options stringlengths 37 300 | correct stringclasses 5
values | annotated_formula stringlengths 7 727 | problem stringlengths 5 967 | rationale stringlengths 1 2.74k | program stringlengths 10 646 |
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a ) β 2 , b ) β 1 , c ) 0 , d ) 1 , e ) 2 | a | add(0.5, negate(3)) | what is the least integer greater than β 3 + 0.5 ? | "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( - 3 ) + ( 0.5 ) = - 2.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from -... | a = 0 + 5
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a ) $ 60 , b ) $ 70 , c ) $ 75 , d ) $ 96 , e ) can not be determined | b | divide(add(50, 90), 2) | if greg buys 3 shirts , 4 trousers and 2 ties , the total cost is $ 90 . if greg buys 7 shirts , 2 trousers and 2 ties , the total cost is $ 50 . how much will it cost him to buy 3 trousers , 5 shirts and 2 ties ? | "solution : 3 x + 4 y + 2 z = 90 7 x + 2 y + 2 z = 50 adding both the equations = 10 x + 6 y + 4 z = 140 5 x + 3 y + 2 z = 70 ans b" | a = 50 + 90
b = a / 2
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a ) 22 % , b ) 23.9 % , c ) 24 % , d ) 25 % , e ) 34 % | b | divide(22, divide(subtract(const_100, 8), const_100)) | in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 8 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ? | "since 8 % of the customers who sample the candyare notcaught , then 88 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.92 = 0.22 ; { % of customers who sample candy } = 0.239 . answer : b ." | a = 100 - 8
b = a / 100
c = 22 / b
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a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | a | divide(multiply(add(4, 3), const_2), 8) | | x + 3 | β | 4 - x | = | 8 + x | how many u solutions will this equation have ? | "| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a" | a = 4 + 3
b = a * 2
c = b / 8
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a ) 12 days , b ) 12 1 / 4 days , c ) 14 days , d ) 24 1 / 2 days , e ) none of these | a | divide(const_1, add(divide(const_1, 21), divide(const_1, 28))) | a sum of money is sufficient to pay a ' s wages for 21 days and b ' s wages for 28 days . the same money is sufficient to pay the wages of both for ? | let total money be rs . x a ' s 1 day ' s wages = rs . x / 21 , b ' s 1 day ' s wages = rs . x / 28 ( a + b ) ' s 1 day ' s wages = rs . ( x / 21 + x / 28 ) = rs . x / 12 ; money is sufficient to pay the wages of both for 12 days . correct option : a | a = 1 / 21
b = 1 / 28
c = a + b
d = 1 / c
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a ) 50 , b ) 80 , c ) 120 , d ) 150 , e ) 100 | a | divide(add(24, multiply(24, divide(2, 3))), subtract(const_1, divide(20, const_100))) | in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 24 . what is the total number of students in the school ? | "explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 24 + 2 / 3 of 24 80 / 100 x = 40 x = 50 . answer : option a" | a = 2 / 3
b = 24 * a
c = 24 + b
d = 20 / 100
e = 1 - d
f = c / e
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a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 54 | c | add(multiply(divide(48, multiply(2, 3)), 3), multiply(divide(48, multiply(2, 3)), 2)) | the l . c . m . of two numbers is 48 . the numbers are in the ratio 2 : 3 . then sum of the number is : | "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 48 or x = 8 . the numbers are 16 and 24 . hence , required sum = ( 16 + 24 ) = 40 . answer : option c" | a = 2 * 3
b = 48 / a
c = b * 3
d = 2 * 3
e = 48 / d
f = e * 2
g = c + f
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a ) r = 21 , b ) r = 22 , c ) r = 23 , d ) 24 , e ) 27 | c | subtract(power(5, 2), 2) | if x + ( 1 / x ) = 5 , what is the value of r = x ^ 2 + ( 1 / x ) ^ 2 ? | "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c" | a = 5 ** 2
b = a - 2
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a ) 21 , b ) 22 , c ) 27 , d ) 26 , e ) 28 | c | add(divide(subtract(56, 1), 2), const_1) | how many multiples of 2 are there between 1 and 56 , exclusive ? | "27 multiples of 2 between 1 and 56 exclusive . from 2 * 1 upto 2 * 27 , ( 1,2 , 3,4 , . . . , 27 ) . hence , 27 multiples ! correct option is c" | a = 56 - 1
b = a / 2
c = b + 1
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a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140 | c | divide(subtract(multiply(39, 120), multiply(120, 15)), subtract(39, 15)) | the average of marks obtained by 120 boys was 39 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ? | "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 39 24 x = 4680 - 1800 = > x = 2880 / 24 x = 120 . hence , the number of boys passed = 120 . answer : c" | a = 39 * 120
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
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['a ) rs . 4233', 'b ) rs . 4350', 'c ) rs . 4457', 'd ) rs . 4670', 'e ) rs . 4756'] | c | multiply(circumface(sqrt(divide(multiply(multiply(const_1000, const_10), 17.56), const_pi))), const_3) | the area of a circular place is 17.56 hectares . find the cost of fencing it at the rate of rs . 3 / meter approximately . | area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . Ο r 2 = 175600 β ( r ) 2 = ( 175600 x ( 7 / 22 ) ) β r = 236.37 m . circumference = 2 Ο r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 3 ) = rs . 4457 . c | a = 1000 * 10
b = a * 17
c = b / math.pi
d = math.sqrt(c)
e = circumface * (
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a ) 1 / 221 , b ) 8 / 221 , c ) 4 / 589 , d ) 4 / 587 , e ) 7 / 654 | a | divide(multiply(divide(52, const_4), divide(52, const_4)), choose(52, const_2)) | from a pack of 52 cards , two cards are drawn at random together at random what is the probability of both the cards being kings ? | "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 2 kings out of 4 n ( e ) = 4 c 2 = ( 4 * 3 ) / ( 2 * 1 ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 1326 = 1 / 221 answer ( a )" | a = 52 / 4
b = 52 / 4
c = a * b
d = math.comb(52, 2)
e = c / d
