation: easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 10 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 a = - 49 . d is the answer .


Question: in what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way ?

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

<gadget id="calculator">24 * (5/18)</gadget>
<output>20/3 = around 6.666667</output>

<gadget id="calculator">52 / (20/3)</gadget>
<output>39/5 = around 7.8</output>
<result>39/5 = around 7.8</result>

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

Explanation: t = 52 / 24 * 18 / 5 = 8 sec answer : c


Question: 6 / 9 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is

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

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

<gadget id="calculator">3 / 9</gadget>
<output>1/3 = around 0.333333</output>

<gadget id="calculator">(7/10) * (1/3)</gadget>
<output>7/30 = around 0.233333</output>

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

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

<gadget id="calculator">6 / 9</gadget>
<output>2/3 = around 0.666667</output>

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

<gadget id="calculator">(2/15) + (7/30)</gadget>
<output>11/30 = around 0.366667</output>

<gadget id="calculator">(7/30) / (11/30)</gadget>
<output>7/11 = around 0.636364</output>

<gadget id="calculator">(7/11) * 100</gadget>
<output>700/11 = around 63.636364</output>
<result>700/11 = around 63.636364</result>

Choices:
A. 64 %
B. 41 %
C. 45 %
D. 72 %
E. 78 %

multiply(divide(multiply(divide(70, const_100), divide(subtract(9, 6), 9)), add(multiply(divide(subtract(const_100, 80), const_100), divide(6, 9)), multiply(divide(70, const_100), divide(subtract(9, 6), 9)))), const_100)

Explanation: total population = 90 ( assume ) . 6 / 9 * 90 = 60 people from montague . 3 / 9 * 90 = 30 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 12 + 21 ) = ~ 64 . answer : a


Question: if a 2 - b 2 = 10 and a * b = 5 , find a 4 + b 4 .

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

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

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

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

Choices:
A. 50
B. 100
C. 150
D. 92
E. 25

add(power(10, const_2), multiply(power(5, const_2), const_2))

Explanation: a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 5 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 100 : substitute a 4 + b 4 = 150 correct answer c


Question: in an office , totally there are 2800 employees and 25 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?

<gadget id="calculator">2_800 * 25</gadget>
<output>70_000</output>

<gadget id="calculator">70_000 / 100</gadget>
<output>700</output>

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

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

<gadget id="calculator">700 * (7/10)</gadget>
<output>490</output>
<result>490</result>

Choices:
A. 390
B. 490
C. 400
D. 460
E. none of these

multiply(divide(multiply(2800, 25), const_100), divide(subtract(const_100, 30), const_100))

Explanation: number of male employees = 2800 * 25 / 100 = 700 required number of male employees who are less than 50 years old = 700 * ( 100 - 30 ) % = 700 * 70 / 100 = 490 . answer : b


Question: when 3 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?

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

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

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

<gadget id="calculator">(1/15) / 2</gadget>
<output>1/30 = around 0.033333</output>

<gadget id="calculator">3 / (1/30)</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 32
B. 81
C. 60
D. 27
E. 90

divide(3, divide(divide(const_1, multiply(const_3, add(const_2, const_3))), const_2))

Explanation: explanation : let the number be 3 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 3 = a / 30 = > a = 90 answer : e


Question: a certain psychologist charges $ 20 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 300 , what is the total charge to a patient who receives only 3 hours of therapy ?

<gadget id="calculator">300 - 20</gadget>
<output>280</output>

<gadget id="calculator">280 / 5</gadget>
<output>56</output>

<gadget id="calculator">56 * 3</gadget>
<output>168</output>

<gadget id="calculator">168 + 20</gadget>
<output>188</output>
<result>188</result>

Choices:
A. $ 120
B. $ 135
C. $ 150
D. $ 165
E. $ 188

add(multiply(divide(subtract(300, 20), 5), 3), 20)

Explanation: "let the charge for first hour = x + 20 then charge for each additional hour = x x + 20 + 4 x = 300 = > 5 x = 280 = > x = 56 total charge for patient for 3 hours of therapy = x + 20 + 2 x = 3 x + 20 = 188 $ answer e"


Question: a bus trip of 550 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?

