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 ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 63 | e | multiply(11, inverse(subtract(1, add(divide(1, 5), divide(2, 3))))) | in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 11 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ? | "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 11 = 63 answer e" | a = 1 / 5
b = 2 / 3
c = a + b
d = 1 - c
e = 1/(d)
f = 11 * e
|
a ) 75 meters , b ) 60 meters , c ) 90 meters , d ) 80 meters , e ) 70 meters | a | multiply(subtract(divide(multiply(42, const_1000), const_3600), divide(subtract(multiply(divide(multiply(42, const_1000), const_3600), 9), multiply(divide(multiply(42, const_1000), const_3600), 5)), add(9, 5))), 9) | a train traveling at 42 kms / hr passes a cyclist going in the same direction in 9 secs . if the cyclist had been going in the opposite direction , the train would have passed him in 5 secs . find the length of the train . | let the length of the train be x meter and the speed of the cyclist is y m / s now when the train and the cyclist are in the same direction , the relative speed is : ( 35 / 3 - y ) m / s [ converting 42 km / h to m / s - 35 / 3 m / s ] now distance / relative speed = 9 seconds substituting the values , we get x + 9 y . . . . . . . . . . . . . . . . . . . . . ( 1 ) similarly calculate the relative speed when they are in the opposite direction the relative speed is ( 35 / 3 + y ) now distance / relative speed is equivalent to 5 seconds substituting the values , we get the equation 3 x - 15 y = 175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 ) solving ( 1 ) and ( 2 ) , we get x = 75 meters answer : a | a = 42 * 1000
b = a / 3600
c = 42 * 1000
d = c / 3600
e = d * 9
f = 42 * 1000
g = f / 3600
h = g * 5
i = e - h
j = 9 + 5
k = i / j
l = b - k
m = l * 9
|
a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 455 , e ) none of these | d | divide(subtract(multiply(30, 350), multiply(15, 245)), 15) | the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 245 , then the mean profit for the last 15 days would be | "average would be : 350 = ( 245 + x ) / 2 on solving , x = 455 . answer : d" | a = 30 * 350
b = 15 * 245
c = a - b
d = c / 15
|
a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 8 , e ) 7 / 6 | d | divide(divide(subtract(8.75, 7.50), subtract(8.75, 5.5)), subtract(const_1, divide(subtract(8.75, 7.50), subtract(8.75, 5.5)))) | in what ratio should a variety of rice costing rs . 5.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ? | "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5.5 ) = 5 / 8 answer : d" | a = 8 - 75
b = 8 - 75
c = a / b
d = 8 - 75
e = 8 - 75
f = d / e
g = 1 - f
h = c / g
|
a ) 62 , b ) 64 , c ) 66 / 7 , d ) 10 , e ) 68 / 7 | e | add(5, divide(subtract(multiply(16, 12), multiply(12, 5)), add(12, 16))) | john can complete a given task in 16 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ? | "in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 16 ) = 5 / 16 of the work . so 11 / 16 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 16 + 1 / 12 = 7 / 48 time taken to complete 11 / 16 of the work = ( 11 / 16 ) / ( 7 / 48 ) = 33 / 7 days . so total number of days taken to complete the work = 33 / 7 + 5 = 68 / 7 days . e" | a = 16 * 12
b = 12 * 5
c = a - b
d = 12 + 16
e = c / d
f = 5 + e
|
a ) 31 , b ) 32 , c ) 33 , d ) 62 , e ) 64 | d | multiply(add(30, const_1), const_2) | what is the least positive integer that is not a factor of 30 ! and is not a prime number ? | a ) 31 is prime and per the question stem we can not use this b ) 32 = 2 * 16 - within 30 ! we have a 2 and 16 so 32 will be a factor of 30 ! c ) 33 = 3 * 11 - again within 30 ! we have a 3 and an 11 so 33 will be a factor of 30 ! d ) 62 = 31 * 2 - bingo 31 is not included in 30 ! e ) 64 = 16 * 4 - both 16 and 4 are multiplied in 30 ! answer is d ! | a = 30 + 1
b = a * 2
|
a ) 698 , b ) 768 , c ) 1430 , d ) 1980 , e ) none | b | add(divide(multiply(const_100, 168), multiply(14, const_2.0)), 168) | if the true discount on a sum due 3 years hence at 14 % per annum be rs . 168 , the sum due is : | "sol . p . w . = 100 * t . d . / r * t = 100 * 168 / 14 * 2 = 600 . ∴ sum = ( p . w . + t . d . ) = rs . ( 600 + 168 ) = rs . 768 . answer b" | a = 100 * 168
b = 14 * 2
c = a / b
d = c + 168
|
a ) 1 , b ) 2 , c ) - 5 , d ) 4 , e ) 5 | c | divide(1, 5) | find the slope of the line perpendicular to the line y = ( 1 / 5 ) x - 7 | two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 5 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 5 ) = - 1 solve for m m = - 5 correct answer c ) - 5 | a = 1 / 5
|
a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08 | c | multiply(2, 9) | each child has 2 pencils and 13 skittles . if there are 9 children , how many pencils are there in total ? | 2 * 9 = 18 . answer is c . | a = 2 * 9
|
a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 160 sec , e ) 276 sec | d | divide(add(1200, 400), divide(1200, 120)) | a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 400 m long ? | "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1600 m t = d / s t = 1600 / 10 t = 160 sec answer : d" | a = 1200 + 400
b = 1200 / 120
c = a / b
|
a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 11 | e | subtract(divide(add(multiply(5, 5), 14), subtract(5, const_1)), subtract(divide(add(multiply(5, 5), 14), subtract(5, const_1)), 5)) | chris age after 14 years will be 5 times his age 5 years back . what is the present age of chris ? | "chris present age = x after 14 years = x + 14 5 years back = x - 5 x + 14 = 5 ( x - 5 ) x = 11 answer is e" | a = 5 * 5
b = a + 14
c = 5 - 1
d = b / c
e = 5 * 5
f = e + 14
g = 5 - 1
h = f / g
i = h - 5
j = d - i
|
