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 ) โ 19 , b ) โ 11 , c ) โ 4 , d ) 4 , e ) 16 | a | add(negate(multiply(add(negate(3), 5), const_2)), multiply(negate(3), 5)) | if x * y = xy โ 2 ( x + y ) for all integers x and y , then 5 * ( โ 3 ) = | 5 * ( - 3 ) = 5 * ( - 3 ) - 2 ( 5 + ( - 3 ) ) = - 15 - 4 = - 19 option ( a ) | a = negate + (
b = a * 5
c = negate + (
|
a ) 50 , b ) 52 , c ) 53 , d ) 55 , e ) 56 | c | subtract(98, subtract(add(floor(divide(98, add(const_4, const_1))), floor(divide(98, const_4))), floor(divide(98, add(const_10, add(const_4, const_1)))))) | two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fourth widget , starting with the fourth , and steven inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by ... | "widgets inspected by lauren : ( ( 96 - 4 ) / 4 ) + 1 = 23 + 1 = 24 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 96 / 12 ) + 1 = 9 total : 24 + 32 - 9 = 45 hence , widgets not inspected : 98 - 45 = 53 option c" | a = 4 + 1
b = 98 / a
c = math.floor(b)
d = 98 / 4
e = math.floor(d)
f = c + e
g = 4 + 1
h = 10 + g
i = 98 / h
j = math.floor(i)
k = f - j
l = 98 - k
|
a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 9 % | e | multiply(2.2, const_4) | on the first of the year , james invested x dollars at proudstar bank in an account that yields 2.2 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays in... | "if the interest were compounded annually instead of quarterly then in one year the interest would be 2.2 * 4 = 8.8 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 8.8 % answer : e ." | a = 2 * 2
|
a ) 36 , b ) 35 , c ) 34 , d ) 38 , e ) 40 | c | multiply(add(subtract(9, const_1), 9), divide(22, add(subtract(6, const_1), 6))) | a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 9 : 00 , how many seconds elaps... | at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 9 strikes , there would be 8 intervals . according to the question , the time spent i... | a = 9 - 1
b = a + 9
c = 6 - 1
d = c + 6
e = 22 / d
f = b * e
|
a ) $ 645.56 , b ) $ 4121.60 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45 | b | subtract(multiply(power(add(divide(divide(4, const_100), 2), const_1), 4), 50000), 50000) | find the compound interest on $ 50000 in 2 years at 4 % per annum , the interest being compounded half - yearly ? | principle = $ 50000 rate = 2 % half yearly = 4 half years amount = 50000 * ( 1 + 2 / 100 ) ^ 4 = 50000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 54121.60 c . i . = 54121.60 - 50000 = $ 4121.60 answer is b | a = 4 / 100
b = a / 2
c = b + 1
d = c ** 4
e = d * 50000
f = e - 50000
|
a ) 4 hours , b ) 2 hours , c ) 3 hours , d ) 2 hours 24 minutes , e ) none | c | divide(subtract(multiply(60, 5), 240), subtract(60, 40)) | i travel the first part of my journey at 40 kmph and the second part at 60 kmph and cover the total distance of 240 km to my destination in 5 hours . how long did the first part of my journey last ? | "explanatory answer the total time of journey = 5 hours . let ' x ' hours be the time that i traveled at 40 kmph therefore , 5 - x hours would be time that i traveled at 60 kmph . hence , i would have covered x * 40 + ( 5 - x ) 60 kms in the 5 hours = 240 kms . solving , for x in the equation 40 x + ( 5 - x ) * 60 = 24... | a = 60 * 5
b = a - 240
c = 60 - 40
d = b / c
|
a ) 81 , b ) 63 , c ) 54 , d ) 36 , e ) 90 | d | divide(divide(factorial(divide(add(sqrt(add(multiply(const_4, multiply(36, const_2)), const_1)), const_1), const_2)), factorial(7)), const_2) | the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ? | nc 2 = 36 = > n * ( n - 1 ) / 2 = 36 by middle term factor and n can not be negative = > n = 9 nc 7 = 9 c 7 = 9 ! / 7 ! * ( 9 - 7 ) ! = 9 * 8 * 7 ! / 7 ! * 2 = 36 so , answer is d . | a = 36 * 2
b = 4 * a
c = b + 1
d = math.sqrt(c)
e = d + 1
f = e / 2
g = math.factorial(f)
h = math.factorial(7)
i = g / h
j = i / 2
|
a ) 17.5 litres , b ) 16.67 litres , c ) 17.67 litres , d ) 16.5 litres , e ) 16 litres | b | multiply(100, subtract(const_1, sqrt(divide(25, 36)))) | a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 25 % . what is the value of x ? | "in 100 l mixture we have 36 l milk and 64 l water . hence m and w are in the ratio of 9 : 16 . x l of solution has been removed . hence we have 36 - 9 / 25 x of milk and 64 - 16 / 25 x of water . for calculation simplicity multiply and divide 9 / 25 x by 4 we get 36 / 100 x since this procedure is repeated 2 times . t... | a = 25 / 36
b = math.sqrt(a)
c = 1 - b
d = 100 * c
|
a ) 2.25 , b ) 3.25 , c ) 4.25 , d ) 14 , e ) 6.25 | d | subtract(power(4, 2), 2) | x + ( 1 / x ) = 4 find x ^ 2 + ( 1 / x ^ 2 ) | "squaring on both sides ( x + 1 / x ) ^ 2 = 4 ^ 2 x ^ 2 + 1 / x ^ 2 = 16 - 2 x ^ 2 + 1 / x ^ 2 = 14 answer : d" | a = 4 ** 2
b = a - 2
|
a ) $ 972 , b ) $ 810 , c ) $ 915 , d ) $ 715 , e ) $ 795 | a | multiply(1200, power(subtract(const_1, divide(10, const_100)), 2)) | a present value of a machine is $ 1200 . its value depletion rate is 10 % per annum then find the machine value after 2 years ? | "p = $ 1200 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1200 * 9 / 10 * 9 / 10 = $ 972 answer is a" | a = 10 / 100
b = 1 - a
c = b ** 2
d = 1200 * c
|
a ) 3 cm , b ) 4 cm , c ) 6 cm , d ) 8 cm , e ) none | d | sqrt(divide(multiply(multiply(const_pi, multiply(16, divide(16, const_2))), const_2), multiply(const_pi, const_4))) | the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 16 cm each . the radius of the sphere is | "solution 4 รฎ r 2 = 2 รฎ 8 x 16 รข โก โ r 2 = ( 8 x 16 / 2 ) รข โก โ 64 รข โก โ r = 8 cm . answer d" | a = 16 / 2
b = 16 * a
c = math.pi * b
d = c * 2
e = math.pi * 4
f = d / e
g = math.sqrt(f)
|
a ) 15 , b ) 16 , c ) 18 , d ) 19 , e ) 17 | e | add(const_10, add(4, const_3)) | for what value of k will the two equations 2 x + 4 = 4 ( x - 2 ) and - x + k = 2 x - 1 have the same solution ? | solve the first equation 2 x + 4 = 4 ( x - 2 ) to obtain . x = 6 substitute x by 6 ( same solution ) in the second equation and solve for k . - 6 + k = 2 ( 6 ) - 1 solve for k . k = 17 correct answer e | a = 4 + 3
b = 10 + a
|
