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 ) 4 , b ) 9 , c ) 15 , d ) 48 , e ) 33 | e | subtract(add(power(6, 2), multiply(6, 2)), add(power(3, const_2), multiply(3, 2))) | the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 6 seconds than it was moving after 3 seconds ? | given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 6 ) = 6 ^ 2 + 2 * 6 = 48 therefore z ( 7 ) - z ( 3 ) = 48 - 15 = 33 km / hr option e | a = 6 ** 2
b = 6 * 2
c = a + b
d = 3 ** 2
e = 3 * 2
f = d + e
g = c - f
|
a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9 | c | divide(subtract(subtract(subtract(subtract(subtract(69, 4), 4), 4), 4), 4), 7) | notebooks are sold in packages of 4 or 7 only . if wilson bought 69 notebooks exactly , what could be the number of large packs wilson bought ? | let number of packs of four = f let number of packs of seven = s 4 f + 7 s = 69 now , we need to test for values of s . since sum 69 is odd and 4 f will always be even , e ca n ' t be even . now , we can test for values e = 3 , 7 and 9 4 * 5 + 7 * 7 = 20 + 49 = 69 answer c | a = 69 - 4
b = a - 4
c = b - 4
d = c - 4
e = d - 4
f = e / 7
|
a ) 228 , b ) 278 , c ) 289 , d ) 500 , e ) 821 | d | divide(340, subtract(const_1, divide(multiply(4, 8), const_100))) | a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 340 less than the sum lent . what was the sum lent ? | "p - 340 = ( p * 4 * 8 ) / 100 p = 500 answer : d" | a = 4 * 8
b = a / 100
c = 1 - b
d = 340 / c
|
a ) 15 / 40 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7 | a | divide(divide(divide(20, const_100), divide(40, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(40, const_100))) | a total of 40 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ] | "let ' take the number of geese to be 100 . male = 40 . female = 60 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 20 = 4 geese ( males ) and now we know out of the total 20 geese , 4 are male , then 16 have to be female . now the ratio part , male geese ratios = 4 / 40 = 1 / 10 . - a female geese ratios = 16 / 60 = 4 / 15 - b cross multiply equations a and b and you get = 15 / 40 . ans a" | a = 20 / 100
b = 40 / 100
c = a / b
d = 2 * 4
e = d * 10
f = e / 100
g = 40 / 100
h = f / g
i = c / h
|
a ) 8 , b ) 10 , c ) 15 , d ) 17 , e ) 21 | b | divide(subtract(multiply(25, 30), 425), add(25, 7.5)) | a contractor isengaged for 30 days on the condition that he receives rs . 25 for eachday he works & fined rs . 7.50 for each day is absent . he gets rs . 425 in all . for how many days was heabsent ? | 30 * 25 = 750 425 - - - - - - - - - - - 325 25 + 7.50 = 32.5 325 / 32.5 = b | a = 25 * 30
b = a - 425
c = 25 + 7
d = b / c
|
a ) 1800 men , b ) 3900 men , c ) 600 men , d ) 3800 men , e ) 900 men | c | subtract(divide(subtract(multiply(2000, 54), multiply(2000, 15)), 30), 2000) | a garrison of 2000 men has provisions for 54 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 30 days more . what is the reinforcement ? | "2000 - - - - 54 2000 - - - - 39 x - - - - - 20 x * 30 = 2000 * 39 x = 2600 2000 - - - - - - - 600 answer : c" | a = 2000 * 54
b = 2000 * 15
c = a - b
d = c / 30
e = d - 2000
|
a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10 | c | add(divide(add(multiply(5, 4), subtract(20, 4)), subtract(5, const_1)), 20) | the ages of two person differ by 20 years . if 4 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively | "let their ages be x and ( x + 20 ) years . then , 5 ( x - 4 ) = ( x + 20 - 4 ) = > 4 x = 36 = > x = 9 their present ages are 29 years and 9 year . answer : c" | a = 5 * 4
b = 20 - 4
c = a + b
d = 5 - 1
e = c / d
f = e + 20
|
a ) 10 , b ) 6 , c ) 4 , d ) 7 , e ) 5 | d | divide(multiply(28, 10), 40) | 28 machines can do a work in 10 days . how many machines are needed to complete the work in 40 days ? | "required number of machines = 28 * 10 / 40 = 7 answer is d" | a = 28 * 10
b = a / 40
|
a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 % | c | multiply(divide(subtract(1400, add(200, 800)), add(200, 800)), const_100) | sandy buys an old scooter for $ 800 and spends $ 200 on its repairs . if sandy sells the scooter for $ 1400 , what is the gain percent ? | "selling price / total cost = 1400 / 1000 = 1.4 the gain percent is 40 % . the answer is c ." | a = 200 + 800
b = 1400 - a
c = 200 + 800
d = b / c
e = d * 100
|
a ) 18 seconds , b ) 26 seconds , c ) 36 seconds , d ) 16 seconds , e ) 46 seconds | c | divide(add(240, 120), multiply(subtract(45, 9), const_0_2778)) | a jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ? | total distance ( d ) = 240 + 120 = 360 meter relative speed ( s ) = 45 - 9 = 36 kmph = 36 * 5 / 18 = 10 mps d = s * t 360 = 10 * t t = 36 seconds answer : c | a = 240 + 120
b = 45 - 9
c = b * const_0_2778
d = a / c
|
a ) 336 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 544 km . | a | multiply(multiply(divide(multiply(15, 24), add(24, 21)), 21), const_2) | a woman complete a journey in 15 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km . | "0.5 x / 21 + 0.5 x / 24 = 15 - - > x / 21 + x / 24 = 30 - - > x = 336 km . a" | a = 15 * 24
b = 24 + 21
c = a / b
d = c * 21
e = d * 2
|
a ) 80 , b ) 100 , c ) 120 , d ) 125 , e ) 135 | d | power(add(3, const_2), 3) | how many 3 - digit integers exist such that all their digits are odd ? | so last digit can be filled in 5 ways - 1 , 3,5 , 7,9 there are 5 possibilities . the answer is 5 ∗ 5 ∗ 5 = 125 the correct answer is d | a = 3 + 2
b = a ** 3
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | divide(subtract(const_1000, const_100), subtract(400, subtract(400, 150))) | matt gets a $ 1,300 commission on a big sale . this commission alone raises his average commission by $ 150 . if matt ' s new average commission is $ 400 , how many sales has matt made ? | "let , average commission = x no . of items sold = y total commission = xy new commission = xy + 1300 new average = ( xy + 1300 ) / ( y + 1 ) = 150 + x i . e . ( xy + 1300 ) = ( y + 1 ) * ( 150 + x ) i . e . ( xy + 1300 ) = ( xy + x + 150 y + 150 ) i . e . ( 1150 ) = ( x + 150 y ) new commission = 400 = 150 + x i . e . x = 250 i . e . y = 6 new sales = y + 1 = 7 answer : option d" | a = 1000 - 100
b = 400 - 150
c = 400 - b
