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 ) 16 , b ) 120 , c ) 160 , d ) 180 , e ) 240 | b | add(multiply(const_100, 3), const_100) | how many 3 - digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number ? | "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 3 ways total = 4 * 10 * 3 = 120 ans : b" | a = 100 * 3
b = a + 100
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a ) 1005 , b ) 1045 , c ) 1075 , d ) 1015 , e ) 1096 | e | add(add(multiply(multiply(20, divide(4, 5)), subtract(subtract(subtract(60, multiply(60, divide(20, const_100))), multiply(60, divide(20, const_100))), 10)), multiply(20, 10)), add(multiply(20, multiply(60, divide(20, const_100))), multiply(20, multiply(60, divide(20, const_100))))) | an automobile parts supplier charges $ 20 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ? | "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 20 * 4 / 5 = 16 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 12 gaskets = 20 * 10 + 16 * 2 = 200 + 32 = 232 2 . he sold 15 % of the gaskets to y = 9 gaskets = 20 * 9 = 180 3 . he sold remaining 65 % to z = 39 gaskets = 20 * 10 = 200 + 16 * 29 = 684 thus , total money earned 232 + 180 + 684 = 1096 answer is e" | a = 4 / 5
b = 20 * a
c = 20 / 100
d = 60 * c
e = 60 - d
f = 20 / 100
g = 60 * f
h = e - g
i = h - 10
j = b * i
k = 20 * 10
l = j + k
m = 20 / 100
n = 60 * m
o = 20 * n
p = 20 / 100
q = 60 * p
r = 20 * q
s = o + r
t = l + s
|
a ) 1288 , b ) 1299 , c ) 10625 , d ) 10000 , e ) 2887 | c | multiply(add(25, const_100), subtract(const_100, 15)) | the length of a rectangle is increased by 25 % and its breadth is decreased by 15 % . what is the effect on its area ? | "100 * 100 = 10000 125 * 85 = 10625 answer : c" | a = 25 + 100
b = 100 - 15
c = a * b
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a ) 42 , b ) 64 , c ) 36 , d ) 72 , e ) 27 | a | divide(subtract(90, multiply(8, 6)), subtract(9, 8)) | suraj has a certain average of runs for 8 innings . in the 9 th innings he scores 90 runs thereby increasing his average by 6 runs . what is his average after the 9 th innings ? | "to improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings . thus , the average after the 9 th innings = 90 - 48 = 42 . answer : a" | a = 8 * 6
b = 90 - a
c = 9 - 8
d = b / c
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a ) 12 days , b ) 10 days , c ) 5 days , d ) 6 days , e ) 15 days | b | divide(multiply(25, 25), add(multiply(divide(25, 20), 38), 15)) | 20 men or 25 women can finish a work in 25 days . how many days 38 men and 15 women will take to finish this job ? | 20 men = 25 women therefore , 1 women = 20 / 25 men = 4 / 5 men 15 women = 4 / 5 * 15 men = 12 men i . e . 38 men + 15 women = 38 men + 12 men = 50 men 1 work done by men = 20 * 25 20 * 25 = 50 * ? number of days = 20 * 25 / 50 = 10 days . b | a = 25 * 25
b = 25 / 20
c = b * 38
d = c + 15
e = a / d
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a ) 90 , b ) 130 , c ) 150 , d ) 140 , e ) 450 | d | add(90, multiply(divide(subtract(940, 90), add(90, 80)), subtract(90, 80))) | two heavily loaded sixteen - wheeler transport trucks are 940 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ? | "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 940 - 90 = 850 k ratio of speeds 9 : 8 - > 850 / 17 = 50 truck a = 90 + 50 * 9 = 540 truck b = 50 * 8 = 400 delta = 140 km answer d" | a = 940 - 90
b = 90 + 80
c = a / b
d = 90 - 80
e = c * d
f = 90 + e
|
a ) 24 , b ) 37 , c ) 28 , d ) 40 , e ) 81 | a | subtract(const_100, subtract(add(32, 56), 12)) | in an examination , 32 % of total students failed in hindi , 56 % failed in english and 12 % in both . the percentage of these who passed in both the subjects is : | "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 32 + 56 â € “ 12 = 76 therefore students who passed = 100 â € “ 76 = 24 . answer : a" | a = 32 + 56
b = a - 12
c = 100 - b
|
a ) 25 , b ) 30 , c ) 50 , d ) 80 , e ) 100 | a | subtract(subtract(250, 80), 20) | of the 250 employees at company x , 80 are full - time , and 175 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ 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 ? | "250 employees 80 are full - time 175 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ 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 ? 250 - 80 = 170 employees not full time 170 - 20 = 150 employees not full time who worked over a year 175 employees have worked at company x for at least a year - 150 employees not full time who worked over a year = 25 full - time employees of company x have worked at the company for at least a year ans a" | a = 250 - 80
b = a - 20
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a ) 22 , b ) 33 , c ) 55 , d ) 77 , e ) 39 | e | subtract(divide(221, add(divide(10, const_100), divide(3, 4))), 221) | a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 221 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ? | "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 221 = > . 1 x + 3 / 4 x = 221 = > x = 260 260 - 221 = pure gala = 39 . e" | a = 10 / 100
b = 3 / 4
c = a + b
d = 221 / c
e = d - 221
|
['a ) 18 cm', 'b ) 20 cm', 'c ) 22 cm', 'd ) 24 cm', 'e ) 25 cm'] | a | sqrt(multiply(216, divide(const_3, const_2))) | the ratio between the perimeter and the breadth of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the length of the rectangle ? | 2 ( l + b ) = 5 b 1 2 l + 2 b = 5 b 3 b = 2 l b = 2 l 3 then , area = 216 cm 2 l x b = 216 l x 2 l = 216 3 l 2 = 324 l = 18 cm . a | a = 3 / 2
b = 216 * a
c = math.sqrt(b)