<gadget id="calculator">550 * 5</gadget>
<output>2_750</output>

<gadget id="calculator">2_750 * 4</gadget>
<output>11_000</output>

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

<gadget id="calculator">11_000 + 25</gadget>
<output>11_025</output>

<gadget id="calculator">11_025 ** (1/2)</gadget>
<output>105</output>

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

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

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

divide(subtract(sqrt(add(multiply(multiply(550, 5), const_4), power(5, const_2))), 5), const_2)

Explanation: the time is the distance / speed . the time difference is 1 hour . 550 / v - 550 / ( v + 5 ) = 1 550 ( v + 5 ) - 550 v = ( v ) ( v + 5 ) 2750 = ( v ) ( v + 5 ) 50 * 55 = ( v ) ( v + 5 ) v = 50 mph the answer is c .


Question: the sum of the squares of 3 consecutive natural number is 2030 . what is the middle number ?

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

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

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

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

add(multiply(multiply(const_4, 3), const_2), const_2)

Explanation: let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26


Question: ( √ 112 + √ 567 ) / √ 175 = ?

<gadget id="calculator">112 ** (1/2)</gadget>
<output>4*sqrt(7) = around 10.583005</output>

<gadget id="calculator">567 ** (1/2)</gadget>
<output>9*sqrt(7) = around 23.811762</output>

<gadget id="calculator">(4*sqrt(7)) + (9*sqrt(7))</gadget>
<output>13*sqrt(7) = around 34.394767</output>

<gadget id="calculator">175 ** (1/2)</gadget>
<output>5*sqrt(7) = around 13.228757</output>

<gadget id="calculator">(13*sqrt(7)) / (5*sqrt(7))</gadget>
<output>13/5 = around 2.6</output>
<result>13/5 = around 2.6</result>

Choices:
A. 2 √ 2
B. 13 / 5
C. 3 √ 2
D. 3 √ 3
E. √ 2

Explanation: ( √ 112 + √ 567 ) / √ 175 = ( 4 √ 7 + 9 √ 7 ) / 5 √ 7 = 13 / 5 hence , the correct answer is b .


Question: a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 percent is cut away . in the second week 20 percent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?

<gadget id="calculator">25 / 100</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">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">30 / 100</gadget>
<output>3/10 = around 0.3</output>

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

<gadget id="calculator">250 * (7/10)</gadget>
<output>175</output>

<gadget id="calculator">(4/5) * 175</gadget>
<output>140</output>

<gadget id="calculator">(3/4) * 140</gadget>
<output>105</output>
<result>105</result>

Choices:
A. 105 kg
B. 103 kg
C. 108 kg
D. 125 kg
E. 117 kg

multiply(subtract(const_1, divide(25, const_100)), multiply(subtract(const_1, divide(20, const_100)), multiply(250, subtract(const_1, divide(30, const_100)))))

Explanation: "a 105 kg 250 × 0.7 × 0.8 × 0.75 = 105 kg ."


Question: dan can do a job alone in 12 hours . annie , working alone , can do the same job in just 9 hours . if dan works alone for 8 hours and then stops , how many hours will it take annie , working alone , to complete the job ?

<gadget id="calculator">8 / 12</gadget>
<output>2/3 = around 0.666667</output>

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

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

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

multiply(subtract(const_1, divide(8, 12)), 9)

Explanation: dan can complete 1 / 12 of the job per hour . in 8 hours , dan completes 8 ( 1 / 12 ) = 2 / 3 of the job . annie can complete 1 / 9 of the job per hour . to complete the job , annie will take 1 / 3 / 1 / 9 = 3 hours . the answer is b .