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a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 67 % | c | multiply(divide(subtract(multiply(const_3, divide(const_1, const_2)), const_1), const_1), const_100) | the length of a rectangle is halved , while its breadth is tripled . wat isthe % change in area ? | "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c" | a = 1 / 2
b = 3 * a
c = b - 1
d = c / 1
e = d * 100
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a ) 43 , b ) 53 , c ) 63 , d ) 65 , e ) 74 | e | subtract(negate(10), multiply(subtract(7,12, 18,25), divide(subtract(7,12, 18,25), subtract(3, 7,12)))) | 3 , 7,12 , 18,25 . . . . . . . . . . . . . . 10 th terms | "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 33 + 9 = 42 42 + 10 = 52 52 + 11 = 63 63 + 11 = 74 answer : e" | a = negate - (
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a ) 127 days , b ) 150 days , c ) 177 days , d ) 187 days , e ) 225 days | b | multiply(divide(multiply(const_1, 100), subtract(multiply(const_1, 100), multiply(10, 5))), multiply(15, 5)) | 10 men and 15 women together can complete a work in 5 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ? | "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 5 15 women ' s 1 day work = ( 1 / 5 - 10 / 100 ) = 1 / 10 1 woman ' s 1 day work = 1 / 150 1 woman alone can complete the work in 150 days . answer : b" | a = 1 * 100
b = 1 * 100
c = 10 * 5
d = b - c
e = a / d
f = 15 * 5
g = e * f
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a ) 1 : 3 , b ) 4 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4 | b | divide(subtract(27, 25), subtract(25, 17)) | two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 25 seconds , what is the ratio of their speeds ? | "let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 25 s = ( 27 x + 17 y ) / ( x + y ) = 25 = ( 27 x + 17 y ) / = 25 ( x + y ) = 2 x = 8 y = x / y = 8 / 2 = 4 / 1 i . e 4 : 1 answer : b" | a = 27 - 25
b = 25 - 17
c = a / b
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a ) s . 48 , b ) s . 50 , c ) s . 55 , d ) s . 60 , e ) s . 70 | a | divide(720, subtract(20, 5)) | on selling 20 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is : | "( c . p . of 20 balls ) - ( s . p . of 20 balls ) = ( c . p . of 5 balls ) c . p . of 15 balls = s . p . of 20 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 15 = rs . 48 . answer : option a" | a = 20 - 5
b = 720 / a
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a ) 5.2 , b ) 5.5 , c ) 7 , d ) 9 , e ) 10 | c | add(13, const_1) | the average of first 13 natural numbers is ? | "sum of 13 natural no . = 182 / 2 = 91 average = 91 / 13 = 7 answer : c" | a = 13 + 1
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a ) 20000 , b ) 24000 , c ) 34000 , d ) 35000 , e ) 30000 | e | multiply(54000, subtract(const_1, divide(multiply(30000, multiply(const_2, multiply(const_2, const_3))), add(multiply(45000, subtract(multiply(const_2, multiply(const_2, const_3)), 2)), multiply(30000, multiply(const_2, multiply(const_2, const_3))))))) | tom opened a shop investing rs . 30000 . jose joined him 2 months later , investing rs . 45000 . they earned a profit of rs . 54000 after completion of one year . what will be jose ' s share of profit ? | sol = ~ s - so anju β s share = [ 5 / 9 ] x 54000 = 30000 e | a = 2 * 3
b = 2 * a
c = 30000 * b
d = 2 * 3
e = 2 * d
f = e - 2
g = 45000 * f
h = 2 * 3
i = 2 * h
j = 30000 * i
k = g + j
l = c / k
m = 1 - l
n = 54000 * m
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a ) 75 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs | a | add(divide(multiply(25, subtract(const_100, 25)), const_100), 75) | fresh grapes contain 75 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 25 kgs of raisins ? | "the weight of non - water in 20 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 75 = 25 % of whole weight ) , so 25 * 0.75 = x * 0.25 - - > x = 75 . answer : a ." | a = 100 - 25
b = 25 * a
c = b / 100
d = c + 75
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a ) 81000 , b ) 22887 , c ) 26877 , d ) 26771 , e ) 17121 | a | add(add(64000, multiply(divide(1, 8), 64000)), multiply(divide(1, 8), add(64000, multiply(divide(1, 8), 64000)))) | every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 64000 ? | 64000 * 9 / 8 * 9 / 8 = 81000 answer : a | a = 1 / 8
b = a * 64000
c = 64000 + b
d = 1 / 8
e = 1 / 8
f = e * 64000
g = 64000 + f
h = d * g
i = c + h
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a ) 298 m , b ) 188 m , c ) 120 m , d ) 160 m , e ) 189 m | d | divide(12, subtract(divide(12, 10), 5)) | a train covers a distance of 12 km in 10 min . if it takes 5 sec to pass a telegraph post , then the length of the train is ? | "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 8 = 160 m . answer : d" | a = 12 / 10
b = a - 5
c = 12 / b
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a ) 334 , b ) 500 , c ) 376 , d ) 288 , e ) 300 | e | divide(285, divide(95, const_100)) | victor gets 95 % marks in examinations . if these are 285 marks , find the maximum marks . | let the maximum marks be m then 95 % of m = 285 β 95 / 100 Γ m = 285 β m = ( 285 Γ 100 ) / 95 β m = 28500 / 95 β m = 300 therefore , maximum marks in the examinations are 300 . answer : e | a = 95 / 100
b = 285 / a
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a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16 | c | divide(subtract(0.75, 0.5), subtract(0.9, 0.5)) | last month , john rejected 0.5 % of the products that he inspected and jane rejected 0.9 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ? | "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.9 ( x ) + 0.5 ( 1 - x ) = 0.75 0.4 x = 0.75 - 0.5 x = 0.25 / 0.4 x = 5 / 8 therefore the answer is c : 5 / 8 ." | a = 0 - 75
b = 0 - 9
c = a / b
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | add(divide(lcm(375, 150), 375), divide(lcm(375, 150), 150)) | a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 375 and $ 150 per unit , respectively . what is the fewest number of computer printers that the company can purchase ? | the smallest amount that the company can spend is the lcm of 375 and 150 , which is 750 for each , which is total 1500 . the number of 1 st type of computers which costing $ 375 = 750 / 375 = 2 . the number of 2 nd type of computers which costing $ 150 = 750 / 150 = 5 . total = 2 + 5 = 7 answer is e . | a = math.lcm(375, 150)