d = a / c
|
a ) 140 meter , b ) 145 meter , c ) 150 meter , d ) 155 meter , e ) 160 meter | c | multiply(100, subtract(const_2, const_1)) | a train speeds past a pole in 15 seconds and a platform 100 meter long in 25 seconds . what is length of the train ? | "explanation : let the length of the train is x meter and speed of the train is y meter / second then x / y = 15 [ because distance / speed = time ] = > y = 15 / x x + 100 / 25 = x / 15 x = 150 meters so length of the train is 150 meters answer is c" | a = 2 - 1
b = 100 * a
|
a ) 0.03375 , b ) 0.03372 , c ) 0.0337 , d ) 0.03377 , e ) 0.03376 | a | divide(multiply(25, 30), 45) | 25 % of 30 % of 45 % is equal to ? | "( 25 / 100 ) * ( 30 / 100 ) * ( 45 / 100 ) 1 / 4 * 3 / 10 * 9 / 20 27 / 800 = 0.03375 answer : a" | a = 25 * 30
b = a / 45
|
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28 | a | multiply(add(divide(20, const_60), divide(20, const_60)), divide(multiply(12, 9), subtract(12, 9))) | a student reached his school late by 20 mins by travelling at a speed of 9 kmph . if he had travelled at a speed of 12 kmph , he would have reached his school 20 mins early . what is the distance between house and school ? | distance = distance either student reaches school before time or after time 9 ( t + 20 / 60 ) = 12 ( t - 20 / 60 ) i . e 9 ( t + 1 / 3 ) = 12 ( t - 1 / 3 ) 9 ( 3 t + 1 ) = 12 ( 3 t - 1 ) t = 7 / 3 put t value in any of distance equation put t = 7 / 3 in 9 ( t + 1 / 3 ) we get 24 km answer : a | a = 20 / const_60
b = 20 / const_60
c = a + b
d = 12 * 9
e = 12 - 9
f = d / e
g = c * f
|
['a ) 0.125', 'b ) 0.25', 'c ) 0.5', 'd ) 0.75', 'e ) not enough information to determine the rate'] | e | divide(840, 0.5) | the volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool . if the surface level of the water is rising at the rate of 0.5 meters per minute , what is the rate w , in cubic meters per minutes , at which the water is flowing into the swimming pool ? | the correct answer is e . there are not enough info to answer the question . a 840 cubic meters rectangle is built from : height * length * width . from the question we know the volume of the pool and the filling rate . a pool can have a height of 10 * width 8.4 * length 10 and have a volume of 840 cubic meters , and it can have a height of 1 meter , width of 100 meters and length of 8.4 . in both cases the pool will fill up in a different rate = e | a = 840 / 0
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a ) 49 , b ) 68 , c ) 60 , d ) 57 , e ) 70 | e | add(add(power(add(add(divide(subtract(subtract(292, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(292, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(292, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(292, const_10), const_2), const_4), const_2), const_2))) | the sum of four consecutive even numbers is 292 . what would be the smallest number ? | "e 70 let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 292 = > x = 37 smallest number is : 2 ( x - 2 ) = 70 ." | a = 292 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 292 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 292 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 292 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
|
a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22 | c | subtract(add(13, 8), const_1) | a student is ranked 13 th from right and 8 th from left . how many are there ? | "13 th from right means = x + 12 8 th from left means = 7 + x total = 12 + 7 + 1 = 20 answer : c" | a = 13 + 8
b = a - 1
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a ) 1728 , b ) 2160 , c ) 2240 , d ) 2268 , e ) 2520 | d | multiply(multiply(multiply(multiply(const_2, const_4), multiply(const_2, const_4)), add(const_4, const_3)), add(const_1, const_4)) | how many 4 - digit odd numbers do not use any digit more than once ? | let a 4 - digit number be represented by abcd here a can have any value between 1 to 9 - so total 9 b can have any value between 0 to 9 , but not a - so total 9 c can have any value between 0 to 9 , but not a or b - so total 8 d can have any value between 0 to 9 , but not a , b or c - so total 7 no . of all possible 4 - digit nos ( without repeating any digit ) = 9 * 9 * 8 * 7 = 4536 half of these would be odd . therefor , no . of odd possible 4 - digit nos ( without repeating any digit ) = 4536 / 2 = 2268 answer should be d . | a = 2 * 4
b = 2 * 4
c = a * b
d = 4 + 3
e = c * d
f = 1 + 4
g = e * f
|
a ) $ 14,000 , b ) $ 15,000 , c ) $ 42,000 , d ) $ 46,000 , e ) $ 50,000 | a | divide(subtract(add(12000, 8000), multiply(2000, 3)), const_1000) | revenues were recorded for store a and store b over a period of 3 months . in the first month , store a ' s revenues were $ 12000 higher than store b ' s revenues . in the second month , store a ' s revenues were $ 8000 higher than store b ' s revenues . if store a ' s average ( arithmetic mean ) monthly revenue for the 3 months was $ 2000 greater than store b ' s average monthly revenue , then store b ' s revenue in the third month was how much greater than store a ' s revenue ? | answer : cit may be tempting to come up with a lot of variables , one each for each month ' s revenue for each company . however , focus on the differences . in the first month , the difference was + 12 in favor of a . ( note that we can drop the thousands since every number in the question is in terms of thousands . ) in the second , the difference was + 8 in favor of a . the average was + 2 in favor of a . with these numbers , use the average formula to find the third month ( t ) : ( 12 + 8 + t ) / 3 = 2 20 + t = 6 t = - 14 since positive numbers indicate a difference in favor of a , negative numbers are in favor of b . - 14 represents a $ 14,000 advantage in favor of store b . choice ( a ) is correct . | a = 12000 + 8000
b = 2000 * 3
c = a - b
d = c / 1000
|