Question: two cars start from the opposite places of a main road , 105 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">105 - 35</gadget>
<output>70</output>

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

<gadget id="calculator">70 - 50</gadget>
<output>20</output>
<result>20</result>

Choices:
A. 65
B. 38
C. 20
D. 28
E. 21

subtract(subtract(105, 35), add(25, 25))

Explanation: answer : c ) 20 km


Question: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 126 , how many more green disks than blue disks are in the bag ?

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

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

<gadget id="calculator">126 / 18</gadget>
<output>7</output>

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

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

Choices:
A. 25
B. 28
C. 30
D. 35
E. 40

multiply(divide(126, add(add(3, 7), 8)), subtract(8, 3))

Explanation: let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 126 - - > x = 7 . g - b = 8 x - 3 x = 5 x = 35 . the answer is d .


Question: ben left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?

<gadget id="calculator">75_000 - 45_000</gadget>
<output>30_000</output>

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

<gadget id="calculator">30_000 / (3/20)</gadget>
<output>200_000</output>

<gadget id="calculator">200_000 / 750</gadget>
<output>800/3 = around 266.666667</output>
<result>800/3 = around 266.666667</result>

Choices:
A. 40
B. 200
C. 266
D. 267
E. 600

divide(divide(subtract(75000, 45000), divide(15, const_100)), 750)

Explanation: in order not to lose money because of the change ben ' s total commission must beat least $ 75,000 - $ 45,000 = $ 30,000 , so total sales must beat least $ 30,000 / 0.15 = $ 200,000 . which means that he must makeat least $ 200,000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d .


Question: if there are 86 workers in a factory , and on a certain day , 72 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .

<gadget id="calculator">72 / 86</gadget>
<output>36/43 = around 0.837209</output>

<gadget id="calculator">(36/43) * 100</gadget>
<output>3_600/43 = around 83.72093</output>
<result>3_600/43 = around 83.72093</result>

Choices:
A. 82.7 %
B. 81.7 %
C. 83.7 %
D. 89.7 %
E. 88.7 %

Explanation: "72 / 86 * 100 = 83.72 83.7 % correct answer c"


Question: x does a work in 20 days . y does the same work in 40 days . in how many days they together will do the same work ?

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

<gadget id="calculator">1 / 40</gadget>
<output>1/40 = around 0.025</output>

<gadget id="calculator">(1/20) + (1/40)</gadget>
<output>3/40 = around 0.075</output>

<gadget id="calculator">1 / (3/40)</gadget>
<output>40/3 = around 13.333333</output>
<result>40/3 = around 13.333333</result>

Choices:
A. 10
B. 12
C. 20
D. 30
E. 13.33

inverse(add(divide(const_1, 20), divide(const_1, 40)))

Explanation: x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 40 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 40 ) = 1 / 13.33 both together will finish the work in 13.33 days . correct option is e


Question: in a school the ratio of boys and girls are in the ration 5 : 6 . 25 % of boys will get scholar ship and 20 % of girls will get scholar ship what % of students wont get scholarship ?

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

<gadget id="calculator">75 / 100</gadget>
<output>3/4 = around 0.75</output>

<gadget id="calculator">5 + 6</gadget>
<output>11</output>

<gadget id="calculator">5 / 11</gadget>
<output>5/11 = around 0.454545</output>

<gadget id="calculator">(3/4) * (5/11)</gadget>
<output>15/44 = around 0.340909</output>

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

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

<gadget id="calculator">6 / 11</gadget>
<output>6/11 = around 0.545455</output>

<gadget id="calculator">(4/5) * (6/11)</gadget>
<output>24/55 = around 0.436364</output>

<gadget id="calculator">(15/44) + (24/55)</gadget>
<output>171/220 = around 0.777273</output>

<gadget id="calculator">(171/220) * 100</gadget>
<output>855/11 = around 77.727273</output>
<result>855/11 = around 77.727273</result>

Choices:
A. 60 %
B. 78 %
C. 88 %
D. 98 %
E. 99 %

multiply(add(multiply(divide(subtract(const_100, 25), const_100), divide(5, add(5, 6))), multiply(divide(subtract(const_100, 20), const_100), divide(6, add(5, 6)))), const_100)

