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 |
|---|---|---|---|---|---|
a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 180 | e | divide(subtract(32, 14), subtract(divide(20, const_100), divide(10, const_100))) | of the diplomats attending a summit conference , 14 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ? | { total } = { french } + { russian } - { both } + { neither } { total } = 14 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 180 . answer : e . | a = 32 - 14
b = 20 / 100
c = 10 / 100
d = b - c
e = a / d
|
a ) 400 , b ) 625 , c ) 1250 , d ) 3200 , e ) 10 000 | d | divide(80, divide(2, 80)) | in a certain pond , 80 fish were caught , tagged , and returned to the pond . a few days later , 80 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ? | "the percent of tagged fish in the second catch is 2 / 80 * 100 = 2.5 % . we are told that 2.5 % approximates the percent of tagged fish in the pond . since there are 80 tagged fish , then we have 0.025 x = 80 - - > x = 3,200 . answer : d ." | a = 2 / 80
b = 80 / a
|
a ) 25 % , b ) 50 % , c ) 100 % , d ) 150 % , e ) none | c | multiply(subtract(divide(subtract(const_100, 50), 25), const_1), const_100) | the cost price of an article is 25 % of the marked price . calculate the gain percent after allowing a discount of 50 % . | "sol . let marked price = rs . 100 . then , c . p . = rs . 25 . s . p = rs . 50 . Γ’ Λ Β΄ gain % = [ 25 / 25 * 100 ] % = 100.0 % . answer c" | a = 100 - 50
b = a / 25
c = b - 1
d = c * 100
|
a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 30 | e | divide(add(40, 20), const_2) | the total marks obtained by a student in mathematics and physics is 40 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together . | "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 40 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 40 + 20 ) / 2 = 30 . answer : e" | a = 40 + 20
b = a / 2
|
['a ) 1 : ( 2 + 6 ^ ( 1 / 2 ) )', 'b ) 1 : ( 4 + 7 ^ ( 1 / 3 ) )', 'c ) ( 2 + 7 ^ ( 1 / 2 ) ) : 1', 'd ) ( 2 + 7 ^ ( 1 / 2 ) ) : 2', 'e ) none of these'] | e | divide(sqrt(const_2), multiply(const_2, add(7, sqrt(const_2)))) | anup manages to draw 7 circles of equal radii with their centres on the diagonal of a square such that two extreme circles touch two sides of the square and each middle circle touches two circles on either side . find the ratio of radius of the circles to the side of the square . | diagonal of square = ( 2 * r ) * 7 + ( 2 ^ ( 1 / 2 ) * r - r ) * 2 diagonal has 7 squares diameters length + little distance between extreme squares to the end point [ form a square of side r from center of extreme circle to the extreme end to find distance ] distance = 2 ^ ( 1 / 2 ) * r - r d = a * 2 ^ ( 1 / 2 ) a = 2 ^ ( 1 / 2 ) * [ 6 * r + 2 ^ ( 1 / 2 ) * r ] r / a = 1 : [ 2 + 6 * 2 ^ ( 1 / 2 ) ] answer is none of the above answer : e | a = math.sqrt(2)
b = math.sqrt(2)
c = 7 + b
d = 2 * c
e = a / d
|
a ) 550 , b ) 600 , c ) 650 , d ) 180 , e ) 750 | d | divide(const_3600, 20) | a light flashes every 20 seconds , how many times will it flash in ? of an hour ? | "1 flash = 20 sec for 1 min = 3 flashes so for 1 hour = 3 * 60 = 180 flashes . answer : d" | a = 3600 / 20
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a ) rs . 200 , b ) rs . 720 , c ) rs . 300 , d ) rs . 150 , e ) none of these | b | multiply(multiply(3, const_4), divide(240, add(3, 1))) | the cost of 3 pens and 5 pencils is rs . 240 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ? | "explanation : let the cost of one pen is β 5 x β and pencil is β x β 3 x 5 x + 5 x = rs . 240 15 x + 5 x = rs . 240 x = 240 / 20 = 12 : . cost of 1 pen = 5 x = 5 x 12 = 60 : . cost of 12 pens , i . e . ( one dozen ) = 60 x 12 = rs . 720 answer : option b" | a = 3 * 4
b = 3 + 1
c = 240 / b
d = a * c
|
a ) $ 16.32 , b ) $ 18.00 , c ) $ 21.60 , d ) $ 24.48 , e ) $ 28.87 | e | multiply(divide(subtract(const_100, 25), const_100), multiply(0.55, 70)) | the regular price per can of a certain brand of soda is $ 0.55 . if the regular price per can is discounted 25 percent when the soda is purchased in 24 - can cases , what is the price of 70 cans of this brand of soda purchased in 24 - can cases ? | "the discounted price of one can of soda is ( 0.75 ) ( $ 0.55 ) , or $ 0.4125 therefore , the price of 70 cans of soda at the discounted price would be ( 70 ) ( $ 0.4125 ) = 28.875 answer : e" | a = 100 - 25
b = a / 100
c = 0 * 55
d = b * c
|
a ) 18 , b ) 16 , c ) 32 , d ) 56 , e ) 60 | b | multiply(divide(divide(add(add(multiply(multiply(const_4, const_2), const_10), multiply(multiply(const_4, const_2), const_100)), multiply(const_12, const_1000)), 230), 7), 2) | the ratio between the number of sheep and the number of horses at the stewart farm is 2 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ? | "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 2 x = 2 * 8 = 16 . hence b" | a = 4 * 2
b = a * 10
c = 4 * 2
d = c * 100
e = b + d
f = 12 * 1000
g = e + f
h = g / 230
i = h / 7
j = i * 2
|
a ) 3600 , b ) 2988 , c ) 2789 , d ) 2887 , e ) 1297 | a | subtract(multiply(add(1500, 100), add(20, const_1)), multiply(1500, 20)) | the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ? | "manager ' s monthly salary rs . ( 1600 * 21 - 1500 * 20 ) = rs . 3600 . answer : a" | a = 1500 + 100
b = 20 + 1
c = a * b
d = 1500 * 20
e = c - d
|
a ) 3 / 2 , b ) 3 / 4 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 5 | c | divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 6))) | a call center has two teams . each member of team a was able to process 6 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ? | "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 6 calls , so total calls for team a = 30 fraction for team b = 40 / ( 40 + 30 ) = 4 / 7 = answer = c" | a = 8 * 5
b = 8 * 5
c = 5 * 6
d = b + c
e = a / d
|