a ) 59 , b ) 83 , c ) 45 , d ) 53 , e ) 64 | a | subtract(multiply(8, 61), subtract(multiply(13, 59), multiply(57, 7))) | the average of 13 numbers is 59 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ? | "sum of all the 13 numbers = 13 * 59 = 767 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 767 = 59 . answer : a" | a = 8 * 61
b = 13 * 59
c = 57 * 7
d = b - c
e = a - d
|
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | c | subtract(add(multiply(reminder(7, 400), 3), reminder(3, 400)), reminder(1, 400)) | x is a positive integer less than 400 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ? | the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 400 n = 23.42 or n = 23 answer : - c | a = reminder * (
b = a + 3
c = b - reminder
|
a ) 287 m , b ) 350 m , c ) 1267 m , d ) 1287 m , e ) 1162.5 m | e | subtract(multiply(speed(300, 8), 39), 300) | a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec . what is the length of the platform ? | "speed = 300 / 8 = 75 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 2 = > x = 1162.5 m . answer : e" | a = speed * (
b = a - 39
|
a ) 33.06 , b ) 34.1 , c ) 34.2 , d ) 24.6 , e ) none of these | a | divide(multiply(multiply(25, add(add(12, 3), const_100)), add(add(12, 3), const_100)), multiply(const_100, const_100)) | the rate of increase of the price of sugar is observed to be 3 percent more than the inflation rate expressed in percentage . the price of sugar , on january 1 , 1994 , is rs . 25 per kg . the inflation rate for the years 1994 and 1995 are expected to be 12 % each . the expected price of sugar on january 1 , 1996 would be | explanation : increase in the price of sugar = ( 12 + 3 ) = 15 % hence , price of the sugar on jan 1 , 1996 = > ( 25 * 115 * 115 ) / ( 100 * 100 ) = rs 33.06 . answer : a | a = 12 + 3
b = a + 100
c = 25 * b
d = 12 + 3
e = d + 100
f = c * e
g = 100 * 100
h = f / g
|
a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75 | e | add(45, multiply(3, 10)) | average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is | explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e | a = 3 * 10
b = 45 + a
|
a ) 22.5 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | a | divide(add(add(add(multiply(5, const_3), add(5, multiply(5, const_2))), multiply(5, const_4)), multiply(add(const_4, const_1), 5)), 5) | find the average of all numbers between 4 and 41 which are divisible by 5 | "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 180 / 8 = 22.5 answer : option a" | a = 5 * 3
b = 5 * 2
c = 5 + b
d = a + c
e = 5 * 4
f = d + e
g = 4 + 1
h = g * 5
i = f + h
j = i / 5
|
a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none | b | log(divide(log(subtract(1, multiply(add(const_4, const_1), const_1000))), log(add(const_4, const_1)))) | the value of log 5 ( 1 / 125 ) is | "solution let log 5 ( 1 / 125 ) = n . then , 5 n = 1 / 125 ‹ = › 5 n = 5 - 3 n = - 3 . answer b" | a = 4 + 1
b = a * 1000
c = 1 - b
d = math.log(c)
e = 4 + 1
f = math.log(e)
g = d / f
h = math.log(g)
|
a ) 65 sec , b ) 16 sec , c ) 18 sec , d ) 13 sec , e ) 76 sec | b | multiply(divide(280, multiply(63, const_1000)), const_3600) | a train 280 m long , running with a speed of 63 km / hr will pass a tree in ? | "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 280 * 2 / 35 = 16 sec answer : b" | a = 63 * 1000
b = 280 / a
c = b * 3600
|
a ) 7 , b ) 8 , c ) 5 , d ) 10 , e ) 9 | e | divide(subtract(12.80, 1), 1.25) | at a certain bowling alley , it costs $ 1 to rent bowling shoes for the day and $ 1.25 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ? | "after renting bowling shoes the person is left with $ 12.80 - $ 1 = $ 11.80 , which is enough for 11.8 / 1.25 < 10 = ~ 9 . answer : e ." | a = 12 - 80
b = a / 1
|
a ) 32 , b ) 30 , c ) 39 , d ) 40 , e ) 42 | b | subtract(54, divide(54, add(const_1, divide(125, const_100)))) | sales price is $ 54 , gross profit is 125 % of cost , what is the value of gross profit ? | "cost + profit = sales cost + ( 125 / 100 ) cost = 54 cost = 24 profit = 54 - 24 = 30 answer ( b )" | a = 125 / 100
b = 1 + a
c = 54 / b
d = 54 - c
|
a ) 288 , b ) 516 , c ) 877 , d ) 278 , e ) 178 | b | add(multiply(divide(60, subtract(21, 22)), 22), multiply(divide(60, subtract(21, 22)), 21)) | two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 22 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ? | "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 22 + 21 = 43 t = 12 d = 43 * 12 = 516 answer : b" | a = 21 - 22
b = 60 / a
c = b * 22
d = 21 - 22
e = 60 / d
f = e * 21
g = c + f
|
a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 % | e | multiply(divide(subtract(const_100, 10), add(20, const_100)), const_100) | marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 10 % . what percent of the projected revenue was the actual revenue ? | "last year revenue = 100 ( assume ) ; this year revenue = 90 ; projected revenue = 120 . actual / projected * 100 = 90 / 120 * 100 = 75 % . answer : e ." | a = 100 - 10
b = 20 + 100
c = a / b
d = c * 100
|
a ) 23 , b ) 28 , c ) 48 , d ) 25 , e ) 99 | d | divide(18750, 750) | if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers | "explanation : h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d" | a = 18750 / 750
|
a ) 42 , b ) 66 , c ) 75 , d ) 112 , e ) 154 | c | multiply(divide(375, add(3, 12)), 3) | in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12 . if the shop carries 375 dogs and bunnies total in stock , how many dogs are there ? | "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 12 x total dogs and bunnies = 15 x . and we are given that 15 x = 375 . hence x = 25 . dogs = 3 x = 3 * 25 = 75 ( option c )" | a = 3 + 12
b = 375 / a
c = b * 3
|