b = a / 375
c = math.lcm(375, 150)
d = c / 150
e = b + d
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a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100 | e | add(multiply(divide(100, const_10), multiply(const_2, const_4)), divide(100, const_10)) | how many integerskgreater than 100 and less than 1200 are there such that if the hundreds and the units digits ofkare reversed , the resulting integer is k + 99 ? | "numbers will be like 102 = > 201 = 102 + 99 203 = > 302 = 103 + 99 so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit . there will be ten pairs of such numbers for every pair there will 10 numbers like for 12 = > 102 , 112,132 , 142,152 , 162,172 , 182,192 . total = 10... | a = 100 / 10
b = 2 * 4
c = a * b
d = 100 / 10
e = c + d
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a ) 21 / 31 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7 | a | add(subtract(1, divide(2, 3)), subtract(divide(2, 3), divide(1, 5))) | a batch of cookies was divided amomg 3 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 5 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin | "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 3 b = 1 / 5 we can solve for g which is 7 / 10 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 7 / 10 + 1 / 3 ) = 7 / 10 x = 21 / ... | a = 2 / 3
b = 1 - a
c = 2 / 3
d = 1 / 5
e = c - d
f = b + e
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a ) 360 , b ) 252 , c ) 280 , d ) 300 , e ) 420 | a | divide(multiply(multiply(30, 42), 60), multiply(multiply(7, 6), 5)) | a grocer is storing soap boxes in cartons that measure 30 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ? | "however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 30 * 42 * 60 dimensions of the soap = 5 * 6 * 7 we get = 6 x 6 x 10 = 360 so the question is why this particular arrangement , in order to maximize number of s... | a = 30 * 42
b = a * 60
c = 7 * 6
d = c * 5
e = b / d
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a ) 4 . , b ) 8 . , c ) 12 . , d ) 16 , e ) 64 | d | power(subtract(5, divide(add(13, 5), const_2)), const_2) | if ( a - b - c + d = 13 ) and ( a + b - c - d = 5 ) , what is the value of ( b - d ) ^ 2 ? | a - b - c + d = 13 - - equation 1 a + b - c - d = 5 - - equation 2 adding 1 and 2 , we get 2 a - 2 c = 18 = > a - c = 9 - - equation 3 using equation 3 in 2 , we get b - d = 5 - 9 = - 4 = > ( b - d ) ^ 2 = 16 answer d | a = 13 + 5
b = a / 2
c = 5 - b
d = c ** 2
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a ) 37 kmph , b ) 34 kmph , c ) 32 kmph , d ) 38 kmph , e ) 76 kmph | c | multiply(const_3_6, divide(225, 15)) | a train 225 m in length crosses a telegraph post in 15 seconds . the speed of the train is ? | "s = 225 / 25 * 18 / 5 = 32 kmph answer : c" | a = 225 / 15
b = const_3_6 * a
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a ) 800 , b ) 500 , c ) 900 , d ) 1600 , e ) 2400 | e | multiply(divide(multiply(multiply(3.6, 0.48), 2.50), multiply(multiply(0.12, 0.09), 0.5)), 3) | find the value of 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] | "answer 3 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3 x 4 x 4 x 50 = 2400 correct option : e" | a = 3 * 6
b = a * 2
c = 0 * 12
d = c * 0
e = b / d
f = e * 3
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a ) 9 , b ) 8 , c ) 10 , d ) 12 , e ) 15 | a | divide(28, divide(add(3.5, 2.8), const_2)) | sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 3.5 per pound , and german chocolate cost $ 2.8 per pound . if the total the she spent on chocolate was $ 28 and both types of chocolate were purchased in whole number of pounds , how many total pounds of ch... | "if there were all the expensive ones , 3.5 . . . . there would be 28 / 3.5 or 8 of them but since 2.8 $ ones are also there , answer has to be > 8 . . if all were 2.8 $ ones , there will be 28 / 2.8 or 10 . . . so only 9 is left answer a . ." | a = 3 + 5
b = a / 2
c = 28 / b
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a ) 127 , b ) 225 , c ) 287 , d ) 450 , e ) 281 | b | divide(multiply(36, 30), divide(multiply(16, 24), 80)) | if 16 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ? | "explanation : let the required no of hectares be x . then men - - - hectares - - - days 16 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 16 * 30 / 24 * 80 x = 225 answer : b" | a = 36 * 30
b = 16 * 24
c = b / 80
d = a / c
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a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | b | add(add(add(divide(15, 3), 1), 1), 15) | a shop sells 1 chocolate at the rate rupee 1 each . you can exchange 3 warppers for one chocolate . if you have rs . 15 , what is the maximum number of chocolates you can get ? | rs . 15 = 15 chocolates 15 wrappers = 5 chocolates 5 wrappers = 1 chocolate ( u have 2 wrappers with you . . ) count this wrapper with already existing wrappers = 15 + 5 + 1 + 1 = 22 chocolates . . answer : b | a = 15 / 3
b = a + 1
c = b + 1
d = c + 15
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a ) 42 , b ) 46 , c ) 50 , d ) 54 , e ) 58 | b | multiply(add(divide(add(subtract(multiply(6, 5), 6), multiply(9, const_2)), subtract(9, 6)), 9), const_2) | jim is now twice as old as fred , who is 9 years older than sam . 6 years ago , jim was 5 times as old as sam . how old is jim now ? | j = 2 f = 2 ( s + 9 ) = 2 s + 18 j - 6 = 5 * ( s - 6 ) ( 2 s + 18 ) - 6 = 5 s - 30 s = 14 and so j = 46 the answer is b . | a = 6 * 5
b = a - 6
c = 9 * 2
d = b + c
e = 9 - 6
f = d / e
g = f + 9
h = g * 2
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a ) 228 , b ) 278 , c ) 300 , d ) 500 , e ) 821 | c | divide(204, subtract(const_1, divide(multiply(4, 8), const_100))) | a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 204 less than the sum lent . what was the sum lent ? | p - 204 = ( p * 4 * 8 ) / 100 p = 300 answer : c | a = 4 * 8
b = a / 100
c = 1 - b
d = 204 / c