a ) 1667 , b ) 6789 , c ) 1200 , d ) 6151 , e ) 1400 | e | divide(1064, subtract(const_1, divide(24, const_100))) | after decreasing 24 % in the price of an article costs rs . 1064 . find the actual cost of an article ? | "cp * ( 76 / 100 ) = 1064 cp = 14 * 100 = > cp = 1400 answer : e" | a = 24 / 100
b = 1 - a
c = 1064 / b
|
a ) a ) 4 , b ) b ) 3 , c ) c ) 5 , d ) d ) 2 , e ) e ) 8 | d | divide(subtract(602, multiply(add(12, 4), divide(1, 8))), 300) | 300 Γ ? + ( 12 + 4 ) Γ 1 / 8 = 602 | explanation : = > 300 Γ ? + ( 12 + 4 ) Γ 1 / 8 = 602 = > 300 Γ ? = 602 - ( 12 + 4 ) Γ 1 / 8 = > 300 Γ ? = 602 - 2 = 600 = > ? = 600 / 300 = 2 answer : option d | a = 12 + 4
b = 1 / 8
c = a * b
d = 602 - c
e = d / 300
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 6 | e | divide(36, add(add(2, 2), 1)) | if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 36 ) which of these integers could be the value of z ? | "solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( β which of these integers β¦ β ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 36 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 37 incorrect c . 2 / 2 = 2 / 3 + 2 / 38 incorrect d . 2 / 3 = 2 / 4 + 2 / 39 incorrect e . 2 / 4 = 2 / 5 + 2 / 40 correct the correct answer is e , because it contains the only value that makes the equation work . notice how quickly this strategy worked in this case" | a = 2 + 2
b = a + 1
c = 36 / b
|
a ) 72 , b ) 75 , c ) 84 , d ) 88 , e ) 90 | b | subtract(inverse(subtract(inverse(35), inverse(60))), const_10) | girl and boy together can complete a piece of work in 35 days while girl alone can complete the same work in 60 days . boy alone will be able to complete the same working in : | subtraction of fraction ab β cd = ad β cbbd girl and boy finish one work with company = 35 days ( girl + boy ) β² s one day β s work = 135 girl alone finish the same work = 60 days girl β² s one day β s work = 160 b β² s one day β s work = ( a + b ) β² s one day β s work - a β² s one day β s work 135 β 160 = 184 hence b alone can complete the work in 84 days | a = 1/(35)
b = 1/(60)
c = a - b
d = 1/(c)
e = d - 10
|
a ) 5.1 , b ) 4.1 , c ) 3.1 , d ) 2.1 , e ) none of these | a | divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | what is 15 percent of 34 | "explanation : it will be 15 % of 34 = ( 15 / 100 ) * 34 = 5.10 answer : option a" | a = 3 + 2
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4
g = 3 + 2
h = f * g
i = 3 + 2
j = i * 2
k = h * j
l = e + k
m = 3 + 3
n = l + m
o = 15 * n
p = o / 100
|
a ) 2288 , b ) 27669 , c ) 1766 , d ) 1000 , e ) 2871 | d | divide(subtract(140, divide(multiply(6, 2500), const_100)), subtract(divide(5, const_100), divide(6, const_100))) | rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 140 . how much was lent at 5 % ? | "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 140 x = 1000 answer : d" | a = 6 * 2500
b = a / 100
c = 140 - b
d = 5 / 100
e = 6 / 100
f = d - e
g = c / f
|
a ) 75142 , b ) 64851 , c ) 5149 , d ) 69993 , e ) none of these | d | subtract(multiply(7, const_1000), 7) | the difference between the local value and the face value of 7 in the numeral 32675149 is ? | "( local value of 7 ) - ( face value of 7 ) = ( 70000 - 7 ) = 69993 d )" | a = 7 * 1000
b = a - 7
|
a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 22 | a | subtract(divide(subtract(multiply(16, 5), 42), const_2), const_2) | the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 16 , and k < m < r < s < t . if t is 42 , what is the greatest possible value of the median of the 5 integers ? | we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 16 which means that in effect , all numbers are equal to 16 . if the largest number is 42 , it is 26 more than 16 . we need r to be maximum so k and m should be as small as possible to get the average of 16 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 15 less than 16 and 2 is 14 less than 16 which means k and m combined are 29 less than the average . 42 is already 26 more than 16 and hence we only have 29 - 26 = 3 extra to distribute between r and s . since s must be greater than r , r can be 16 + 1 = 17 and s can be 16 + 2 = 18 . so r is 17 . answer ( a ) | a = 16 * 5
b = a - 42
c = b / 2
d = c - 2
|
a ) 21 , b ) 23 , c ) 25 , d ) 27 , e ) 29 | a | add(10, add(const_0_25, add(const_0_33, divide(divide(231, 10), const_2)))) | a rectangular field has a length 10 meters more than it is width . if the area of the field is 231 , what is the length ( in meters ) of the rectangular field ? | "area = l * w = ( l ) * ( l - 10 ) = 231 trial and error : 20 * 10 = 200 ( too low ) 21 * 11 = 231 the length is 21 meters . the answer is a ." | a = 231 / 10
b = a / 2
c = const_0_33 + b
d = const_0_25 + c
e = 10 + d
|
a ) 22 , b ) 20 , c ) 90 , d ) 80 , e ) 11 | d | multiply(divide(subtract(1080, 600), 600), const_100) | a cycle is bought for rs . 600 and sold for rs . 1080 , find the gain percent ? | "600 - - - - 180 100 - - - - ? = > 80 % answer : d" | a = 1080 - 600
b = a / 600
c = b * 100
|
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12 | c | add(subtract(divide(86, 7), 3), const_1) | how many integers are between 3 and 86 / 7 , inclusive ? | "86 / 7 = 12 . xx we are not concerned about the exact value of 86 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 3 and 86 / 7 would be 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 total number of integers = 10 option c if we need to find the number of integers between two numbers n and m , where m > n the number of integers = m - n + 1 in the given question , the number of integers = 12 - 3 + 1 = 10 answer : c" | a = 86 / 7
b = a - 3
c = b + 1
|
a ) 0 kmph , b ) 3.5 kmph , c ) 16 kmph , d ) 2.5 kmph , e ) 26 kmph | b | divide(subtract(15, 8), const_2) | a man goes downstream at 15 kmph , and upstream 8 kmph . the speed of the stream is | "speed of the stream = 1 / 2 ( 15 - 8 ) kmph = 3.5 kmph . correct option : b" | a = 15 - 8
b = a / 2