a ) 14.4 , b ) 120 , c ) 50.4 , d ) 60 , e ) 90 | b | divide(multiply(4, 9), divide(30, const_100)) | 30 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ? | "30 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 30 ) * 100 = 120 square feet answer : option b" | a = 4 * 9
b = 30 / 100
c = a / b
|
a ) 647 , b ) 698 , c ) 758 , d ) 847 , e ) 976 | c | subtract(830, divide(multiply(subtract(854, 830), 3), 4)) | a sum of money at simple interest amounts to rs . 830 in 3 years and to rs . 854 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 854 - 830 ) = rs . 24 . s . i . for 3 years = rs . ( 24 x 3 ) = rs . 72 . principal = rs . ( 830 - 72 ) = rs . 758 . answer : c" | a = 854 - 830
b = a * 3
c = b / 4
d = 830 - c
|
a ) 1.2 hrs , b ) 1.8 hrs , c ) 2.4 hrs , d ) 3.0 hrs , e ) none of these | c | inverse(add(divide(const_1, 4), divide(const_1, 6))) | a person p takes 4 hrs time to complete a job and q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job ? | explanation : p ’ s 1 hr work = 1 / 4 q ’ s 1 hr work = 1 / 6 ( p + q ) ’ s 1 hr work = 1 / 4 + 1 / 6 = 5 / 12 = > time = 12 / 5 = 2.4 hrs answer : option c | a = 1 / 4
b = 1 / 6
c = a + b
d = 1/(c)
|
a ) 20 % , b ) 27 % , c ) 31 % , d ) 43 % , e ) none | a | subtract(const_100, multiply(divide(add(8, const_100), add(35, const_100)), const_100)) | a shopkeeper fixes the marked price of an item 35 % above its cost price . the percentage of discount allowed to gain 8 % is | solution let c . p = rs . 100 then , marked price = rs . 135 , s . p = rs . 108 . discount % = ( 27 / 135 × 100 ) % = 20 % answer a | a = 8 + 100
b = 35 + 100
c = a / b
d = c * 100
e = 100 - d
|
a ) 20 % loss , b ) 37.5 % profit , c ) 37.5 % loss , d ) 30.33 % loss , e ) none of these | b | multiply(const_100, divide(subtract(const_100, divide(multiply(const_100, 16), 22)), divide(multiply(const_100, 16), 22))) | if the cost price of 22 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ? | "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 22 articles = rs . 22 . selling price of 16 articles = rs . 22 therefore , selling price of 22 articles is : - = > 22 / 16 ã — 22 = > 30.25 . therefore , profit = selling price - cost price . = > 30.25 â ˆ ’ 22 = 8.25 hence , the percentage of profit = profit x 100 / c . p . = > 8.25 / 22 ã — 100 . = > 37.5 % profit . answer : b" | a = 100 * 16
b = a / 22
c = 100 - b
d = 100 * 16
e = d / 22
f = c / e
g = 100 * f
|
a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none | d | divide(10, divide(multiply(multiply(2, multiply(multiply(add(2, const_3), 2), const_3)), 2), 10)) | six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ? | "l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d" | a = 2 + 3
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / 10
g = 10 / f
|
a ) 4 % , b ) 7 % , c ) 8 % , d ) 3 % , e ) 1 % | c | divide(multiply(divide(4, 5), const_100), 10) | at what rate percent per annum will the simple interest on a sum of money be 4 / 5 of the amount in 10 years ? | "let sum = x . then , s . i . = 4 x / 5 , time = 10 years . rate = ( 100 * 4 x ) / ( x * 5 * 10 ) = 8 % answer : c" | a = 4 / 5
b = a * 100
c = b / 10
|
a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60 | c | divide(subtract(divide(70, const_2), sqrt(subtract(multiply(divide(70, const_2), divide(70, const_2)), multiply(const_4, 300)))), const_2) | the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle . | "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c" | a = 70 / 2
b = 70 / 2
c = 70 / 2
d = b * c
e = 4 * 300
f = d - e
g = math.sqrt(f)
h = a - g
i = h / 2
|
a ) 1 km , b ) 1.5 km , c ) 5 km , d ) 3.2 km , e ) 2.4 km | e | divide(multiply(subtract(5, 1), const_3), 5) | a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ? | speed of down stream = 5 + 1 = 6 kmph speed of upstream = 5 - 1 = 4 kmph let the required distance be xkm x / 6 + x / 4 = 1 2 x + 3 x = 12 x = 2.4 km answer is e | a = 5 - 1
b = a * 3
c = b / 5
|
a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8927 | e | divide(divide(multiply(4106.25, const_100), 9), 5) | a sum fetched a total simple interest of $ 4106.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ? | "e 8927 principal = $ 100 x 4106.25 / 9 x 5 = $ 410625 / 45 = $ 8927 ." | a = 4106 * 25
b = a / 9
c = b / 5
|
a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025 | c | divide(add(divide(multiply(300, const_100), 30), 300), divide(75, const_100)) | a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ? | 300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer | a = 300 * 100
b = a / 30
c = b + 300
d = 75 / 100
e = c / d
|
a ) $ 480 , b ) $ 450 , c ) $ 928 , d ) $ 870 , e ) $ 660 | c | add(divide(multiply(divide(add(832, 448), const_2), 45), const_100), divide(add(832, 448), const_2)) | the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 45 % profit ? | "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 145 % of $ 640 = $ 928 . c" | a = 832 + 448
b = a / 2
c = b * 45
d = c / 100
e = 832 + 448
f = e / 2
g = d + f
|
a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4 | c | divide(multiply(const_2, multiply(50, 30)), add(50, 30)) | a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ? | explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c | a = 50 * 30
b = 2 * a
c = 50 + 30
d = b / c
|
a ) 4680250 , b ) 4685850 , c ) 4680315 , d ) 4685975 , e ) none of these | c | multiply(divide(4685, 999), const_100) | 4685 * 999 | "explanation : 4685 * ( 1000 - 1 ) = 4685000 - 4685 = 4680315 option c" | a = 4685 / 999
b = a * 100
|
a ) 48 , b ) 46 , c ) 54 , d ) 58 , e ) 62 | a | add(add(subtract(40, const_3), 7), subtract(10, 7)) | 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 5 like all . how many people like apple ? | "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 5 40 + 10 + 5 - 7 = 48 like apple answer : a" | a = 40 - 3