Explanation: boys : girls = > 5 x : 6 x total no . of students including boys nd girls = 5 x + 6 x = 11 x 25 % of boys = > 5 x * 25 / 100 = 5 x / 4 20 % of girls = > 6 x * 20 / 100 = 6 x / 5 no . of students who are getting scholarship = > 5 x / 4 + 6 x / 5 = 49 x / 20 no . of students who are not getting scholarship = 11 x - 49 x / 20 = 171 x / 20 % of students not getting scolorship = > 171 x / 20 / 11 x * 100 = > 100 * 171 x / 220 x = 77.7 % answer : b


Question: a start walking from a place at a uniform speed of 7 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .

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

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

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

<gadget id="calculator">(5/9) + 7</gadget>
<output>68/9 = around 7.555556</output>
<result>68/9 = around 7.555556</result>

Choices:
A. 4.7 kmph
B. 7.6 kmph
C. 4 kmph
D. 7 kmph
E. 5.3 kmph

add(divide(1, divide(add(const_60, 48), const_60)), 7)

Explanation: distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 7 + 5 / 9 = 7.55 answer b


Question: find large number from below question the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

<gadget id="calculator">1_355 - 15</gadget>
<output>1_340</output>

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

<gadget id="calculator">1_340 / 5</gadget>
<output>268</output>

<gadget id="calculator">268 * 6</gadget>
<output>1_608</output>
<result>1_608</result>

Choices:
A. 1235
B. 1345
C. 1678
D. 1767
E. 1623

multiply(divide(subtract(1355, 15), subtract(6, const_1)), 6)

Explanation: "let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 large number = 268 + 1355 = 1623 e"


Question: solve below question 2 x + 1 = - 13

<gadget id="calculator">13 + 1</gadget>
<output>14</output>

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

<gadget id="calculator">(-14) / 2</gadget>
<output>-7</output>
<result>-7</result>

Choices:
A. - 8
B. - 9
C. 9
D. 8
E. - 7

Explanation: "2 x + 1 = - 13 x = - 7 e"


Question: car a is 16 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?

<gadget id="calculator">16 + 8</gadget>
<output>24</output>

<gadget id="calculator">58 - 50</gadget>
<output>8</output>

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

Choices:
A. 1.5
B. 2.0
C. 2.5
D. 3.0
E. 3.5

Explanation: relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it ' ll need 24 / 8 = 3 hours . answer : d


Question: if x + y = 290 , x - y = 200 , for integers of x and y , y = ?

<gadget id="calculator">290 + 200</gadget>
<output>490</output>

<gadget id="calculator">490 / 2</gadget>
<output>245</output>
<result>245</result>

Choices:
A. 200
B. 245
C. 50
D. 115
E. 150

Explanation: "x + y = 290 x - y = 200 2 x = 90 x = 45 y = 245 answer is b"


Question: the bankers discount of a certain sum of money is rs . 18 and the true discount on the same sum for the same time is rs . 15 . the sum due is :

<gadget id="calculator">15 * 18</gadget>
<output>270</output>

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

<gadget id="calculator">270 / 3</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 89
B. 90
C. 91
D. 92
E. 93

divide(multiply(15, 18), subtract(18, 15))

Explanation: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 18 * 15 ) / 18 - 15 ; 90 answer : b"


Question: the mean of 50 observations is 200 . but later he found that there is decrements of 34 from each observations . what is the the updated mean is ?