a ) 7297 , b ) 6425 , c ) 2871 , d ) 6725 , e ) 2981 | b | divide(7967, add(const_1, divide(24, const_100))) | the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 7967 for a computer table , then what was the cost price of the computer table ? | "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 7967 ( 100 / 124 ) = rs . 6425 . answer : b" | a = 24 / 100
b = 1 + a
c = 7967 / b
|
a ) 16 , b ) 18 , c ) 17 , d ) 12 , e ) 12 | d | subtract(const_100, subtract(add(const_100, 10), divide(multiply(add(const_100, 10), 20), const_100))) | a fair price shopkeeper takes 10 % profit on his goods . he lost 20 % goods during theft . his loss percent is ? | "suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 80 . s . p . of each item = rs . 1.10 total sale = 1.10 * 80 = rs . 88 hence , loss % = 12 / 100 * 100 = 12 % answer : d" | a = 100 + 10
b = 100 + 10
c = b * 20
d = c / 100
e = a - d
f = 100 - e
|
a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 80 kg , e ) none of these | d | multiply(multiply(multiply(4, 2), divide(1, const_100)), const_1000) | a boat having a length 4 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is : | "explanation : volume of water displaced = ( 4 x 2 x 0.01 ) m 3 = 0.08 m 3 . โด mass of man = volume of water displaced x density of water = ( 0.08 x 1000 ) kg = 80 kg . answer : d" | a = 4 * 2
b = 1 / 100
c = a * b
d = c * 1000
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | d | subtract(divide(add(divide(210, 6), divide(7, 4)), 6), const_2) | for an international mathematics olympiad , country d will send 6 delegates in total โ two will be supervisors and 4 will be contestants . there are 210 ways in which the 6 delegates can be chosen and there are 7 candidates competing for the 4 contestants โ places available . how many candidates are competing for the t... | option a wrong as 2 supervisor need to be selected . going by statement : 4 contestant chosen from 7 - - 7 c 4 = = 35 and total ways = 210 consider 2 supervisor will be chosen from : x people . so as per question : 35 * x = 210 x = 6 so by using options , option a already decided wrong . option b 2 c 2 will be 1 not 6 ... | a = 210 / 6
b = 7 / 4
c = a + b
d = c / 6
e = d - 2
|
a ) 15 % , b ) 16 % , c ) 25 % , d ) 30 % , e ) 40 % | b | divide(divide(multiply(40, 80), multiply(80, 80)), add(divide(multiply(40, 80), multiply(80, 80)), 8)) | a certain car can travel 40 minutes on a gallon of gasoline at 80 miles per hour . if the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end , then what percent of the tank was used to travel 80 miles at 80 mph ? | "total time for travelling 80 miles @ 60 mph = 80 / 80 = 1 hour = 60 minutes . given , the car uses 1 gallon for every 40 minutes of driving @ 80 mph . thus in 60 minutes it will use = 1.5 gallons . thus , full tank = 1.5 + 8 = 9.5 gallons - - - > 1.5 / 9.5 = 16 % of the fuel used . b is the correct answer ." | a = 40 * 80
b = 80 * 80
c = a / b
d = 40 * 80
e = 80 * 80
f = d / e
g = f + 8
h = c / g
|
['a ) 50', 'b ) 60', 'c ) 70', 'd ) 80', 'e ) 90'] | c | divide(700, divide(add(12, 8), const_2)) | the cross - section of a water channel is a trapezium in shape . if the channel is 12 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 700 square meters , what is the depth of the channel ( in meters ) ? | 1 / 2 * d * ( 12 + 8 ) = 700 d = 70 the answer is c . | a = 12 + 8
b = a / 2
c = 700 / b
|
a ) 6 , b ) 6.5 , c ) 7.25 , d ) 7.5 , e ) 8 | b | divide(subtract(292, multiply(3.2, 10)), 40) | cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 292 runs ? | "required run rate = 262 - ( 3.2 x 10 ) = 250 = 6.5 40 40 b" | a = 3 * 2
b = 292 - a
c = b / 40
|
a ) 17523 , b ) 2788 , c ) 1750 , d ) 2787 , e ) 29899 | c | divide(multiply(divide(divide(add(divide(multiply(4000, 10), const_100), divide(multiply(add(4000, divide(multiply(4000, 10), const_100)), 10), const_100)), 2), 3), const_100), 8) | simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on rs . 4000 for 2 years at 10 % per annum . the sum placed on simple interest is : | "explanation : c . i . = rs . [ 4000 * ( 1 + 10 / 100 ) ^ 2 - 4000 ] = rs . 840 sum = rs . ( 420 * 100 ) / 3 * 8 = rs . 1750 \ answer : c ) rs , 1750" | a = 4000 * 10
b = a / 100
c = 4000 * 10
d = c / 100
e = 4000 + d
f = e * 10
g = f / 100
h = b + g
i = h / 2
j = i / 3
k = j * 100
l = k / 8
|
a ) 26 , b ) 35 , c ) 39 , d ) 51 , e ) 55 | d | multiply(subtract(20, const_4), const_3) | the product z of two prime numbers is between 20 and 56 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 14 but less than 30 then what is z ? | "the smallest possible product is 51 which is 3 * 17 . all other products are too big . the answer is d ." | a = 20 - 4
b = a * 3
|
a ) 574580 , b ) 574200 , c ) 584250 , d ) 576460 , e ) none of these | b | multiply(divide(5800, 99), const_100) | 5800 * 99 | "explanation : 5800 * ( 100 - 1 ) = 580000 - 5800 = 574200 option b" | a = 5800 / 99
b = a * 100
|
a ) 8 , b ) 9 , c ) 10 , d ) 12 , e ) 15 | c | divide(add(115, 85), multiply(const_2, const_10)) | 3 numbers are such that the second is as much lesser than thr third as the first is lesser than the second . if the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number | explanation : its a bit funny sum . if you see the first sentence actually it saying that the numbers are in a . p . now as the first two numbers product is 85 so if you take factor 85 you get 5 and 17 . . now as per option 17 can not be the middle number so from intuition and seeing the option only 10 could be the mid... | a = 115 + 85
b = 2 * 10
c = a / b
|
a ) 280 , b ) 250 , c ) 260 , d ) 270 , e ) 300 | b | divide(200, subtract(const_1, divide(20, const_100))) | after decreasing 20 % in the price of an article costs rs . 200 . find the actual cost of an article ? | "cp * ( 80 / 100 ) = 200 cp = 2.5 * 100 = > cp = 250 answer : b" | a = 20 / 100
b = 1 - a
c = 200 / b
|
a ) 298 , b ) 237 , c ) 306 , d ) 876 , e ) 291 | c | subtract(subtract(480, divide(multiply(480, 15), const_100)), divide(multiply(subtract(480, divide(multiply(480, 15), const_100)), 25), const_100)) | the sale price sarees listed for rs . 480 after successive discount is 15 % and 25 % is ? | "480 * ( 85 / 100 ) * ( 75 / 100 ) = 306 answer : c" | a = 480 * 15
b = a / 100
c = 480 - b
d = 480 * 15
