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 ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days | e | divide(const_1, add(multiply(4, divide(divide(const_1, 6), 24)), multiply(8, divide(divide(const_1, 6), 16)))) | 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ? | "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 4 girls = 8 Γ£ β 6 / 4 + 12 = 12 + 4 = 16 girls 9 days to complete the work answer : option e" | a = 1 / 6
b = a / 24
c = 4 * b
d = 1 / 6
e = d / 16
f = 8 * e
g = c + f
h = 1 / g
|
a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 16 | e | divide(subtract(630, multiply(75, 2.00)), 30) | 30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen . | "since average price of a pencil = 2 β΄ price of 75 pencils = 150 β΄ price of 30 pens = ( 630 β 150 ) = 480 β΄ average price of a pen = 480 β 60 = 16 answer e" | a = 75 * 2
b = 630 - a
c = b / 30
|
a ) 5.55 % , b ) 5.65 % , c ) 5.75 % , d ) 5.85 % , e ) 5.95 % | e | multiply(divide(multiply(multiply(const_100, const_100), divide(5, const_100)), subtract(multiply(const_100, const_100), add(multiply(add(const_2, const_3), multiply(multiply(add(const_2, const_3), const_2), const_100)), multiply(add(const_2, const_3), const_100)))), const_100) | a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 1,600 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ? | "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8400 = 5 / 84 which is about 5.95 % the answer is e ." | a = 100 * 100
b = 5 / 100
c = a * b
d = 100 * 100
e = 2 + 3
f = 2 + 3
g = f * 2
h = g * 100
i = e * h
j = 2 + 3
k = j * 100
l = i + k
m = d - l
n = c / m
o = n * 100
|
a ) 215 , b ) 212 , c ) 278 , d ) 279 , e ) 222 | b | multiply(circumface(divide(34, const_2)), 2) | find the cost of fencing around a circular field of diameter 34 m at the rate of rs . 2 a meter ? | "2 * 22 / 7 * 17 = 106 106 * 2 = rs . 212 answer : b" | a = 34 / 2
b = circumface * (
|
a ) 33 , b ) 37 , c ) 40 , d ) 38 , e ) 27 | c | multiply(divide(add(multiply(2, divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2))), multiply(2, divide(40, const_60))), divide(40, const_60)), divide(add(multiply(2, divide(40, const_60)), multiply(3, divide(40, const_60))), subtract(3, 2))) | a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the the distance in km ? | "let the distance be x km , the speed in which he moved = v kmph time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes β xv β xv + 3 = 4060 β x [ 1 v β 1 v + 3 ] = 23 β x [ v + 3 β vv ( v + 3 ) ] = 23 β 2 v ( v + 3 ) = 9 x . . . . . . . . . . . . . . . . ( equation 1 ) time taken wh... | a = 40 / const_60
b = 2 * a
c = 40 / const_60
d = 3 * c
e = b + d
f = 3 - 2
g = e / f
h = 2 * g
i = 40 / const_60
j = 2 * i
k = h + j
l = 40 / const_60
m = k / l
n = 40 / const_60
o = 2 * n
p = 40 / const_60
q = 3 * p
r = o + q
s = 3 - 2
t = r / s
u = m * t
|
a ) 200 , b ) 240 , c ) 50 , d ) 115 , e ) 150 | b | divide(add(280, 200), const_2) | if x + y = 280 , x - y = 200 , for integers of x and y , y = ? | "x + y = 280 x - y = 200 2 x = 80 x = 40 y = 240 answer is b" | a = 280 + 200
b = a / 2
|
a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9 | c | subtract(const_1, divide(const_2, 10)) | there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ? | number of students = 10 number of ways 10 students can sit around a circular table = ( 10 - 1 ) ! = 9 ! number of ways a and d sit together ( consider a and d as one entity ) = ( 9 - 1 ) ! = 8 ! * 2 number of ways a and d do not sit together = 9 ! - ( 8 ! * 2 ) probability = ( 9 ! - ( 8 ! * 2 ) ) / 9 ! = 1 - 2 / 9 = 7 ... | a = 2 / 10
b = 1 - a
|
a ) 2 / 3 , b ) 3 / 7 , c ) 8 / 15 , d ) 3 / 8 , e ) 4 / 7 | c | divide(multiply(divide(2, 3), 8), 10) | a pipe can empty 2 / 3 rd of a cistern in 10 mins . in 8 mins , what part of the cistern will be empty ? | "2 / 3 - - - - 10 ? - - - - - 8 = = > 8 / 15 c" | a = 2 / 3
b = a * 8
c = b / 10
|
a ) $ 18.33 , b ) $ 22.33 , c ) $ 28.33 , d ) $ 26.23 , e ) $ 16.23 | a | multiply(divide(multiply(const_2, 10), add(110, 10)), 110) | if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is : | s . i . on $ ( 110 - 10 ) for a certain time = $ 10 . s . i . on $ 100 for double the time = $ 20 . t . d . on $ 120 = $ ( 120 - 100 ) = $ 20 . t . d . on $ 110 = $ ( 20 / 120 * 100 ) = $ 18.33 answer : a | a = 2 * 10
b = 110 + 10
c = a / b
d = c * 110
|