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a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44 | e | multiply(divide(20, const_100), multiply(divide(20, 300), 300)) | 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ? | "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 44 ( 44 - 12 ) must be those with four screens or more e is the answer" | a = 20 / 100
b = 20 / 300
c = b * 300
d = a * c
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | c | subtract(max(3, 2), const_1) | on a two - dimensional coordinate plane , the line q = x ^ 2 - x ^ 3 touches the x - axis in how many places ? | "apparently it ' s q = x ^ 2 - x ^ 3 instead of q = x ^ 2 - q ^ 3 . in this case : the x - intercept is the value ( s ) of x for q = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ." | a = max(3)
b = a - 1
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a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 24 | e | subtract(multiply(divide(const_100, 60), divide(multiply(60, 84), const_100)), 60) | there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 60 % | "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 60 / 100 = 50.40 so x = 18.75 answer : e" | a = 100 / 60
b = 60 * 84
c = b / 100
d = a * c
e = d - 60
|
a ) 16 , b ) 18 , c ) 13 , d ) 20 , e ) 22 | c | subtract(divide(subtract(multiply(10, 5), 20), const_2), const_2) | the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 10 , and k < m < r < s < t . if t is 20 , 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 10 which means that in effect , all numbers are equal to 10 . if the largest number is 20 , it is 10 more than 20 . we need r to be maximum so k and m should be as small as possible to get the average of 10 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average . 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s . since s must be greater than r , r can be 10 + 3 = 13 and s can be 10 + 4 = 14 . so r is 13 . answer ( c )" | a = 10 * 5
b = a - 20
c = b / 2
d = c - 2
|
a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20 | a | multiply(10, divide(15, subtract(15, 10))) | if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ? | "let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a" | a = 15 - 10
b = 15 / a
c = 10 * b
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a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | a | multiply(log(divide(multiply(multiply(add(const_4, const_1), 1,000), const_100), 1,000)), 1) | the population of a bacteria culture doubles every 1 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria | "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 1 minutes so answer is 9 * 1 = 9 minutes answer ( a )" | a = 4 + 1
b = a * 1
c = b * 100
d = c / 1
e = math.log(d)
f = e * 1
|
a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28 | b | divide(48, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(48, 2))))), 2)) | a rectangular tiled patio is composed of 48 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 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ? | "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b" | a = negate + (
b = 4 ** 2
c = 48 * 2
d = 4 * c
e = b + d
f = math.sqrt(e)
g = a / f
h = 48 / g
|
a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8 | a | add(add(const_4, const_3), const_2) | what is the units digit of 28 ! + 50 ! + 3 ! + 4 ! ? | "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 4 = 10 the units digit is 0 . the answer is a ." | a = 4 + 3
b = a + 2
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a ) s . 177 , b ) s . 168 , c ) s . 144 , d ) s . 129 , e ) s . 112 | b | add(divide(119, subtract(const_1, divide(15, const_100))), multiply(divide(119, subtract(const_1, divide(15, const_100))), divide(20, const_100))) | a shopkeeper loses 15 % , if an article is sold for rs . 119 . what should be the selling price of the article to gain 20 % ? | "given that sp = rs . 119 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 119 ) / 85 = rs . 140 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 140 * 120 ) / 100 = rs . 168 answer : b" | a = 15 / 100
b = 1 - a
c = 119 / b
d = 15 / 100
e = 1 - d
f = 119 / e
g = 20 / 100
h = f * g
i = c + h
|
a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) none of these | d | divide(divide(const_1, multiply(10, 6)), divide(const_1, multiply(6, const_10))) | eight women can do a work in 10 days . ten men can complete the same work in 6 days . what is the ratio between the capacity of a man and a woman ? | "explanation : ( 8 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 80 ( 10 ã — 6 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 60 so , required ratio = 1 / 80 : 1 / 60 = 4 : 3 answer : d" | a = 10 * 6
b = 1 / a
c = 6 * 10
d = 1 / c
e = b / d
|
a ) $ 525 , b ) $ 550.50 , c ) $ 1080.02 , d ) $ 522.3 , e ) $ 1020.2 | d | multiply(divide(2350, add(add(inverse(6), inverse(8)), inverse(12))), inverse(6)) | x , y and z , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2350 , what will be z ' s share of the earnings ? | "the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2350 = $ 522.3 hence : d" | a = 1/(6)
b = 1/(8)
c = a + b
d = 1/(12)
e = c + d
f = 2350 / e
g = 1/(6)
h = f * g
|