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a ) 36 , b ) 40 , c ) 48 , d ) 32 , e ) 56 | b | add(multiply(divide(2, multiply(48, 2)), 2), multiply(divide(2, multiply(48, 2)), 48)) | the l . c . m . of 2 numbers is 48 . the numbers are in the ratio 2 : 3 . find their sum ? | "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 48 x = 8 the numbers are = 16 and 24 required sum = 16 + 24 = 40 answer is b" | a = 48 * 2
b = 2 / a
c = b * 2
d = 48 * 2
e = 2 / d
f = e * 48
g = c + f
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a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 39.1 , e ) 33.8 | d | multiply(divide(subtract(69.0, 42.0), 69.0), const_100) | the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 42.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ? | "$ 69 - $ 42 = 27 $ ( 27 / 69 ) * 100 = 39.13 % answer : d" | a = 69 - 0
b = a / 69
c = b * 100
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a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 6 | c | divide(factorial(subtract(add(const_4, 2), const_1)), multiply(factorial(2), factorial(subtract(const_4, const_1)))) | how many positive integers less than 100 have a remainder of 2 when divided by 13 ? | "take the multiples of 13 and add 2 0 x 13 + 2 = 2 . . . . 13 x 7 + 2 = 93 there are 14 numbers answer c" | a = 4 + 2
b = a - 1
c = math.factorial(b)
d = math.factorial(2)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
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a ) 105600 yards , b ) 35200 yards , c ) 39520 yards , d ) 42560 yards , e ) 41520 yards | a | divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 60), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2))) | convert 60 miles into yards ? | "1 mile = 1760 yards 60 miles = 60 * 1760 = 105600 yards answer is a" | a = 3 + 2
b = a * 2
c = 3 + 2
d = c * 2
e = b * d
f = e * 60
g = 3 + 2
h = g * 2
i = 3 + 2
j = i * 2
k = h * j
l = f / k
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a ) $ 4.50 , b ) $ 10.2 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 5.60 | b | add(3.2, multiply(divide(subtract(10.8, 3.2), add(5, subtract(sqrt(const_2), 1))), 5)) | the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 10.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn c... | i tried using time / rate approach : - initial price difference = 10.80 - 3.20 = 7.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled ... | a = 10 - 8
b = math.sqrt(2)
c = b - 1
d = 5 + c
e = a / d
f = e * 5
g = 3 + 2
|
a ) 3 , b ) 16 , c ) 75 , d ) 24 , e ) 26 | e | subtract(add(subtract(300, 200), const_1), add(add(add(divide(subtract(300, 200), 2), const_1), add(floor(subtract(add(divide(subtract(300, 200), 3), const_1), add(multiply(5, 3), 2))), const_1)), subtract(add(divide(subtract(300, 200), 5), const_1), multiply(5, 3)))) | how many positive integers e between 200 and 300 ( both inclusive ) are not divisible by 2 , 3 or 5 ? | 1 ) i figured there are 101 integers ( 300 - 200 + 1 = 101 ) . since the set begins with an even and ends with an even , there are 51 evens . 2 ) question says integers are not divisible by 2 , leaving all of the odds ( 101 - 51 = 50 integers ) . 3 ) question says integers are not divisible by 5 , removing all the inte... | a = 300 - 200
b = a + 1
c = 300 - 200
d = c / 2
e = d + 1
f = 300 - 200
g = f / 3
h = g + 1
i = 5 * 3
j = i + 2
k = h - j
l = math.floor(k)
m = l + 1
n = e + m
o = 300 - 200
p = o / 5
q = p + 1
r = 5 * 3
s = q - r
t = n + s
u = b - t
|
a ) 280 , b ) 284 , c ) 292 , d ) 320 , e ) 322 | e | multiply(23, 14) | the hcf of two numbers is 23 and the other two factors of their lcm are 13 and 14 . what is the largest number ? | hcf of the two numbers = 23 since hcf will be always a factor of lcm , 23 is a factor of the lcm . given that other two factors in the lcm are 13 and 14 . hence factors of the lcm are 23 , 13 , 14 so , numbers can be taken as ( 23 Γ 13 ) and ( 23 Γ 14 ) = 299 and 322 hence , largest number = 322 e ) | a = 23 * 14
|
a ) 1 / 2 , b ) 2 / 3 , c ) 1 / 5 , d ) 1 / 6 , e ) none of these | b | divide(subtract(const_6, 2), const_6) | in a throw of dice what is the probability of ge Γ¦ Β« ng number greater than 2 | explanation : number greater than 2 is 3 , 4 , 5 & 6 , so only 4 number total cases of dice = [ 1,2 , 3,4 , 5,6 ] so probability = 4 / 6 = 2 / 3 answer : b | a = 6 - 2
b = a / 6
|
a ) 15 , b ) 20 , c ) 10 , d ) 5 , e ) 8 | d | multiply(subtract(multiply(add(const_1, divide(50, const_100)), subtract(const_1, divide(30, const_100))), const_1), const_100) | a retailer purchases shirts from a wholesaler and then sells the shirts in her store at a retail price that is 50 percent greater than the wholesale price . if the retailer decreases the retail price by 30 percent this will have the same effect as increasing the wholesale price by what percent ? | answer : d = 5 . assume rs . 100 to be the price at which the retailer buys from wholesaler . 50 % increase makes retail price = 150 . now 30 % decrease - > ( 1 - 30 / 100 ) * 150 = 105 . now compared to the wholesale price of 100 , 5 % increase is what will have the same effect as increasing the wholesale price . | a = 50 / 100
b = 1 + a
c = 30 / 100
d = 1 - c
e = b * d
f = e - 1
g = f * 100
|
a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17 | e | floor(divide(172, 10)) | on dividing 172 by a number , the quotient is 10 and the remainder is 2 . find the divisor . | "d = ( d - r ) / q = ( 172 - 2 ) / 10 = 170 / 10 = 17 e" | a = 172 / 10
b = math.floor(a)
|
a ) 25 % , b ) 33 1 / 3 % , c ) 83 1 / 3 % , d ) 33 4 / 3 % , e ) 73 1 / 3 % | a | divide(multiply(const_100, const_100), multiply(4, const_100)) | in what time a sum of money double itself at 4 % per annum simple interest ? | "p = ( p * 4 * r ) / 100 r = 25 % answer : a" | a = 100 * 100
b = 4 * 100
c = a / b
|
a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120 | e | divide(48, subtract(divide(3, 4), divide(35, const_100))) | a big container is 35 % full with water . if 48 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ? | "48 liters is 40 % of the capacity c . 48 = 0.4 c c = 48 / 0.4 = 120 liters . the answer is e ." | a = 3 / 4
b = 35 / 100