e = d / 100
f = 480 - e
g = f * 25
h = g / 100
i = c - h
|
a ) โ 7 , b ) 7 , c ) 10 , d ) 12 , e ) 16 | e | multiply(7, 4) | the sum of all solutions for x in the equation x ^ 2 โ 8 x + 21 = | x โ 4 | + 7 is equal to : | "x ^ 2 - 8 x + 14 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 10 = 0 x = 6,5 , 3,2 we test all 4 values in original equation , all ok . thus , sum = 6 + 5 + 3 + 2 = 16 ans ( e )" | a = 7 * 4
|
a ) rs . 40 , b ) rs . 70 , c ) rs . 90 , d ) rs . 100 , e ) rs . 120 | b | subtract(add(divide(600, 5), divide(910, 7)), divide(1620, 9)) | p , q and r together earn rs . 1620 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ? | "explanation : amount earned by p , q and r in 1 day = 1620 / 9 = 180 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + ... | a = 600 / 5
b = 910 / 7
c = a + b
d = 1620 / 9
e = c - d
|
a ) 351 , b ) 425 , c ) 748 , d ) 854 , e ) 945 | e | multiply(multiply(15, 3), 9) | a certain university will select 1 of 9 candidates eligible to fill a position in the mathematics department and 2 of 15 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidat... | "1 c 9 * 2 c 15 = 9 * 105 = 945 the answer is ( e )" | a = 15 * 3
b = a * 9
|
a ) 54 mins , b ) 55 mins , c ) 56 mins , d ) 57 mins , e ) 58 mins | a | add(45, multiply(divide(subtract(multiply(6, divide(45, const_60)), multiply(4, divide(45, const_60))), add(4, 6)), const_60)) | two motor cycles a & b are started from one point at 4 kmph & 6 kmph ; after 45 min b starts returning , at what time they will meet ? | distance covered by a in 45 mins = 3 kms . distance covered by b in 45 mins = 4.5 kms . distance between and b after 45 mins = 1.5 kms . relative speed when b is returning = 4 + 6 = 10 kmph distance between a and b is covered in 1.5 / 10 = 0.15 hrs = 9 mins so they will meet again after 54 mins from starting time . ans... | a = 45 / const_60
b = 6 * a
c = 45 / const_60
d = 4 * c
e = b - d
f = 4 + 6
g = e / f
h = g * const_60
i = 45 + h
|
a ) 20 , b ) 120 , c ) 360 , d ) 6000 , e ) 820 | d | divide(multiply(120, 1000), 20) | if 20 % of a number = 1000 , then 120 % of that number will be ? | "let the number x . then , 20 % of x = 1000 x = ( 1000 * 100 ) / 20 = 5000 120 % of x = ( 120 / 100 * 5000 ) = 6000 . answer : d" | a = 120 * 1000
b = a / 20
|
a ) 80 , b ) 90 , c ) 100 , d ) 120 , e ) 140 | c | divide(subtract(multiply(120, 35), multiply(120, 15)), subtract(39, 15)) | the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidates who passed the examination is ? | "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 โ 24 y = 4200 - 1800 โด y = 2400 / 24 = 100 c" | a = 120 * 35
b = 120 * 15
c = a - b
d = 39 - 15
e = c / d
|
a ) 288 , b ) 262 , c ) 72 , d ) 205 , e ) 164 | e | multiply(divide(32, 40), add(add(const_100, 65), 40)) | a certain sum of money is divided among a , b and c so that for each rs . a has , b has 65 paisa and c 40 paisa . if c ' s share is rs . 32 , find the sum of money ? | "a : b : c = 100 : 65 : 40 = 20 : 13 : 8 8 - - - - 32 41 - - - - ? = > rs . 164 answer : e" | a = 32 / 40
b = 100 + 65
c = b + 40
d = a * c
|
a ) 40 % , b ) 33 8 / 3 % , c ) 33 1 / 3 % , d ) 33 2 / 3 % , e ) 33 1 / 2 % | a | subtract(const_100, divide(multiply(945, const_100), 675)) | an article is bought for rs . 675 and sold for rs . 945 , find the gain percent ? | "675 - - - - 270 100 - - - - ? = > 40 % answer : a" | a = 945 * 100
b = a / 675
c = 100 - b
|
a ) 2.04 % , b ) 6.12 % , c ) 8 % , d ) 8.25 % , e ) 10 % | b | multiply(1.5, const_4) | on the first of the year , james invested x dollars at proudstar bank in an account that yields 1.5 % in interest every quarter year . at the end of the year , during which he made no additional deposits or withdrawals , he had y dollars in the account . if james had invested the same amount in an account which pays in... | "if the interest were compounded annually instead of quarterly then in one year the interest would be 1.5 * 4 = 6 % . now , since the interest is compounded quarterly then there would be interest earned on interest ( very small amount ) thus the actual interest would be a little bit more than 6 % . answer : b ." | a = 1 * 5
|
a ) 181 / 3 , b ) 182 / 3 , c ) 183 / 3 , d ) 184 / 3 , e ) 182 / 5 | b | add(add(multiply(divide(63, add(multiply(const_2, subtract(13, 5)), subtract(add(6, 15), const_2))), subtract(13, 5)), multiply(subtract(23, const_1), divide(63, add(multiply(const_2, subtract(13, 5)), subtract(add(6, 15), const_2))))), const_4) | a 1 , a 5 , a 13 ( terms of ap ) are in gp and a 6 + a 15 = 63 . find a 23 | a 1 a 5 = a 1 + 4 d a 13 = a 1 + 12 d now a 5 / a 1 = a 13 / a 5 - - - - > > a 1 = 4 d . . . . . . . . ( 1 ) given a 6 + a 15 = 63 - - - - > a 1 + 5 d + a 1 + 14 d = 63 - - - - > 2 a 1 + 19 d = 63 - - - - > 8 d + 19 d = 63 from ( 1 ) - - - - > d = 63 / 27 = 7 / 3 so a = 4 d = 4 * 7 / 3 = 28 / 3 from ( 1 ) a 23 = a 1 + ... | a = 13 - 5
b = 2 * a
c = 6 + 15
d = c - 2
e = b + d
f = 63 / e
g = 13 - 5
h = f * g
i = 23 - 1
j = 13 - 5
k = 2 * j
l = 6 + 15
m = l - 2
n = k + m
o = 63 / n
p = i * o
q = h + p
r = q + 4
|
a ) 5 / 24 , b ) 7 / 12 , c ) 7 / 24 , d ) 8 / 24 , e ) 9 / 24 | b | subtract(divide(3, 4), divide(3, 18)) | if 3 / p = 4 & 3 / q = 18 then p - q = ? | "p = 3 / 4 , q = 3 / 18 = > q = 1 / 6 therefore p - q = ( 3 / 4 ) - ( 1 / 6 ) = 7 / 12 answer : b" | a = 3 / 4
b = 3 / 18
c = a - b
|
a ) 11 , b ) 13 , c ) 15 , d ) data inadequate , e ) none | d | subtract(63, multiply(29, const_2)) | a number when divided by 899 gives a remainder 63 . if the same number is divided by 29 , the remainder will be | "sol . number = ( 31 x q ) + 29 . given data is inadequate . answer d" | a = 29 * 2
b = 63 - a
|
a ) 11 , b ) 17 , c ) 18 , d ) 101 , e ) 30 | e | sqrt(divide(2700, const_3)) | the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2700 sq m , then what is the breadth of the rectangular plot ? | "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2700 3 b 2 = 2700 b 2 = 900 = 30 ( b > 0 ) b = 30 m . answer : e" | a = 2700 / 3
b = math.sqrt(a)
|