a ) 14 , 7 , b ) 10 , 5 , c ) 13 , 8 , d ) 12 , 8 , e ) 8 , 12 | c | add(subtract(add(multiply(const_3, 5), multiply(const_3, 7)), multiply(4, 7)), 5) | a is older than b by 5 years . 7 years hence , thrice a ' s age shall be equal to 4 times that of b . find their present ages . | explanation : let the present ages of a and b be ' a ' and ' b ' respectively . 3 ( a + 7 ) = 4 ( ( b + 7 ) - - - ( 1 ) = > 3 a - 4 b = 7 - - - - - - - ( 1 ) a - b = 5 - - - - - - - ( 2 ) solving ( 1 ) and ( 2 ) we get b = 8 substituting b = 8 in second equation , we get a = 13 . answer : c = > 2 a = 32 = > a = 16 . answer : c | a = 3 * 5
b = 3 * 7
c = a + b
d = 4 * 7
e = c - d
f = e + 5
|
a ) 40 , b ) 99 , c ) 88 , d ) 44 , e ) 11 | a | add(multiply(multiply(3, 5), const_100), multiply(4, 5)) | three numbers are in the ratio 3 : 4 : 5 and their l . c . m is 2400 . their h . c . f is ? | "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 * 40 ) , ( 4 * 40 ) and ( 5 * 40 ) . hence , required h . c . f = 40 . answer : a" | a = 3 * 5
b = a * 100
c = 4 * 5
d = b + c
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a ) a ) 10 , b ) b ) 8 , c ) c ) 6 , d ) d ) 4 , e ) e ) 2 | a | subtract(20, multiply(2, 5)) | what is x if x + 2 y = 20 and y = 5 ? | "x = 20 - 2 y x = 20 - 10 . x = 10 answer : a" | a = 2 * 5
b = 20 - a
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a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8 | b | divide(subtract(multiply(34, 2), 40), 2) | a certain experimental mathematics program was tried out in 2 classes in each of 34 elementary schools and involved 40 teachers . each of the classes had 1 teacher and each of the teachers taught at least 1 , but not more than 3 , of the classes . if the number of teachers who taught 3 classes is n , then the least and greatest possible values of n , respectively , are | one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 34 * 2 = 68 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 68 - 40 = 28 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 28 / 2 = 14 . so the greatest possible value of the # of teachers who had 3 classes is 14 . only answer b has this option . | a = 34 * 2
b = a - 40
c = b / 2
|
a ) 15 seconds , b ) 18 seconds , c ) 24 seconds , d ) 30 seconds , e ) 45 seconds | c | divide(48, subtract(5, 3)) | nicky and cristina are running a race . since cristina is faster than nicky , she gives him a 48 meter head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? | "used pluging in method say t is the time for cristina to catch up with nicky , the equation will be as under : for nicky = n = 3 * t + 48 for cristina = c = 5 * t @ t = 24 , n = 120 c = 120 right answer ans : c" | a = 5 - 3
b = 48 / a
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a ) 100 km , b ) 150 km , c ) 50 km , d ) 120 km , e ) 200 km | d | multiply(6, 20) | a walks at 10 kmph and 6 hours after his start , b cycles after him at 20 kmph . how far from the start does b catch up with a ? | suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 6 hours . x / 10 - x / 20 = 6 x = 120 km answer is d | a = 6 * 20
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a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130 | d | factorial(const_3) | how many words , with or without meaning , can be formed using all letters of the word sharp using each letter exactly once ? | "the word sharp has exactly 5 letters which are all different . therefore the number of words that can be formed = number of permutations of 5 letters taken all at a time . = p ( 5 , 5 ) = 5 ! = 5 x 4 x 3 x 2 × 1 = 120 answer : d" | a = math.factorial(3)
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a ) 600 , b ) 720 , c ) 760 , d ) 620 , e ) 700 | c | add(multiply(80, 8), multiply(subtract(80, 20), multiply(8, divide(25, const_100)))) | mary works in a restaurant a maximum of 80 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ? | "mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 60 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 60 ) = $ 600 . the total amount is $ 160 + $ 600 = $ 760 answer c 360 ." | a = 80 * 8
b = 80 - 20
c = 25 / 100
d = 8 * c
e = b * d
f = a + e
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a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4 | a | divide(add(divide(subtract(multiply(4, 2), 5), subtract(multiply(2, 2), const_1)), subtract(4, multiply(2, divide(subtract(multiply(4, 2), 5), subtract(multiply(2, 2), const_1))))), 3) | if 2 x + y = 4 and x + 2 y = 5 , then ( x + y ) / 3 = | "we have two equations : 2 x + y = 4 x + 2 y = 5 notice that something nice happens when we add them . we get : 3 x + 3 y = 9 divide both sides by 3 to get : x + y = 3 so , ( x + y ) / 3 = 3 / 3 = 1 answer : a" | a = 4 * 2
b = a - 5
c = 2 * 2
d = c - 1
e = b / d
f = 4 * 2
g = f - 5
h = 2 * 2
i = h - 1
j = g / i
k = 2 * j
l = 4 - k
m = e + l
n = m / 3
|
a ) 858 , b ) 859 , c ) 869 , d ) 4320 , e ) none of these | a | subtract(lcm(lcm(lcm(24, 32), 36), 54), 6) | the least number which when increased by 6 each divisible by each one of 24 , 32 , 36 and 54 is : | "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 5 = 864 - 6 = 858 . answer a" | a = math.lcm(24, 32)
b = math.lcm(a, 36)
c = math.lcm(b, 54)
d = c - 6
|
a ) a ) 59 , b ) b ) 61 , c ) c ) 63 , d ) d ) 65 , e ) e ) 90 | e | divide(add(81, 100), const_2) | find the mean proportional between 81 & 100 ? | "formula = √ a × b a = 81 and b = 100 √ 81 × 100 = 9 × 10 = 90 e" | a = 81 + 100
b = a / 2
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a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 45 | e | divide(add(30, 60), const_2) | a man can row upstream at 30 kmph and downstream at 60 kmph , and then find the speed of the man in still water ? | "us = 30 ds = 60 m = ( 30 + 60 ) / 2 = 45 answer : e" | a = 30 + 60
b = a / 2
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a ) 25 , b ) 30 , c ) 28 , d ) 36 , e ) 42 | d | subtract(multiply(16, const_2), multiply(2, const_2)) | if the average ( arithmetic mean ) of 2 a + 16 , 3 a - 8 is 94 , what is the value of a ? | "am of 2 a + 16 , 3 a - 8 = 2 a + 16 + 3 a - 8 / 2 = 5 a + 8 / 2 given that 5 a + 8 / 2 = 94 a = 36 answer is d" | a = 16 * 2
b = 2 * 2
c = a - b