c = a - b
d = 48 / c
|
a ) 2 / 3 , b ) 3 / 4 , c ) 7 / 19 , d ) 8 / 21 , e ) 10 / 21 | d | divide(8, add(add(8, 7), 6)) | in a box , there are 8 orange , 7 black and 6 white balls . if one ball is picked up randomly . what is the probability that it is neither orange nor white ? | total balls are 21 and neither black nor white . so favor case will be only 8 c 1 and total case 21 c 1 probability will be 8 c 1 / 21 c 1 = 8 / 21 answer : d | a = 8 + 7
b = a + 6
c = 8 / b
|
a ) 48 , b ) 64 , c ) 36 , d ) 72 , e ) 27 | c | divide(subtract(96, multiply(12, 5)), subtract(13, 12)) | suraj has a certain average of runs for 12 innings . in the 13 th innings he scores 96 runs thereby increasing his average by 5 runs . what is his average after the 13 th innings ? | "to improve his average by 5 runs per innings he has to contribute 12 x 5 = 60 runs for the previous 12 innings . thus , the average after the 13 th innings = 96 - 60 = 36 . answer : c" | a = 12 * 5
b = 96 - a
c = 13 - 12
d = b / c
|
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | b | divide(multiply(150, const_100), add(150, const_100)) | total number of boys and girls in a school is 150 . if the number of boys is x , then girls become x % of the total number of students . the number of boys is | explanation : clearly , x % of 150 = 150 - x [ as x is number of boys ] = > x + x / 100 β 150 = 150 = > 5 / 2 x = 150 = > x = 60 option b | a = 150 * 100
b = 150 + 100
c = a / b
|
a ) 2 years , b ) 5 years , c ) 7 years , d ) 8 years , e ) 10 years | e | divide(subtract(60000, 20000), multiply(20000, divide(20, const_100))) | $ 20000 will become $ 60000 at 20 % p . a . find the time ? | "si = simple interest = a - p = 60000 - 20000 = $ 40000 r = 100 si / pt = 100 * 40000 / 20000 * 20 = 10 years answer is e" | a = 60000 - 20000
b = 20 / 100
c = 20000 * b
d = a / c
|
a ) 9 : 8 , b ) 8 : 9 , c ) 6 : 2 , d ) 2 : 3 , e ) 1 : 2 | b | divide(divide(multiply(const_4, 3), multiply(3, 3)), divide(multiply(3, const_4), multiply(2, const_4))) | a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 6 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 3 . what is the ratio of luxury cars to sport utility vehicles ? | the ratio of economy to luxury cars is 6 : 2 - - > e : l = 6 : 2 = 30 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 3 - - > e : s = 5 : 3 = 30 : 18 . thus , l : s = 10 : 18 = 5 : 6 . answer : b . | a = 4 * 3
b = 3 * 3
c = a / b
d = 3 * 4
e = 2 * 4
f = d / e
g = c / f
|
a ) - 2 , b ) 10 , c ) - 1 , d ) 3 , e ) 0 | c | divide(subtract(negate(const_1), 3), subtract(subtract(power(negate(const_1), const_2), multiply(8, negate(const_1))), 20)) | what is the smallest integer that satisfies the inequality ( ( x - 3 ) / ( x ^ 2 - 8 x - 20 ) ) > 0 ? | let us factorize the denominator and rewrite the expression as ( x Γ’ Λ β 3 ) / ( ( x Γ’ Λ β 10 ) ( x + 2 ) ) > 0 equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good . the values that are relevant to us are x = 3 , x = 10 and x = - 2 .... | a = negate - (
b = a / 3
|
a ) 35 , b ) 30 , c ) 25 , d ) 20 , e ) 15 | e | subtract(add(add(20, 40), 60), add(add(multiply(5, const_3), 10), 80)) | the average ( arithmetic mean ) of 20 , 40 , and 60 is 5 more than the average of 10 , 80 , and what number ? | a 1 = 120 / 3 = 40 a 2 = a 1 - 5 = 35 sum of second list = 35 * 3 = 105 therefore the number = 105 - 90 = 15 e | a = 20 + 40
b = a + 60
c = 5 * 3
d = c + 10
e = d + 80
f = b - e
|
a ) 25 , b ) 42 , c ) 45 , d ) 49 , e ) 54 | a | divide(power(105, 3), multiply(multiply(21, 49), 45)) | if a = 105 and a ^ 3 = 21 * 49 * 45 * b , what is the value of b ? | "first step will be to break down all the numbers into their prime factors . 105 = 3 * 5 * 7 21 = 7 * 3 49 = 7 * 7 45 = 3 * 3 * 5 so , ( 105 ) ^ 3 = 3 * 7 * 7 * 7 * 3 * 3 * 5 * b therefore ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 * 7 ^ 3 * b therefore , b = 3 ^ 3 * 5 ^ 3 * 7 ^ 3 / 3 ^ 3 * 5 * 7 ^ 3 b = 5 ^ 2 = 25 correct answer a... | a = 105 ** 3
b = 21 * 49
c = b * 45
d = a / c
|
a ) 54.0 , b ) 54.9 , c ) 92.5 , d ) 57.0 , e ) 63.0 | c | add(add(multiply(divide(subtract(const_100, 20), const_100), 30), 30), multiply(divide(add(const_100, 25), const_100), 30)) | james took a 3 - hour bike ride . in the second hour he traveled 30 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ? | let the distance travelled in the first hour be x . thus , 1.2 x = 30 , x = 25 . now , the distance travelled in the 3 rd hour = 30 + 1 / 4 Γ’ Λ β 30 = 37.5 the only option ending with a 0.5 in the decimal place is c . answer : c | a = 100 - 20
b = a / 100
c = b * 30
d = c + 30
e = 100 + 25
f = e / 100
g = f * 30
h = d + g
|
a ) 1 , b ) 5 , c ) 3 , d ) 2 , e ) 4 | e | subtract(3, divide(subtract(44, 20), add(10, 20))) | calculate the value of n from the below equation : n ^ 3 Γ’ Λ β 10 n + 20 = 44 | "use elimination method to find the correct option . you find that of all the options when 4 is the correct value for n answer : e" | a = 44 - 20
b = 10 + 20
c = a / b
d = 3 - c
|
a ) a ) 5.61 , b ) b ) 3.42 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24 | b | max(multiply(subtract(add(45, 9), const_1), subtract(divide(9, 35), divide(9, 45))), const_4) | due to construction , the speed limit along an 9 - mile section of highway is reduced from 45 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? | "old time in minutes to cross 9 miles stretch = 9 * 60 / 45 = 9 * 4 / 3 = 12 new time in minutes to cross 9 miles stretch = 9 * 60 / 35 = 9 * 12 / 7 = 15.42 time difference = 3.42 ans : b" | a = 45 + 9
b = a - 1
c = 9 / 35
d = 9 / 45
e = c - d
f = b * e
g = max(f)
|
a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25 | c | divide(5, 3) | a number x is multiplied by 5 , and this product is then divided by 3 . if the positive square root of the result of these two operations equals x , what is the value of x if x β 0 ? | "sqrt ( 5 x / 3 ) to be perfect square x has to 5 / 3 ans : c" | a = 5 / 3