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a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 9.00 , e ) $ 20.00 | d | subtract(20, multiply(subtract(12, const_1), 1)) | if 12 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 1.00 , then the maximum possible amount any one person could have contributed is | d for me 11 people with 1 $ each - > maximum = 9 | a = 12 - 1
b = a * 1
c = 20 - b
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a ) $ 98,000 , b ) $ 106,000 , c ) $ 112,000 , d ) $ 118,000 , e ) $ 123,000 | e | divide(multiply(const_100, multiply(const_100, add(const_1, 4))), add(divide(25, const_100), multiply(multiply(divide(25, const_100), subtract(const_1, divide(25, const_100))), const_2))) | the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 76,875 , how much profit did the business make ? | "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = $ 76,875 p = $ 123,000 the answer is e ." | a = 1 + 4
b = 100 * a
c = 100 * b
d = 25 / 100
e = 25 / 100
f = 25 / 100
g = 1 - f
h = e * g
i = h * 2
j = d + i
k = c / j
|
a ) 30 days , b ) 35 days , c ) 40 days , d ) 45 days , e ) 50 days | a | divide(subtract(10, add(divide(10, 40), divide(10, 40))), divide(10, 40)) | a and b can do a piece of work in 40 days and 40 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ? | "explanation : ( a + b ) β s 10 days work = 10 [ 1 / 40 + 1 / 40 ] = 10 [ 1 + 1 / 40 ] = 1 / 2 a complete remaining work in 1 / 2 * 40 = 20 total work = 10 + 20 = 30 days answer : option a" | a = 10 / 40
b = 10 / 40
c = a + b
d = 10 - c
e = 10 / 40
f = d / e
|
a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 12.5 | e | divide(subtract(282, multiply(10, 3.2)), 20) | in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 20 overs to reach the target of 282 runs ? | "explanation : runs scored in the first 10 overs = 10 Γ 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 20 run rate needed = 250 / 20 = 12.5 answer : option e" | a = 10 * 3
b = 282 - a
c = b / 20
|
a ) 35 % , b ) 37.5 % , c ) 45 % , d ) 47.5 % , e ) 50 % | e | multiply(divide(add(multiply(40, divide(30, const_100)), multiply(80, divide(40, const_100))), add(40, 80)), const_100) | a car dealership has 40 cars on the lot , 30 % of which are silver . if the dealership receives a new shipment of 80 cars , 40 % of which are not silver , what percentage of total number of cars are silver ? | "number of silver cars before shipment = 30 % of 40 = 12 number of silver cars after shipment = 60 % of 80 = 48 total number of silver cars out of 120 = 48 + 12 = 60 , which is 50 % e is my answer ." | a = 30 / 100
b = 40 * a
c = 40 / 100
d = 80 * c
e = b + d
f = 40 + 80
g = e / f
h = g * 100
|
a ) 1.25 , b ) 1.75 , c ) 2.25 , d ) 2.75 , e ) 3.25 | c | add(divide(divide(12, const_2), 4), divide(divide(12, const_2), 8)) | a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 12 km , if the person completes half of the distance by walking and the other half by running ? | "time = 6 / 4 + 6 / 8 = 18 / 8 = 2.25 hours the answer is c ." | a = 12 / 2
b = a / 4
c = 12 / 2
d = c / 8
e = b + d
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a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 54 | c | add(divide(add(subtract(subtract(5, const_1), const_1), add(50, subtract(5, const_1))), const_3), const_3) | the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 5 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ? | "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 5 th year = 50 , 6 th year = 50 - 5 = 45 . the correct answer is c ." | a = 5 - 1
b = a - 1
c = 5 - 1
d = 50 + c
e = b + d
f = e / 3
g = f + 3
|
a ) 13 : 6 , b ) 13 : 5 , c ) 11 : 6 , d ) 11 : 5 , e ) 12 : 5 | c | divide(divide(subtract(20, 42), subtract(32, 42)), subtract(const_1, divide(subtract(20, 42), subtract(32, 42)))) | in what ratio must rice of rs . 32 per kg be mixed with rice of rs . 42 per kg so that cost of mixture is rs . 20 per kg ? | "( 20 - 42 ) / ( 32 - 20 ) = 22 / 12 = 11 : 6 answer : c" | a = 20 - 42
b = 32 - 42
c = a / b
d = 20 - 42
e = 32 - 42
f = d / e
g = 1 - f
h = c / g
|
a ) 1 / 5 , b ) 2 / 7 , c ) 2 / 5 , d ) 1 / 7 , e ) 3 / 5 | b | divide(25, add(10, 25)) | in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ? | "total draws = prizes + blanks = 10 + 25 = 35 probability of getting a prize = 10 / 35 = 2 / 7 correct option is b" | a = 10 + 25
b = 25 / a
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a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 72 , e ) e ) 36 | d | divide(multiply(48, 3), subtract(3, const_1)) | if the number is divided by 3 , it reduced by 48 . the number is | "explanation : let the number be x . then , x - ( x / 3 ) = 48 = > 2 x / 3 = 48 = > x = 72 answer : option d" | a = 48 * 3
b = 3 - 1
c = a / b
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a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 480 cm | e | add(triangle_perimeter(80, 80, 80), triangle_perimeter(80, 80, 80)) | an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 80 cm , find the sum of the perimeters of all the triangles . | "we have 80 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 40 and continues . so we have 80 , 40,20 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 80 / 1 - ( 1 / 2 ) = 160 equilateral triangle perimeter is 3 a = 3 * 160 = 480 . so option e ." | a = triangle_perimeter + (
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a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 25 | e | divide(subtract(multiply(26, 2), 2), 2) | if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 , then n = | "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 26 = > 4 x 2 ^ 2 n = 4 ^ 26 = 2 ^ 52 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 52 = > 2 ^ ( 2 n + 2 ) = 2 ^ 52 = > 2 n + 2 = 52 = > n = 25 so . answer will be e" | a = 26 * 2
b = a - 2
c = b / 2
|
a ) a ) 4.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20 | a | divide(subtract(34, power(5, 2)), 2) | if a - b = 5 and a 2 + b 2 = 34 , find the value of ab . | "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 34 - 25 = 9 ab = 4.5 . answer : a" | a = 5 ** 2
b = 34 - a
c = b / 2
|