b = a + 7
c = 10 - 7
d = b + c
|
a ) 13000 , b ) 6250 , c ) 10000 , d ) 5000 , e ) none of these | b | subtract(subtract(multiply(multiply(5, const_1000), const_100), add(multiply(75000, const_2), 75000)), subtract(subtract(multiply(divide(subtract(56, 1), 56), multiply(multiply(5, const_1000), const_100)), multiply(multiply(75000, const_2), divide(subtract(56, 1), 56))), 75000)) | a textile manufacturing firm employees 56 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 56 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is : | "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 55 / 56 ) â ˆ ’ 150000 ã — ( 55 / 56 ) â ˆ ’ 75000 . = > rs 2 , 68,750 decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 68,750 = > rs . 6,250 answer : b" | a = 5 * 1000
b = a * 100
c = 75000 * 2
d = c + 75000
e = b - d
f = 56 - 1
g = f / 56
h = 5 * 1000
i = h * 100
j = g * i
k = 75000 * 2
l = 56 - 1
m = l / 56
n = k * m
o = j - n
p = o - 75000
q = e - p
|
a ) 4436 toys , b ) 5487 toys , c ) 1101 toys , d ) 2354 toys , e ) 1375 toys | c | divide(5505, 5) | a factory produces 5505 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ? | to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 5505 / 5 = 1101 toys correct answer c | a = 5505 / 5
|
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | c | divide(multiply(multiply(8, 8), 24), multiply(12, 16)) | 8 men , working 8 hours a day can complete a work in 24 days . how many hours a day must 12 men work to complete the same work in 16 days ? | "the number of hours required to complete the work is 8 * 8 * 24 = 1536 12 × 16 × ( x ) = 1536 x = 8 the answer is c ." | a = 8 * 8
b = a * 24
c = 12 * 16
d = b / c
|
a ) 72 , b ) 180 , c ) 70 , d ) 90 , e ) 140 | d | multiply(add(9, 1), add(1, 8)) | in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 9 , 1 ) , ( 1 , 1 ) , ( 1 , - 8 ) and ( - 9 , - 8 ) ? | "length of side 1 = 9 + 1 = 10 length of side 2 = 8 + 1 = 9 area of rectangle = 10 * 9 = 90 d is the answer" | a = 9 + 1
b = 1 + 8
c = a * b
|
a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 14 / 19 , e ) 1 / 2 | d | divide(add(3, 1), const_10) | company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 1 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ? | "# of basic stereos was 1 / 3 of total and # of deluxe stereos was 2 / 3 of total , let ' s assume total = 15 , then basic = 5 and deluxe = 10 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 5 * 1 = 5 and total time for deluxe would be 10 * 7 / 5 = 14 - - > total time for both of them would be 5 + 14 = 19 - - > deluxe / total = 14 / 19 . answer : d ." | a = 3 + 1
b = a / 10
|
a ) 76 seconds , b ) 18 seconds , c ) 40 seconds , d ) 48 seconds , e ) 45 seconds | d | divide(add(460, 140), divide(multiply(45, const_1000), const_3600)) | a train is 460 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ? | "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 460 + 140 = 600 meter time = distance / speed = 600 * ( 2 / 25 ) = 48 seconds answer : d" | a = 460 + 140
b = 45 * 1000
c = b / 3600
d = a / c
|
a ) 18 , b ) 135 , c ) 175 , d ) 216 , e ) 250 | b | add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 6)) | joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 6 of the remaining paint . how many gallons of paint has joe used ? | "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 6 ) * 270 = 45 gallons total paint used = 135 gallons . option b" | a = 360 / 4
b = a * 1
c = 360 / 4
d = c * 1
e = 360 - d
f = e / 6
g = b + f
|
a ) 72 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 59 kmph | a | subtract(multiply(14, multiply(180, const_0_2778)), 100) | a train 100 m long crosses a platform 180 m long in 14 sec ; find the speed of the train ? | "d = 100 + 180 = 280 t = 14 s = 280 / 14 * 18 / 5 = 72 kmph answer : a" | a = 180 * const_0_2778
b = 14 * a
c = b - 100
|
a ) 60 - 65 , b ) 55 - 58 , c ) 51 - 59 , d ) 39 - 41 , e ) 38 - 40 | c | add(divide(multiply(48.75, 5), const_100), 48.75) | a meal cost $ 48.75 adn there was no tax . if the tip was more than 5 pc but less than 20 pc of the price , then the total amount paid should be : | "5 % ( 48.75 ) = 2.4375 20 % ( 48.75 ) = 9.75 total amount could have been 48.75 + 2.4375 and 48.75 + 9.75 = > could have been between 51.1875 and 58.5 = > approximately between 51 and 59 answer is c ." | a = 48 * 75
b = a / 100
c = b + 48
|
a ) 5.2 , b ) 7.4 , c ) 13.7 , d ) 21.2 , e ) 28.7 | c | divide(383.6, 28) | on a map , 1 inch represents 28 miles . how many c inches would be necessary to represent a distance of 383.6 miles ? | "c inches necessary to represent a distance of 383.6 miles = 383.6 / 28 = 13.7 answer c" | a = 383 / 6
|
a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 . | c | add(divide(1430, add(divide(1430, add(add(const_10, const_10), const_2)), 45)), 9) | a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many apples f did each person get before 45 people joined the feast ? | "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons f = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c" | a = 10 + 10
b = a + 2
c = 1430 / b
d = c + 45
e = 1430 / d
f = e + 9
|
a ) a ) 15 , b ) b ) 10 , c ) c ) 14 , d ) d ) 12 , e ) e ) 11 | c | divide(1232, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14)) | if the wheel is 14 cm then the number of revolutions to cover a distance of 1232 cm is ? | "2 * 22 / 7 * 14 * x = 1232 = > x = 14 answer : c" | a = 3 * 100
b = 1 * 10
c = a + b
d = c + 4
e = d / 100
f = 2 * e
g = f * 14
h = 1232 / g
|