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a ) 210 , b ) 225 , c ) 200 , d ) 250 , e ) 300 | c | divide(add(10, 40), divide(subtract(const_100, 75), const_100)) | a group of students was interviewed for that if it was asked whether or not they speak french and / or english . among those who speak french , 10 speak english well , while 40 of them do not speak english . if 75 % of students do not speak french , how many students were surveyed ? | "number of students who speak french are 40 + 10 = 50 of total students , the percentage of students who do not speak french was 75 % - - > percentage of who do is 25 % 50 - - - - - - - 25 % x - - - - - - - 100 % x = 50 * 100 / 25 = 200 = number of all students answer is c" | a = 10 + 40
b = 100 - 75
c = b / 100
d = a / c
|
a ) a ) 150 m , b ) b ) 270 m , c ) c ) 180 m , d ) d ) 158 m , e ) e ) 350 m | b | subtract(multiply(250, divide(15, divide(15, const_3))), multiply(120, divide(20, divide(15, const_3)))) | a train crosses a platform of 120 m in 15 sec , same train crosses another platform of length 250 m in 20 sec . then find the length of the train ? | "length of the train be ‘ x ’ x + 120 / 15 = x + 250 / 20 4 x + 480 = 3 x + 750 x = 270 m answer : b" | a = 15 / 3
b = 15 / a
c = 250 * b
d = 15 / 3
e = 20 / d
f = 120 * e
g = c - f
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a ) 21 , b ) 56 , c ) 76 , d ) 84 , e ) 85 | a | add(multiply(multiply(3, const_4.0), const_100), multiply(4, 36)) | two numbers are in the ratio 3 : 4 . if their l . c . m . is 36 . what is sum of the numbers ? | "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 36 = > 12 x = 36 = > x = 36 / 12 = 3 sum of the numbers = 3 x + 4 x = 7 x = 7 x 3 = 21 answer : option a" | a = 3 * 4
b = a * 100
c = 4 * 36
d = b + c
|
a ) 2.5 sec , b ) 3 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec | b | divide(120, multiply(144, const_0_2778)) | in what time will a train 120 m long cross an electric pole , it its speed be 144 km / hr ? | "speed = 144 * 5 / 18 = 40 m / sec time taken = 120 / 40 = 3 sec . answer : b" | a = 144 * const_0_2778
b = 120 / a
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a ) 32435453 , b ) 1234554 , c ) 76768786 , d ) 97979797 , e ) 75868656 | b | subtract(1234562, multiply(multiply(12, 3), 2)) | evaluate : 1234562 - 12 * 3 * 2 = ? | "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1234562 - 12 * 3 * 2 = 1234562 - 8 = 1234554 correct answer b" | a = 12 * 3
b = a * 2
c = 1234562 - b
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a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130 | d | divide(multiply(add(33, divide(1, 3)), 360), const_100) | 33 1 / 3 % of 360 ? | "33 1 / 3 % = 1 / 3 1 / 3 × 360 = 120 d )" | a = 1 / 3
b = 33 + a
c = b * 360
d = c / 100
|
a ) 196 sq m , b ) 286 sq m , c ) 298 sq m , d ) 267 sq m , e ) 231 sq m | a | divide(square_area(14), const_2) | what is the area of a square field whose sides have a length of 14 meters ? | "14 * 14 = 196 sq m the answer is a ." | a = square_area / (
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a ) 10 , b ) 40 , c ) 15 , d ) 18 , e ) 20 | b | multiply(32, inverse(subtract(const_1, divide(8, 40)))) | x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 32 days . how long will y take to complete the work ? | "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 32 days whole work will be done by y in 32 * 5 / 4 = 40 days answer is b" | a = 8 / 40
b = 1 - a
c = 1/(b)
d = 32 * c
|
a ) 239 , b ) 247 , c ) 277 , d ) 270 , e ) 898 | d | divide(multiply(divide(multiply(1800, const_2), const_3), const_3), add(const_2, const_3)) | a man traveled a total distance of 1800 km . he traveled one - third of the whole trip by plane and the distance traveled by train is three - fifth of the distance traveled by bus . if he traveled by train , plane and bus , then find the distance traveled by bus ? | "explanation : total distance traveled = 1800 km . distance traveled by plane = 600 km . distance traveled by bus = x distance traveled by train = 3 x / 5 = > x + 3 x / 5 + 600 = 1800 = > 8 x / 5 = 1200 = > x = 750 km . answer : d" | a = 1800 * 2
b = a / 3
c = b * 3
d = 2 + 3
e = c / d
|
a ) 0 , b ) 1 , c ) 36 , d ) 120 , e ) 524 | b | subtract(power(3, subtract(const_1, const_1)), power(subtract(const_1, const_1), 3)) | if k is a non - negative integer and 12 ^ k is a divisor of 856,736 then 3 ^ k - k ^ 3 = | "8 + 5 + 6 + 7 + 3 + 6 = 35 , so this number is not divisible by 3 and thus not divisible by 12 . therefore , k = 0 3 ^ k - k ^ 3 = 1 - 0 = 1 the answer is b ." | a = 1 - 1
b = 3 ** a
c = 1 - 1
d = c ** 3
e = b - d
|
['a ) 126', 'b ) 156', 'c ) 190', 'd ) 300', 'e ) 260'] | d | multiply(add(divide(subtract(divide(divide(1950, 6.5), const_2), const_10), const_2), add(divide(subtract(divide(divide(1950, 6.5), const_2), const_10), const_2), const_10)), const_2) | the length of a rectangular plot is 10 mtr more than its width . the cost of fencing the plot along its perimeter at the rate of rs . 6.5 mtr is rs . 1950 . the perimeter of the plot is ? | sol . let width = x , length = ( 10 + x ) perimeter = 2 ( x + ( 10 + x ) ) = 2 ( 2 x = 10 ) & 2 ( 2 x + 10 ) * 6.5 = 1950 x = 70 required perimeter = 2 ( 70 + 80 ) = 300 d | a = 1950 / 6
b = a / 2
c = b - 10
d = c / 2
e = 1950 / 6
f = e / 2
g = f - 10
h = g / 2
i = h + 10
j = d + i
k = j * 2
|
a ) 8.7 days , b ) 2.0 days , c ) 6.6 days , d ) 7.7 days , e ) 4.8 days | e | divide(multiply(8, 6), divide(subtract(multiply(8, 6), multiply(add(divide(multiply(8, 6), 8), divide(multiply(8, 6), 6)), 2)), 2)) | a can do a piece of work in 8 days . b can do it in 6 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ? | "c = 1 / 2 - 1 / 8 - 1 / 8 = 5 / 24 = > 4.8 days answer : e" | a = 8 * 6
b = 8 * 6
c = 8 * 6
d = c / 8
e = 8 * 6
f = e / 6
g = d + f
h = g * 2
i = b - h
j = i / 2
k = a / j
|
a ) 342 km , b ) 390 km , c ) 642 km , d ) 742 km , e ) 382 km | b | divide(add(add(30, multiply(2, 10)), 30), 2) | a car started running at a speed of 30 km / hr and the speed of the car was increased by 2 km / hr at the end of every hour . find the total distance covered by the car in the first 10 hours of the journey . | "the total distance covered by the car in the first 10 hours = 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48 = sum of 10 terms in ap whose first term is 30 and last term is 48 = 10 / 2 [ 30 + 48 ] = 390 km . answer : b" | a = 2 * 10
b = 30 + a
c = b + 30
d = c / 2
|