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a ) $ 4720 , b ) $ 4840 , c ) $ 4920 , d ) $ 5080 , e ) $ 5160 | b | multiply(4000, power(add(const_1, divide(10, const_100)), const_2)) | what amount does an investor receive if the investor invests $ 4000 at 10 % p . a . compound interest for two years , compounding done annually ? | "a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 5000 = 1.21 * 5000 = 4840 the answer is b ." | a = 10 / 100
b = 1 + a
c = b ** 2
d = 4000 * c
|
a ) $ 14,755 , b ) $ 15,430 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155 | b | multiply(divide(const_3, const_4), const_1000) | a store owner estimates that the average price of type a products will increase by 40 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owne... | "cost of type a products next year = 1.40 * 4500 = 6300 cost of type b products next year = 1.1 * 8300 = 9130 total 6300 + 9130 = 15430 option b" | a = 3 / 4
b = a * 1000
|
a ) 3 , b ) 9 , c ) 12 , d ) 18 , e ) 24 | e | multiply(divide(9, 3), add(add(4, 3), 1)) | the school soccer team looks at their record and finds that they win , lose , and tie games in a ratio of 4 : 3 : 1 . how many games did they play if they lost 9 games ? | the ratio is 4 wins : 3 losses : 1 tie . think of ratio as ` ` parts . ' ' divide 9 ( total losses ) by 3 ( ratio losses ) to find 1 ` ` part ' ' of the ratio . 9 / 3 = 3 this means the team tied 3 games . multiply 3 ( 1 ` ` part ' ' of ratio ) by 4 ( ratio wins ) to find total wins . 3 * 4 = 12 . this mean the team wo... | a = 9 / 3
b = 4 + 3
c = b + 1
d = a * c
|
a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 54 | e | add(multiply(divide(9, subtract(divide(9, 10), divide(3, 4))), divide(3, 4)), 9) | if 9 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ? | "let the capacity of the tank = c ( 3 / 4 ) c + 9 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 9 = > ( 3 / 20 ) c = 9 = > c = ( 9 * 20 ) / 3 = 60 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 9 = 45 + 9 = 54 answer e" | a = 9 / 10
b = 3 / 4
c = a - b
d = 9 / c
e = 3 / 4
f = d * e
g = f + 9
|
a ) 18 , b ) 36 , c ) 72 , d ) 0 , e ) 1 | a | multiply(divide(99, add(const_10, const_1)), const_2) | what is the remainder when 121212 . . . . . . . ( 300 ) digits is divided by 99 . | 12 / 99 = 12 1212 / 99 = 24 121212 / 99 = 36 . . . 121212 . . . ( 300 ) / 99 = ( 12 * 300 ) % 99 = 36 if they say 300 digits then ( 12 * 150 ) % 99 = 18 answer : a | a = 10 + 1
b = 99 / a
c = b * 2
|
a ) 22 , b ) 99 , c ) 27 , d ) 36 , e ) 20 | d | multiply(4, 9) | walking 9 / 8 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? | "speed ratio = 1 : 9 / 8 = 8 : 9 time ratio = 9 : 8 1 - - - - - - - - 9 4 - - - - - - - - - ? 36 m . answer : d" | a = 4 * 9
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a ) 47 , b ) 47.03 , c ) 48.03 , d ) 48 , e ) 49 | c | subtract(multiply(55, 30), multiply(48, 30)) | the average of 30 numbers is 48 . if three numbers namely 45 , 55 and 43 are discarded , the average of remaining numbers is ? | "explanation : total of 30 numbers = 30 * 48 = 1440 average o 27 numbers = 1440 - ( 45 + 55 + 43 ) / 27 = 48.03 answer : option c" | a = 55 * 30
b = 48 * 30
c = a - b
|
a ) 5 kmph , b ) 7 kmph , c ) 9 kmph , d ) 8 kmph , e ) 10 kmph | e | divide(subtract(divide(95, 2), divide(45, 2)), const_2) | a man rows his boat 95 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ? | "speed downstream = d / t = 95 / ( 2 1 / 2 ) = 38 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 38 - 18 ) / 2 = 10 kmph answer : e" | a = 95 / 2
b = 45 / 2
c = a - b
d = c / 2
|
a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 60,000 , e ) $ 75,000 | d | divide(add(multiply(multiply(multiply(const_3, const_3), const_10), multiply(const_100, const_10)), multiply(multiply(const_3, const_10), multiply(const_100, const_10))), add(75, 15)) | a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 210,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ? | "another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 7 a * 1 + a * 5 ) / 6 = 12 a / 6 = 2 a = 60000 answer is d . $ 60,000" | a = 3 * 3
b = a * 10
c = 100 * 10
d = b * c
e = 3 * 10
f = 100 * 10
g = e * f
h = d + g
i = 75 + 15
j = h / i
|
a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23 | a | divide(subtract(multiply(18, 18), 1), 17) | a batsman scored 1 runs in his 18 th innings and that makes his average 18 . find his average upto the 17 th innings ? | avg = sum of the value / no . of the value 18 = ( sum of the first 17 innings score + 1 ) / 18 ( 18 * 18 - 1 ) = sum of the first 17 innings score sum of the first 17 innings score = 323 ave upto 17 innings = 323 / 17 = 19 answer : a | a = 18 * 18
b = a - 1
c = b / 17
|
a ) 4 , b ) 4.5 , c ) 6 , d ) 6.25 , e ) 7.2 | e | divide(multiply(9, const_60), add(15, const_60)) | if jack walked 9 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ? | "distance walked in 1 hour and 15 mins = 9 miles speed per hour = distance / time = 9 / ( 5 / 4 ) = 7.2 miles per hour answer e" | a = 9 * const_60
b = 15 + const_60
c = a / b
|
a ) 90 , b ) 129 , c ) 120 , d ) 160 , e ) 200 | b | divide(add(110, 148), 2) | a student chose a number , multiplied it by 2 , then subtracted 148 from the result and got 110 . what was the number he chose ? | "solution : let x be the number he chose , then 2 * x * 148 = 110 2 x = 258 x = 129 correct answer b" | a = 110 + 148
b = a / 2
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a ) 27 , b ) 3 , c ) 6 , d ) 8 , e ) 12 | b | divide(divide(multiply(multiply(8, 12), 3), 12), 8) | a crate measures 3 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still... | "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 3 for the surface 8 * 12 face . volume = 27 pi answer b" | a = 8 * 12
b = a * 3
c = b / 12
d = c / 8
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | e | subtract(add(3.4, 10.7), 1.6) | if [ x ] is the greatest integer less than or equal to x , what is the value of [ 1.6 ] + [ - 3.4 ] + [ 10.7 ] ? | "you are asked what the closest lesser integer value to [ x ] is . [ 1.6 ] = 1.0 [ - 3.4 ] = - 4.0 [ 10.7 ] = 10.0 therefore , answer is : 1.0 - 4.0 + 10.0 = 7.0 option e ." | a = 3 + 4
b = a - 1