<gadget id="calculator">200 - 34</gadget>
<output>166</output>
<result>166</result>

Choices:
A. 165
B. 166
C. 190
D. 198
E. 199

Explanation: "166 answer is b"


Question: the sum of first 45 natural numbers is

<gadget id="calculator">45 + 1</gadget>
<output>46</output>

<gadget id="calculator">45 * 46</gadget>
<output>2_070</output>

<gadget id="calculator">2_070 / 2</gadget>
<output>1_035</output>
<result>1_035</result>

Choices:
A. 1035
B. 1280
C. 2070
D. 2140
E. none

divide(multiply(45, add(45, const_1)), const_2)

Explanation: solution we know that ( 1 + 2 + 3 + . . . . . + 45 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 45 ) = ( 45 × 46 / 2 ) = 1035 . answer a


Question: what is the dividend . divisor 13 , the quotient is 17 and the remainder is 1

<gadget id="calculator">13 * 17</gadget>
<output>221</output>

<gadget id="calculator">221 + 1</gadget>
<output>222</output>
<result>222</result>

Choices:
A. 222
B. 224
C. 226
D. 228
E. 230

Explanation: "a = d * q + r a = 13 * 17 + 1 a = 221 + 1 a = 222"


Question: a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is :

<gadget id="calculator">20 * 6.5</gadget>
<output>130</output>
<result>130</result>

Choices:
A. 125 km
B. 130 km
C. 135 km
D. 140 km
E. none

Explanation: "sol . let the total journey be x km . then 3 x / 5 + 7 x / 20 + 6.5 = x ⇔ 12 x + 7 x + 20 * 6.5 = 20 x ⇔ x = 130 km . answer b"


Question: there are 300 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .

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

<gadget id="calculator">300 / (2/5)</gadget>
<output>750</output>
<result>750</result>

Choices:
A. 650
B. 700
C. 750
D. 800
E. none of these

Explanation: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 200 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 300 = 2 / 5 t , or 2 / 5 ( t - m ) = 300 , from here we get that t - m = 750 , that would be total number of female employees and the answer ( c )


Question: the true discount on a bill of rs . 2260 is rs . 360 . what is the banker ' s discount ?

<gadget id="calculator">2_260 - 360</gadget>
<output>1_900</output>

<gadget id="calculator">360 / 1_900</gadget>
<output>18/95 = around 0.189474</output>

<gadget id="calculator">(18/95) * 2_260</gadget>
<output>8_136/19 = around 428.210526</output>
<result>8_136/19 = around 428.210526</result>

Choices:
A. rs . 428
B. rs . 422
C. rs . 412
D. rs . 442
E. none of these

Explanation: "explanation : f = rs . 2260 td = rs . 360 pw = f - td = 2260 - 360 = rs . 1900 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1900 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2260 for unexpired time = 360 / 1900 × 2260 = 0.19 × 2260 = rs . 428 answer : option a"


Question: in the first 20 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 30 overs to reach the target of 302 runs ?

<gadget id="calculator">20 * 4.8</gadget>
<output>96</output>

<gadget id="calculator">302 - 96</gadget>
<output>206</output>

<gadget id="calculator">206 / 30</gadget>
<output>103/15 = around 6.866667</output>
<result>103/15 = around 6.866667</result>

Choices:
A. 5
B. 6.25
C. 6.75
D. 6.87
E. 7.25

divide(subtract(302, multiply(20, 4.8)), 30)

Explanation: required run rate = 302 - ( 4.8 x 20 ) / 30 = 206 / 30 = 6.87 option d


Question: a trader sells 85 meters of cloth for rs . 8500 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?

<gadget id="calculator">8_500 / 85</gadget>
<output>100</output>

<gadget id="calculator">100 - 15</gadget>
<output>85</output>
<result>85</result>

Choices:
A. rs . 80
B. rs . 85
C. rs . 90
D. rs . 95
E. none of these

Explanation: "sp of 1 m of cloth = 8500 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 15 = rs . 85 . answer : b"


Question: anne bought doughnuts for a class breakfast party . she bought 9 chocolate doughnuts , 7 coconut doughnuts , and 9 jam - filled doughnuts . how many doughnuts did anne buy in all ?

<gadget id="calculator">9 + 7</gadget>
<output>16</output>

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

Choices:
A. 25
B. 36
C. 39
D. 21
E. 11

Explanation: "add the numbers of doughnuts . 9 + 7 + 9 = 25 . answer is a ."


Question: the length of a rectangle i s two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?