a ) 91 , b ) 10 , c ) 1001 , d ) 1911 , e ) none of these | b | gcd(1230, 920) | the maximum number of students among them 1230 pens and 920 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is : | "explanation : required number of students = h . c . f of 1230 and 920 = 10 . answer : b" | a = math.gcd(1230, 920)
|
a ) 25650 , b ) 25750 , c ) 26550 , d ) 26750 , e ) 29925 | e | multiply(900, multiply(7, 4.75)) | the length of a room is 7 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre . | "area = 7 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 7 × 4.75 × 900 = 7 × 4275 = rs . 29925 answer is e" | a = 7 * 4
b = 900 * a
|
a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4 sec , e ) 12 sec | e | divide(110, multiply(add(27, 6), const_0_2778)) | a train 110 m long is running with a speed of 27 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ? | "speed of train relative to man = 27 + 6 = 33 km / hr . = 33 * 5 / 18 = 9.1667 m / sec . time taken to pass the men = 110 / 9.1667 = 12 sec . answer : e" | a = 27 + 6
b = a * const_0_2778
c = 110 / b
|
a ) 10 days , b ) 11 days , c ) 13 days , d ) 21 days , e ) 31 days | b | add(divide(subtract(const_1, multiply(add(divide(const_1, 24), divide(const_1, 30)), 4)), add(divide(const_1, multiply(add(const_2, const_3), multiply(const_2, const_4))), add(divide(const_1, 24), divide(const_1, 30)))), 4) | a , b and c can do a piece of work in 24 days , 30 days and 60 days respectively . they began the work together but c left 4 days before the completion of the work . in how many days was the work completed ? | one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 60 = 11 / 120 work done by a and b together in the last 4 days = 4 * ( 1 / 24 + 1 / 30 ) = 3 / 10 remaining work = 7 / 10 the number of days required for this initial work = 7 days . the total number of days required = 4 + 7 = 11 days . answer : b | a = 1 / 24
b = 1 / 30
c = a + b
d = c * 4
e = 1 - d
f = 2 + 3
g = 2 * 4
h = f * g
i = 1 / h
j = 1 / 24
k = 1 / 30
l = j + k
m = i + l
n = e / m
o = n + 4
|
a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 125 | a | divide(subtract(550, divide(550, add(divide(10, const_100), const_1))), 10) | machine p and machine q are each used to manufacture 550 sprockets . it takes machine p 10 hours longer to produce 550 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ? | "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 550 / x = 550 / 1.1 x + 10 1.1 ( 550 ) = 550 + 11 x 11 x = 55 x = 5 the answer is a ." | a = 10 / 100
b = a + 1
c = 550 / b
d = 550 - c
e = d / 10
|
a ) 29.2 % , b ) 12.5 % , c ) 13 % , d ) 11.3 % , e ) none of these | a | multiply(divide(7, multiply(multiply(const_4, const_3), const_2)), const_100) | what percent of a day is 7 hours ? | explanation : solution : required percentage = ( 7 / 100 * 24 ) = 29.2 % answer : a | a = 4 * 3
b = a * 2
c = 7 / b
d = c * 100
|
a ) 9 . , b ) 12 . , c ) 15 . , d ) 16 . , e ) 25 | e | add(4, multiply(10, 2)) | if 4 xz + yw = 5 and xw + yz = 10 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ? | "( 2 x + y ) * ( 2 z + w ) = 5 + 2 ( 10 ) = 25 answer : e" | a = 10 * 2
b = 4 + a
|
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9 | b | divide(multiply(110, 130), multiply(70, 30)) | rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is : | "area of tile = 70 * 30 = 2100 area of floor = 130 * 110 = 14300 no of tiles = 14300 / 2100 = 6.8 so , the no of tile = 6 answer : b" | a = 110 * 130
b = 70 * 30
c = a / b
|
a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1951602 , d ) d ) 1943236 , e ) e ) 1951604 | d | multiply(divide(1394, 1394), const_100) | 1394 x 1394 = ? | "1394 x 1394 = ( 1394 ) 2 = ( 1400 - 6 ) 2 = ( 1400 ) 2 + ( 6 ) 2 - ( 2 x 1400 x 6 ) = 1960000 + 36 - 16800 = 1960036 - 16800 = 1943236 . answer : d" | a = 1394 / 1394
b = a * 100
|
['a ) 226.3', 'b ) 226.2', 'c ) 228.2', 'd ) 227', 'e ) 226'] | a | subtract(circle_area(add(divide(34, const_2), 2)), circle_area(divide(34, const_2))) | a circular ground whose diameter is 34 metres , has a 2 metre - broad garden around it . what is the area of the garden in square metres ? | req . area = ï € [ ( 19 ) 2 â € “ ( 17 ) 2 ] = 22 â „ 7 ã — ( 36 ã — 2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 ã — 36 ã — 2 ) / 7 = 226.3 sq m answer a | a = 34 / 2
b = a + 2
c = circle_area - (
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a ) a ) 47.095 , b ) b ) 47.752 , c ) c ) 47.806 , d ) d ) 47.95 , e ) of the above | c | subtract(add(3889, 12.808), 3854.002) | 3889 + 12.808 - ? = 3854.002 | let 3889 + 12.808 - x = 3854.002 . then x = ( 3889 + 12.808 ) - 3854.002 = 3901.808 - 3854.002 = 47.806 . answer = c | a = 3889 + 12
b = a - 3854
|
a ) 12 days , b ) 15 days , c ) 20 days , d ) 18 days , e ) 22 days | a | divide(const_1, add(divide(const_1, 20), divide(const_1, 30))) | a sum of money is sufficient to pay a ' s wages for 20 days and b ' s wages for 30 days . the same money is sufficient to pay the wages of both for ? | "let the total money be $ x a ' s 1 day work = $ x / 20 b ' s 1 day work = $ x / 30 a + b 1 day work = $ x / 12 money is sufficient to pay the wages of both for 12 days answer is a" | a = 1 / 20
b = 1 / 30
c = a + b
d = 1 / c
|
a ) 6.8 , b ) 7.1 , c ) 7.2 , d ) 7.5 , e ) 8.0 | a | divide(multiply(multiply(6, 8), const_2), add(6, 8)) | a river boat leaves silver town and travels upstream to gold town at an average speed of 6 kilometers per hour . it returns by the same route at an average speed of 8 kilometers per hour . what is the average speed for the round - trip in kilometers per hour ? | "pick a number which is lcm of 8 and 6 = 24 . upstream time = 24 / 6 = 4 hrs downstream time = 24 / 8 = 3 hrs total time = 7 hrs total distance = 48 average speed = 48 / 7 = 6.8 km / hr" | a = 6 * 8
b = a * 2
c = 6 + 8
d = b / c
|
['a ) 42.25 sq cm', 'b ) 45.25 sq cm', 'c ) 43.25 sq cm', 'd ) 50.25 sq cm', 'e ) 52.25 sq cm'] | a | power(subtract(subtract(7, const_0_25), const_0_25), const_2) | the sides of a square region , measured to the nearest centimeter , are 7 centimeters long . the least possible value of the actual area of the square region is | though there might be some technicalities concerning the termnearest ( as 6.5 is equidistant from both 6 and 7 ) the answer still should be a : 6.5 ^ 2 = 42.25 . answer : a | a = 7 - const_0_25