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a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20 | e | multiply(divide(75, subtract(multiply(137, 2), 61)), 2) | a firm is comprised of partners and associates in a ratio of 2 : 61 . if 75 more associates were hired , the ratio of partners to associates would be 4 : 137 . how many partners are currently in the firm ? | "the ratio 2 : 61 = 4 : 122 so the ratio changed from 4 : 122 to 4 : 137 . 137 - 122 = 15 which is 1 / 5 of the increase in 75 associates . the ratio changed from 20 : 610 to 20 : 685 . thus the number of partners is 20 . the answer is e ." | a = 137 * 2
b = a - 61
c = 75 / b
d = c * 2
|
a ) 20 , b ) 25 , c ) 27 , d ) 22 , e ) 17 | b | subtract(37, multiply(multiply(18, 3), 2)) | evaluate : 37 - 18 Γ· 3 Γ 2 = | "according to order of operations , 18 Γ· 3 Γ 2 ( division and multiplication ) is done first from left to right 18 Γ· 3 Γ 2 = 6 Γ 2 = 12 hence 37 - 18 Γ· 3 Γ 2 = 37 - 12 = 25 correct answer b ) 25" | a = 18 * 3
b = a * 2
c = 37 - b
|
a ) 271 , b ) 266 , c ) 400 , d ) 277 , e ) 232 | c | subtract(multiply(25, multiply(90, const_0_2778)), 225) | a train 225 m long running at 90 kmph crosses a platform in 25 sec . what is the length of the platform ? | "length of the platform = 90 * 5 / 18 * 25 = 625 β 225 = 400 answer : c" | a = 90 * const_0_2778
b = 25 * a
c = b - 225
|
a ) 22 , b ) 389 , c ) 38 , d ) 45 , e ) 01 | d | multiply(divide(add(add(add(const_10, 20), multiply(divide(41, const_100), const_1000)), const_1000), multiply(add(200, 120), const_10)), const_100) | in an election only two candidates contested 20 % of the voters did not vote and 120 votes were declared as invalid . the winner got 200 votes more than his opponent thus he secured 41 % votes of the total voters on the voter list . percentage votes of the defeated candidate out of the total votes casted is : | let there be x voters and k votes goes to loser then 0.8 x - 120 = k + ( k + 200 ) k + 200 = 0.41 x \ inline \ rightarrow k = 1440 and ( k + 200 ) = 1640 therefore \ inline \ frac { 1440 } { 3200 } \ times 100 = 45 % answer : d ) 45 % | a = 10 + 20
b = 41 / 100
c = b * 1000
d = a + c
e = d + 1000
f = 200 + 120
g = f * 10
h = e / g
i = h * 100
|
a ) 800 , b ) 700 , c ) 360 , d ) 370 , e ) 380 | b | subtract(multiply(speed(600, 18), 39), 600) | a 600 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ? | "speed = 600 / 18 = 100 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 100 / 3 = > x = 1300 m . l = 1300 - 600 = 700 m answer : option b" | a = speed * (
b = a - 39
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a ) 11 , b ) 12 , c ) 13.2 , d ) none , e ) can not be determined | a | divide(187, divide(187, 17)) | 17 times a number gives 187 . the number is | "explanation : let the number be ' n ' 17 Γ n = 187 β n = 11 correct option : a" | a = 187 / 17
b = 187 / a
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a ) 8.5 , b ) 6.6 , c ) 7.6 , d ) 6.4 , e ) 5.7 | b | divide(0.0008154, 0.00205) | 0.0008154 / 0.00205 x 16.5 = ? | "explanation : ? = 0.0008154 / 0.00205 x 16.5 = 6.6 answer : option b" | a = 0 / 8154
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a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6 | c | add(divide(subtract(52, divide(subtract(divide(add(14, 2), 2), 2), 2)), add(subtract(divide(add(14, 2), 2), 2), divide(add(14, 2), 2))), divide(const_1, 2)) | tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , ho... | "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its s... | a = 14 + 2
b = a / 2
c = b - 2
d = c / 2
e = 52 - d
f = 14 + 2
g = f / 2
h = g - 2
i = 14 + 2
j = i / 2
k = h + j
l = e / k
m = 1 / 2
n = l + m
|
a ) 32 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph | a | subtract(multiply(divide(280, 9), const_3_6), 80) | a man sitting in a train which is traveling at 80 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ? | "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 80 ) kmph = 32 kmph . answer : a" | a = 280 / 9
b = a * const_3_6
c = b - 80
|
a ) 80 , b ) 100 , c ) 110 , d ) 120 , e ) 140 | d | multiply(multiply(3, const_10), const_4) | howmany 3 digit numbers are there tens digit place is more than hundreds digit place and units place less than hundreds digit place ? | we have numbers { 01 , 23 , 45 , 67 , 89 } now we would decide the cases on behalf of value of hundred place digit . and accordingly choose unit ' s digit and ten ' s digit . value of hundred place digit must be choosen in such a manner that there should exist a greater digit for ten ' s place and a smaller digit for u... | a = 3 * 10
b = a * 4
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a ) none , b ) one , c ) two , d ) three , e ) four | e | subtract(15, multiply(3, const_4)) | a = 7 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ? | "this is a tricky worded question and i think the answer is should be d not c . . . here is my reason : the stem says that x is a positive integer such that has no factor grater than 2 and less than x itself . the stem wants to say that x is a prime number . because any prime number has no factor grater than 1 and itse... | a = 3 * 4
b = 15 - a
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a ) 70 , b ) 76 , c ) 78 , d ) 80 , e ) 88 | b | subtract(multiply(add(32, 4), add(10, const_1)), multiply(10, 32)) | average of 10 matches is 32 , how many runs one should should score to increase his average by 4 runs . | "explanation : average after 11 innings should be 36 so , required score = ( 11 * 36 ) - ( 10 * 32 ) = 396 - 320 = 76 answer : option b" | a = 32 + 4
b = 10 + 1
c = a * b
d = 10 * 32
e = c - d
|
a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200 | c | divide(subtract(300, 244), subtract(const_1, divide(65, const_100))) | a particular library has 300 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 65 percent of books that were loaned out are returned and there are 244 books in the sp... | "the total number of books is 300 . let x be the number of books which were loaned out . 65 % of books that were loaned out are returned . 35 % of books that were loaned out are not returned . now , there are 244 books , thus the number of un - returned books is 300 - 244 = 56 books . 0.35 x = 56 x = 160 the answer is ... | a = 300 - 244