a ) 334 , b ) 160 , c ) 387 , d ) 278 , e ) 112 | b | divide(multiply(sqrt(16), 120), sqrt(9)) | two trains a and b start simultaneously in the opposite direction from two points p and q and arrive at their destinations 16 and 9 hours respectively after their meeting each other . at what speed does the second train b travel if the first train travels at 120 km / h | answer : b ) 160 km / h | a = math.sqrt(16)
b = a * 120
c = math.sqrt(9)
d = b / c
|
a ) 12 days , b ) 10 days , c ) 9 days , d ) 8 days , e ) 11 days | a | inverse(subtract(inverse(3), add(inverse(6), inverse(12)))) | a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 12 days , how long will a woman take to complete the work ? | "explanation : ( 1 man + 1 woman + 1 boy ) โ s 1 day โ s work = 1 / 3 1 man โ s 1 day work = 1 / 6 1 boy โ s 1 day โ s work = 1 / 1 ( 1 man + 1 boy ) โ s 1 day โ s work = 1 / 6 + 1 / 12 = 1 / 4 therefore , 1 woman โ s 1 day โ s work = 1 / 3 โ 1 / 4 = 1 / 12 therefore , the woman alone can finish the work in 12 days . a... | a = 1/(3)
b = 1/(6)
c = 1/(12)
d = b + c
e = a - d
f = 1/(e)
|
a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.83 feet | e | divide(add(add(multiply(add(2, 6), 2), 6), 12), add(2, 6)) | carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 6 inches tall . carmen places her sculpture on a base that is 12 inches tall . how tall are the sculpture andbase together ? | "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 12 = 44 46 / 12 = 3.83 feet answer : e" | a = 2 + 6
b = a * 2
c = b + 6
d = c + 12
e = 2 + 6
f = d / e
|
a ) rs . 960 , b ) rs . 250 , c ) rs . 300 , d ) rs . 150 , e ) none of these | a | multiply(multiply(3, const_4), divide(340, add(3, 1))) | the cost of 3 pens and 5 pencils is rs . 340 . also the cost of one pen and one pencil is in the ratio of 4 : 1 respectively . what is the cost of one dozen pens ? | "explanation : let the cost of one pen is โ 4 x โ and pencil is โ x โ 3 x 4 x + 5 x = rs . 340 12 x + 5 x = rs . 340 x = 340 / 17 = 20 : . cost of 1 pen = 4 x = 4 x 20 = 80 : . cost of 12 pens , i . e . ( one dozen ) = 80 x 12 = rs . 960 answer : option a" | a = 3 * 4
b = 3 + 1
c = 340 / b
d = a * c
|
a ) $ 8250 , b ) $ 8350 , c ) $ 8650 , d ) $ 8450 , e ) $ 8500 | a | multiply(400, multiply(5.5, 3.75)) | the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 400 per sq . metre . | "area = 5.5 ร 3.75 sq . metre . cost for 1 sq . metre . = $ 400 hence , total cost = 5.5 ร 3.75 ร 400 = $ 8250 a" | a = 5 * 5
b = 400 * a
|
a ) 45 , b ) 56 , c ) 60.4 , d ) 85 , e ) 90 | c | add(multiply(power(2, multiply(divide(60, 10), subtract(const_1, 2))), 120), 60) | the temperature of a certain cup of coffee 10 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 ( 2 ^ - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 8... | "answer : b the temperature of coffee 10 minutes after it was poured ( 120 f ) will help in solving the constant โ a โ . 120 = 120 ( 2 ^ 10 a ) + 60 2 ^ - 1 = 2 ^ 10 a a = - 1 / 10 the temperature of coffee 80 minutes after it was poured is : f = 120 ( 2 ^ - 80 / 10 ) + 60 f = 120 * 1 / 256 + 60 f = 15 / 32 + 60 f = 19... | a = 60 / 10
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
|
a ) 35 , b ) 50 , c ) 100 , d ) 120 , e ) 150 | a | subtract(subtract(multiply(11, 20), multiply(5, 22)), multiply(5, 15)) | the average of 11 results is 20 . the average of first 5 of them is 15 and that of last 5 is 22 . find the 6 th result ? | "6 th result = sum of 11 results - sum of 10 results = 11 * 20 - 5 * 15 - 5 * 22 = 220 - 75 - 110 = 35 answer is a" | a = 11 * 20
b = 5 * 22
c = a - b
d = 5 * 15
e = c - d
|
a ) 0 , b ) 2 / 15 , c ) 2 / 5 , d ) 9 / 20 , e ) 5 / 6 | e | divide(5, 6) | 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 - 5 / 6 = | we need to determine the result of 1 / 3 + 1 / 2 - 5 / 6 + 1 / 5 + 1 / 4 - 9 / 20 let โ s add the given fractions in two groups . in the group of the first three fractions , notice that 1 / 3 and 1 / 2 share a common denominator of 6 with 5 / 6 . 1 / 2 + 1 / 3 = 3 / 6 + 2 / 6 = 5 / 6 thus , 5 / 6 โ 5 / 6 = 0 looking at... | a = 5 / 6
|
a ) 11 , b ) 15 , c ) 20 , d ) 38 , e ) 56 | a | multiply(power(const_2, 210), factorial(210)) | the product of three consecutive numbers is 210 . then the sum of the smallest two numbers is ? | "product of three numbers = 210 210 = 2 * 3 * 5 * 7 = 5 * 6 * 7 . so , the three numbers are 5 , 6 and 7 . and sum of smallest of these two = 5 + 6 = 11 . answer : option a" | a = 2 ** 210
b = math.factorial(210)
c = a * b
|
a ) 14 , b ) 52 , c ) 54 , d ) 180 , e ) 240 | b | add(add(divide(240, 40), divide(240, 40)), 40) | frank the fencemaker needs to fence in a rectangular yard . he fences in the entire yard , except for one full side of the yard , which equals 40 feet . the yard has an area of 240 square feet . how many feet offence does frank use ? | "area = length x breadth 240 = 40 x breadth so , breadth = 6 units fencing required is - breadth + breadth + length 6 + 6 + 40 = > 52 feet answer must be ( b ) 52" | a = 240 / 40
b = 240 / 40
c = a + b
d = c + 40
|
a ) 250 , b ) 277 , c ) 278 , d ) 200 , e ) 288 | a | divide(subtract(multiply(334, 25), multiply(71, const_100)), subtract(25, 20)) | the total of 334 of 20 paise and 25 paise make a sum of rs . 71 . the no of 20 paise coins is | "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 334 - x ) . 0.20 * ( x ) + 0.25 ( 334 - x ) = 71 = > x = 250 . . answer : a ) 250" | a = 334 * 25
b = 71 * 100
c = a - b
d = 25 - 20
e = c / d
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | a | power(2, 2) | the function f ( n ) is defined as the product of all the consecutive positive integers between 1 and n ^ 2 , inclusive , whereas the function g ( n ) is defined as the product of the squares of all the consecutive positive integers between 1 and n , inclusive . the exponent on 3 in the prime factorization of f ( 3 ) /... | "f ( 3 ) / g ( 3 ) = product ( 1 to 3 ^ 2 ) / 1.2 ^ 2.3 ^ 2 = 1 . 2.3 . 4.5 . 6.7 . 8.9 / 1 . 4.9 = 1 . 2.3 . ( 2 ^ 2 ) . 5 . ( 2.3 ) . 7 . ( 2 ^ 3 ) . 9 / 1 . ( 2 ^ 2 ) . 9 = 1 . ( 2 ^ 7 ) . 3.5 . 7.9 / 1 . ( 2 ^ 2 ) . 9 loof for 2 ^ 7 / 2 ^ 2 = 2 ^ 5 - - - - exponent 1 answer : a" | a = 2 ** 2
|