['a ) 9', 'b ) 7', 'c ) 4', 'd ) 8', 'e ) 6'] | c | floor(sqrt(divide(divide(surface_cube(6.5), const_4), const_pi))) | the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number . | first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 6.5 cm each . the surface area of 1 side of the cube is 42.25 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes surface area is 253.5 cm . now we know that the surface area of the ball is 253.5 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 4 . then divide by pi . then determine the square root of the answer . the radius is 4.460 . rounding to the nearest whole number the radius is 4 . the correct answer is ( c ) . | a = surface_cube / (
b = a / 4
c = math.sqrt(b)
d = math.floor(c)
|
a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7 | a | divide(multiply(3, multiply(divide(2, subtract(multiply(divide(add(const_100, 20), const_100), 3), divide(7, 5))), divide(7, 5))), add(divide(2, subtract(multiply(divide(add(const_100, 20), const_100), 3), divide(7, 5))), 6)) | ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 ) | "let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a" | a = 100 + 20
b = a / 100
c = b * 3
d = 7 / 5
e = c - d
f = 2 / e
g = 7 / 5
h = f * g
i = 3 * h
j = 100 + 20
k = j / 100
l = k * 3
m = 7 / 5
n = l - m
o = 2 / n
p = o + 6
q = i / p
|
a ) 1.0 , b ) 9.6 , c ) 3.5 , d ) 3.2 , e ) 5.1 | c | add(divide(add(add(add(add(9, 17), 25), 28), 29), add(const_4, const_1)), 25) | if a = { 9 , 17 , 25 , 28 , 29 , 30 } , how much less is the mean of the numbers in a than the median of the numbers in s ? | "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 9 + 17 + 25 + 28 + 29 + 30 ) / 6 = 23 median = ( 25 + 28 ) / 2 = 26.5 difference = 3.5 option c" | a = 9 + 17
b = a + 25
c = b + 28
d = c + 29
e = 4 + 1
f = d / e
g = f + 25
|
a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500 | c | subtract(add(700, 600), 1000) | a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ? | "a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c" | a = 700 + 600
b = a - 1000
|
a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140 | b | add(multiply(add(multiply(add(divide(1, 2), add(divide(1, 4), divide(1, 3))), 25), 25), 2), const_10) | sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 10 more than 1 / 4 of the fine and peter paid $ 10 less than 1 / 3 of the fine , leaving pay $ 25 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ? | "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 10 ] + [ ( 1 / 3 ) f – 10 ] + [ ( 1 / 2 ) f – 25 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 25 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 300 12 f = 13 f – 300 – f = – 300 f = 300 well , if the fine cost $ 300 , then sam paid the part not covered by joe or peter . half the fine is $ 150 , and sam paid $ 25 less than this : $ 125 answer = b" | a = 1 / 2
b = 1 / 4
c = 1 / 3
d = b + c
e = a + d
f = e * 25
g = f + 25
h = g * 2
i = h + 10
|
a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52 | c | divide(multiply(const_4, const_3), 52) | from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ? | "the total number of cards is 52 . the number of kings is 4 . p ( king ) = 4 / 52 = 1 / 13 the answer is c ." | a = 4 * 3
b = a / 52
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a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36 | a | divide(multiply(18, 2), const_4) | if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k = | "i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear" | a = 18 * 2
b = a / 4
|
a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820 | d | add(300, multiply(divide(300, 5), 8)) | in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is | "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d" | a = 300 / 5
b = a * 8
c = 300 + b
|
a ) 298 , b ) 237 , c ) 248 , d ) 876 , e ) 291 | c | subtract(subtract(390, divide(multiply(390, 15), const_100)), divide(multiply(subtract(390, divide(multiply(390, 15), const_100)), 25), const_100)) | the sale price sarees listed for rs . 390 after successive discount is 15 % and 25 % is ? | "390 * ( 85 / 100 ) * ( 75 / 100 ) = 248 answer : c" | a = 390 * 15
b = a / 100
c = 390 - b
d = 390 * 15
e = d / 100
f = 390 - e
g = f * 25
h = g / 100
i = c - h
|
a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2 | c | multiply(divide(1, 9), 9) | a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ? | explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c | a = 1 / 9
b = a * 9
|
a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7 | b | subtract(10, divide(25, 5)) | a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ? | "explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b" | a = 25 / 5
b = 10 - a
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a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991 | e | subtract(multiply(add(5, const_1), 7000), add(add(add(add(6435, 6927), 6855), 7230), 6562)) | a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ? | "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e" | a = 5 + 1
b = a * 7000
c = 6435 + 6927
d = c + 6855
e = d + 7230
f = e + 6562
g = b - f
|
a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches | e | multiply(30, divide(1.5, add(const_1, 1.5))) | during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ? | "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e" | a = 1 + 1
b = 1 / 5
c = 30 * b
|
a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42 | c | subtract(45, multiply(const_2, divide(divide(45, const_2), add(const_1, const_4)))) | let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ? | "the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ." | a = 45 / 2
b = 1 + 4
c = a / b
d = 2 * c
e = 45 - d
|