a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 20 | d | divide(subtract(40, 4), const_2) | if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ? | let the two integers equal x and y , and then create the following equation and simplify : xy + 4 = 40 xy = 36 so x and y are a pair of integers that equal 36 . try adding all possible combinations of two integers that multiply out to 36 : 1 Γ 36 = 36 1 + 36 = 37 2 Γ 18 = 36 2 + 18 = 20 3 Γ 12 = 36 3 + 12 = 15 4 Γ 9 = ... | a = 40 - 4
b = a / 2
|
a ) 40 , b ) 87 , c ) 48 , d ) 21 , e ) 14 | c | divide(460, multiply(subtract(45, 140), const_0_2778)) | a train 460 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ? | "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 460 + 140 = 600 m required time = 600 * 2 / 25 = 48 sec answer : c" | a = 45 - 140
b = a * const_0_2778
c = 460 / b
|
a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these | a | add(multiply(8, 2.5), 45) | the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ? | "a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg ." | a = 8 * 2
b = a + 45
|
a ) s . 247 , b ) s . 248 , c ) s . 264 , d ) s . 329 , e ) s . 412 | c | add(divide(187, subtract(const_1, divide(15, const_100))), multiply(divide(187, subtract(const_1, divide(15, const_100))), divide(20, const_100))) | a shopkeeper loses 15 % , if an article is sold for rs . 187 . what should be the selling price of the article to gain 20 % ? | "given that sp = rs . 187 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 187 ) / 85 = 20 * 6 = rs . 220 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 220 * 120 ) / 100 = rs . 264 answer : c" | a = 15 / 100
b = 1 - a
c = 187 / b
d = 15 / 100
e = 1 - d
f = 187 / e
g = 20 / 100
h = f * g
i = c + h
|
a ) - 11 , b ) - 5 , c ) 0 , d ) 5 , e ) 11 | c | multiply(negate(multiply(divide(65, 2), 2)), 11) | if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ? | "( i ) 9 a - 11 b = 65 ( ii ) 2 a + 22 b = - 65 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ." | a = 65 / 2
b = a * 2
c = negate * (
|
a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35 | a | divide(add(add(add(multiply(5, const_3), add(5, multiply(5, const_2))), multiply(5, const_4)), multiply(add(const_4, const_1), 5)), 5) | find the average of all numbers between 1 and 76 which are divisible by 5 | "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 ) / 15 = 600 / 15 = 40 answer : option a" | a = 5 * 3
b = 5 * 2
c = 5 + b
d = a + c
e = 5 * 4
f = d + e
g = 4 + 1
h = g * 5
i = f + h
j = i / 5
|
a ) 40 , b ) 60.5 , c ) 52 , d ) 55 , e ) 36 | b | add(subtract(134, multiply(3.5, 22)), 3.5) | a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning . | explanation : let the average after 22 nd innings = x then average after 21 th innings = ( x - 3.5 ) therefore 21 ( x - 3.5 ) + 134 = 22 x therefore x = 60.5 answer : b | a = 3 * 5
b = 134 - a
c = b + 3
|
a ) 22 % , b ) 24 percent , c ) 25 % , d ) 28 % , e ) 27 % | b | multiply(divide(add(multiply(divide(20, const_100), 500), multiply(divide(30, const_100), subtract(800, 500))), 800), const_100) | for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 30 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman β s commission was approximately what percent of the total amoun... | "total sales = 800 commission = ( 20 / 100 ) * 500 + ( 30 / 100 ) * 300 = 100 + 90 = 190 % commission = ( 190 / 800 ) * 100 = 23.7 ~ 24 % answer is b" | a = 20 / 100
b = a * 500
c = 30 / 100
d = 800 - 500
e = c * d
f = b + e
g = f / 800
h = g * 100
|
a ) 21 , b ) 20 , c ) 22 , d ) 19 , e ) 24 | b | divide(subtract(subtract(subtract(subtract(135, const_1), const_2), const_3), const_4), 6) | in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 6 rows in all and a total of 135 bricks in the wall , how many bricks does the bottom row contain ? | "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 = 135 6 x - 15 = 135 6 x = 120 x = 20 answer : b" | a = 135 - 1
b = a - 2
c = b - 3
d = c - 4
e = d / 6
|
a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 59 , e ) 52.9 | d | divide(add(multiply(25, 50), multiply(40, 65)), add(25, 40)) | the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ? | "sum of the marks for the class of 25 students = 25 * 50 = 1250 sum of the marks for the class of 40 students = 40 * 65 = 2600 sum of the marks for the class of 65 students = 1250 + 2600 = 3850 average marks of all the students = 4850 / 65 = 59 . answer : d" | a = 25 * 50
b = 40 * 65
c = a + b
d = 25 + 40
e = c / d
|
a ) 18 , b ) 750 , c ) 23 , d ) 120 , e ) none of these | c | divide(circle_area(divide(34, multiply(2, const_pi))), 4) | how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ? | "circumference of circular bed = 34 cm area of circular bed = ( 34 ) 2 Γ’ Β β 4 Γ― β¬ space for each plant = 4 cm 2 Γ’ Λ Β΄ required number of plants = ( 34 ) 2 Γ’ Β β 4 Γ― β¬ Γ£ Β· 4 = 22.98 = 23 ( approx ) answer c" | a = 2 * math.pi