a ) rs 18221.76 , b ) rs 18123.30 , c ) rs 18123.40 , d ) rs 18123.50 , e ) none of these | a | subtract(multiply(multiply(multiply(const_4, const_100), const_100), power(add(const_1, divide(12, const_100)), 3)), multiply(multiply(const_4, const_100), const_100)) | what will be the compound interest on rs . 45000 after 3 years at the rate of 12 % per annum | "explanation : ( 45000 ร ( 1 + 12 / 100 ) 3 ) = > 45000 ร 28 / 25 ร 28 / 25 ร 28 / 25 = > 63221.76 so compound interest will be 63221.76 - 45000 = rs 18221.76 option a" | a = 4 * 100
b = a * 100
c = 12 / 100
d = 1 + c
e = d ** 3
f = b * e
g = 4 * 100
h = g * 100
i = f - h
|
a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 169 | e | add(floor(divide(337, 2)), const_1) | the guests at a football banquet consumed a total of 337 pounds of food . if no individual guest consumed more than 2 pounds of food , what is the minimum number of guests that could have attended the banquet ? | "to minimize one quantity maximize other . 168 * 2 ( max possible amount of food a guest could consume ) = 336 pounds , so there must be more than 168 guests , next integer is 169 . answer : e ." | a = 337 / 2
b = math.floor(a)
c = b + 1
|
a ) 2430 , b ) 2700 , c ) 3300 , d ) 4860 , e ) 5400 | b | multiply(divide(factorial(divide(10, 2)), const_2), divide(factorial(10), multiply(factorial(subtract(10, 2)), factorial(2)))) | a plant manager must assign 10 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 2 new workers . how many different ways can she assign the new workers ? | "my take selecting team of 2 out of 10 to assign to the shifts = 10 c 2 = 45 ways . now 2 out of 10 means total of 5 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 5 * 4 * 3 * 2 * 1 = 120 here alt and alt are the same : so 120 / 2 = 60 ways . total ways of selecting... | a = 10 / 2
b = math.factorial(a)
c = b / 2
d = math.factorial(10)
e = 10 - 2
f = math.factorial(e)
g = math.factorial(2)
h = f * g
i = d / h
j = c * i
|
a ) 1 / 18 , b ) 1 / 14 , c ) 5 / 18 , d ) 1 / 15 , e ) 1 / 16 | c | divide(choose(5, const_2), choose(add(5, 4), const_2)) | there are 5 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes | taking 2 red shoe the probability is 5 c 2 from 9 shoes probability of taking 2 red shoes is 5 c 2 / 9 c 2 = 5 / 18 answer : c | a = math.comb(5, 2)
b = 5 + 4
c = math.comb(b, 2)
d = a / c
|
a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250 | e | divide(200, divide(4, divide(const_10, const_2))) | to fill a tank , 200 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 4 - fifths of its present ? | let the capacity of 1 bucket = x . then , the capacity of tank = 200 x . new capacity of bucket = 4 / 5 x therefore , required number of buckets = ( 200 x ) / ( 4 x / 5 ) = ( 200 x ) x 5 / 4 x = 1000 / 4 = 250 answer is e . | a = 10 / 2
b = 4 / a
c = 200 / b
|
a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 9 , d ) 1 / 12 , e ) 1 / 13 | c | divide(const_2, choose(add(const_3, const_3), const_3)) | what is the probability of getting a sum 9 from two throw of a dice ? | "in two throws of die , n ( s ) = 36 let e = event of getting a sum 9 = { ( 3,6 ) , ( 4,5 ) , ( 5,4 ) , ( 6,3 ) } p ( e ) = 4 / 36 = 1 / 9 answer c 1 / 9" | a = 3 + 3
b = math.comb(a, 3)
c = 2 / b
|
a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32 | c | multiply(divide(7, 9), add(31, const_4)) | john was 31 years old when he married betty . they just celebrated their fifth wedding anniversary , and betty ' s age is now 7 / 9 of john ' s . how old is betty ? | "assume betty ' s age on marriage = x years . john ' s age on marriage = 31 john ' s age after 5 years = 36 years . betty ' s age after 5 years = x + 5 given : x + 5 = 7 / 9 ( 36 ) = 28 therefore betty ' s current age = 28 option c" | a = 7 / 9
b = 31 + 4
c = a * b
|
a ) a ) 1040 , b ) b ) 1145 , c ) c ) 1055 , d ) d ) 1060 , e ) e ) 1075 | b | add(multiply(8, 70), multiply(9, 65)) | tom purchased 8 kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 65 per kg . how much amount did he pay to the shopkeeper ? | "cost of 8 kg apples = 70 ร 8 = 560 . cost of 9 kg of mangoes = 65 ร 9 = 585 . total cost he has to pay = 560 + 585 = 1145 . b )" | a = 8 * 70
b = 9 * 65
c = a + b
|
a ) 2 km , b ) 4 km , c ) 5 km , d ) 2.25 km , e ) none of these | d | divide(divide(90, const_60), add(inverse(add(4, 2)), inverse(subtract(4, 2)))) | a man can row 4 kmph is still water . if the river is running at 2 kmph it takes 90 min to row to a place and back . how far is the place | explanation : speed in still water = 4 kmph speed of the stream = 2 kmph speed upstream = ( 4 - 2 ) = 2 kmph speed downstream = ( 4 + 2 ) = 6 kmph total time = 90 minutes = 90 โ 60 hour = 3 โ 2 hour let l be the distance . then ( l / 6 ) + ( l / 2 ) = 32 = > l + 3 l = 9 = > 4 l = 9 = > l = 9 โ 4 = 2.25 km . answer : op... | a = 90 / const_60
b = 4 + 2
c = 1/(b)
d = 4 - 2
e = 1/(d)
f = c + e
g = a / f
|
a ) 1 , b ) 2 , c ) 5 , d ) 6 , e ) 8 | a | subtract(multiply(add(floor(divide(929, 30)), const_1), 30), 929) | what is the least number should be added to 929 , so the sum of the number is completely divisible by 30 ? | "( 929 / 30 ) gives remainder 29 29 + 1 = 30 , so we need to add 1 answer : a" | a = 929 / 30
b = math.floor(a)
c = b + 1
d = c * 30
e = d - 929
|
a ) 288 , b ) 378 , c ) 342 , d ) 662 , e ) 262 | b | subtract(subtract(495, divide(multiply(495, 15), const_100)), divide(multiply(subtract(495, divide(multiply(495, 15), const_100)), 10), const_100)) | the sale price sarees listed for rs . 495 after successive discount is 15 % and 10 % is ? | "495 * ( 85 / 100 ) * ( 90 / 100 ) = 378 answer : b" | a = 495 * 15
b = a / 100
c = 495 - b
d = 495 * 15
e = d / 100
f = 495 - e
g = f * 10
h = g / 100
i = c - h
|
a ) 5 , b ) 7 , c ) 9 , d ) 8 , e ) 12 | d | add(divide(subtract(multiply(floor(divide(119, 11)), 11), multiply(add(floor(divide(29, 11)), const_1), 11)), 11), const_1) | how many numbers from 29 to 119 are exactly divisible by 11 ? | "29 / 11 = 2 and 119 / 11 = 10 = = > 10 - 2 = 8 numbers answer : d" | a = 119 / 11
b = math.floor(a)
c = b * 11
d = 29 / 11
e = math.floor(d)
f = e + 1
g = f * 11
h = c - g
i = h / 11
j = i + 1
|