a ) 16 % , b ) 83.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 % | b | multiply(divide(subtract(110, 60), 60), const_100) | john makes $ 60 a week from his job . he earns a raise and now makes $ 110 a week . what is the % increase ? | "increase = ( 50 / 60 ) * 100 = ( 5 / 6 ) * 100 = 83.33 % . b" | a = 110 - 60
b = a / 60
c = b * 100
|
a ) 25 , b ) 30 , c ) 28 , d ) 24 , e ) 32 | a | divide(multiply(subtract(35, 10), 10), subtract(35, subtract(35, 10))) | a certain number of workers can do a work in 35 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ? | "number of workers = 10 * ( 35 - 10 ) / 10 = 25 answer is a" | a = 35 - 10
b = a * 10
c = 35 - 10
d = 35 - c
e = b / d
|
a ) 64 , b ) 1 / 8 , c ) 1 , d ) 8 , e ) 1 / 64 | b | divide(const_1, power(2, 3)) | in the formula a = ( 2 r ) ^ 3 , if r is halved , then a is multiplied by ? | say r = 2 = > a 1 = 64 when r = 1 ; v 2 = 8 v 2 = 1 / 8 * v 1 . answer : b | a = 2 ** 3
b = 1 / a
|
a ) 328897 , b ) 120000 , c ) 118000 , d ) 277768 , e ) 188871 | c | add(multiply(multiply(subtract(const_1, divide(20, const_100)), subtract(const_1, divide(20, const_100))), add(multiply(multiply(const_100, const_100), sqrt(const_100)), multiply(multiply(divide(sqrt(const_100), const_2), const_100), const_100))), multiply(multiply(add(20, const_2), const_100), sqrt(const_100))) | the value of a machine depreciates at 20 % per annum . if its present value is rs . 1 , 50,000 , at what price should it be sold after two years such that a profit of rs . 22,000 is made ? | the value of the machine after two years = 0.8 * 0.8 * 1 , 50,000 = rs . 96,000 sp such that a profit of rs . 22,000 is made = 96,000 + 24,000 = rs . 1 , 18,000 answer : c | a = 20 / 100
b = 1 - a
c = 20 / 100
d = 1 - c
e = b * d
f = 100 * 100
g = math.sqrt(100)
h = f * g
i = math.sqrt(100)
j = i / 2
k = j * 100
l = k * 100
m = h + l
n = e * m
o = 20 + 2
p = o * 100
q = math.sqrt(100)
r = p * q
s = n + r
|
a ) 11 , b ) 31 , c ) 99 , d ) 77 , e ) 18 | b | multiply(divide(subtract(1180, 900), 900), const_100) | a cycle is bought for rs . 900 and sold for rs . 1180 , find the gain percent ? | "900 - - - - 280 100 - - - - ? = > 31 % answer : b" | a = 1180 - 900
b = a / 900
c = b * 100
|
a ) 40 , b ) 50 , c ) 28 , d ) 38 , e ) 48 | b | multiply(subtract(33, 8), const_2) | all the students of class are told to sit in circle shape . here the boy at the 8 th position is exactly opposite to 33 th boy . total number of boys in the class ? | "as half the circle shape consist of 33 - 8 = 25 boys , so total number of boys in full circle = 2 * 25 = 50 answer : b" | a = 33 - 8
b = a * 2
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a ) 17 / 2900 , b ) 2683 / 2700 , c ) 2496 / 2700 , d ) 2369 / 2700 , e ) 198 / 270 | b | divide(subtract(multiply(choose(45, const_1), choose(60, const_1)), choose(17, const_1)), multiply(choose(45, const_1), choose(60, const_1))) | 45 girls and 60 boys are present at a party . there are 17 girl - boy are in relationship among them . if a girl and a boy is selected at random , what is the probability that they will be not a couple ? | in how many ways we can select a girl and a boy from 45 lady and 60 gentlemen ? in 45 * 60 = 2,700 ways . we have a total of 17 couples so , the probability of selecting a couple is 17 / 2,700 = 17 / 2700 . probability of there will not be a couple = 1 - ( 17 / 2700 ) = 2683 / 2700 ans - b | a = math.comb(45, 1)
b = math.comb(60, 1)
c = a * b
d = math.comb(17, 1)
e = c - d
f = math.comb(45, 1)
g = math.comb(60, 1)
h = f * g
i = e / h
|
a ) 11 / 4 , b ) 2 / 3 , c ) 3 / 2 , d ) 4 / 5 , e ) 4 / 7 | a | divide(divide(11, 15), divide(2, 15)) | if p ( a ) = 2 / 15 , p ( b ) = 4 / 15 , and p ( a Γ’ Λ Βͺ b ) = 11 / 15 find p ( a | b ) | "p ( a | b ) = p ( a Γ’ Λ Βͺ b ) / p ( b ) p ( a | b ) = ( 11 / 15 ) / ( 4 / 15 ) = 11 / 4 . a" | a = 11 / 15
b = 2 / 15
c = a / b
|
a ) 82.1 sec . , b ) 12.2 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec . | b | divide(add(110, 134), multiply(72, const_0_2778)) | how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 134 m length ? | "speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 134 = 244 m . required time = 244 / 20 = 12.2 sec . answer : b" | a = 110 + 134
b = 72 * const_0_2778
c = a / b
|
a ) 12 % , b ) 25 % , c ) 26 % , d ) 27 % , e ) 28 % | b | multiply(divide(70, 280), const_100) | what percent is 70 of 280 ? | "70 / 280 = 1 / 4 1 / 4 Γ 100 = 25 % b" | a = 70 / 280
b = a * 100
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a ) 1 , b ) 10 , c ) 19 , d ) 20 , e ) 21 | d | subtract(multiply(divide(40, const_2), add(divide(40, const_2), 1)), multiply(divide(add(39, 1), const_2), add(divide(subtract(39, 1), 2), 1))) | ifaequals the sum of the even integers from 2 to 40 , inclusive , andbequals the sum of the odd integers from 1 to 39 , inclusive , what is the value of a - b ? | this is a solution from beatthegmat : even numbers : ( 40 - 2 ) / 2 + 1 = 20 even integers . ( 40 + 2 ) / 2 = 21 is the average of the even set . sum = avg * ( # of elements ) = 21 * 20 = 420 = a odd numbers : ( 39 - 1 ) / 2 + 1 = 20 odd integers . ( 39 + 1 ) / 2 = 20 is the average of the odd set . sum = avg * ( # of elements ) = 20 * 20 = 400 = b a - b = 420 - 400 = 20 . answer : d | a = 40 / 2
b = 40 / 2
c = b + 1
d = a * c
e = 39 + 1
f = e / 2
g = 39 - 1
h = g / 2
i = h + 1
j = f * i
k = d - j
|
a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 300 | e | multiply(divide(multiply(90, const_1000), const_3600), 12) | a train running at the speed of 90 km / hr crosses a pole in 12 seconds . find the length of the train ? | "speed = 90 * ( 5 / 18 ) m / sec = 75 / 3 m / sec length of train ( distance ) = speed * time ( 75 / 3 ) * 12 = 300 meter answer : e" | a = 90 * 1000
b = a / 3600
c = b * 12
|