b = 34 / a
c = circle_area / (
|
a ) 550 , b ) 882 , c ) 772 , d ) 652 , e ) 271 | a | add(500, multiply(500, divide(10, const_100))) | a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 10 % ? | "cost price = rs . 500 profit = 10 % of 500 = rs . 50 selling price = cost price + profit = 500 + 50 = 550 answer : a" | a = 10 / 100
b = 500 * a
c = 500 + b
|
a ) 5 miles , b ) 8 miles , c ) 6 miles , d ) 13 miles , e ) 12 miles | d | multiply(divide(subtract(30, divide(multiply(add(5, 1), 24), const_60)), add(5, add(5, 1))), 5) | stacy and helon are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than helon ' s constant rate of 5 miles / hour . if helon starts her journey 24 minutes after stacy , how far from the original destination has helon walked when the two meet... | original distance between s and h = 30 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 30 - - - > t = 138 / 55 hours . thus h h... | a = 5 + 1
b = a * 24
c = b / const_60
d = 30 - c
e = 5 + 1
f = 5 + e
g = d / f
h = g * 5
|
a ) 14.05 , b ) 14.02 , c ) 277 , d ) 288 , e ) 222 | a | multiply(0.30103, divide(0.30103, 0.4771)) | if log 2 = 0.30103 and log 3 = 0.4771 , find the number of digits in ( 648 ) 5 | "log ( 648 ) 5 = 5 log ( 648 ) = 5 log ( 81 Γ 8 ) = 5 [ log ( 81 ) + log ( 8 ) ] = 5 [ log ( 34 ) + log ( 23 ) ] = 5 [ 4 log ( 3 ) + 3 log ( 2 ) ] = 5 [ 4 Γ 0.4771 + 3 Γ 0.30103 ] = 5 ( 1.9084 + 0.90309 ) = 5 Γ 2.81149 β 14.05 answer : a" | a = 0 / 30103
b = 0 * 30103
|
['a ) 15 : 12', 'b ) 15 : 14', 'c ) 15 : 16', 'd ) 15 : 22', 'e ) none of these'] | c | sqrt(divide(225, 256)) | if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is : | explanation : a 2 / b 2 = 225 / 256 = 15 / 16 < = > 4 a / 4 b = 4 β 15 / 4 β 16 = 15 / 16 = 15 : 16 option c | a = 225 / 256
b = math.sqrt(a)
|
a ) 49 , b ) 30 , c ) 29 , d ) 31 , e ) 32 | b | subtract(12702, multiply(floor(divide(12702, 99)), 99)) | what least number must be subtracted from 12702 to get number exactly 99 ? | "explanation : divide the given number by 99 and find the remainder . if you subtract the remainder from the given number then it is exactly divisible by 99 . 99 ) 12702 ( 128 99 280 198 822 792 30 required number is 30 . answer is b" | a = 12702 / 99
b = math.floor(a)
c = b * 99
d = 12702 - c
|
a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108 | a | add(40, multiply(divide(20, const_100), 40)) | if x is 20 percent greater than 40 , then x = | "x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a" | a = 20 / 100
b = a * 40
c = 40 + b
|
a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810 | a | multiply(divide(add(14, 56), const_2), divide(add(subtract(56, 14), 2), 2)) | in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ? | "the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a ." | a = 14 + 56
b = a / 2
c = 56 - 14
d = c + 2
e = d / 2
f = b * e
|
a ) 36 , b ) 96 , c ) 100 , d ) 76 , e ) 72 | b | multiply(multiply(divide(60, subtract(const_1, divide(2, 3))), divide(2, 3)), divide(4, 5)) | a certain automobile company β s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 60 vehicles that are not speedsters , how many speedster convert... | "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 60 vehicles . hence 2 / 3 constitutes 120 speedster convertibls = 120 * 4 / 5 = 96 b" | a = 2 / 3
b = 1 - a
c = 60 / b
d = 2 / 3
e = c * d
f = 4 / 5
g = e * f
|
a ) 20 lb , b ) 18 lb , c ) 12 lb , d ) 15 lb , e ) 5 lb | c | divide(12, const_1) | a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ? | "sol . 12 Γ· 1 = 12 . answer : c" | a = 12 / 1
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a ) 620 , b ) 610 , c ) 630 , d ) 625 , e ) 635 | a | add(multiply(divide(1320, add(60, multiply(75, divide(80, 120)))), 25), multiply(multiply(divide(1320, add(60, multiply(75, divide(80, 120)))), divide(80, 120)), 40)) | the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is | "let the price of one apple = a and price of one orange = b the price of 80 apples is equal to that of 120 oranges 80 a = 120 b = > 2 a = 3 b β b = 2 a / 3 - - - - - ( equation 1 ) price of 60 apples and 75 oranges together is rs . 1320 = > 60 a + 75 b = 1320 = > 4 a + 5 b = 88 β 4 a + 5 ( 2 a ) / 3 = 88 ( β΅ substitute... | a = 80 / 120
b = 75 * a
c = 60 + b
d = 1320 / c
e = d * 25
f = 80 / 120
g = 75 * f
h = 60 + g
i = 1320 / h
j = 80 / 120
k = i * j
l = k * 40
m = e + l
|