['a ) 3.11545466', 'b ) 0.76678113', 'c ) 0.11785113', 'd ) 2.11785113', 'e ) 0.11786667'] | c | divide(sqrt(const_2), add(const_10, const_2)) | what is the volume of an tetrahedron with edge length of 1 ? | the answer is sqr ( 2 ) / 12 = 0.11785113 the following can be derived using the pythagorean theorem : the height of a face is 3.5 / 2 . the area of any face is 3.5 / 4 . the distance from any corner to the center of a joining face is 1 / 3.5 . the height of the tetrahedron is ( 2 / 3 ) . 5 the area is 1 / 3 * base * height = ( 1 / 3 ) * 3.5 / 4 * ( 2 / 3 ) . 5 = 21 / 2 / 12 . the above cube has sides of length 1 / sqr ( 2 ) . the area formed by the diagonals along four of the faces as shown in the diagram is a tetrahedrom . left over are four pyramids . the base of each pyramid is half of the side of the cube and the height is the height of the cube . thus the area of each pyramid is : 1 / 2 * ( 1 / sqr ( 2 ) ) 2 * 1 / sqr ( 2 ) * 1 / 3 = ( 12 * sqr ( 2 ) ) - 1 the total area of the cube is ( 1 / sqr ( 2 ) ) 3 = ( 2 * sqr ( 2 ) ) - 1 the area of the tetrahedrom is thus ( 2 * sqr ( 2 ) ) - 1 - 4 * ( 12 * sqr ( 2 ) ) - 1 = 3 / ( 6 * sqr ( 2 ) ) - 2 / ( 6 * sqr ( 2 ) ) = 1 / ( 6 * sqr ( 2 ) ) = sqr ( 2 ) / 12 correct answer c | a = math.sqrt(2)
b = 10 + 2
c = a / b
|
a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16 | a | add(divide(subtract(const_1, add(add(power(divide(const_1, const_2), 2), multiply(2, power(divide(const_1, const_2), 2))), multiply(multiply(2, const_3), power(divide(const_1, const_2), 2)))), const_10), subtract(const_1, add(add(power(divide(const_1, const_2), 2), multiply(2, power(divide(const_1, const_2), 2))), multiply(multiply(2, const_3), power(divide(const_1, const_2), 2))))) | an exam consists of 2 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ? | "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 1 / 16 . a" | a = 1 / 2
b = a ** 2
c = 1 / 2
d = c ** 2
e = 2 * d
f = b + e
g = 2 * 3
h = 1 / 2
i = h ** 2
j = g * i
k = f + j
l = 1 - k
m = l / 10
n = 1 / 2
o = n ** 2
p = 1 / 2
q = p ** 2
r = 2 * q
s = o + r
t = 2 * 3
u = 1 / 2
v = u ** 2
w = t * v
x = s + w
y = 1 - x
z = m + y
|
a ) 87 , b ) 98 , c ) 32 , d ) 28 , e ) 37 | c | divide(add(add(20, 28), multiply(8, 2)), const_2) | the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 28 years . find the average age of the women ? | "20 + 28 + 8 * 2 = 64 / 2 = 32 answer : c" | a = 20 + 28
b = 8 * 2
c = a + b
d = c / 2
|
a ) 2 , b ) 2.4 , c ) 1.2 , d ) 2.1 , e ) 2.7 | b | divide(subtract(divide(divide(multiply(600, 6), const_1000), divide(20, const_60)), const_1), const_4) | a girl was riding her scooter . her father wanted to calculate her speed . he knew that the street was 600 meters from end to end . he saw his daughter make the roundtrip 6 times . it took her 20 minutes to complete those 6 trips . how fast was the girl riding her scooter in kilometers per hour ? | the distance of the street was 600 meters . the made the roundtrip 6 times , which would be 2 trips for each roundtrip . multiply 12 times 600 to get the total distance . 600 * 12 = 7200 meters of 7.2 km . the question asked for the speed in km / hour and 20 minutes is one third of an hour . multiply 7200 by 1 / 3 to get approximately 2400 meters . correct answer is b | a = 600 * 6
b = a / 1000
c = 20 / const_60
d = b / c
e = d - 1
f = e / 4
|
a ) 2 : 3 , b ) 6 : 7 , c ) 8 : 9 , d ) 8 : 3 , e ) it can not be determined from the information given | e | divide(add(2, 6), add(3, 6)) | the ratio of two quantities is 2 : 3 . if each of the quantities is increased by 6 , what is the ratio of the new quantities ? | "let quantities are 2 x and 3 x ratio of quantities after each is increased by 6 = ( 2 x + 6 ) / ( 3 x + 6 ) for x = 1 , ( 2 x + 6 ) / ( 3 x + 6 ) = 8 / 9 for x = 2 , ( 2 x + 6 ) / ( 3 x + 6 ) = 10 / 12 the value of final expression is dependent on the value of x which ca n ' t be determined as per given information . hence , the answer can not be determined answer : option e" | a = 2 + 6
b = 3 + 6
c = a / b
|
a ) 2.2 , b ) 2.3 , c ) 2.4 , d ) 2.5 , e ) 2.6 | c | divide(add(subtract(2.5, 0.5), add(2.5, 0.5)), const_2) | a rower whose speed is 2.5 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 0.5 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ? | time upstream = d / 2 time downstream = d / 3 total time = d / 2 + d / 3 = 5 d / 6 average speed = 2 d / ( 5 d / 6 ) = 2.4 km / hr the answer is c . | a = 2 - 5
b = 2 + 5
c = a + b
d = c / 2
|
a ) 8 : 6 , b ) 7 : 6 , c ) 5 : 6 , d ) 7 : 5 , e ) 6 : 7 | b | divide(add(6.25, divide(divide(4.5, 3), const_2)), add(4.5, divide(4.5, 3))) | in what ratio should a variety of wheat costing rs . 3 per kg be mixed with another variety of wheat costing rs . 6.25 per kg to obtain a mixture costing rs . 4.50 per kg ? | let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 6.25 - 4.50 ) / ( 4.50 - 3 ) = 7 / 6 answer : b | a = 4 / 5
b = a / 2
c = 6 + 25
d = 4 / 5
e = 4 + 5
f = c / e
|
a ) 21 . , b ) 28 . , c ) 35 . , d ) 49 . , e ) 6 . | e | add(const_3, const_2) | in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,3 ) , ( 8,3 ) , ( 4,5 ) , ( 7,5 ) ? | "delta x will give us the dimension of one side of the parallelogram = 8 - 5 = 3 unit delta y will give us the dimension of the other side of parallelogram = 5 - 3 = 2 unit area of parallelogram = 3 * 2 = 6 answer is e" | a = 3 + 2
|
a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25 | d | divide(subtract(add(27, add(27, 3)), multiply(3, 3)), const_2) | the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ? | let the average age of the whole team be x years . 11 x - ( 27 + 30 ) = 9 ( x - 1 ) 11 x - 9 x = 48 2 x = 48 x = 24 . the average age of the team is 24 years . the answer is d . | a = 27 + 3
b = 27 + a
c = 3 * 3
d = b - c
e = d / 2
|