b = 65 / 100
c = 1 - b
d = a / c
|
a ) 57 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 38 , e ) 47 | a | subtract(58, const_1) | in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 58 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ? | "so 57 days answer a = 57" | a = 58 - 1
|
a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3 | e | divide(divide(factorial(6), multiply(factorial(2), factorial(1))), factorial(6)) | joshua and jose work at an auto repair center with 1 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ? | "two methods 1 ) probability of chosing josh first = 1 / 3 probability of chosing jose second = 1 / 2 total = 1 / 6 probability of chosing jose first = 1 / 3 probability of chosing josh second = 1 / 2 total = 1 / 6 final = 1 / 6 + 1 / 6 = 1 / 3 e" | a = math.factorial(6)
b = math.factorial(2)
c = math.factorial(1)
d = b * c
e = a / d
f = math.factorial(6)
g = e / f
|
a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29 | b | add(subtract(multiply(sqrt(169), const_2), multiply(const_2, 1)), 1) | what is the value of n if the sum of the consecutive odd intergers e from 1 to n equals 169 ? | "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of... | a = math.sqrt(169)
b = a * 2
c = 2 * 1
d = b - c
e = d + 1
|
a ) 7858 , b ) 8301 , c ) 14667 , d ) 63840 , e ) 146,667 | e | divide(multiply(subtract(3.25, 2.85), divide(55000, multiply(const_10, const_100))), subtract(2.8, 2.65)) | joseph completes work worth $ 3.25 in hour and his cost to company per hour is $ 2.85 . ray completes worth worth of $ 2.80 in an hour and his cost to company is $ 2.65 per hour . if joseph works for 55000 hours , how many must ray work so that company makes at least as much in total gross profit as in case of joseph ? | joseph : profit / hour = 3.25 - 2.85 = 0.4 : no of hours = 55,000 : gross profit = 55,000 * 0.4 = 22,000 ray : profit / hour = 0.15 : gross profit = 22,000 : no of hours = 22,000 / 0.15 = 220,000 / 1.5 ( only closes is 146,667 ) answer e | a = 3 - 25
b = 10 * 100
c = 55000 / b
d = a * c
e = 2 - 8
f = d / e
|
a ) 95 , b ) 50 , c ) 12 , d ) 13 , e ) 67 | a | divide(divide(subtract(250, multiply(multiply(5, const_0_2778), 5)), 5), const_0_2778) | a train 250 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is : | "speed of the train relative to man = ( 250 / 10 ) m / sec = ( 25 ) m / sec . [ ( 25 ) * ( 18 / 5 ) ] km / hr = 90 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 90 = = > x = 95 km / hr . answer : option a" | a = 5 * const_0_2778
b = a * 5
c = 250 - b
d = c / 5
e = d / const_0_2778
|
a ) 20 , b ) 30 , c ) 10 , d ) 80 , e ) 100 | c | subtract(subtract(200, 50), 10) | of the 200 employees at company x , 50 are full - time , and 150 have worked at company x for at least a year . there are 10 employees at company x who aren β t full - time and haven β t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ... | "200 employees 50 are full - time 150 have worked at company x for at least a year 10 employees at company x who aren β t full - time and haven β t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 200 - 50 = 150 employees not full tim... | a = 200 - 50
b = a - 10
|
a ) 26630 , b ) 26640 , c ) 36644 , d ) 31944 , e ) 26844 | d | multiply(24000, add(const_1, divide(multiply(3, 10), const_100))) | population is 24000 . population increases by 10 % every year , then the population after 3 years is ? | "population after 1 st year = 24000 * 10 / 100 = 2400 = = = > 24000 + 2400 = 26400 population after 2 nd year = 26400 * 10 / 100 = 2640 = = = > 26400 + 2640 = 29040 population after 3 rd year = 29040 * 10 / 100 = 2904 = = = > 29040 + 2904 = 31944 answer : d" | a = 3 * 10
b = a / 100
c = 1 + b
d = 24000 * c
|
a ) 278 , b ) 900 , c ) 278 , d ) 450 , e ) 772 | b | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(2, 150))) | a man purchased 3 blankets @ rs . 100 each , 2 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "10 * 150 = 1500 3 * 100 + 2 * 150 = 600 1500 β 600 = 900 answer : b" | a = 10 * 150
b = 3 * 100
c = 2 * 150
d = b + c
e = a - d
|
a ) 170 , b ) 172 , c ) 174 , d ) 176 , e ) 178 | c | add(4, lcm(34, 5)) | find the least number which when divided by 34 and 5 leaves a remainder of 4 in each case . | "the least number which when divided by different divisors leaving the same remainder in each case = lcm ( different divisors ) + remainder left in each case . hence the required least number = lcm ( 31 , 5 ) + 4 = 174 . answer : c" | a = math.lcm(34, 5)
b = 4 + a
|
a ) 1 / pi , b ) sqrt ( 2 / pi ) , c ) sqrt ( 4.5 / pi ) , d ) 2 / sqrt ( pi ) , e ) pi / 2 | c | sqrt(divide(divide(square_area(3), 2), const_pi)) | an artist wishes to paint a circular region on a square poster that is 3 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ? | "area of the poster is 3 x 3 = 9 1 / 2 the area = 4.5 pi * r ^ 2 = 4.5 r ^ 2 = 4.5 / pi r = sqrt ( 4.5 / pi ) answer ( c )" | a = square_area / (
b = a / 2
c = math.sqrt(b)
|
a ) 10.9 sec , b ) 14.8 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 9.27 sec | e | divide(add(120, 150), multiply(add(60, 40), const_0_2778)) | two trains 120 m and 150 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ? | "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 120 + 150 = 270 m . required time = 270 * 9 / 250 = 9.27 = 9.27 sec . answer : e" | a = 120 + 150
b = 60 + 40
c = b * const_0_2778
d = a / c
|
a ) 96 kmph , b ) 94 kmph , c ) 92 kmph , d ) 86 kmph , e ) 72 kmph | e | multiply(divide(160, 8), const_3_6) | a 160 meter long train crosses a man standing on the platform in 8 sec . what is the speed of the train ? | "s = 160 / 8 * 18 / 5 = 72 kmph answer : e" | a = 160 / 8
b = a * const_3_6
|
a ) 2 . , b ) 4 . , c ) 5 . , d ) 6 , e ) 18 . | e | divide(multiply(12, 18), 12) | 18 beavers , working together in a constant pace , can build a dam in 12 hours . how many hours will it take 12 beavers that work at the same pace , to build the same dam ? | "total work = 18 * 12 = 216 beaver hours 12 beaver * x = 216 beaver hours x = 216 / 12 = 18 answer : e" | a = 12 * 18
b = a / 12
|
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