<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">1_225 ** (1/2)</gadget>
<output>35</output>

<gadget id="calculator">(2/5) * 35</gadget>
<output>14</output>

<gadget id="calculator">14 * 10</gadget>
<output>140</output>
<result>140</result>

Choices:
A. 140 sq . units
B. 149
C. 148
D. 17
E. 143

multiply(multiply(divide(const_2, add(const_2, const_3)), sqrt(1225)), 10)

Explanation: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : option a


Question: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?

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

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

Choices:
A. 8.1
B. 8.9
C. 8.6
D. 8.3
E. 9.0

Explanation: distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 10 miles per hour time = t 2 = distance / speed = x / 10 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 8 = x ( 1 / 10 + 1 / 8 ) = = 9 x / 40 speed = 2 x / ( 9 x / 40 ) = 80 / 9 = 8.9 answer : b


Question: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 38 years . what is molly ' s age right now ?

<gadget id="calculator">38 - 6</gadget>
<output>32</output>

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

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

Choices:
A. 15
B. 18
C. 21
D. 24
E. 27

Explanation: now , sandy is 38 - 6 = 32 molly ' s age is ( 3 / 4 ) * 32 = 24 the answer is d .


Question: in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?

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

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

<gadget id="calculator">(3/4) * 60</gadget>
<output>45</output>

<gadget id="calculator">60 - 45</gadget>
<output>15</output>

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

<gadget id="calculator">(5/6) * 40</gadget>
<output>100/3 = around 33.333333</output>

<gadget id="calculator">40 - (100/3)</gadget>
<output>20/3 = around 6.666667</output>

<gadget id="calculator">15 + (20/3)</gadget>
<output>65/3 = around 21.666667</output>
<result>65/3 = around 21.666667</result>

Choices:
A. 10 %
B. 12 %
C. 15 %
D. 18 %
E. 22 %

add(subtract(subtract(const_100, 40), multiply(divide(3, 4), subtract(const_100, 40))), subtract(40, multiply(divide(5, 6), 40)))

Explanation: "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 2 / 5 = 1 / 15 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 15 = 13 / 60 which is about 22 % the answer is e ."


Question: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 45 more revolutions than gear p ?

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

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

<gadget id="calculator">(2/3) - (1/6)</gadget>
<output>1/2 = around 0.5</output>

<gadget id="calculator">45 / (1/2)</gadget>
<output>90</output>
<result>90</result>

Choices:
A. 45
B. 80
C. 90
D. 100
E. 120

divide(45, subtract(divide(40, const_60), divide(10, const_60)))

Explanation: "gear q makes 30 more revolutions each 60 seconds . the time to make 45 = 30 * 1.5 more revolutions is 60 * 1.5 = 90 seconds . the answer is c ."


Question: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 6 ” 3 ?

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

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

Choices:
A. 5
B. 3
C. 2
D. 1
E. 0

Explanation: 6 ” 3 = 9 - 6 = 3 answer : b


Question: the sides of a square region , measured to the nearest centimeter , are 4 centimeters long . the least possible value of the actual area of the square region is

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

<gadget id="calculator">4 - (1/4)</gadget>
<output>15/4 = around 3.75</output>

<gadget id="calculator">(15/4) - (1/4)</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">(7/2) ** 2</gadget>
<output>49/4 = around 12.25</output>
<result>49/4 = around 12.25</result>

Choices:
A. 15.25 sq cm
B. 18.25 sq cm
C. 12.25 sq cm
D. 21.25 sq cm
E. 25.25 sq cm

power(subtract(subtract(4, const_0_25), const_0_25), const_2)

Explanation: "though there might be some technicalities concerning the termnearest ( as 3.5 is equidistant from both 3 and 4 ) the answer still should be : 3.5 ^ 2 = 12.25 . answer : c"


Question: what sum of money will produce rs . 80 as simple interest in 4 years at 3 1 / 2 percent ?