a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8 | d | add(2, 5) | what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ? | "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 6 + 1 = 7 x = 5 - - > result = 1 + 7 + 0 = 8 x = 2 - - > result = 2 + 4 + 3 = 9 so minimum value of the expression occurs at x = 4 and the resultant value = 7 answer : d" | a = 2 + 5
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a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg | d | add(65, multiply(8, 4)) | the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ? | "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d" | a = 8 * 4
b = 65 + a
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a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 27 kmph | e | multiply(const_3_6, divide(120, 16)) | a train 120 m in length crosses a telegraph post in 16 seconds . the speed of the train is ? | "s = 120 / 16 * 18 / 5 = 27 kmph answer : e" | a = 120 / 16
b = const_3_6 * a
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a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16 | b | floor(subtract(divide(300, 40), divide(50, 10))) | subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 25 pages . | "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 25 / 2.5 ) = 10 hrs answer : b" | a = 300 / 40
b = 50 / 10
c = a - b
d = math.floor(c)
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a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none | c | subtract(add(25, 17), const_2) | if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ? | "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ." | a = 25 + 17
b = a - 2
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a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729 | a | multiply(square_perimeter(sqrt(289)), 54) | what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ? | "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a" | a = math.sqrt(289)
b = square_perimeter * (
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a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28 | c | subtract(const_60, multiply(const_60, divide(33, 45))) | excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ? | "explanation : t = 12 / 45 * 60 = 16 answer : option c" | a = 33 / 45
b = const_60 * a
c = const_60 - b
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a ) 70 hours , b ) 40 / 9 hours , c ) 9 hours , d ) 16 hours , e ) 20 hours | b | divide(const_1, add(divide(const_1, 8), divide(const_1, 10))) | worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long should it take both a and b , working together but independently , to do the same job ? | "a ’ s 1 hour ' s work = 1 / 8 b ' s 1 hour ' s work = 1 / 10 ( a + b ) ' s 1 hour ' s work = ( 1 / 8 ) + ( 1 / 10 ) = 9 / 40 both a and b will finish the work in 40 / 9 days . answer b 40 / 9 hours" | a = 1 / 8
b = 1 / 10
c = a + b
d = 1 / c
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a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 70 | d | multiply(60, const_1) | rectangle dimensions were given , 2 doors dimensions given , 2 windows dimensions given . 70 cm wide wallpaper to be covered on the walls of this room . cost of wallpaper is 60 per meter . . calculate total cost | area of room = ( l * b ) m ^ 2 area of door + window = ( d + w ) m ^ 2 remaining area = ( ( l * b ) - ( d + w ) ) m ^ 2 so length = remaining area / 0.70 m total cost = length * 60 - - - ans and total cost = 60 answer : d | a = 60 * 1
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a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7 | b | inverse(6) | set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ? | number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b | a = 1/(6)
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a ) 42 , b ) 48 , c ) 56 , d ) 64 , e ) 72 | c | subtract(divide(multiply(subtract(subtract(subtract(const_100, multiply(divide(160, 800), const_100)), 23), subtract(const_100, 75)), 800), const_100), divide(multiply(subtract(const_100, 75), 800), const_100)) | in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 23 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ? | 200 are sophomores . the number of freshmen is 600 - 160 - 0.23 ( 800 ) = 256 the answer is c . | a = 160 / 800
b = a * 100
c = 100 - b
d = c - 23
e = 100 - 75
f = d - e
g = f * 800
h = g / 100
i = 100 - 75
j = i * 800
k = j / 100
l = h - k
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a ) $ 0.94 , b ) $ 0.97 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20 | b | multiply(add(const_1, divide(9, const_100)), divide(0.80, divide(subtract(const_100, 10), const_100))) | the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 9 percent of the cost of the tomatoes . | "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.09 * 80 90 x - 80 = 7.2 90 x = 87.2 x = 87.2 / 90 = 0.968 x is slightly under 0.9688 = 0.97 answer : b" | a = 9 / 100
b = 1 + a
c = 100 - 10
d = c / 100
e = 0 / 80
f = b * e
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a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666 | d | multiply(power(divide(const_1, const_2), 3), 3) | if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ? | "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 h thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : d" | a = 1 / 2
b = a ** 3
c = b * 3
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a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these | c | add(multiply(10, 2.5), 50) | the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ? | "explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c" | a = 10 * 2
b = a + 50