b = a - const_0_25
c = b ** 2
|
a ) 19 / 11628 , b ) 36 / 11628 , c ) 613 / 11628 , d ) 6113 / 11628 , e ) 63 / 11628 | e | divide(add(add(divide(factorial(6), factorial(5)), divide(factorial(5), factorial(5))), divide(factorial(8), multiply(factorial(subtract(8, 5)), factorial(5)))), divide(factorial(add(add(6, 5), 8)), multiply(factorial(5), factorial(subtract(add(add(6, 5), 8), 5))))) | a box contains 6 white , 5 red and 8 white marbles . 5 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ? | explanation : total marbles in a box = 6 black + 5 red + 8 green marbles = 19 marbles 5 marbles are drawn from 19 marbles at random . therefore , n ( s ) = 19 c 5 = 11628 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 5 + 5 c 5 + 8 c 5 = 6 + 1 + 56 = 63 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 63 / 11628 answer : e | a = math.factorial(6)
b = math.factorial(5)
c = a / b
d = math.factorial(5)
e = math.factorial(5)
f = d / e
g = c + f
h = math.factorial(8)
i = 8 - 5
j = math.factorial(i)
k = math.factorial(5)
l = j * k
m = h / l
n = g + m
o = 6 + 5
p = o + 8
q = math.factorial(p)
r = math.factorial(5)
s = 6 + 5
t = s + 8
u = t - 5
v = math.factorial(u)
w = r * v
x = q / w
y = n / x
|
a ) 11025 , b ) 23889 , c ) 29088 , d ) 1999 , e ) 17710 | a | multiply(divide(105, 2), const_100) | 105 * 2 | "here d = 5 . 100 + 2 × × 5 / 25 = 11025 answer : a" | a = 105 / 2
b = a * 100
|
a ) 32 , b ) 42 , c ) 83 , d ) 71 , e ) 92 | b | subtract(add(power(43, 43), 43), multiply(44, floor(divide(add(power(43, 43), 43), 44)))) | what will be the reminder when ( 43 ^ 43 + 43 ) is divided by 44 ? | "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 43 ^ 43 + 1 ) will be divisible by ( 43 + 1 ) ; ( 43 ^ 43 + 1 ) + 42 when divided by 44 will give 42 as remainder . correct option : b" | a = 43 ** 43
b = a + 43
c = 43 ** 43
d = c + 43
e = d / 44
f = math.floor(e)
g = 44 * f
h = b - g
|
a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30 | d | multiply(4, divide(40, add(4, 6))) | maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 40 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ? | "time taken = total distance / relative speed total distance = 40 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 40 / 10 = 4 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 4 = 24 kms . . . answer - d" | a = 4 + 6
b = 40 / a
c = 4 * b
|
a ) 238 , b ) 290 , c ) 278 , d ) 200 , e ) 288 | b | divide(subtract(multiply(342, 25), multiply(71, const_100)), subtract(25, 20)) | the total of 342 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 = ( 342 - x ) . 0.20 * ( x ) + 0.25 ( 342 - x ) = 71 = > x = 290 . . answer : b ) 290" | a = 342 * 25
b = 71 * 100
c = a - b
d = 25 - 20
e = c / d
|
a ) 10 % , b ) 45.8 % , c ) 25 % , d ) 52 % , e ) none of these | b | subtract(multiply(divide(350, add(225, 15)), const_100), const_100) | a retailer buys a radio for rs 225 . his overhead expenses are rs 15 . he sellis the radio for rs 350 . the profit percent of the retailer is | "explanation : cost price = ( 225 + 15 ) = 240 sell price = 350 gain = ( 110 / 240 ) * 100 = 45.8 % . answer : b" | a = 225 + 15
b = 350 / a
c = b * 100
d = c - 100
|
a ) 32 kmph , b ) 34 kmph , c ) 40 kmph , d ) 45 kmph , e ) 65 kmph | c | divide(add(35, 45), const_2) | a man can row upstream at 35 kmph and downstream at 45 kmph , and then find the speed of the man in still water ? | "us = 35 ds = 45 m = ( 35 + 45 ) / 2 = 40 answer : c" | a = 35 + 45
b = a / 2
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a ) 230 m , b ) 240 m , c ) 250 m , d ) 260 m , e ) 280 m | e | subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 220) | a 220 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 ? | speed = ( 120 + 80 ) km / h ( because direction is opposite hence relative velocity is added ) = 500 / 9 m / s time = 9 sec let the lenght of second train is x total distance covered = 220 + x therefore , d = speed * time thus 220 + x = 500 / 9 * 9 x = 500 - 220 = 280 m answer : e | a = 120 + 80
b = a * const_0_2778
c = b * 9
d = c - 220
|
a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) none of these | c | divide(multiply(multiply(multiply(5, 76.5), 10), 80), multiply(multiply(21.25, 30), 4)) | if 80 lamps can be lighted 5 hours per day for 10 days for rs . 21.25 , then the number of lamps which can be lighted 4 hours daily for 30 days for rs . 76.50 , is ? | explanation : ( hrs / day 4 : 5 ) : ( money 21.25 : 76.50 ) : ( days 30 : 10 ) : : 80 : x 4 * 21.25 * 30 * x = 5 * 76.50 * 10 * 80 so x = 120 answer : c | a = 5 * 76
b = a * 10
c = b * 80
d = 21 * 25
e = d * 4
f = c / e
|
a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 16 | a | divide(20, const_2) | in a group of ducks and cows , the total number of legs are 20 more than twice the no . of heads . find the total no . of buffaloes . | "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 20 = > 2 x = 20 = > x = 10 a" | a = 20 / 2
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a ) 27 kg , b ) 20 kg , c ) 26 kg , d ) 31 kg , e ) 35 kg | a | subtract(add(multiply(40, const_2), multiply(41, const_2)), multiply(45, const_3)) | the average weight of a , b and c is 45 kg . if the average weight of a and b be 40 kg and that of b and c be 41 kg , then the weight of b is : | "let d sum of a , b , c is 3 * 45 = 135 and sum of a and b s 2 * 40 = 80 sum of b and c is 2 * 41 = 82 hence 80 + 82 - 135 = 27 ans = 27 answer : a" | a = 40 * 2
b = 41 * 2
c = a + b
d = 45 * 3
e = c - d
|
a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540 | a | divide(multiply(divide(multiply(100, 10), subtract(15, 10)), const_100), 10) | i sold a book at a profit of 10 % . had i sold it for $ 100 more , 15 % would have been gained . find the cost price ? | "115 % of cost - 110 % of cost = $ 100 5 % of cost = $ 100 cost = 100 * 100 / 5 = $ 2000 answer is a" | a = 100 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
|