a ) 4 : 3 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 9 , e ) none | d | divide(7, add(2, 7)) | two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ? | let the c . p . of spirit be re . 1 litre . spirit in 1 litre mix . of a = 5 / 7 litre , c . p . of 1 litre mix . in a = re . 5 / 7 spirit in 1 litre mix . of b = 7 / 13 litre , c . p . of 1 litre mix . in b = re . 7 / 13 spirit in 1 litre mix . of c = 8 / 13 litre , mean price = re . 8 / 13 . by the rule of alligation... | a = 2 + 7
b = 7 / a
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a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 18 inches , e ) 66 inches | d | divide(add(multiply(7, const_12), 6), 5) | a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part . | "explanation : total length of scale in inches = ( 7 * 12 ) + 6 = 90 inches length of each of the 5 parts = 90 / 5 = 18 inches answer : d" | a = 7 * 12
b = a + 6
c = b / 5
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['a ) 18', 'b ) 6', 'c ) 27', 'd ) 48', 'e ) 36'] | e | multiply(multiply(multiply(const_2, const_2), const_3), const_3) | a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ? | volume of cube = lbh = 3 new cube l , b , h are increases of 3 l , 2 b , 2 h new volume of cube = 3 l * 2 b * 2 h = 12 lbh = 12 * 3 = 36 answer : e | a = 2 * 2
b = a * 3
c = b * 3
|
a ) $ 2.25 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.50 , e ) $ 3.75 | a | divide(multiply(multiply(3, 5), 0.60), const_4) | having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is this student β s weekly allowance ? | "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 60 cents ( 4 / 15 ) x = 60 x = $ 2.25 the answer is a ." | a = 3 * 5
b = a * 0
c = b / 4
|
a ) 91 , b ) 30 , c ) 45 , d ) 60 , e ) 90 | a | divide(multiply(14, subtract(14, const_1)), const_2) | there are 14 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ? | "10 players are there . two players play one game with one another . so 14 c 2 = 14 * 13 / 2 = 91 so option a is correct" | a = 14 - 1
b = 14 * a
c = b / 2
|
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90 | b | divide(multiply(30, divide(40, const_100)), subtract(divide(80, const_100), divide(60, const_100))) | a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ? | "60 % is 20 % - points above 40 % and 20 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 1 . so the team played a total of 30 + 30 = 60 games . the answer is b ." | a = 40 / 100
b = 30 * a
c = 80 / 100
d = 60 / 100
e = c - d
f = b / e
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a ) 2 : 5 , b ) 1 : 3 , c ) 2 : 7 , d ) 3 : 4 , e ) 1 : 5 | c | divide(subtract(4, 2), subtract(11, 4)) | cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ? | "2 % is 2 % - points below 4 % and 11 % is 7 % - points above 4 % . the ratio of a : b should be 2 : 7 . the answer is c ." | a = 4 - 2
b = 11 - 4
c = a / b
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a ) 30 , b ) 35 , c ) 37 , d ) 41 , e ) 43 | b | add(multiply(3, divide(subtract(10, divide(10, const_2)), subtract(3, divide(4, const_2)))), multiply(4, divide(subtract(10, divide(10, const_2)), subtract(3, divide(4, const_2))))) | 10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages | explanation : let a ' s age 10 years ago = x years . then , b ' s age 10 years ago = 2 x years . ( x + 10 ) / ( 2 x + lo ) = 3 / 4 = > x = 5 . so , the total of their present ages = ( x + 10 + 2 x + 10 ) = ( 3 x + 20 ) = 35 years . answer : option b | a = 10 / 2
b = 10 - a
c = 4 / 2
d = 3 - c
e = b / d
f = 3 * e
g = 10 / 2
h = 10 - g
i = 4 / 2
j = 3 - i
k = h / j
l = 4 * k
m = f + l
|
['a ) 5', 'b ) 6', 'c ) 9', 'd ) 13', 'e ) 28'] | c | divide(126, divide(add(negate(4), sqrt(add(power(4, const_2), multiply(4, multiply(126, 2))))), const_2)) | a rectangular tiled patio is composed of 126 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 126 tiles , and it will still be rectangular . how many rows are in the tile patio before ... | suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 126 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , n... | a = negate + (
b = 4 ** 2
c = 126 * 2
d = 4 * c
e = b + d
f = math.sqrt(e)
g = a / f
h = 126 / g
|
a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14 | c | subtract(39, subtract(add(26, 20), 17)) | in a class of 39 students 26 play football and play 20 long tennis , if 17 play above , many play neither ? | "26 + 20 - 17 = 29 39 - 29 = 10 play neither answer is c" | a = 26 + 20
b = a - 17
c = 39 - b