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a ) 6 km , b ) 7 km , c ) 7.2 km , d ) 8 km , e ) 8.4 km | c | multiply(divide(24, const_60), add(15, 3)) | the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hourr . the distance travelled downstream in 24 mins is ? | "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = 2460 × 18 = 2 × 185 = 7.2 km c" | a = 24 / const_60
b = 15 + 3
c = a * b
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a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15 | d | add(divide(8, 1), divide(4, 1)) | if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ? | "tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ." | a = 8 / 1
b = 4 / 1
c = a + b
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a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 23 | d | divide(add(22, 42), const_2) | a man can row upstream at 22 kmph and downstream at 42 kmph , and then find the speed of the man in still water ? | "us = 22 ds = 42 m = ( 42 + 22 ) / 2 = 32 answer : d" | a = 22 + 42
b = a / 2
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a ) 5 , b ) 15 , c ) 25 , d ) 35 , e ) 45 | c | multiply(const_4, const_4) | if the side length of square b is five times that of square a , the area of square b is how many times the area of square a ? | "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 5 x ) ^ 2 = 25 x ^ 2 . the answer is c ." | a = 4 * 4
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a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg | d | add(multiply(2, 20), 40) | the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man . | total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d | a = 2 * 20
b = a + 40
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['a ) 9', 'b ) 8', 'c ) 4', 'd ) 10', 'e ) 11'] | e | subtract(subtract(310, 138), subtract(255, 94)) | in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ? | take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e | a = 310 - 138
b = 255 - 94
c = a - b
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a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185 | c | multiply(divide(const_100, 8), 14) | a 14 % stock yielding 8 % is quoted at ? | "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 14 , money invested = 100 × 14 / 8 = rs . 175 ie , market value of the stock = rs . 175 answer is c ." | a = 100 / 8
b = a * 14
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a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25 | a | divide(multiply(subtract(26, 6), 3), 4) | at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ? | let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a | a = 26 - 6
b = a * 3
c = b / 4
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a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days | b | multiply(const_3, 5) | working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose | "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 15 x + y = 30 so xy = 150 the answer choices are : 26 days 15 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 15 days for jose and 10 days for jane . answer : b" | a = 3 * 5
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a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 % | e | multiply(divide(add(multiply(divide(20, 100), 1,100), 100), 1,000), 100) | two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1,000 ? | "investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %" | a = 20 / 100
b = a * 1
c = b + 100
d = c / 1
e = d * 100
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a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145 | a | divide(add(645, 25), add(add(3, const_1), const_1)) | a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ? | a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a | a = 645 + 25
b = 3 + 1
c = b + 1
d = a / c
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a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 . | d | power(subtract(3, divide(add(13, 3), 2)), 2) | if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ? | "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d" | a = 13 + 3
b = a / 2
c = 3 - b
d = c ** 2
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a ) 61 % , b ) 62 % , c ) 65 % , d ) 64 % , e ) 50 % | a | subtract(const_100, add(20, multiply(20, subtract(const_1, divide(5, const_100))))) | dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ? | say dhoni ' s earning last month was $ 100 . dhoni spent 20 percent of his earning last month on rent - - > $ 20 on rent ; 5 percent less than what he spent on rent to purchase a new dishwasher - - > $ 20 * 0.95 = $ 19 on the dishwasher . left over amount 100 - ( 20 + 19 ) = $ 61 answer : a | a = 5 / 100
b = 1 - a
c = 20 * b
d = 20 + c
e = 100 - d
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a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 % | e | multiply(divide(20, subtract(const_100, 20)), const_100) | if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ? | "excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )" | a = 100 - 20
b = 20 / a
c = b * 100
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a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | c | add(subtract(15, const_10), const_1) | a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ? | 2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c | a = 15 - 10
b = a + 1
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a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg | c | add(56, 8) | the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ? | the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c | a = 56 + 8