a ) 1200 , b ) 1240 , c ) 1852 , d ) 3200 , e ) 2500 | e | divide(multiply(2, const_100), 0.08) | an inspector rejects 0.08 % of the meters as defective . how many will he examine to reject 2 ? | "then , 0.08 % of x = 2 ( 8 / 100 ) * ( 1 / 100 ) x = 2 x = ( 2 * 100 * 100 ) / 8 = 2500 answer is e" | a = 2 * 100
b = a / 0
|
a ) 1 : 2 , b ) 3 : 4 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these | c | divide(subtract(15.8, 15.4), subtract(16.4, 15.8)) | the average age of a class is 15.8 years . the average age of the boys in the class is 16.4 years and that of the girls is 15.4 years . what is the ratio of boys to girls in the class ? | "let number of boys = x ; let number of girls = y total numbers of students = x + y ( x + y ) × 15.8 = 16.4 x + 15.4 y 0.6 x = 0.4 y x / y = 0.4 / 0.6 = 2 / 3 answer : c" | a = 15 - 8
b = 16 - 4
c = a / b
|
a ) 4 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 % | a | divide(const_100, 25) | in how many years will a sum of money doubles itself at 25 % per annum on simple interest ? | "p = ( p * 25 * r ) / 100 r = 4 % answer : a" | a = 100 / 25
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a ) 343 , b ) 729 , c ) 829 , d ) 929 , e ) 727 | a | power(7, 3) | log 3 n + log 7 n what is 3 digit number n that will be whole number | no of values n can take is 1 7 ^ 3 = 343 answer : a | a = 7 ** 3
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a ) 30 / 71 , b ) 4 / 7 , c ) 5 / 43 , d ) 1 / 2 , e ) 1 / 5 | c | subtract(divide(1, 5), subtract(subtract(const_1, add(add(divide(2, 7), divide(1, 5)), divide(1, 7))), divide(2, 7))) | at the a - street fish market a vendor sells fresh caught fish . his store is filled with 2 / 7 bass , 1 / 5 tuna , 1 / 7 trout , and the rest are catfish . if a customer just bought 1 / 7 of all the tuna and 1 / 7 of all the catfish , and a fisherman arrived to restock the bass , doubling the number of bass , what proportion of fish now in the store are trout ? | bass = 2 / 7 = 10 / 35 tuna = 1 / 5 = 7 / 35 trout = 1 / 7 = 5 / 35 catfish = 1 - ( 10 / 35 + 7 / 35 + 5 / 35 ) = 13 / 35 purchased : tuna = 7 / 35 - ( 7 / 35 ) ( 1 / 7 ) = 6 / 35 , and catfish = 13 / 35 - ( 13 / 35 ) ( 1 / 7 ) = 12 / 35 stocked : doubling the number of bass ( 2 ) ( 10 / 35 ) = 20 / 35 now : 20 + 6 + 5 + 12 = 43 trout proportion is now 5 / 43 . answer : c | a = 1 / 5
b = 2 / 7
c = 1 / 5
d = b + c
e = 1 / 7
f = d + e
g = 1 - f
h = 2 / 7
i = g - h
j = a - i
|
a ) s . 5,000 , b ) s . 5,500 , c ) s . 5,700 , d ) s . 6,000 , e ) s . 7,500 | d | divide(multiply(20000, divide(multiply(15000, multiply(const_12, const_2)), add(add(multiply(20000, multiply(const_12, const_2)), multiply(15000, multiply(const_12, const_2))), multiply(subtract(multiply(const_12, const_2), 6), 20000)))), const_12) | a and b started a business in partnership investing rs . 20000 and rs . 15000 respectively . after 6 months , c joined them with rs . 20000 . whatwill be b ' s share in total profit of rs . 20000 earned at the end of 2 years from the startingof the business ? | a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 20000 x 3 / 10 = rs . 6,000 . d | a = 12 * 2
b = 15000 * a
c = 12 * 2
d = 20000 * c
e = 12 * 2
f = 15000 * e
g = d + f
h = 12 * 2
i = h - 6
j = i * 20000
k = g + j
l = b / k
m = 20000 * l
n = m / 12
|
a ) 17 , b ) 18 , c ) 16 , d ) 19 , e ) 14 | a | subtract(add(multiply(divide(323, divide(323, 2)), const_4), const_10), const_1) | the product of two positive integers is 323 and their difference is 2 . what is the smaller number ? | let ' s use trial and error to find the two numbers . 20 * 18 = 360 ( too high ) 19 * 17 = 323 the answer is a . | a = 323 / 2
b = 323 / a
c = b * 4
d = c + 10
e = d - 1
|
a ) 12 kg , b ) 14 kg , c ) 15 kg , d ) 20 kg , e ) 18 kg | b | multiply(divide(35, 5), 2) | an alloy is to contain steel and iron in the ratio 5 : 2 . the iron required to be melted with 35 kg of steel is ? | let the required quantity of steel be x kg 5 : 2 : : 35 : x 5 x = 2 * 35 x = 14 kg answer is b | a = 35 / 5
b = a * 2
|
a ) 220 km , b ) 224 km , c ) 230 km , d ) 400 km , e ) 234 km | d | multiply(const_2, divide(multiply(multiply(20, 10), 30), add(20, 10))) | a man complete a journey in 30 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 10 km / hr . find the total journey in km . | 0.5 x / 20 + 0.5 x / 10 = 30 - - > x / 20 + x / 10 = 60 - - > 3 x = 20 x 60 - - > x = ( 60 x 20 ) / 3 = 400 km . answer : d | a = 20 * 10
b = a * 30
c = 20 + 10
d = b / c
e = 2 * d
|
a ) 52 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph | a | subtract(multiply(divide(280, 9), const_3_6), 60) | a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ? | "relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 60 ) kmph = 52 kmph . answer : a" | a = 280 / 9
b = a * const_3_6
c = b - 60
|
a ) 2 , b ) 20 , c ) 0.2 , d ) 0.02 , e ) none of these | d | multiply(divide(0.0006, 0.03), const_100) | 0.0006 ? = 0.03 | "explanation : required answer = 0.0006 / 0.03 = 0.06 / 3 = 0.02 . answer : option d" | a = 0 / 6
b = a * 100
|
a ) 11 , b ) 49 , c ) 88 , d ) 65 , e ) 22 | b | divide(divide(subtract(125, multiply(multiply(4, const_0_2778), 4)), 10), const_0_2778) | a train 125 m long passes a man , running at 4 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ? | "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 4 ) km / hr . x - 4 = 45 = = > x = 49 km / hr . answer : b" | a = 4 * const_0_2778
b = a * 4
c = 125 - b
d = c / 10
e = d / const_0_2778
|
a ) 72 / 17 , b ) 17 / 72 , c ) 14 / 24 , d ) 24 / 56 , e ) 34 / 56 | a | divide(multiply(9, 8), add(9, 8)) | it would take one machine 9 hours to complete a large production order and another machine 8 hours to complete the same order . how many hours would it take both machines , working simultaneously at their respective constant rates , to complete the order ? | the rate of the first machine is 1 / 9 job per hour ; the rate of the second machine is 1 / 8 job per hour ; thus , the combined rate of the machines is 1 / 9 + 1 / 8 = 17 / 72 job per hour , which means that it takes 1 / ( 17 / 72 ) = 72 / 17 hours both machines to do the job . answer : a . | a = 9 * 8
b = 9 + 8
c = a / b
|
a ) 1964 , b ) 1984 , c ) 2964 , d ) 2984 , e ) none of these | d | subtract(3034, divide(1002, 20.04)) | 3034 − ( 1002 ÷ 20.04 ) = ? | "explanation : = 3034 − ( 1002 / 2004 × 100 ) = 3034 − 50 = 2984 option d" | a = 1002 / 20