a ) 58 , b ) 70 , c ) 63 , d ) 65 , e ) 72 | c | divide(multiply(subtract(multiply(divide(add(6, 2), 2), 4), 2), add(multiply(divide(add(6, 2), 2), subtract(4, 2)), const_1)), const_2) | the points a ( 0 , 0 ) , b ( 0 , 4 a - 2 ) and c ( 2 a + 1 , 2 a + 6 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ? | 1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 6 ) now 4 a - 2 = 2 a + 6 2 a = 8 . a = 4 therefore , a ( 0,0 ) ; b ( 0,14 ) ; c ( 9,14 ) 1 / 2 * 9 * 14 = 63 answer : c | a = 6 + 2
b = a / 2
c = b * 4
d = c - 2
e = 6 + 2
f = e / 2
g = 4 - 2
h = f * g
i = h + 1
j = d * i
k = j / 2
|
a ) 1050 , b ) 1220 , c ) 2500 , d ) 1060 , e ) 1110 | c | divide(900, subtract(const_1, divide(multiply(8, 8), const_100))) | a fellow borrowed a certain sum of money at 8 % per annum at simple interest and in 8 years the interest amounted to rs . 900 less than the sum lent . what was the sum lent ? | "p - 900 = ( p * 8 * 8 ) / 100 p = 2500 answer : c" | a = 8 * 8
b = a / 100
c = 1 - b
d = 900 / c
|
a ) 6 days , b ) 18 days , c ) 21 days , d ) 30 days , e ) 13 days | d | multiply(const_3, 3) | aarti can do a piece of work in 3 days . in how many days will she complete 10 time of work of same type ? | "we have the important relation , more work , more time ( days ) a piece of work can be done in 3 days . 10 times of work of same type can be done in 3 x 10 = 30 days answer d" | a = 3 * 3
|
a ) 457 km , b ) 444 km , c ) 547 km , d ) 600 km , e ) 453 km | d | add(multiply(divide(60, subtract(21, 29)), 29), multiply(divide(60, subtract(21, 29)), 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 29 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 = 29 + 21 = 50 t = 12 d = 50 * 12 = 600 answer : d" | a = 21 - 29
b = 60 / a
c = b * 29
d = 21 - 29
e = 60 / d
f = e * 21
g = c + f
|
a ) 20 % , b ) 40 % , c ) 50 % , d ) 53.85 % , e ) 100 % | d | subtract(const_100, divide(subtract(const_100, 40), add(const_1, divide(30, const_100)))) | when sold at a 40 % discount , a sweater nets the merchant a 30 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ? | "we should be careful about what are we measuring % on / what is the base . . let the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 30 % . . therefore the wholesale purchase cost = x . . . . 1.3 x = 60 or x = 46.15 . . . marked price was 100 so . . . so answer is 53.85 % . . d" | a = 100 - 40
b = 30 / 100
c = 1 + b
d = a / c
e = 100 - d
|
a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30 | d | multiply(subtract(9, 10), 10) | what is the greatest positive integer x such that 3 ^ x is a factor of 9 ^ 10 ? | "9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 the answer is d . 20" | a = 9 - 10
b = a * 10
|
a ) 1360 , b ) 1450 , c ) 1600 , d ) 947 , e ) none | d | divide(multiply(85, 78), subtract(85, 78)) | the simple interest and the true discount on a certain sum for a given time and at a given rate are rs . 85 and rs . 78 respectively . the sum is : | sol . sum = s . i . * t . d . / ( s . i ) - ( t . d . ) = 85 * 78 / ( 85 - 78 ) = rs . 947 . answer d | a = 85 * 78
b = 85 - 78
c = a / b
|
a ) 22 , b ) 60 , c ) 99 , d ) 88 , e ) 11 | b | multiply(divide(subtract(1080, 675), 675), const_100) | a cycle is bought for rs . 675 and sold for rs . 1080 , find the gain percent ? | "675 - - - - 180 100 - - - - ? = > 60 % answer : b" | a = 1080 - 675
b = a / 675
c = b * 100
|
a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) none of these | c | sqrt(multiply(add(4, divide(1, 2)), 8)) | two workers a and b are engaged to do a work . a working alone takes 8 hours more to complete the job than if both worked together . if b worked alone , he would need 4 1 / 2 hours more to complete the job than they both working together . what time would they take to do the work together ? | let a and be together take x hours to complete the work . then , a alone takes ( x + 8 ) hrs and b alone takes ( x + 9 / 2 ) hrs to complete the work . then , 1 / ( x + 8 ) + 1 / ( x + 9 / 2 ) = 1 / x , 1 / ( x + 8 ) + 2 / ( 2 x + 9 ) = 1 / x x ( 4 x + 25 ) = ( x + 8 ) ( 2 x + 9 ) 2 x ^ 2 = 72 , x ^ 2 = 36 , x = 6 corr... | a = 1 / 2
b = 4 + a
c = b * 8
d = math.sqrt(c)
|
a ) 28 , b ) 40 , c ) 68 , d ) 88 , e ) 78 | a | add(multiply(divide(80, 20), const_2), 20) | a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 80 sq . feet , how many feet of fencing will be required ? | "we have : l = 20 ft and lb = 80 sq . ft . so , b = 4 ft . length of fencing = ( l + 2 b ) = ( 20 + 8 ) ft = 28 ft . answer : a" | a = 80 / 20
b = a * 2
c = b + 20
|
a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) 15 | a | divide(const_1, add(divide(const_1, 6), divide(const_1, 12))) | a can do a work in 6 days . b can do in 12 days . if both a & b are working together in how many days they can finish the work ? | 1 day work of a = 1 / 6 1 day work of b = 1 / 12 1 day work of a & b = 1 / 6 + 1 / 12 = 1 / 4 a & b finish the work in 4 days answer is a | a = 1 / 6
b = 1 / 12
c = a + b
d = 1 / c
|
a ) 8 , b ) 10 , c ) 12 , d ) 12 , e ) 16 | a | lcm(2, 3) | if 2 and 3 are positive integers , then 2 * 3 + 2 is | answer : a | a = math.lcm(2, 3)
|
a ) 230 m , b ) 240 m , c ) 260 m , d ) 320 m , e ) 330 m | c | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 240) | a 240 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ? | "relative speed = ( 120 + 80 ) km / hr = ( 200 x ( 5 / 18 ) ) m / sec = ( 500 / 9 ) m / sec . let the length of the other train be x metres . then , ( x + 240 ) / 9 = 500 / 9 x + 240 = 500 x = 260 . c" | a = 120 + 80
b = a * const_0_2778
c = b * 9
d = c - 240
|
a ) 10 % , b ) 25 % , c ) 64 % , d ) 42 % , e ) 17 % | b | multiply(divide(subtract(600, add(add(add(add(25, 70), 100), 110), 145)), 600), const_100) | kavi had a stock of 600 bags in his bookshop . he sold 25 on monday , 70 on tuesday , 100 on wednesday , 110 on thursday and 145 on friday . what percentage of the bags were not sold ? | let n be the total number of bags sold . hence n = 25 + 70 + 100 + 110 + 145 = 450 let m be the bags not sold m = 600 - n = 600 - 450 = 150 percentage bags not sold / total number of bags = 150 / 600 = 0.25 = 25 % correct answer b | a = 25 + 70
b = a + 100
c = b + 110
d = c + 145
e = 600 - d
f = e / 600
g = f * 100
|