a ) 15.5 sec , b ) 8.4 sec , c ) 33.6 sec , d ) 31.11 sec , e ) 16.8 sec | d | divide(multiply(add(20, 15), divide(multiply(20, 10), 15)), 15) | two cars , car 1 and car 2 move towards each other from e and y respectively with respective speeds of 20 m / s and 15 m / s . after meeting each other car 1 reaches y in 10 seconds . in how many seconds does car 2 reach e starting from y ? | e - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | - - - - - - - - - - - - - - - - - - - - - - - - - - - - y car a ( 20 mps ) - - - - - - - - - - - - - - - - - - - - - - - - - > p < - - - - - - - - - - - - - - - car b ( 15 mps ) let 2 cars meet each other at point p in t seconds . car 1 covers distance = 20 t . car 2 covers distance = 15 t . so , total distance ey = 35 t . from p , car 1 reaches onto y in 10 secs . so it covers 15 t further . so , 15 t / 20 = 10 so t = 40 / 3 sec and total distance = ( 35 * 40 ) / 3 hence car 2 will cover total distance in ( 35 * 40 ) / ( 3 * 15 ) = 31.11 sec approx . answer d | a = 20 + 15
b = 20 * 10
c = b / 15
d = a * c
e = d / 15
|
['a ) 114', 'b ) 150', 'c ) 129', 'd ) 25', 'e ) 57'] | c | add(25, divide(circumface(25), const_2)) | the radius of a semicircular plot is 25 . what is the approximate perimeter of the plot ? | perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 25 + 2 * 25 = 128.50 approximately 129 answer c | a = circumface / (
b = 25 + a
|
a ) one , b ) two , c ) three , d ) four , e ) five | d | divide(lcm(10, 4), add(const_3, const_2)) | how many two - digit whole numbers yield a remainder of 3 when divided by 10 and also yield a remainder of 3 when divided by 4 ? options : | numbers giving remainder 3 when divided by 10 = 13,23 , 33,43 , 53,63 , 73,83 , 93 numbers giving remainder 3 when divided by 4 = alternate numbers ( coloured in red ) = 4 correct option : d | a = math.lcm(10, 4)
b = 3 + 2
c = a / b
|
a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11 | b | add(divide(25, 5), const_2) | on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number t of races we need to conduct to get the top 3 fastest horses ? | "t = 7 is the correct answer . good solution buneul . b" | a = 25 / 5
b = a + 2
|
a ) 80 , b ) 117 , c ) 95 , d ) 100 , e ) 108 | b | multiply(multiply(multiply(const_100, divide(add(const_100, 20), const_100)), divide(subtract(const_100, 25), const_100)), divide(add(const_100, 30), const_100)) | from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 30 percent . what percent of the stock Γ’ β¬ β’ s 2007 starting price was the price of the stock at the end of 2009 ? | "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 30 % = 90 * 1.3 = 117 thus ratio = 117 / 100 = 1.17 ( in % terms = 117 % ) . thus b is the correct answer ." | a = 100 + 20
b = a / 100
c = 100 * b
d = 100 - 25
e = d / 100
f = c * e
g = 100 + 30
h = g / 100
i = f * h
|
a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28 | b | divide(40, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(40, 2))))), 2)) | a rectangular tiled patio is composed of 40 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 40 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? | "r * c = 70 and ( 6 + 4 ) ( c - 2 ) = 70 - - > r = 6 and c = 6 . answer : b ." | a = negate + (
b = 4 ** 2
c = 40 * 2
d = 4 * c
e = b + d
f = math.sqrt(e)
g = a / f
h = 40 / g
|
a ) 26 , b ) 30 , c ) 34 , d ) 38 , e ) 42 | c | add(add(10, 12), 12) | set s consists of integers { 6 , 7 , 10 , 12 , 15 } . if integer n is included in the set , the average ( arithmetic mean ) of set s will increase by 40 % . what is the value of integer n ? | "the average of the numbers in set s is 10 . if we increase the mean by 40 % , the new mean is 14 . thus , on average , 5 numbers increase by 4 . therefore n = 14 + 20 = 34 the answer is c ." | a = 10 + 12
b = a + 12
|
a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138 | d | divide(1224, subtract(43, 34)) | a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1224 . find the number to be multiplied . | "let the required number be x . then , 43 x β 34 x = 1224 or 9 x = 1224 or x = 136 . required number = 136 . answer : d" | a = 43 - 34
b = 1224 / a
|
a ) $ 10 , b ) $ 20 , c ) $ 25 , d ) $ 30 , e ) $ 40 | b | subtract(subtract(multiply(500, power(add(divide(20, const_100), const_1), 2)), 500), multiply(multiply(500, divide(20, const_100)), 2)) | what will be the difference between simple and compound interest @ 20 % per annum on a sum of $ 500 after 2 years ? | "s . i . = 500 * 20 * 2 / 100 = $ 200 c . i . = 500 * ( 1 + 20 / 100 ) ^ 2 - 500 = $ 220 difference = 220 - 200 = $ 20 answer is b" | a = 20 / 100
b = a + 1
c = b ** 2
d = 500 * c
e = d - 500
f = 20 / 100
g = 500 * f
h = g * 2
i = e - h
|
a ) $ 1116.3 , b ) $ 3583.3 , c ) $ 3283.3 , d ) $ 3683.3 , e ) $ 2683.3 | d | subtract(divide(650, divide(15, const_100)), 650) | martins made a part payment of $ 650 toward buying a brand new washing machine , which represents 15 % of the total cost of the washing machine , how much remains to be paid ? | explanation : let ' s start with what the total price of the washing machine would be . if 15 % is equal to $ 650 then 100 % equals $ x . we just have to multiply $ 650 by 6.67 to get total amount = $ 4333.3 . out of this amount we then need to deduct the amount already paid which was $ 650 so we have $ 4333.3 - $ 650 = $ 3683.3 answer : option d | a = 15 / 100
b = 650 / a
c = b - 650
|
a ) 43,200 , b ) 19,600 , c ) 20,000 , d ) 20,400 , e ) 20,800 | a | multiply(multiply(divide(300, add(const_2, const_3)), const_3), multiply(divide(300, add(const_2, const_3)), const_4)) | a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 300 feet . what is its area , in square feet ? | "you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 300 , you can deduce the following a = 180 b = 240 180 x 240 = 43,200 a is the answer ." | a = 2 + 3
b = 300 / a
c = b * 3
d = 2 + 3
e = 300 / d
f = e * 4
g = c * f
|
a ) 600 , b ) 1200 , c ) 1500 , d ) 1600 , e ) 2000 | e | multiply(divide(5, 6), multiply(10, divide(multiply(8, 60), subtract(10, 8)))) | in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 6 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ? | "sugar : flour = 5 : 6 = 25 : 30 ; flour : soda = 10 : 1 = 30 : 3 ; thus we have that sugar : flour : soda = 25 x : 30 x : 3 x . also given that 30 x / ( 3 x + 60 ) = 8 / 1 - - > x = 80 - - > sugar = 25 x = 2,000 . answer : e ." | a = 5 / 6