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a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91 | c | divide(2, subtract(subtract(subtract(const_1, divide(1, 3)), multiply(divide(2, 5), subtract(const_1, divide(1, 3)))), multiply(divide(2, 3), subtract(subtract(const_1, divide(1, 3)), multiply(divide(2, 5), subtract(const_1, divide(1, 3))))))) | there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ? | sol : if x sweets were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 2 x × 2 / 3 × 3 / 5 × 1 / 3 = 2 x = 15 answer : c | a = 1 / 3
b = 1 - a
c = 2 / 5
d = 1 / 3
e = 1 - d
f = c * e
g = b - f
h = 2 / 3
i = 1 / 3
j = 1 - i
k = 2 / 5
l = 1 / 3
m = 1 - l
n = k * m
o = j - n
p = h * o
q = g - p
r = 2 / q
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a ) 11 % , b ) 20 % , c ) 27 % , d ) 32 % , e ) 49 % | a | multiply(divide(90, 90), const_100) | the cost of 100 articles is equal to selling price of 90 . find the gain or loss percent ? | "c . p . of each article be $ 1 c . p . of 90 articles = 100 gain % = 10 / 90 * 100 = 11 % approximately answer is a" | a = 90 / 90
b = a * 100
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a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91 | d | add(multiply(divide(9, add(5, 9)), divide(subtract(9, const_1), subtract(add(5, 9), const_1))), multiply(divide(subtract(5, const_1), subtract(add(5, 9), const_1)), divide(5, add(5, 9)))) | a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ? | "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d ." | a = 5 + 9
b = 9 / a
c = 9 - 1
d = 5 + 9
e = d - 1
f = c / e
g = b * f
h = 5 - 1
i = 5 + 9
j = i - 1
k = h / j
l = 5 + 9
m = 5 / l
n = k * m
o = g + n
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a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15 | d | divide(add(223, 43), 17) | a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ? | "223 + 43 = 266 / 17 = 11 ( remainder ) d" | a = 223 + 43
b = a / 17
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a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60 | c | multiply(400, divide(25, const_100)) | find the 25 % of rs . 400 . | "explanation : 25 % of 400 = > 25 / 100 * 400 = rs . 100 answer : c" | a = 25 / 100
b = 400 * a
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a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 % | a | multiply(divide(10, subtract(40, 10)), const_100) | a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ? | "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) – ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs . 4000 profit % = 10 / 30 × 100 = 33.33 % profit of 33.33 % was made by the merchant . a" | a = 40 - 10
b = 10 / a
c = b * 100
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a ) rs . 90000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these | a | divide(9000, divide(subtract(const_100, add(add(50, 25), 15)), const_100)) | ajay spends 50 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 15 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income . | savings 10 % - 9000 expenditure 90 % - 81000 total - 90000 answer : a | a = 50 + 25
b = a + 15
c = 100 - b
d = c / 100
e = 9000 / d
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a ) 288 , b ) 4500 , c ) 7200 , d ) 864 , e ) 9640 | b | multiply(divide(const_4, 3), power(3, 3)) | the measurement of a rectangular box with lid is 50 cmx 30 cmx 38 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere ) | "d = 30 , r = 15 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 15 * 15 * 15 = 4500 π cm 3 answer : b" | a = 4 / 3
b = 3 ** 3
c = a * b
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a ) rs . 3000 , b ) rs . 4000 , c ) rs . 3500 , d ) rs . 4500 , e ) rs . 6000 | b | multiply(divide(105, 16), const_100) | if an article is sold at 12 % profit instead of 16 % profit , then the profit would be rs . 105 less . what is the cost price ? | "explanation : let the cost price of an article be rs . x . ( 16 % of x ) - ( 12 % of x ) = 105 16 x / 100 - 12 x / 100 = 105 = > 4 x = 160 * 100 = > x = 1500 cost price = rs . 4000 answer : b" | a = 105 / 16
b = a * 100
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a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5 | b | divide(subtract(16, 9), subtract(19, 16)) | gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ? | "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b" | a = 16 - 9
b = 19 - 16
c = a / b
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a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735 | e | divide(multiply(choose(7, 5), choose(7, 4)), 7) | a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ? | "there 7 questions in part a out of which 5 question can be chosen as = 7 c 5 . similarly , 4 questions can be chosen from 7 questions of part b as = 7 c 4 . hence , total number of ways , = 7 c 5 * 7 c 4 = [ 7 ! / ( 2 ! 5 ! ) ] * [ 7 ! / ( 3 ! * 4 ! ) ] = { 21 } * { 7 * 6 * 5 * 4 / ( 4 * 3 * 2 * 1 ) } = 735 . e" | a = math.comb(7, 5)
b = math.comb(7, 4)
c = a * b
d = c / 7
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a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28 | d | divide(subtract(multiply(60, const_4), 200), const_2) | a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be : | "explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d" | a = 60 * 4
b = a - 200
c = b / 2