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a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2 | e | divide(divide(18, const_3), const_3) | if a * b denotes the greatest common divisor of a and b , then ( ( 12 * 16 ) * ( 18 * 12 ) ) = ? | "the greatest common divisor of 12 and 16 is 4 . hence 12 * 16 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 12 is 6 . hence 18 * 12 = 6 . hence ( ( 12 * 16 ) * ( 18 * 12 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e ." | a = 18 / 3
b = a / 3
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a ) 20 , b ) 19 , c ) 18 , d ) 17 , e ) 16 | a | divide(multiply(24, 15), 18) | if 24 men take 15 days to to complete a job , in how many days can 18 men finish that work ? | ans . 20 days | a = 24 * 15
b = a / 18
|
a ) 1200 ft , b ) 800 ft , c ) 900 ft , d ) 1000 ft , e ) 1500 ft | a | multiply(40, add(divide(multiply(40, divide(const_10, const_2)), const_3), divide(const_10, const_2))) | the circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long . what is the distance travelled by the cart , when the front wheel has done five more revolutions than the rear wheel ? | "total distance - x x / 40 - x / 48 = 5 x = 1200 ft answer a" | a = 10 / 2
b = 40 * a
c = b / 3
d = 10 / 2
e = c + d
f = 40 * e
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a ) 110 kmph , b ) 120 kmph , c ) 108 kmph , d ) 100 kmph , e ) 98 kmph | c | multiply(divide(600, subtract(30, 10)), const_3_6) | a train requires 10 seconds to pass a pole while it requires 30 seconds to cross a stationary train which is 600 mtrs long . find the speed of the train . | "in 10 s the train crosses the pole and in 30 sec the train crosses one more stationary train in 20 sec the train travels a distance of 600 mtrs speed = 600 / 20 = 30 m / s = 30 ( 3600 / 1000 ) = 30 * 18 / 5 = 108 kmph answer : c" | a = 30 - 10
b = 600 / a
c = b * const_3_6
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a ) 76 , b ) 80 , c ) 85 , d ) 87 , e ) 89 | b | subtract(multiply(add(10, const_1), add(4, 36)), multiply(10, 36)) | the average of runs of a cricket player of 10 innings was 36 . how many runs must he make in his next innings so as to increase his average of runs by 4 ? | "explanation : average = total runs / no . of innings = 36 so , total = average x no . of innings = 36 x 10 = 360 . now increase in avg = 4 runs . so , new avg = 36 + 4 = 40 runs total runs = new avg x new no . of innings = 40 x 11 = 440 runs made in the 11 th inning = 440 - 360 = 80 answer : b" | a = 10 + 1
b = 4 + 36
c = a * b
d = 10 * 36
e = c - d
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a ) 78 % , b ) 66 % , c ) 62 % , d ) 64 % , e ) 60 % | b | multiply(divide(subtract(800, add(add(add(62, 62), add(60, 48)), 40)), 800), const_100) | john had a stock of 800 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ? | "let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 800 - n = 1400 - 272 = 528 percentage books not sold / total number of books = 528 / 800 = 0.66 = 66 % correct answer b" | a = 62 + 62
b = 60 + 48
c = a + b
d = c + 40
e = 800 - d
f = e / 800
g = f * 100
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a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 15,000 , e ) e ) 11,100 | d | multiply(multiply(const_4, const_2), const_100) | a certain city with a population of 180,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ? | "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 180 k x = 15,000 answer : d" | a = 4 * 2
b = a * 100
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a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | c | add(const_3, const_3) | a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 100 that is both a prime and a palindrome . what is the sum of the digits of p ? | "given that p is smallest integer greater than 200 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime n... | a = 3 + 3
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a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 12 , e ) e ) 15 | a | divide(divide(6, subtract(divide(40, const_60), divide(20, const_60))), const_3) | circular gears l and r start to rotate at the same time at the same rate . gear l makes 20 complete revolutions per minute and gear r makes 40 revolutions per minute . how many seconds after the gears start to rotate will gear r have made exactly 6 more revolutions than gear l ? | gear l - - 20 rotations per 60 seconds - - 2 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 2 rotations hence every 6 seconds the difference between the number of rotations ... | a = 40 / const_60
b = 20 / const_60
c = a - b
d = 6 / c
e = d / 3