a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9 | d | divide(subtract(divide(85, 2), divide(45, 2)), const_2) | a man rows his boat 85 km downstream and 45 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ? | "speed downstream = d / t = 85 / ( 2 1 / 2 ) = 34 kmph speed upstream = d / t = 45 / ( 2 1 / 2 ) = 18 kmph the speed of the stream = ( 34 - 18 ) / 2 = 8 kmph answer : d" | a = 85 / 2
b = 45 / 2
c = a - b
d = c / 2
|
a ) 1 / 7 , b ) 3 , c ) 12 / 3 , d ) 6 / 6 , e ) 1 | a | divide(multiply(1, const_1), subtract(multiply(const_2, const_4), 1)) | if f ( x ) = 1 / x and x is a natural number , what can not be the answer for f ( f ( x ) ) ? | answer a is impossible because the invers of 1 / x is x , and the only way to have something other than a natural number is to input something other than a natural number . with the specification that only natural numbers may be used 1 / 7 is not a possibility for f ( f ( x ) ) | a = 1 * 1
b = 2 * 4
c = b - 1
d = a / c
|
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4 | e | subtract(add(const_2, const_3), const_2) | the product of the squares of two positive integers is 900 . how many pairs of positive integers satisfy this condition ? | "ans : e - 4 pairs ( x ห 2 ) ( y ห 2 ) = 900 [ square root both sides ] xy = 30 20 = 1 x 30 , 3 x 10 , 6 x 5 , 5 x 6 , 10 x 3 , 30 x 1 , 15 x 2 , 2 x 15 cancel the repeats this leaves us with exactly 4 options . hence , e" | a = 2 + 3
b = a - 2
|
a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4 | c | divide(divide(divide(lcm(23, 57), 57), const_4), const_4) | what is the least value of x . so that 23 x 57 is divisible by 3 . | "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 3 + x + 5 + 7 = 17 + x least value of x may be 1 therefore 17 + 1 = 18 is divisible by 3 . answer : option c" | a = math.lcm(23, 57)
b = a / 57
c = b / 4
d = c / 4
|
a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these | d | divide(divide(const_1, multiply(10, 4)), divide(const_1, multiply(4, const_10))) | six women can do a work in 10 days . ten men can complete the same work in 4 days . what is the ratio between the capacity of a man and a woman ? | "explanation : ( 6 รฃ โ 10 ) women can complete the work in 1 day . รข ห ยด 1 woman ' s 1 day ' s work = 1 / 60 ( 10 รฃ โ 4 ) men can complete the work in 1 day . รข ห ยด 1 man ' s 1 day ' s work = 1 / 40 so , required ratio = 1 / 60 : 1 / 40 = 3 : 2 answer : d" | a = 10 * 4
b = 1 / a
c = 4 * 10
d = 1 / c
e = b / d
|
a ) 32 , b ) 42 , c ) 52 , d ) 62 , e ) 72 | c | subtract(subtract(subtract(add(multiply(5, 28), 232), multiply(5, 28)), multiply(5, 28)), multiply(const_4, const_10)) | if 28 less than 5 times a certain number is 232 . what is the number ? | 5 x โ 28 subtraction is built backwards , multiply the unknown by 5 5 x โ 28 = 232 is translates to equals + 28 + 28 add 28 to both sides 5 x = 260 the variable ismultiplied by 5 5 5 divide both sides by 5 x = 52 the number is 52 . correct answer c | a = 5 * 28
b = a + 232
c = 5 * 28
d = b - c
e = 5 * 28
f = d - e
g = 4 * 10
h = f - g
|
a ) 1217 , b ) 1348.2 , c ) 1210 , d ) 1212 , e ) 1312 | b | multiply(subtract(power(23, const_2), power(const_10, const_2)), divide(add(multiply(const_10, const_2), const_2), add(const_4, const_3))) | a rope of which a calf is tied is increased from 10 m to 23 m , how much additional grassy ground shall it graze ? | ฯ ( 232 โ 102 ) = 1348.2 answer : b | a = 23 ** 2
b = 10 ** 2
c = a - b
d = 10 * 2
e = d + 2
f = 4 + 3
g = e / f
h = c * g
|
a ) 50 kg , b ) 60 kg , c ) 70 kg , d ) 80 kg , e ) none of these | b | multiply(multiply(multiply(3, 2), divide(1, const_100)), const_1000) | a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets into it . the mass of the man is : | explanation : in this type of question , first we will calculate the volume of water displaces then will multiply with the density of water . volume of water displaced = 3 * 2 * 0.01 = 0.06 m cube mass of man = volume of water displaced * density of water = 0.06 * 1000 = 60 kg option b | a = 3 * 2
b = 1 / 100
c = a * b
d = c * 1000
|
a ) 60 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 % | a | multiply(multiply(power(divide(6, 10), const_2), divide(10, 6)), const_100) | tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 6 meters , and the interior of tank b has a height of 6 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ? | "the radius of tank a is 6 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 36 / ( 4 * pi ^ 2 ) = 180 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 6 * pi * 100 / ( 4 * pi ^ 2 ) = 300 / ( 2 * pi ) tank a / tank b = 180 / 300 = 6 / 10 = 60 % the answer is a ." | a = 6 / 10
b = a ** 2
c = 10 / 6
d = b * c
e = d * 100
|
a ) 12 % , b ) 14 % , c ) 16 % , d ) 20 % , e ) 23 % | e | subtract(const_100, divide(multiply(add(const_100, 10), subtract(const_100, 30)), const_100)) | the tax on a commodity is diminished by 30 % but its consumption is increased by 10 % . find the decrease percent in the revenue derived from it ? | "explanation : 100 * 100 = 10000 70 * 110 = 7700 10000 - - - - - - - 2300 100 - - - - - - - ? = 23 % e )" | a = 100 + 10
b = 100 - 30
c = a * b
d = c / 100
e = 100 - d
|
a ) 3.6 sec , b ) 18 sec , c ) 36 sec , d ) 39 sec , e ) none of these | d | multiply(multiply(divide(divide(add(270, 120), const_1000), subtract(45, 9)), const_60), const_60) | a jogger running at 9 kmph along side a railway track is 270 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? | "speed of train relative to jogger = ( 45 โ 9 ) km / h = 36 km / h = ( 36 ร 5 โ 18 ) m / sec = 10 m / sec distance to be covered = ( 270 + 120 ) m = 390 m . โด time taken = ( 390 โ 10 ) sec = 39 sec . answer d" | a = 270 + 120
b = a / 1000
c = 45 - 9
d = b / c
e = d * const_60
f = e * const_60
|
a ) 20 , b ) 87 , c ) 266 , d ) 288 , e ) 11 | a | subtract(divide(multiply(add(39, const_1), add(add(39, const_1), const_1)), const_2), 800) | some consecutive natural numbers , starting with 1 , are written on the board . now , one of the numbers was erased and the average of the remaining numbers is 800 / 39 . find the number which was erased . | we know that average of n consecutive numbes average = n ร ( n + 1 ) 2 n = ( n + 1 ) 2 n ร ( n + 1 ) 2 n = ( n + 1 ) 2 if the given n is sufficiently large , the average does not change much even though we exclude one or two numbers from it . so the approximate number of observations is almost double to the average ( r... | a = 39 + 1