b = 8 * 60
c = 10 - 8
d = b / c
e = 10 * d
f = a * e
|
a ) 202 , b ) 203 , c ) 204 , d ) 205 , e ) 206 | b | multiply(19, 399) | the h . c . f of two numbers is 19 and their l . c . m is 4263 . if one of the numbers is 399 , then the other is ? | "other number = ( 19 * 4263 ) / 399 = 203 . answer : b" | a = 19 * 399
|
a ) 30 % , b ) 47 % , c ) 90 % , d ) 100 % , e ) none of these | b | multiply(const_100, divide(subtract(add(multiply(const_100, divide(110, const_100)), const_100), multiply(const_100, add(const_1, divide(12, const_100)))), add(multiply(const_100, divide(110, const_100)), const_100))) | in a restaurant , the profit is 110 % of the cost . if the cost increases by 12 % but the selling price remains constant , approximately what percentage of the selling price is the profit ? | explanation : let c . p . = rs . 100 . then , profit = rs . 110 , s . p . = rs . 210 . new c . p . = 112 % of rs . 100 = rs . 112 new s . p . = rs . 210 . profit = rs . ( 210 - 112 ) = rs . 98 . required percentage = ( 98 / 210 * 100 ) % = 47 % appox answer : b | a = 110 / 100
b = 100 * a
c = b + 100
d = 12 / 100
e = 1 + d
f = 100 * e
g = c - f
h = 110 / 100
i = 100 * h
j = i + 100
k = g / j
l = 100 * k
|
a ) 3 / 5 , b ) 4 / 5 , c ) 11 / 15 , d ) 16 / 25 , e ) 19 / 25 | d | divide(multiply(4, 4), add(multiply(4, 4), multiply(3, 3))) | at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 3 / 4 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ? | "let x be the number of workers on the day crew . let y be the number of boxes loaded by each member of the day crew . then the number of boxes loaded by the day crew is xy . the number of boxes loaded by the night crew is ( 3 x / 4 ) ( 3 y / 4 ) = 9 xy / 16 the total number of boxes is xy + 9 xy / 16 = 25 xy / 16 the fraction loaded by the day crew is xy / ( 25 xy / 16 ) = 16 / 25 the answer is d ." | a = 4 * 4
b = 4 * 4
c = 3 * 3
d = b + c
e = a / d
|
a ) 22 , b ) 99 , c ) 27 , d ) 24 , e ) 20 | d | multiply(4, 6) | walking 6 / 5 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ? | "speed ratio = 1 : 6 / 5 = 5 : 6 time ratio = 6 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? 24 m . answer : d" | a = 4 * 6
|
a ) 11 , b ) 30 , c ) 29 , d ) 88 , e ) 61 | c | divide(500, multiply(subtract(66, 3), const_0_2778)) | how many seconds will a 500 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 66 km / hr ? | "speed of train relative to man = 66 - 3 = 63 km / hr . = 63 * 5 / 18 = 35 / 2 m / sec . time taken to pass the man = 500 * 2 / 35 = 28.57 sec . approx . 29 sec answer : c" | a = 66 - 3
b = a * const_0_2778
c = 500 / b
|
a ) 4 , b ) 16 , c ) 64 , d ) 256 , e ) 1024 | e | multiply(power(const_2.0, 4), power(4, 3)) | what number times ( 1 β 4 ) ^ 2 will give the value of 4 ^ 3 ? | "x * ( 1 / 4 ) ^ 2 = 4 ^ 3 x = 4 ^ 2 * 4 ^ 3 = 4 ^ 5 = 1024 the answer is e ." | a = 2 ** 0
b = 4 ** 3
c = a * b
|
a ) 2 , b ) 9 , c ) 6 , d ) 3 , e ) 5 | b | multiply(6, add(const_1, divide(25, const_100))) | a vendor bought toffees at 6 for a rupee . how many for a rupee must he sell to gain 25 % ? | "c . p . of 6 toffees = re . 1 s . p . of 6 toffees = 150 % of re . 1 = rs . 3 / 2 for rs . 3 / 2 , toffees sold = 6 . for re . 1 , toffees sold = 6 x 3 / 2 = 9 . answer b" | a = 25 / 100
b = 1 + a
c = 6 * b
|
a ) 300 , b ) 350 , c ) 400 , d ) 450 , e ) 500 | c | divide(divide(152, const_2), divide(19, const_100)) | one night 19 percent of the female officers on a police force were on duty . if 152 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ? | "let x be the number of female police officers on the police force . the number of female police officers on duty was 76 . 0.19 x = 76 x = 400 the answer is c ." | a = 152 / 2
b = 19 / 100
c = a / b
|
a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36 | a | add(divide(70, add(0.75, 6)), divide(70, add(0.75, 6))) | a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 6 tons ? | "the weight of one car and one truck is 6.75 tons . 70 / 6.75 = 10 plus a remainder the ferry could carry 10 cars and 10 trucks for a total of 20 vehicles . the answer is a ." | a = 0 + 75
b = 70 / a
c = 0 + 75
d = 70 / c
e = b + d
|
a ) 280 meter , b ) 240 meter , c ) 225 meter , d ) 200 meter , e ) none of these | c | multiply(multiply(const_0_2778, 54), subtract(35, 20)) | a train passes a platform in 35 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is | "explanation : speed of the train = 54 km / hr = ( 54 Γ 10 ) / 35 m / s = 15 m / s length of the train = speed Γ time taken to cross the man = 15 Γ 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 35 = > 300 + l = 15 Γ 35 = 525 = > l = 525 - 300 = 225 meter answer : option c" | a = const_0_2778 * 54
b = 35 - 20
c = a * b
|
a ) 26 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 40 % | a | multiply(divide(add(multiply(divide(20, 100), 400), multiply(100, divide(50, 100))), add(400, 100)), 100) | a grocer has 400 pounds of coffee in stock , 20 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 50 percent is decaffeinated , what percent , by weight , of the grocer β s stock of coffee is decaffeinated ? | "1 . 20 % of 400 = 80 pounds of decaffeinated coffee 2 . 50 % of 100 = 50 pounds of decaffeinated coffee 3 . wt have 130 pounds of decaffeinated out of 500 pounds , that means 130 / 500 * 100 % = 26 % . the correct answer is a ." | a = 20 / 100
b = a * 400
c = 50 / 100
d = 100 * c
e = b + d
f = 400 + 100
g = e / f
h = g * 100
|
a ) s . 7500 , b ) s . 8000 , c ) s . 8280 , d ) s . 9000 , e ) s . 6000 | c | divide(divide(3220, subtract(const_1, divide(5, const_12))), divide(2, 3)) | praveen starts business with rs . 3220 and after 5 months , hari joins with praveen as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is hari β s contribution in the capital ? | "let hari β s capital be rs . x . then , 3220 * 12 / 7 x = 2 / 3 = > 14 x = 115920 = > x = 8280 . answer : c" | a = 5 / 12