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12 | b | multiply(divide(subtract(180, divide(240, const_2)), 40), const_2) | angelina walked 180 meters from her home to the grocery at a constant speed . she then walked 240 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ? | "let the speed be x . . . so time taken from home to grocery = 180 / x . . the speed to gym = 2 x . . so time taken = 240 / 2 x = 120 / x . . its given 180 / x - 120 / x = 40 . . 60 / x = 40 = > 40 x = 60 = > x = 60 / 40 x = 1.5 m / secs . . so grocery to gym = 2 * 1.5 = 3 m / s . . . answer : b" | a = 240 / 2
b = 180 - a
c = b / 40
d = c * 2
|
a ) 12 , b ) 7 , c ) 9 , d ) 15 , e ) 3 | e | divide(150, 50) | i have 150 pieces of cake . there are 50 friends in my house . i would like to give each friend the same amount of cake , how much should i give to each friend ? | 150 / 50 = 3 the answer is e . | a = 150 / 50
|
a ) 3022 , b ) 3040 , c ) 3099 , d ) 3088 , e ) 3066 | b | subtract(divide(multiply(760, subtract(22, const_2)), 4), 760) | there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 4 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 4 x * 4 = 760 * 20 x = 3800 760 - - - - - - - 3040 answer : b" | a = 22 - 2
b = 760 * a
c = b / 4
d = c - 760
|
a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 % | b | multiply(divide(subtract(1260, add(300, 900)), add(300, 900)), const_100) | sandy buys an old scooter for $ 900 and spends $ 300 on its repairs . if sandy sells the scooter for $ 1260 , what is the gain percent ? | "selling price / total cost = 1260 / 1200 = 1.05 the gain percent is 5 % . the answer is b ." | a = 300 + 900
b = 1260 - a
c = 300 + 900
d = b / c
e = d * 100
|
a ) 5568 , b ) 6369 , c ) 8736 , d ) 5635 , e ) 6734 | c | divide(multiply(divide(multiply(8000, add(const_100, 4)), const_100), add(const_100, 5)), const_100) | find the amount on rs . 8000 in 2 years , the rate of interest being 4 % per first year and 5 % for the second year ? | "8000 * 104 / 100 * 105 / 100 = > 8736 answer : c" | a = 100 + 4
b = 8000 * a
c = b / 100
d = 100 + 5
e = c * d
f = e / 100
|
a ) 22.5 , b ) 27.5 , c ) 32.5 , d ) 37.5 , e ) none | c | multiply(divide(subtract(multiply(divide(25, const_100), 1000), multiply(divide(20, const_100), multiply(1000, divide(60, const_100)))), subtract(1000, multiply(1000, divide(60, const_100)))), const_100) | of the 1000 inhabitants of a town , 60 % are males of whom 20 % are literate . if , of all the inhabitants , 25 % are literate , then what percent of the females of the town are literate ? | sol . number of males = 60 % of 1000 = 600 . number of females = ( 1000 - 600 ) = 400 . number of literates = 25 % of 1000 = 250 . number of literate males = 20 % of 600 = 120 . number of literate females = ( 250 - 120 ) = 130 . ∴ required percentage = ( 130 / 400 x 100 ) % = 32.5 % answer c | a = 25 / 100
b = a * 1000
c = 20 / 100
d = 60 / 100
e = 1000 * d
f = c * e
g = b - f
h = 60 / 100
i = 1000 * h
j = 1000 - i
k = g / j
l = k * 100
|
a ) 10 litres , b ) 17 litres , c ) 15 litres , d ) 18 litres , e ) none of these | b | divide(20, add(1, divide(1, 2))) | how much water must be added to 68 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ? | "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 68 litres of milk = ( 1 ⁄ 4 × 68 ) litres = 17 litres . answer b" | a = 1 / 2
b = 1 + a
c = 20 / b
|
a ) 197 , b ) 280 , c ) 189 , d ) 278 , e ) 350 | e | divide(multiply(600, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19))) | i bought two books ; for rs . 600 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ? | "x * ( 85 / 100 ) = ( 600 - x ) 119 / 100 x = 350 answer : e" | a = 100 + 19
b = 600 * a
c = 100 - 15
d = 100 + 19
e = c + d
f = b / e
|
a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6 | c | divide(power(2, 2), multiply(choose(4, 2), choose(2, 1))) | if x is to be chosen at random from the set { 1 , 2 , 3 , 4 } and y is to be chosen at random from the set { 5 , 6 , 7 , 8 } , what is the probability that xy will be even ? | "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 1 / 2 . answer : c ." | a = 2 ** 2
b = math.comb(4, 2)
c = math.comb(2, 1)
d = b * c
e = a / d
|
a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2 | d | subtract(divide(divide(84, const_1), const_3), const_3) | in how many ways can the integer 84 be expressed as a product of two different positive integers ? | "84 = ( 2 ^ 2 ) * 3 * 7 since 84 is not a perfect square , no of ways = 4 answer d" | a = 84 / 1
b = a / 3
c = b - 3
|
a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 144 | e | divide(multiply(power(12, 3), power(6, 2)), 432) | find the value of y from ( 12 ) ^ 3 x 6 ^ 2 ÷ 432 = y ? | "144 e" | a = 12 ** 3
b = 6 ** 2
c = a * b
d = c / 432
|
a ) 25 % , b ) 50 % , c ) 20 % , d ) 75 % , e ) 30 % | d | subtract(divide(35, divide(20, const_100)), const_100) | a man buys an article for $ 20 . and sells it for $ 35 . find the gain percent ? | "c . p . = $ 20 s . p . = $ 35 gain = $ 15 gain % = 15 / 20 * 100 = 75 % answer is d" | a = 20 / 100
b = 35 / a
c = b - 100
|
a ) 4 h , b ) 5 h , c ) 7 h , d ) 9 h , e ) 8 h | d | add(divide(80, const_10), const_1) | a ball dropped from h height and moves 80 % of height each time . total distance covered is | first time distance is h second time 80 h / 100 = 4 h / 5 similarly third time 80 % of 4 h / 5 = h ( 4 ^ 2 ) / ( 5 ^ 2 ) and so on . . . this will lead to infinite terms of geometric progression i . e h + 2 * 4 h / 5 + 2 * 16 h / 25 . . . . . . . . . . . . sum = h + 2 * 4 h / ( 5 ( 1 - 4 / 5 ) ) = 9 h answer : d | a = 80 / 10
b = a + 1
|
a ) 101 , b ) 116 , c ) 119 , d ) 116 , e ) 32 | d | multiply(73196, 631) | calculate 73196 ÷ ? = 631 | "answer let 62976 / x = 631 then x = 62976 / 631 = 116 option : d" | a = 73196 * 631
|