b = 39 + 1
c = b + 1
d = a * c
e = d / 2
f = e - 800
|
a ) 50 cm 2 , b ) 100 cm 2 , c ) 150 cm 2 , d ) 200 cm 2 , e ) 250 cm 2 | a | multiply(multiply(divide(const_1, const_2), add(3, 7)), 10) | find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm ? | "1 / 2 * 10 ( 7 + 3 ) = 50 cm 2 answer : a" | a = 1 / 2
b = 3 + 7
c = a * b
d = c * 10
|
a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50 | d | divide(rectangle_area(15, 24), 8) | carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 15 inches by 24 inches and jordan ' s rectangle is 8 inches long , how wide is jordan ' s rectangle , in inches ? | "area of first rectangle is 15 * 24 = 360 hence area of second would be 8 x = 360 x x = 45 answer is d" | a = rectangle_area / (
|
a ) 2327 , b ) 2757 , c ) 3147 , d ) 3587 , e ) 3997 | c | add(lcm(lcm(18, 70), lcm(25, 21)), 3) | what is the smallest number which when increased by 3 is divisible by 18 , 70 , 25 and 21 ? | "when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is c ." | a = math.lcm(18, 70)
b = math.lcm(25, 21)
c = math.lcm(a, b)
d = c + 3
|
a ) 2 m , b ) 3 m , c ) 4 m , d ) 5 m , e ) 1.5 m | c | divide(multiply(10, 10), subtract(rectangle_area(10, 10), rectangle_area(5, 10))) | the dimensions of a field are 10 m by 10 m . a pit 10 m long , 5 m wide and 4 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ? | "the volume of the earth removed is 10 * 5 * 4 = 200 m ^ 3 . the remaining area of the field is 10 * 10 - 10 * 5 = 50 m ^ 2 . 200 m ^ 3 of the earth evenly spread over the area of 50 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 200 / 50 = 4 m . answer : c" | a = 10 * 10
b = rectangle_area - (
c = a / b
|
a ) 25.5 % , b ) 21.5 % , c ) 17.5 % , d ) 13.5 % , e ) 9.5 % | c | add(subtract(subtract(const_100, 60), multiply(divide(3, 4), subtract(const_100, 60))), subtract(60, multiply(divide(7, 8), 60))) | in a survey of parents , exactly 7 / 8 of the mothers and 3 / 4 of the fathers held full - time jobs . if 60 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ? | "fathers without full - time jobs are 1 / 4 * 2 / 5 = 2 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 8 * 3 / 5 = 3 / 40 of all the parents surveyed . the percent of parents without full - time jobs is 2 / 20 + 3 / 40 = 7 / 40 = 17.5 % the answer is c ." | a = 100 - 60
b = 3 / 4
c = 100 - 60
d = b * c
e = a - d
f = 7 / 8
g = f * 60
h = 60 - g
i = e + h
|
a ) 6 hours , b ) 5 hours , c ) 5.5 hours , d ) 8 hours , e ) none | c | divide(add(296, 6.5), add(divide(296, 8), 18)) | a truck covers a distance of 296 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 6.5 km more than that travelled by the truck ? | explanation : speed of the truck = distance / time = 296 / 8 = 37 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 37 + 18 ) = 55 kmph distance travelled by car = 296 + 6.5 = 302.5 km time taken by car = distance / speed = 302.5 / 55 = 5.5 hours . answer โ c | a = 296 + 6
b = 296 / 8
c = b + 18
d = a / c
|
a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10 | e | divide(choose(12, 3), choose(add(12, 12), 3)) | a bag contains 12 red jellybeans and 12 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ? | "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total o... | a = math.comb(12, 3)
b = 12 + 12
c = math.comb(b, 3)
d = a / c
|
a ) 7500 , b ) 20000 , c ) 2775 , d ) 5496 , e ) 6851 | b | divide(16000, subtract(subtract(const_1, divide(10, const_100)), divide(10, const_100))) | a candidate got 10 % of the votes polled and he lost to his rival by 16000 votes . how many votes were cast ? | "10 % - - - - - - - - - - - l 90 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 80 % - - - - - - - - - - 16000 100 % - - - - - - - - - ? = > 20000 answer : b" | a = 10 / 100
b = 1 - a
c = 10 / 100
d = b - c
e = 16000 / d
|
a ) 3.4 km , b ) 2.9 km , c ) 2.4 km , d ) 2.6 km , e ) 2.8 km | c | multiply(divide(multiply(8, 9), subtract(9, 8)), divide(add(14, 16), const_60)) | if i walk at 8 km / h , i miss the bus by 14 minutes . if i walk at 9 km / h , i reach 16 minutes before the arrival of the bus . how far i walk to reach the bus stand ? | d = product of speed difference of time / difference of speed d = 8 x 9 / 60 [ 14 รข ห โ ( รข ห โ 16 ) / 9 - 8 ] [ here , รข โฌ โ ve sign indicates before the schedule time ] รข โก โ d = 2.4 km answer c | a = 8 * 9
b = 9 - 8
c = a / b
d = 14 + 16
e = d / const_60
f = c * e
|
['a ) l = 2 , w = 9', 'b ) l = 5 , w = 8', 'c ) l = 6 , w = 4', 'd ) l = 1 , w = 7', 'e ) l = 2 , w = 3'] | c | add(divide(subtract(divide(20, const_2), 2), const_2), 2) | the length of a rectangle is 2 cm more than the width of the rectangle . the perimeter of the rectangle is 20 cm . find the length and the width of the rectangle . | let length l = x , width w = x โ 2 and perimeter = p โด p = 2 l + 2 w = 2 x + 2 ( x โ 2 ) 20 = 2 x + 2 x โ 4 4 x = 24 x = 6 l = 6 cm and w = l โ 2 = 4 cm answer is c . | a = 20 / 2
b = a - 2
c = b / 2
d = c + 2
|
a ) 24 , b ) 55 , c ) 77 , d ) 99 , e ) 01 | a | multiply(divide(subtract(10, const_1), subtract(4, const_1)), 8) | a certain sum becomes 4 times itself at simple interest in 8 years . in how many years does it become 10 times itself ? | let the sum be rs . x , then it becomes rs . 4 x in eight years rs . 3 x is the interest on x for eight years . r = ( 100 * 3 x ) / ( x * 8 ) = 300 / 8 % if the sum becomes ten times itself , then interest is 9 x . the required time period = ( 100 * 9 x ) / ( x * 300 / 8 ) = ( 100 * 9 x * 8 ) / ( x * 300 ) = 24 years .... | a = 10 - 1
b = 4 - 1
c = a / b
d = c * 8
|
a ) 290 / 289 , b ) 26 / 25 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these | b | add(power(divide(const_1, const_1), const_2), power(divide(const_1, 5), const_2)) | product of two natural numbers is 5 . then , the sum of reciprocals of their squares is | "explanation : if the numbers are a , b , then ab = 5 , as 17 is a prime number , so a = 1 , b = 5 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 5 ( 2 ) = 26 / 25 option b" | a = 1 / 1
b = a ** 2
c = 1 / 5
d = c ** 2
e = b + d
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.