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a ) 16 , b ) 17 , c ) 43 , d ) 19 , e ) 20 | c | subtract(divide(multiply(62, 150), const_100), divide(multiply(20, 250), const_100)) | what is the difference between 62 % of 150 nd 20 % of 250 . | ( 62 / 100 ) * 150 â € “ ( 20 / 100 ) * 250 93 - 50 = 43 answer : c | a = 62 * 150
b = a / 100
c = 20 * 250
d = c / 100
e = b - d
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a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25 | b | multiply(divide(add(multiply(50, divide(10, const_100)), multiply(25, divide(20, const_100))), const_100), const_100) | of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ? | "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b" | a = 10 / 100
b = 50 * a
c = 20 / 100
d = 25 * c
e = b + d
f = e / 100
g = f * 100
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a ) 62 , b ) 181 , c ) 170 , d ) 171 , e ) 50 | d | add(power(11, 2), multiply(power(5, 2), 2)) | if a 2 - b 2 = 11 and a * b = 5 , find a 4 + b 4 . | "a 2 - b 2 = 11 : given a 4 + b 4 - 2 a 2 b 2 = 112 : square both sides and expand . a * b = 2 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 121 : substitute a 4 + b 4 = 171 correct answer d" | a = 11 ** 2
b = 5 ** 2
c = b * 2
d = a + c
|
a ) 90 % , b ) 99 % , c ) 100 % , d ) 101 % , e ) 110 % | b | multiply(10, 10) | on july 1 of last year , total employees at company e was decreased by 10 percent . without any change in the salaries of the remaining employees , the average ( arithmetic mean ) employee salary was 10 percent more after the decrease in the number of employees than before the decrease . the total of the combined salaries of all the employees at company e after july 1 last year was what percent of that before july 1 last year ? | "let the number of employees before jul 1 be 100 then av sal 1 = total 1 / 100 after jul 1 employees = 90 av sal 2 = total 2 / 90 now from the question av 2 = av 1 + 10 % total 2 / 90 = total 1 / 100 + 1 / 10 * total 1 / 100 total 2 / 90 = 11 total 1 / 1000 total 2 = 99 total 1 / 100 now percent = total 2 / total 1 * 100 = 99 total 1 / total 1 = 99 answer : b" | a = 10 * 10
|
a ) - 5 , b ) - 6 , c ) - 7 , d ) - 8 , e ) - 10 | d | floor(divide(19, negate(3))) | if q and d are both integers , q > d , and - 3 q > 19 , then the largest value of d would be ? | no , your thinking is incorrect . when we know that q > d and q < - 6.33 , the largest value of q can be - 7 while if q = - 7 , then largest value of d < - 7 will be - 8 . for negative numbers , - 7 > - 8 and - 8 > - 10 . you are right in saying that d can take any value less than - 7 - - - > d could be - 8 , - 9 , - 10 . . . . and out of all these values , - 8 is the greatest . look at the numbers on the number line . for any 2 numbers , the ones on the right are greater than the ones on the left : . . . . . . . - 11 - 10 - 9 - 8 - 7 - 6 - 5 . . . . . 0 1 2 3 4 5 6 . . . ( - 11 < - 10 , - 10 < - 8 , 4 < 5 etc ) . so , as per the question if d < q and q = - 7 , then d ' s largest ' possible ' value has to be - 8 . - 10 is smaller than - 8 = d | a = 19 / negate
b = math.floor(a)
|
a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 229 , e ) e ) 302 | d | divide(195, divide(subtract(const_100, 15), const_100)) | a small company reduced its faculty by approximately 15 percent to 195 employees . what was the original number of employees ? | "if x is the original number of employees , then after 15 % reduction in employees number is . 85 x but we are given . 85 x = 195 x = 229 so the original number of employees is 229 correct answer - d" | a = 100 - 15
b = a / 100
c = 195 / b
|
a ) 20 , b ) 21 , c ) 27 , d ) 23 , e ) 24 | c | divide(subtract(30, subtract(multiply(const_2, const_2), const_2)), subtract(const_2, const_1)) | a man is 30 years older than his son . in three years , his age will be twice the age of his son . the present age of his son is : | "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 3 = 2 ( x + 3 ) x + 33 = 2 x + 6 x = 27 . answer : c" | a = 2 * 2
b = a - 2
c = 30 - b
d = 2 - 1
e = c / d
|
a ) 70 % , b ) 60 % , c ) 50 % , d ) 40 % , e ) 30 % | c | multiply(divide(subtract(180, 120), 120), const_100) | henry earns $ 120 a week from his job . his income increased and now makes $ 180 a week . what is the percent increase ? | increase = ( 60 / 120 ) * 100 = ( 1 / 2 ) * 100 = 50 % . c | a = 180 - 120
b = a / 120
c = b * 100
|
a ) 144 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph | a | subtract(multiply(6, multiply(120, const_0_2778)), 120) | a train 120 m long crosses a platform 120 m long in 6 sec ; find the speed of the train ? | "d = 120 + 120 = 240 t = 6 s = 240 / 6 * 18 / 5 = 144 kmph answer : a" | a = 120 * const_0_2778
b = 6 * a
c = b - 120
|
a ) 52 , b ) 75 , c ) 92 , d ) 100 , e ) 184 | d | divide(multiply(300, divide(40, subtract(48, 36))), divide(add(36, 48), subtract(48, 36))) | an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 48 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ? | "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 48 - 40 ) / ( 40 - 36 ) = 8 / 4 = 2 / 1 = number of microtron stocks / number of dynaco stocks so for every 2 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 3 ) th i . e . 300 / 3 = 100 must be dynaco stock . answer ( d )" | a = 48 - 36
b = 40 / a
c = 300 * b
d = 36 + 48
e = 48 - 36
f = d / e
g = c / f
|
a ) a . 20 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24 | a | add(add(add(add(add(add(add(add(add(add(add(add(const_1, add(3, 3)), const_1), const_1), const_1), const_1), 3), const_1), const_1), const_1), const_1), const_1), const_1) | working at constant rate , pump x pumped out half of the water in a flooded basement in 3 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ? | "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 20 hours a" | a = 3 + 3