b = 3034 - a
|
a ) 5 , b ) 6 , c ) 8 , d ) 7 , e ) 4 | a | divide(subtract(57, multiply(const_3, 9)), multiply(const_3, const_2)) | a number is doubled and 9 is added . if the resultant is trebled , it becomes 57 . what is that number ? | "let the number be x . then , 3 ( 2 x + 9 ) = 57 2 x = 10 = > x = 5 answer : a" | a = 3 * 9
b = 57 - a
c = 3 * 2
d = b / c
|
a ) 12 , b ) 15 , c ) 17 , d ) 137 , e ) 147 | b | divide(multiply(add(multiply(5, const_100), 76), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(5, const_100), 76), add(multiply(4, const_100), 32)), gcd(add(multiply(5, const_100), 76), add(multiply(4, const_100), 32)))) | a room is 5 meters 76 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room . | "let us calculate both the length and width of the room in centimeters . length = 5 meters and 76 centimeters = 576 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 576 and 432 = 144 thus , the number of square tiles required = ( 576 x 432 ) / ( 144 x 144 ) = 4 x 3 = 12 answer : b" | a = 5 * 100
b = a + 76
c = 4 * 100
d = c + 32
e = b * d
f = 5 * 100
g = f + 76
h = 4 * 100
i = h + 32
j = math.gcd(g, i)
k = 5 * 100
l = k + 76
m = 4 * 100
n = m + 32
o = math.gcd(l, n)
p = j * o
q = e / p
|
a ) 10 : 00 , b ) 10 : 30 , c ) 11 : 00 , d ) 11 : 30 , e ) 12 : 00 | a | add(divide(70, subtract(80, 70)), 3) | a train sets off at 2 : 00 pm at the speed of 70 km / h . another train starts at 3 : 00 pm in the same direction at the rate of 80 km / h . at what time will the second train catch the first train ? | in one hour the first train travels 70 km . the second train catches the first train at a rate of 80 km / h - 70 km / h = 10 km / h . the second train will catch the first train in 70 / 10 = 7 hours , so at 10 : 00 pm . the answer is a . | a = 80 - 70
b = 70 / a
c = b + 3
|
a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 3 hours 24 minutes , e ) none | d | divide(68, add(15, 5)) | a boat can travel with a speed of 15 km / hr in still water . if the speed of the stream is 5 km / hr . find the time taken by the boat to go 68 km downstream ? | "solution speed downstream = ( 15 + 5 ) km / hr = 20 km / hr . time taken to travel 68 km downstream = ( 68 / 20 ) hrs = 3 hrs 24 minutes . answer d" | a = 15 + 5
b = 68 / a
|
a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13 | b | add(9, const_1) | mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 9 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ? | "if n = 10 mark sold 1 box and ann sold 8 boxes total 9 < 10 answer : b" | a = 9 + 1
|
a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 54 liters , e ) 34 liters | d | multiply(divide(135, add(3, 2)), 2) | 135 liters of a mixture of milk and water contains in the ratio 3 : 2 . how much water should now be added so that the ratio of milk and water becomes 3 : 4 ? | "milk = 3 / 5 * 135 = 81 liters water = 54 liters 81 : ( 54 + p ) = 3 : 4 162 + 3 p = 324 = > p = 54 54 liters of water are to be added for the ratio become 3 : 4 . answer : d" | a = 3 + 2
b = 135 / a
c = b * 2
|
a ) 13 , b ) 10 , c ) 11 , d ) 5 , e ) 14 | d | divide(add(17, subtract(power(17, const_2), multiply(60, const_4))), const_2) | 17 times a positive integer is more than its square by 60 , then the positive integer is | "explanation : let the number be x . then , 17 x = x 2 + 60 = > x 2 - 17 x + 60 = 0 = > ( x - 12 ) ( x - 5 ) = 0 = > x = 5 or 12 answer : option d" | a = 17 ** 2
b = 60 * 4
c = a - b
d = 17 + c
e = d / 2
|
a ) 3 / 40000 , b ) 1 / 3600 , c ) 1 / 20000 , d ) 1 / 60 , e ) 1 / 15 | c | divide(1, const_3) | a certain junior class has 1000 students and a certain senior class has 800 students . among these students , there are 40 siblings pairs each consisting of 1 junior and 1 senior . if 1 student is to be selected at random from each class , what is the probability that the 2 students selected will be a sibling pair ? | "let ' s see pick 40 / 1000 first then we can only pick 1 other pair from the 800 so total will be 40 / 800 * 1000 simplify and you get 1 / 20000 answer is c" | a = 1 / 3
|
a ) 1 / 13 , b ) 2 / 13 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 23 | c | divide(subtract(52, multiply(const_4, const_4)), 52) | a card is drawn from a pack of 52 cards . the probability of getting a queen of club or a king of heart is | "explanation : total number of cases = 52 favourable cases = 2 probability = 2 / 56 = 1 / 26 answer is c" | a = 4 * 4
b = 52 - a
c = b / 52
|
['a ) 14', 'b ) 47', 'c ) 54', 'd ) 180', 'e ) 64'] | e | add(add(divide(480, 40), divide(480, 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 480 square feet . how many feet offence does frank use ? | area = length x breadth 480 = 40 x breadth so , breadth = 12 units fencing required is - breadth + breadth + length 12 + 12 + 40 = > 64 feet answer must be ( e ) 64 | a = 480 / 40
b = 480 / 40
c = a + b
d = c + 40
|
a ) 3 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m | a | power(divide(6804, multiply(multiply(6, 7), 6)), divide(const_1, const_3)) | the height of the wall is 6 times its width and length of the wall is 7 times its height . if the volume of the wall be 6804 cu . m . its width is | "explanation : let width = x then , height = 6 x and length = 42 x 42 x ã — 6 x ã — x = 6804 x = 3 answer : a" | a = 6 * 7
b = a * 6
c = 6804 / b
d = 1 / 3
e = c ** d
|
a ) 66 , b ) 35 , c ) 42 , d ) 27 , e ) 11 | b | divide(multiply(divide(add(const_4, const_3), add(add(const_4, const_3), const_2)), 90), const_2) | 90 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ? | x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 90 = 35 answer : b | a = 4 + 3
b = 4 + 3
c = b + 2
d = a / c
e = d * 90
f = e / 2
|
a ) 8 hrs , b ) 10 hrs , c ) 12 hrs , d ) 15 hrs , e ) 6 hrs | e | multiply(divide(1, 3), 9) | a train running at 1 / 3 of its own speed reached a place in 9 hours . how much time could be saved if the train would have run at its own speed ? | "time taken if run its own speed = 1 / 3 * 9 = 3 hrs time saved = 9 - 3 = 6 hrs answer : e" | a = 1 / 3
b = a * 9
|
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