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a ) 12 , b ) 3 , c ) 6 , d ) 9 , e ) 10 | b | add(multiply(4, const_100), multiply(multiply(subtract(const_1, multiply(add(divide(const_1, 4), divide(const_1, 12)), const_2)), 4), const_60)) | two pipes a and b can fill a tank in 4 and 12 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ? | "part filled by a in 1 min . = 14 part filled by b in 1 min . = 1 / 12 part filled by ( a + b ) in 1 min . = 1 / 4 + 1 / 12 = 1 / 3 . both the pipes can fill the tank in 3 minutes . answer : b" | a = 4 * 100
b = 1 / 4
c = 1 / 12
d = b + c
e = d * 2
f = 1 - e
g = f * 4
h = g * const_60
i = a + h
|
a ) 130 , b ) 132 , c ) 134 , d ) 136 , e ) 138 | c | divide(1206, subtract(43, 34)) | a girl was asked to multiply a certain number by 43 . she multiplied it by 34 and got his answer less than the correct one by 1206 . find the number to be multiplied . | "let the required number be x . then , 43 x β 34 x = 1206 or 9 x = 1206 or x = 134 . required number = 134 . answer : c" | a = 43 - 34
b = 1206 / a
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a ) 25 , b ) 66 , c ) 18 , d ) 37 , e ) 01 | d | divide(multiply(divide(multiply(18.5, 50), const_100), const_100), 25) | a company pays 18.5 % dividend to its investors . if an investor buys rs . 50 shares and gets 25 % on investment , at what price did the investor buy the shares ? | "explanation : dividend on 1 share = ( 18.5 * 50 ) / 100 = rs . 9.25 rs . 25 is income on an investment of rs . 100 rs . 9.25 is income on an investment of rs . ( 9.25 * 100 ) / 25 = rs . 37 answer : d" | a = 18 * 5
b = a / 100
c = b * 100
d = c / 25
|
a ) 12.9 , b ) 12.5 , c ) 12.6 , d ) 12.2 , e ) 12.1 | e | divide(multiply(20, 1000), add(1000, 650)) | 1000 men have provisions for 20 days . if 650 more men join them , for how many days will the provisions last now ? | "1000 * 20 = 1650 * x x = 12.1 answer : e" | a = 20 * 1000
b = 1000 + 650
c = a / b
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a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 100000 | e | divide(multiply(90000, const_100), subtract(const_100, 10)) | david ' s bank ' s saving amount is decreased 10 % due to loan payment and current balance is rs . 90000 . find the actual balance before deduction ? | 10 % decreased 90 % balance = 90000 100 % = 90000 / 90 * 100 = 100000 answer : e | a = 90000 * 100
b = 100 - 10
c = a / b
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a ) s . 800 , b ) s . 2400 , c ) s . 4000 , d ) s . 5500 , e ) s . 4200 | d | multiply(subtract(multiply(divide(2200, 2), 3), 2200), 5) | the ratio of incomes of two person p 1 and p 2 is 5 : 4 and the ratio of their expenditures is 3 : 2 . if at the end of the year , each saves rs . 2200 , then what is the income of p 1 ? | "let the income of p 1 and p 2 be rs . 5 x and rs . 4 x respectively and let their expenditures be rs . 3 y and 2 y respectively . then , 5 x β 3 y = 2200 β¦ ( i ) and 4 x β 2 y = 2200 β¦ β¦ . . ( ii ) on multiplying ( i ) by 2 , ( ii ) by 3 and subtracting , we get : 2 x = 2200 - > x = 1100 p 1 β s income = rs 5 * 1100 =... | a = 2200 / 2
b = a * 3
c = b - 2200
d = c * 5
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a ) 81 , b ) 81.5 , c ) 82 , d ) 84.5 , e ) none of these | b | divide(add(multiply(83, subtract(79, 76)), add(multiply(85, subtract(81, 76)), multiply(76, subtract(83, 79)))), add(subtract(81, 76), add(subtract(83, 79), subtract(79, 76)))) | 3 math classes : x , y , and z , take an algebra test . the average score in class x is 83 . the average score in class y is 76 . the average score in class z is 85 . the average score of all students in classes x and y together is 79 . the average score of all students in classes y and z together is 81 . what is the a... | explanation : let the number of students in classes x , y and z be a , b and c respectively . then total of x = 83 a total of y = 76 b total of z = 85 c and , ( 83 a + 76 b ) / ( a + b ) = 79 . i . e 4 a = 3 b . also , ( 76 b + 85 c ) / ( b + c ) = 81 . i . e 4 c = 5 b . hence , b = ( 4 / 3 ) a , c = ( 5 / 4 ) b = ( 5 ... | a = 79 - 76
b = 83 * a
c = 81 - 76
d = 85 * c
e = 83 - 79
f = 76 * e
g = d + f
h = b + g
i = 81 - 76
j = 83 - 79
k = 79 - 76
l = j + k
m = i + l
n = h / m
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a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8 | b | divide(subtract(const_1, add(multiply(divide(const_1, 4), const_2), multiply(divide(const_1, 14), const_2))), divide(const_1, 14)) | a can finish a piece of work in 4 days . b can do it in 14 days . they work together for two days and then a goes away . in how many days will b finish the work ? | "2 / 4 + ( 2 + x ) / 14 = 1 = > x = 5 days answer : b" | a = 1 / 4