b = 1 + a
c = b + 1
d = c + 1
e = d + 1
f = e + 1
g = f + 3
h = g + 1
i = h + 1
j = i + 1
k = j + 1
l = k + 1
m = l + 1
|
a ) 2 cm , b ) 5 / 2 cm , c ) 5 cm , d ) 15 / 2 cm , e ) none of the these | d | add(add(10, 12), 10) | two spherical balls lie on the ground touching . if one of the balls has a radius of 10 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ? | "similar triangle properties . . 2 / r + 10 = 10 / r - 10 giving r = 15 / 2 . answer : d" | a = 10 + 12
b = a + 10
|
a ) 1 / 1000 , b ) 1 / 506 , c ) 253 / 500 , d ) 253 / 1000 , e ) none of these | a | divide(subtract(add(multiply(753, 753), multiply(247, 247)), multiply(753, 247)), add(multiply(multiply(753, 753), 753), multiply(multiply(247, 247), 247))) | ( 753 x 753 + 247 x 247 - 753 x 247 ) / ( 753 x 753 x 753 + 247 x 247 x 247 ) = ? | given exp . = ( a ^ 2 + b ^ 2 - ab ) / ( a ^ 3 + b ^ 3 ) = 1 / ( a + b ) = 1 / ( 753 + 247 ) = 1 / 1000 answer : a | a = 753 * 753
b = 247 * 247
c = a + b
d = 753 * 247
e = c - d
f = 753 * 753
g = f * 753
h = 247 * 247
i = h * 247
j = g + i
k = e / j
|
a ) 6 min , b ) 5 min , c ) 5.5 min , d ) 4 min , e ) 3 min | a | divide(7201, multiply(1.2, const_1000)) | the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 1.2 km / hr ? | "area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 1.2 km / hour = 1200 m / hour = 20 m / min time taken by lady to cross the field diagonally = 120 / 20 = 6 min answer a" | a = 1 * 2
b = 7201 / a
|
a ) 144 min , b ) 145 min , c ) 150 min , d ) 200 min , e ) 250 min | a | multiply(add(const_1, const_4), 36) | one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 36 minutes , then the slower pipe alone will be able to fill the tank in : | "slower pipe alone fill the tank = x faster pipe will fill in x / 3 min 1 / x + 3 / x = 1 / 36 x = 144 min answer a" | a = 1 + 4
b = a * 36
|
a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 14 % | c | subtract(const_100, divide(multiply(add(const_100, 9), subtract(const_100, 22)), const_100)) | the tax on a commodity is diminished by 22 % but its consumption is increased by 9 % . find the decrease percent in the revenue derived from it ? | "100 * 100 = 10000 78 * 109 = 8502 10000 - - - - - - - 1200 100 - - - - - - - ? = 15 % answer : c" | a = 100 + 9
b = 100 - 22
c = a * b
d = c / 100
e = 100 - d
|
a ) 3 / 8 , b ) 5 / 12 , c ) 7 / 24 , d ) 11 / 36 , e ) 13 / 48 | c | add(divide(1, 6), divide(1, 8)) | each of the three people individually can complete a certain job in 4 , 6 , and 8 hours , respectively . what is the lowest fraction of the job that can be done in 1 hour by 2 of the people working together at their respective rates ? | "the two slowest people work at rates of 1 / 6 and 1 / 8 of the job per hour . the sum of these rates is 1 / 6 + 1 / 8 = 7 / 24 of the job per hour . the answer is c ." | a = 1 / 6
b = 1 / 8
c = a + b
|
a ) 2.4 km , b ) 2.9 km , c ) 3.4 km , d ) 1.9 km , e ) 5.6 km | d | divide(multiply(subtract(4, 1), const_3), 4) | a man can row at 4 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | "explanation : speed in still water = 4 kmph speed of the current = 1 kmph speed downstream = ( 4 + 1 ) = 5 kmph speed upstream = ( 4 - 1 ) = 3 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 5 + x / 3 = 1 â ‡ ’ 3 x + 5 x = 15 â ‡ ’ 8 x = 15 â ‡ ’ x = 1.9 km answer : option d" | a = 4 - 1
b = a * 3
c = b / 4
|
a ) 80 % , b ) 85 % , c ) 96 % , d ) 125 % , e ) 150 % | c | subtract(const_100, multiply(divide(add(20, const_100), add(25, const_100)), const_100)) | two numbers are respectively 20 % and 25 % more than a third number . the percentage that is first of the second is ? | "explanation : i ii iii 120 125 100 125 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 96 % answer is c" | a = 20 + 100
b = 25 + 100
c = a / b
d = c * 100
e = 100 - d
|
a ) 289 , b ) 400 , c ) 200 , d ) 288 , e ) 111 | b | divide(subtract(360, 340), divide(5, const_100)) | if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is | "explanation : let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : b" | a = 360 - 340
b = 5 / 100
c = a / b
|
a ) 19 % , b ) 10 % , c ) 21 % , d ) 16 % , e ) none | c | add(15, multiply(subtract(15, 10), divide(6, 5))) | weights of two friends ram and shyam are in the ratio 6 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ? | "solution : given ratio of ram and shayam ' s weight = 6 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 6 / 5 or , x = 21 % . answer : option c" | a = 15 - 10
b = 6 / 5
c = a * b
d = 15 + c
|
a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6 | e | divide(84, 36) | how many of the positive factors of 36 , 84 and how many common factors are there in numbers ? | "factors of 36 - 1 , 2 , 3 , 4 , 6 , 9 , 12 , 18 , 36 factors of 84 - 1 , 2 , 3 , 4 , 6 , 7 , 12 , 14 , 21 , 28 , 42 , 84 comparing both , we have six common factors of 36 and 84 - 1,2 , 3,4 , 6,12 , answer ( e )" | a = 84 / 36
|
a ) 475 , b ) 234 , c ) 289 , d ) 345 , e ) none of these | a | divide(divide(multiply(multiply(const_100, const_100), 9.5), const_100), const_4) | jaclyn buys $ 20 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter | "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 475 answer : a" | a = 100 * 100
b = a * 9
c = b / 100
d = c / 4
|
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