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

<gadget id="calculator">3 + (1/2)</gadget>
<output>7/2 = around 3.5</output>

<gadget id="calculator">4 * (7/2)</gadget>
<output>14</output>

<gadget id="calculator">14 / 100</gadget>
<output>7/50 = around 0.14</output>

<gadget id="calculator">80 / (7/50)</gadget>
<output>4_000/7 = around 571.428571</output>
<result>4_000/7 = around 571.428571</result>

Choices:
A. 263
B. 571.4
C. 367
D. 368
E. 339

divide(80, divide(multiply(4, add(3, divide(1, 2))), const_100))

Explanation: "80 = ( p * 4 * 7 / 2 ) / 100 p = 571.4 answer : b"


Question: two - third of a positive number and 144 / 216 of its reciprocal are equal . the number is :

<gadget id="calculator">144 * 3</gadget>
<output>432</output>

<gadget id="calculator">216 * 2</gadget>
<output>432</output>

<gadget id="calculator">432 / 432</gadget>
<output>1</output>

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

Choices:
A. 5 / 12
B. 12 / 5
C. 25 / 144
D. 144 / 25
E. 1

sqrt(divide(multiply(144, const_3), multiply(216, const_2)))

Explanation: "let the number be x . then , 2 / 3 x = 144 / 216 * 1 / x x 2 = 144 / 216 * 3 / 2 = 144 / 144 x = 1 answer : e"


Question: from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is ?

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

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

<gadget id="calculator">(4/5) ** 3</gadget>
<output>64/125 = around 0.512</output>

<gadget id="calculator">(64/125) * 100</gadget>
<output>256/5 = around 51.2</output>
<result>256/5 = around 51.2</result>

Choices:
A. 45 %
B. 49.6 %
C. 51.2 %
D. 55 %
E. 60.3 %

multiply(power(divide(subtract(const_100, 20), const_100), const_3), const_100)

Explanation: let the total quantity of original milk = 1000 gm milk after 1 st operation = 80 % of 1000 = 800 gm milk after second operation = 80 % of 800 = 640 gm milk after third operation = 80 % of 640 = 512 gm strength of final mixture = 51.2 % answer is c


Question: after 6 games , team b had an average of 70 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?

<gadget id="calculator">6 * 70</gadget>
<output>420</output>

<gadget id="calculator">420 + 47</gadget>
<output>467</output>

<gadget id="calculator">500 - 467</gadget>
<output>33</output>
<result>33</result>

Choices:
A. 85
B. 74
C. 67
D. 33
E. 28

Explanation: "( 6 * 70 ) + 47 + x > 500 420 + 47 + x > 500 467 + x > 500 = > x > 33 option d"


Question: if a ' s height is 40 % less than that of b , how much percent b ' s height is more than that of a ?

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

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

<gadget id="calculator">(2/3) * 100</gadget>
<output>200/3 = around 66.666667</output>
<result>200/3 = around 66.666667</result>

Choices:
A. 66.66 %
B. 66.68 %
C. 66.766 %
D. 86.66 %
E. 66.65 %

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

Explanation: "excess of b ' s height over a ' s = [ ( 40 / ( 100 - 40 ) ] x 100 % = 66.66 % answer : a ) 66.66 %"


Question: how long will a boy take to run round a square field of side 35 meters , if he runs at the rate of 9 km / hr ?

<gadget id="calculator">35 * 4</gadget>
<output>140</output>

<gadget id="calculator">1_000 / 3_600</gadget>
<output>5/18 = around 0.277778</output>

<gadget id="calculator">9 * (5/18)</gadget>
<output>5/2 = around 2.5</output>

<gadget id="calculator">140 / (5/2)</gadget>
<output>56</output>
<result>56</result>

Choices:
A. 22
B. 38
C. 37
D. 56
E. 28

divide(multiply(35, const_4), multiply(9, divide(const_1000, const_3600)))

Explanation: answer : d ) 56 sec


Question: how many prime numbers are between 25 / 3 and 84 / 6 ?

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

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

Explanation: "25 / 3 = 8 . xxx 84 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"