b = a * 2
c = 1 / 14
d = c * 2
e = b + d
f = 1 - e
g = 1 / 14
h = f / g
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a ) 4.37 % , b ) 7.3 % , c ) 7.6 % , d ) 8.75 % , e ) none | b | add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, const_3)), const_1000)), 1), const_10), const_100), const_4) | the population of a town increased from 1 , 34,000 to 2 , 32,500 in a decade . the average percent increase of population per year is : | "explanation : increase in 10 years = ( 232500 - 134000 ) = 98500 . increase % = ( 98500 / 134000 x 100 ) % = 73 % . required average = ( 73 / 10 ) % = 7.3 % . answer : option b" | a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 2 + 3
f = e * 100
g = d - f
h = 3 + 4
i = h * 10
j = 2 + 3
k = i + j
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
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a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | c | subtract(divide(30, const_2), 1) | if r is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of r ? | answer is c . numbers in format of 3 ^ k in the series from 1 to 30 inclusive r are : 3 * 1 , 3 * 2 , 3 * 3 , 3 * 4 , 3 * 5 , 3 * 3 * 2 , 3 * 7 , 3 * 8 , 3 * 3 * 3 , 3 * 10 . total number of 3 = 13 . so k = 14 . | a = 30 / 2
b = a - 1
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a ) 33 , b ) 30 , c ) 36 , d ) 28 , e ) 26 | a | divide(subtract(460, multiply(8, 41)), const_4) | rs . 460 was divided among 41 boys and girls such that each boy rs . 12 and each girl got rs . 8 . what is the number of boys ? | explanation : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - solution 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - assume that the number of b... | a = 8 * 41
b = 460 - a
c = b / 4
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a ) 12 , b ) 27 , c ) 29 , d ) 55 , e ) 95 | e | add(divide(18000, 200), 5) | a shopkeeper sells 200 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ? | sp per metre = 18000 / 200 = rs . 90 loss per metre = rs . 5 cp per metre = 90 + 5 = rs . 95 . answer : e | a = 18000 / 200
b = a + 5
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a ) 29 , b ) 27 , c ) 28 , d ) 24 , e ) 21 | a | add(add(multiply(2, 11), 5), 2) | find the total number of prime factors in the expression ( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 . | "( 4 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = ( 2 x 2 ) ^ 11 x ( 7 ) ^ 5 x ( 11 ) ^ 2 = 2 ^ 11 x 2 ^ 11 x 7 ^ 5 x 11 ^ 2 = 2 ^ 22 x 7 ^ 5 x 11 ^ 2 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer is a ." | a = 2 * 11
b = a + 5
c = b + 2
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a ) 3.0 , b ) 5.0 , c ) 5.5 , d ) 6.5 , e ) 6.75 | e | multiply(45, divide(15, 100)) | a glucose solution contains 15 grams of glucose per 100 cubic centimeters of solution . if 45 cubic centimeters of the solution were poured into an empty container , how many grams of glucose would be in the container ? | "construct an equation : 15 / 100 = x / 45 - > x = 6.75 answer : e ." | a = 15 / 100
b = 45 * a
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a ) 22 , b ) 12 , c ) 7.5 , d ) 99 , e ) 21 | c | divide(multiply(120, const_2), add(speed(120, 15), speed(120, 5))) | two trains of equal lengths take 5 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ? | "speed of the first train = 120 / 5 = 24 m / sec . speed of the second train = 120 / 15 = 8 m / sec . relative speed = 24 + 8 = 32 m / sec . required time = ( 120 + 120 ) / 32 = 7.5 sec . answer : c" | a = 120 * 2
b = speed + (
c = a / b
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a ) 6 , b ) 6.6 , c ) 8.8 , d ) 100 , e ) 110 | c | divide(880, divide(multiply(multiply(10, 880), divide(add(const_100, 10), const_100)), subtract(multiply(880, divide(add(const_100, 10), const_100)), 880))) | machine a and machine b are each used to manufacture 880 sprockets . it takes machine a 10 hours longer to produce 880 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ? | "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 880 qt = 800 for a : ( t + 10 ) ( q ) = 880 qt + 10 q = 880 800 + 10 q = 880 q = 8 so a can produce 8 / hour . then b can produce = 8 ( 1.1 ) = 8.8 / hour . c" | a = 10 * 880
b = 100 + 10
c = b / 100
d = a * c
e = 100 + 10
f = e / 100
g = 880 * f
h = g - 880
i = d / h
j = 880 / i