a ) 12.5 , b ) 8.01 , c ) 7.5 , d ) 26 , e ) 22 | a | multiply(multiply(multiply(const_0_2778, subtract(60, 20)), 50), inverse(multiply(const_0_2778, add(60, 20)))) | two trains of equal length , running with the speeds of 60 and 20 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ? | "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 20 = 80 * 5 / 18 t = 2500 / 9 * 18 / 400 = 12.5 sec . answer : a" | a = 60 - 20
b = const_0_2778 * a
c = b * 50
d = 60 + 20
e = const_0_2778 * d
f = 1/(e)
g = c * f
|
a ) – 20 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14 | a | subtract(negate(2), multiply(2, subtract(2, negate(2)))) | on the number line , the number p is twice as many units from - 2 as - 2 is from 7 . if p is less than – 2 , what is the value of p ? | "distance between - 2 and 7 = 9 since number p is twice as many units from - 2 as - 2 is from 7 , therefore p can be - 20 since , p is less than - 2 , the value of p = - 20 answer a" | a = negate - (
|
a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2 | d | subtract(4, 1) | find value for x from below equation ? x + 1 = 4 | "1 . subtract 1 from both sides : x + 1 - 1 = 4 - 1 2 . simplify both sides : x = 3 d" | a = 4 - 1
|
a ) 1650 , b ) 1324 , c ) 1245 , d ) 1300 , e ) 1635 | a | multiply(divide(subtract(1325, 5), subtract(5, const_1)), 5) | find large number from below question the difference of two numbers is 1325 . on dividing the larger number by the smaller , we get 5 as quotient and the 5 as remainder | "let the smaller number be x . then larger number = ( x + 1325 ) . x + 1325 = 5 x + 5 4 x = 1320 x = 330 large number = 330 + 1320 = 1650 answer : a" | a = 1325 - 5
b = 5 - 1
c = a / b
d = c * 5
|
a ) 5 : 1 , b ) 10 : 5 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2 | d | divide(multiply(4, 5), multiply(1, 2)) | jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 4 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ? | "u / i = 4 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 20 : 10 : 2 i . e . u : b = 20 : 2 answer : option d" | a = 4 * 5
b = 1 * 2
c = a / b
|
a ) 55 , b ) 42 , c ) 43 , d ) 44 , e ) 45 | a | divide(factorial(11), multiply(factorial(subtract(11, const_2)), factorial(const_2))) | if 11 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes | "n ( n - 1 ) / 2 = 11 * 10 / 2 = 55 answer : a" | a = math.factorial(11)
b = 11 - 2
c = math.factorial(b)
d = math.factorial(2)
e = c * d
f = a / e
|
a ) 10.6 , b ) 11.3 , c ) 12.7 , d ) 13.4 , e ) 14.5 | a | divide(0.0005215, 0.000305) | 0.0005215 / 0.000305 x 6.2 = ? | "explanation : ? = 0.0005215 / 0.000305 x 6.2 = 10.6 answer : option a" | a = 0 / 5215
|
a ) 20 % , b ) 24 % , c ) 30 % , d ) 27 % , e ) 79 % | d | divide(multiply(subtract(add(add(const_100, 10), multiply(add(const_100, 10), divide(25, const_100))), const_100), const_100), add(add(const_100, 10), multiply(add(const_100, 10), divide(25, const_100)))) | the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 25 % . by approximately what percent would the output now have to be decreased in order to restore the original output ? | "the original output increases by 10 % and then 25 % . total % change = a + b + ab / 100 total % change = 10 + 25 + 10 * 25 / 100 = 37.5 % now , you want to change it to 0 , so , 0 = 37.5 + x + 37.5 x / 100 x = - 37.5 ( 100 ) / 137.5 = 27 % approximately answer is d" | a = 100 + 10
b = 100 + 10
c = 25 / 100
d = b * c
e = a + d
f = e - 100
g = f * 100
h = 100 + 10
i = 100 + 10
j = 25 / 100
k = i * j
l = h + k
m = g / l
|
a ) 4 : 3 , b ) 9 : 2 , c ) 18 : 20 , d ) 1 : 4 , e ) 18 : 4 | a | divide(add(multiply(multiply(const_3, const_3), add(multiply(const_3, const_3), const_1)), 2), multiply(2, add(multiply(const_3, const_3), const_1))) | a and b started a business investing rs . 24,000 and rs 18,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ? | "a : b = 24000 : 18000 = 8 : 6 = 4 : 3 answer : a" | a = 3 * 3
b = 3 * 3
c = b + 1
d = a * c
e = d + 2
f = 3 * 3
g = f + 1
h = 2 * g
i = e / h
|
a ) 14.29 , b ) 14.21 , c ) 14.22 , d ) 14.27 , e ) 14.23 | b | divide(283, 1983) | find 283 / 1983 × 100 | "never start finding common factors . adjust the denominator to 2000 . so we are introducing an error of 17 which is 171983 = 1117171983 = 1117 th of the denominator . 283002000 = 14.15283002000 = 14.15 but this answer is slightly less than actual answer . now 14 . 1511714.15117 = 0.12 approximately . adding 0.12 to 14.25 gives 14.27 . option b is correct ." | a = 283 / 1983
|
a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 280 | e | divide(multiply(342, 10), add(2, 10)) | compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 342 grams of compound x ? | "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 342 gms of x have 342 * 10 / 12 = 280 gms of b and 342 - 280 = 62 gms of a . cross check : - a / b = 62 / 280 = 2 / 10 ( as given ) ans e" | a = 342 * 10
b = 2 + 10
c = a / b
|
a ) 50 % , b ) 33.33 % , c ) 40 % , d ) 16.66 % , e ) 12.5 % | c | multiply(subtract(divide(4, 5), multiply(divide(4, 5), divide(1, 2))), const_100) | a certain article of clothing was discounted during a special sale to 4 / 5 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ? | "say the original retail price of the item was $ 200 . the price after the first sale = 4 / 5 * $ 200 = $ 160 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 160 - 100 ) / 150 = 1 / 3 = 40 % . answer : c ." | a = 4 / 5
b = 4 / 5
c = 1 / 2
d = b * c
e = a - d
f = e * 100
|
a ) 5000 , b ) 6000 , c ) 7000 , d ) 8000 , e ) 9000 | a | subtract(40000, multiply(divide(7, 8), 40000)) | income and expenditure of a person are in the ratio 8 : 7 . if the income of the person is rs . 40000 , then find his savings ? | "let the income and the expenditure of the person be rs . 8 x and rs . 7 x respectively . income , 8 x = 40000 = > x = 5000 savings = income - expenditure = 8 x - 7 x = x so , savings = rs . 5000 . answer : a" | a = 7 / 8