b = 1 - a
c = 3220 / b
d = 2 / 3
e = c / d
|
a ) 30 , b ) 35 , c ) 40 , d ) 50 , e ) 60 | c | divide(160, const_10) | how many integers from 22 to 160 , inclusive , are divisible by 3 but not divisible by 7 ? | "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 22 to 160 , inclusive is ( 147 - 42 ) / 21 + 1 = 6 ; 46 - 6 = 40 . answer : c ." | a = 160 / 10
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a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 14.25 hours , e ) 16 hours | c | divide(multiply(6, 8), 4) | 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 4 such machines to perform the same job ? | let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 4 machines 4 units of work ( 4 machines ) - - - > 1 hour for 48 units of work 4 * 12 - - - > 1 * 12 hours c 12 hours | a = 6 * 8
b = a / 4
|
a ) 7000 , b ) 7200 , c ) 7400 , d ) 7600 , e ) 7800 | a | divide(2100, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100))) | a candidate got 35 % of the votes and lost to the rival by 2100 votes . how many votes were cast ? | "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 2100 10 % = 700 100 % of the votes = 7000 answer : a" | a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 2100 / d
|
a ) a ) 11 , b ) b ) 3 , c ) c ) 2 , d ) d ) 1 , e ) e ) 6 | b | divide(subtract(25, 1), 3) | if you write down all the numbers from 1 to 25 , then how many times do you write 3 ? | "explanation : explanation : clearly , from 1 to 25 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 so , required number = 3 answer : b" | a = 25 - 1
b = a / 3
|
a ) 9 , b ) 36 , c ) 122 , d ) 3 , e ) 1 | d | divide(sqrt(81), 3) | what is the square root of 81 , divided by 3 ? | "square root is a number times itself square root of 81 = 6 , 9 / 3 = 3 ( d ) 3" | a = math.sqrt(81)
b = a / 3
|
a ) 151 , b ) 149 , c ) 152 , d ) 251 , e ) none of the above | d | divide(add(multiply(30, 250), subtract(165, 135)), 30) | the mean of 30 values was 250 . it was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean . find the correct mean . | "corrected mean = 250 Γ 30 β 135 + 165 / 30 = 7500 β 135 + 165 / 30 = 7530 / 30 = 251 answer d" | a = 30 * 250
b = 165 - 135
c = a + b
d = c / 30
|
a ) 9.3 , b ) 9.6 , c ) 9.8 , d ) 10.1 , e ) 10.3 | c | divide(add(9, 11), add(divide(9, 11), divide(11, 9))) | a cyclist rides a bicycle 9 km at an average speed of 11 km / hr and again travels 11 km at an average speed of 9 km / hr . what is the average speed for the entire trip ? | "distance = 20 km time = 9 / 11 + 11 / 9 = ( 81 + 121 ) / 99 = 202 / 99 hours average speed = ( 20 * 99 ) / 202 = 9.8 km / h the answer is c ." | a = 9 + 11
b = 9 / 11
c = 11 / 9
d = b + c
e = a / d
|
a ) 29 , b ) 28 , c ) 30 , d ) 32 , e ) 23 | b | divide(add(26, 30), const_2) | a man can row upstream at 26 kmph and downstream at 30 kmph , and then find the speed of the man in still water ? | "us = 26 ds = 30 m = ( 30 + 26 ) / 2 = 28 answer : b" | a = 26 + 30
b = a / 2
|
a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34 | d | subtract(60, subtract(add(35, 23), 31)) | in a group of 60 people , 35 have visited iceland and 23 have visited norway . if 31 people have visited both iceland and norway , how many people have visited neither country ? | this is an example of a standard overlapping sets question . it has no ' twists ' to it , so you ' ll likely find using the overlapping sets formula to be a fairly easy approach . if you ' re not familiar with it , then here is the formula : 60 = 35 + 23 - 31 + ( # in neither group ) = 33 the prompt gives you all of the numbers you need to get to the correct answer . just plug in and solve . d | a = 35 + 23
b = a - 31
c = 60 - b
|
a ) 23 , b ) 27 , c ) 25 , d ) 35 , e ) 15 | c | divide(divide(multiply(5000, 5), const_100), 10) | a reduction of 5 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 5000 , what is the reduced price for kg ? | "5000 * ( 5 / 100 ) = 250 - - - - 10 ? - - - - 1 = > rs . 25 answer : c" | a = 5000 * 5
b = a / 100
c = b / 10
|
a ) 200 , b ) 228 , c ) 182 , d ) 102 , e ) 128 | b | add(power(10, 2), multiply(power(8, 2), 2)) | if a 2 - b 2 = 10 and a * b = 8 , find a 4 + b 4 . | "a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 8 : given a 2 b 2 = 82 : square both sides . a 4 + b 4 - 2 ( 64 ) = 100 : substitute a 4 + b 4 = 228 correct answer b" | a = 10 ** 2
b = 8 ** 2
c = b * 2
d = a + c
|
a ) 6400 , b ) 8000 , c ) 5000 , d ) 4980 , e ) 4960 | a | add(divide(divide(80, divide(divide(divide(divide(divide(80, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(80, divide(divide(divide(divide(divide(80, const_2), const_2), const_2), const_2), const_2)), const_2)))) | find the sum of first 80 odd numbers | "explanation : n 2 = 802 = 6400 answer : option a" | a = 80 / 2
b = a / 2
c = b / 2
d = c / 2
e = d / 2
f = 80 / e
g = f / 2
h = 80 / 2
i = h / 2
j = i / 2
k = j / 2
l = k / 2
m = 80 / l
n = m / 2
o = math.sqrt(n)
p = 1 + o
q = g + p
|
a ) 51 , b ) 55 , c ) 59 , d ) 71 , e ) 92 | a | add(37, multiply(subtract(const_1, divide(const_1, const_3)), subtract(58, 37))) | of 58 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | total = 58 thrower = 37 rest = 58 - 37 = 21 left handed = 21 / 3 = 7 right handed = 14 if all thrower are right handed then total right handed is 37 + 14 = 51 so a . 51 is the right answer | a = 1 / 3
b = 1 - a
c = 58 - 37
d = b * c
e = 37 + d
|
a ) s . 9621 , b ) s . 6921 , c ) s . 10721 , d ) s . 6261 , e ) s . 6361 | c | multiply(8000, power(add(const_1, divide(5, const_100)), 6)) | the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 6 years is | "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 6 = rs 10721 answer : c" | a = 5 / 100
b = 1 + a
c = b ** 6
d = 8000 * c
|
a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500 | c | floor(divide(divide(subtract(590, multiply(const_1000, divide(8, const_100))), subtract(divide(10, const_100), divide(8, const_100))), const_1000)) | angelo and isabella are both salespersons . in any given week , angelo makes $ 590 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ? | let the weekly sales of both = x 590 + ( x β 1000 ) 8 / 100 = 10 / 100 x x = 25500 answer : c | a = 8 / 100
b = 1000 * a
c = 590 - b
d = 10 / 100
e = 8 / 100
f = d - e
g = c / f
h = g / 1000
i = math.floor(h)
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | subtract(add(const_2, const_3), const_2) | the product of the squares of two positive integers is 1600 . how many pairs of positive integers satisfy this condition ? | "ans : e - 4 pairs ( x Λ 2 ) ( y Λ 2 ) = 1600 [ square root both sides ] xy = 40 40 = 1 x 40 , 4 x 10 , 40 x 1 , 10 x 4 , 5 x 8 , 8 x 5 , 20 x 2 , 2 x 20 cancel the repeats this leaves us with exactly 4 options . hence , e" | a = 2 + 3
b = a - 2
|
a ) 20 % , b ) 30 % , c ) 50 % , d ) 60 % , e ) 80 % | e | multiply(divide(20, 25), const_100) | what percent is 20 % of 25 % ? | required percentage = 20 % / 25 % * 100 = 20 / 25 * 100 = 80 % answer is e | a = 20 / 25
b = a * 100
|
a ) 16 , b ) 36 , c ) 42 , d ) 48 , e ) 54 | a | divide(24, subtract(divide(const_1, divide(40, const_100)), const_1)) | walking at 40 % of his usual speed a man takes 24 minutes more to cover a distance . what is his usual time to cover this distance ? | speed is inversly proprtional to time walking at 40 % of speed meand 2 / 5 s takes 5 / 2 t . it takes 24 minutes extra to cover the distance . then 5 / 2 t = t + 24 5 t = 2 t + 48 3 t = 48 t = 16 . option a is correct | a = 40 / 100
b = 1 / a
c = b - 1
d = 24 / c
|
a ) 75 , b ) 110 , c ) 125 , d ) 175 , e ) 225 | b | divide(subtract(multiply(divide(660, const_3), const_4), 660), const_2) | there are 660 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ? | "female = x male = 660 - x x / 2 + 660 - x / 4 = 1 / 3 * ( 660 ) = 220 x = 220 x / 2 = 110 is supposed to be the answer m is missing something correct option b" | a = 660 / 3
b = a * 4
c = b - 660
d = c / 2
|
a ) 10.66 kmph , b ) 11.66 kmph , c ) 21.66 kmph , d ) 12.66 kmph , e ) 11.96 kmph | b | multiply(divide(10, const_60), 70) | the speed of a train is 70 kmph . what is the distance covered by it in 10 minutes ? | "70 * 10 / 60 = 11.66 kmph answer : b" | a = 10 / const_60
b = a * 70
|
['a ) 1 / 4', 'b ) 3 / 8', 'c ) 1 / 2', 'd ) 3 / 5', 'e ) 2'] | d | divide(multiply(multiply(const_1, const_1), multiply(const_2, const_3)), add(multiply(multiply(const_1, const_1), const_2), multiply(multiply(const_1, const_2), const_4))) | what is the ratio e of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ? | one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area e = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d ) | a = 1 * 1
b = 2 * 3
c = a * b
d = 1 * 1
e = d * 2
f = 1 * 2
g = f * 4
h = e + g
i = c / h
|
a ) 4 , b ) 2 , c ) 9 / 2 , d ) - 9 / 2 , e ) - 8 / 2 | c | divide(power(3, 2), 2) | if the operation @ is defined for all a and b by the equation a @ b = ( a ^ b ) / 2 , then ( 3 @ 2 ) = ? | work within the parenthesis first so solve ( 3 @ 2 ) first ( 3 @ 2 ) = ( 3 ^ 2 ) / 2 = 9 / 2 so 9 / 2 is the answer . . . . this question is merely testing order of operations remember pemdas answer : c | a = 3 ** 2
b = a / 2
|
a ) 4.25 hr , b ) 5.25 hr , c ) 3 hr , d ) 2.25 hr , e ) 2.50 hr | c | divide(54, add(10, 8)) | a boat can travel with a speed of 10 km / hr in still water . if the speed of the stream is 8 km / hr , find the time taken by the boat to go 54 km downstream . | "speed of boat in still water = 10 km / hr speed of the stream = 8 km / hr speed downstream = ( 10 + 8 ) = 18 km / hr time taken to travel 68 km downstream = 54 Γ’ Β β 18 = 17 Γ’ Β β 4 = 3 hours answer is c" | a = 10 + 8
b = 54 / a
|
a ) 799 , b ) 800 , c ) 801 , d ) 802 , e ) 803 | b | divide(multiply(9600, 400), 4800) | there is enough provisions for 9600 women in an army camp for 400 days . if there were 4800 men less , how long will the provision last ? | we have , m 1 d 1 = m 2 d 2 9600 * 400 = 4800 * d 2 d 2 = 9600 * 400 / 4800 = 800 days . answer : b | a = 9600 * 400
b = a / 4800
|
a ) 8 , b ) 5 , c ) 11 , d ) 3 , e ) 4 | d | divide(sqrt(multiply(add(6, 2), add(15, 3))), add(3, 1)) | if a * b * c = ( β ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 3 . | "6 * 15 * 3 = ( β ( 6 + 2 ) ( 15 + 3 ) ) / ( 3 + 1 ) = ( β 8 * 18 ) / 4 = ( β 144 ) / 4 = 12 / 4 = 3 . answer is d ." | a = 6 + 2
b = 15 + 3
c = a * b
d = math.sqrt(c)
e = 3 + 1
f = d / e
|
a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 48 | e | divide(subtract(multiply(const_3, 60), 60), const_3) | shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 60 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ? | "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 48 hence answer is e" | a = 3 * 60
b = a - 60
c = b / 3
|
a ) 240 , b ) 288 , c ) 277 , d ) 357 , e ) 361 | d | multiply(divide(630, add(add(multiply(6000, 8), multiply(subtract(6000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(6000, 8), multiply(subtract(6000, 1000), subtract(const_12, 8)))) | a and b began business with rs . 6000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 630 find the share of a . | "( 6 * 8 + 5 * 4 ) : ( 4 * 8 + 5 * 4 ) 17 : 13 17 / 30 * 630 = 357 answer : d" | a = 6000 * 8
b = 6000 - 1000
c = 12 - 8
d = b * c
e = a + d
f = 4000 * 8
g = 4000 + 1000
h = 12 - 8
i = g * h
j = f + i
k = e + j
l = 630 / k
m = 6000 * 8
n = 6000 - 1000
o = 12 - 8
p = n * o
q = m + p
r = l * q
|
a ) 295 , b ) 199 , c ) 676 , d ) 156 , e ) 122 | a | multiply(divide(950, add(add(multiply(12, 8), multiply(16, 9)), multiply(18, 6))), multiply(16, 9)) | a , b and c rents a pasture for rs . 950 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ? | "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 950 = 295 answer : a" | a = 12 * 8
b = 16 * 9
c = a + b
d = 18 * 6
e = c + d
f = 950 / e
g = 16 * 9
h = f * g
|
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