b = a * 40000
c = 40000 - b
|
a ) 220 , b ) 230 , c ) 500 , d ) 560 , e ) 1000 | e | divide(multiply(multiply(subtract(3.50, 3), const_1000), const_100), 50) | workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.50 lacs . how many workers were they ? | "n * 50 = ( 350000 - 300000 ) = 50000 n = 50000 / 50 = 1000 e" | a = 3 - 50
b = a * 1000
c = b * 100
d = c / 50
|
a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17 | c | divide(factorial(subtract(add(const_4, 01), const_1)), multiply(factorial(01), factorial(subtract(const_4, const_1)))) | how many positive integers less than 60 have a reminder 01 when divided by 4 ? | "1 also gives the remainder of 1 when divided by 4 . so , there are total of 15 numbers . answer : c ." | a = 4 + 1
b = a - 1
c = math.factorial(b)
d = math.factorial(1)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 1 , b ) 22 1 / 7 , c ) 2 , d ) 22 1 / 2 , e ) 3 | a | divide(subtract(divide(100, 10), divide(200, 25)), const_2) | a boat goes 100 km downstream in 10 hours , and 200 km upstream in 25 hours . the speed of the stream is ? | "100 - - - 10 ds = 10 ? - - - - 1 200 - - - - 30 us = 8 ? - - - - - 1 s = ( 10 - 8 ) / 2 = 1 kmph . answer : a" | a = 100 / 10
b = 200 / 25
c = a - b
d = c / 2
|
a ) 188 , b ) 216 , c ) 156 , d ) 680 , e ) 121 | d | divide(subtract(multiply(1000, divide(20, const_100)), 30), divide(25, const_100)) | if 25 % of x is 30 less than 20 % of 1000 , then x is ? | "25 % of x = x / 4 ; 20 % of 1000 = 20 / 100 * 1000 = 200 given that , x / 4 = 200 - 30 = > x / 4 = 170 = > x = 680 . answer : d" | a = 20 / 100
b = 1000 * a
c = b - 30
d = 25 / 100
e = c / d
|
a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50 | b | divide(360, multiply(multiply(const_3, const_3), const_2)) | mr . bhaskar is on tour and he has rs . 360 for his expenses . if he exceeds his tour by 4 days , he must cut down his daily expenses by rs . 3 . for how many days is mr . bhaskar on tour ? | if his tour is for x days and he is spending rs y per day , then xy = 360 x = 360 / y or y = 360 / x ( x + 4 ) * ( y - 3 ) = 360 or xy + 4 y - 3 x - 12 = 360 or 4 y - 3 x - 12 = 0 4 * 360 / x - 3 x - 12 = 0 solving it , we get x = 20 answer : b | a = 3 * 3
b = a * 2
c = 360 / b
|
a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14 | d | divide(multiply(3, 5), divide(multiply(add(3, 5), add(5, const_2)), const_2)) | a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability z that out of the two , one is white and one is blue ? | "the required probability z = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ." | a = 3 * 5
b = 3 + 5
c = 5 + 2
d = b * c
e = d / 2
f = a / e
|
a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none | e | multiply(multiply(multiply(5, 3), divide(1, const_100)), const_1000) | a boat having a length 5 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is | "solution volume of water displaced = ( 5 x 3 x 0.01 ) m 3 = 0.15 m 3 . mass of man = volume of water displaced × density of water = ( 0.15 × 1000 ) kg = 150 kg . answer e" | a = 5 * 3
b = 1 / 100
c = a * b
d = c * 1000
|
a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35 | c | add(subtract(75, multiply(3, 15)), 3) | a batsman in his 15 th inning makes a score of 75 and their by increasing his average by 3 . what is his average after the 15 th inning ? | "14 x + 75 = 15 ( x + 3 ) x = 30 + 3 = 33 answer : c" | a = 3 * 15
b = 75 - a
c = b + 3
|
a ) 1050 , b ) 2770 , c ) 1550 , d ) 5102 , e ) 5000 | a | subtract(multiply(const_10, 150), add(multiply(3, 100), multiply(1, 150))) | a man purchased 3 blankets @ rs . 100 each , 1 blankets @ rs . 150 each and two blankets at a certain rate which is now slipped off from his memory . but he remembers that the average price of the blankets was rs . 150 . find the unknown rate of two blankets ? | "10 * 150 = 1500 3 * 100 + 1 * 150 = 450 1500 – 450 = 1050 answer : a" | a = 10 * 150
b = 3 * 100
c = 1 * 150
d = b + c
e = a - d
|
a ) 41 , b ) 10 , c ) 31 , d ) 16 , e ) 17 | c | divide(60, divide(multiply(multiply(2, multiply(multiply(add(const_2, const_3), 2), const_3)), 2), const_60)) | five bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8,10 seconds respectively . in 60 minutes , how many times do they toll together ? | l . c . m of 2 , 4,6 , 8,10 is 240 . i . e after each 2 min they will toll together . so in 60 min they will toll 30 times . as they have initially tolled once , the answer will be 30 + 1 = 31 . answer : c | a = 2 + 3
b = a * 2
c = b * 3
d = 2 * c
e = d * 2
f = e / const_60
g = 60 / f
|
a ) 4069 , b ) 6048 , c ) 1000 , d ) 4096 , e ) 4060 | d | divide(power(power(4, const_2), const_3), power(4, const_3)) | a cube of side 4 meter length is cut into small cubes of side 25 cm each . how many such small cubes can be obtained ? | "along one edge , the number of small cubes that can be cut = 400 / 25 = 16 along each edge 16 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 16 * 16 * 16 = 4096 answer : d" | a = 4 ** 2
b = a ** 3
c = 4 ** 3
d = b / c
|
a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24 | a | divide(log(divide(multiply(const_3, const_10), add(const_4, const_1))), log(power(divide(multiply(const_2, const_10), add(const_4, const_1)), divide(const_1, 10)))) | on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ? | "24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ." | a = 3 * 10
b = 4 + 1
c = a / b
d = math.log(c)
e = 2 * 10
f = 4 + 1
g = e / f
h = 1 / 10
i = g ** h
j = math.log(i)
k = d / j
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.