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a ) 160 , b ) 150 , c ) 100 , d ) 66 , e ) 50 | d | divide(subtract(multiply(204, divide(16, const_100)), 30), subtract(divide(16, const_100), divide(12, const_100))) | an empty fuel tank with a capacity of 204 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ? | "say there are a gallons of fuel a in the tank , then there would be 204 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 204 - a gallons of fuel b is 0.16 ( 204 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 204 - a ) = 30 - - > a =... | a = 16 / 100
b = 204 * a
c = b - 30
d = 16 / 100
e = 12 / 100
f = d - e
g = c / f
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a ) 4676 , b ) 4678 , c ) 9950 , d ) 9504 , e ) 9936 | c | multiply(floor(divide(power(const_10, 4), 50)), 50) | what is the largest 4 digit number exactly divisible by 50 ? | "largest 4 digit number = 9999 9999 Γ· 50 = 199 , remainder = 49 hence largest 4 digit number exactly divisible by 50 = 9999 - 49 = 9950 answer : c" | a = 10 ** 4
b = a / 50
c = math.floor(b)
d = c * 50
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a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105 | d | multiply(divide(add(subtract(55, 40), 7.5), subtract(55, 40)), const_60) | if teena is driving at 55 miles per hour and is currently 7.5 miles behind poe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of poe ? | "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . poe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena ca... | a = 55 - 40
b = a + 7
c = 55 - 40
d = b / c
e = d * const_60
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a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 % | d | divide(multiply(subtract(1512, 1400), const_100), 1400) | the compound interest earned on a sum for the second and the third years are $ 1400 and $ 1512 respectively . what is the rate of interest ? | "1512 - 1400 = 112 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 112 ) / ( 1400 ) = 8 % the answer is d ." | a = 1512 - 1400
b = a * 100
c = b / 1400
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a ) 86 , b ) 90 , c ) 92 , d ) 94 , e ) 96 | a | add(multiply(add(multiply(6, const_3), 2), divide(add(multiply(6, const_3), 2), 5)), 6) | in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is | "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 . a" | a = 6 * 3
b = a + 2
c = 6 * 3
d = c + 2
e = d / 5
f = b * e
g = f + 6
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a ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 7 | a | divide(multiply(44, 432), 31) | a number when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 31 | "explanation : p Γ· 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 option a" | a = 44 * 432
b = a / 31
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a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 250 | e | add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(160, 120), 120), 120), 3)), 120)) | if $ 120 invested at a certain rate of simple interest amounts to $ 160 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? | "120 amounts to 160 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 160 120 + 120 * ( r / 100 ) * ( 3 ) = 160 = > r = 100 / 9 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) 250 answer is e ." | a = 150 * 6
b = 160 - 120
c = b * 120
d = c / 120
e = d / 3
f = a * e
g = f / 120
h = 150 + g
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a ) 4.5 % , b ) 5.5 % , c ) 6.5 % , d ) 8.75 % , e ) none | a | add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(1, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(1, const_3)), const_1000)), 1), const_10), const_100), const_4) | the population of a town increased from 1 , 33,400 to 1 , 93,500 in a decade . the average percent increase of population per year is : | "explanation : increase in 10 years = ( 193500 - 133400 ) = 60100 . increase % = ( 60100 / 133400 x 100 ) % = 45 % . required average = ( 45 / 10 ) % = 4.5 % . answer : option a" | a = 10 * 1000
b = a * 10
c = b - 1000
d = c - 1000
e = 1 + 3
f = e * 100
g = d - f
h = 3 + 4
i = h * 10
j = 1 + 3
k = i + j
l = k * 1000
m = g / l
n = m - 1
o = n / 10
p = o * 100
q = p + 4
|
a ) a ) 1200000 , b ) b ) 562000 , c ) c ) 800000 , d ) d ) 500000 , e ) e ) 652000 | a | multiply(divide(60000, subtract(const_100, add(add(multiply(20, 3), 30), 5))), const_100) | a person distributed 20 % of his income to his 3 children each . he deposited 30 % of his income to his wife ' s account . he donated 5 % of remaining amount to an orphan house . finally he has $ 60000 . find his total income ? | "3 children got = 3 * 20 % = 60 % wife got = 30 % orphan house = 5 % total = 60 + 30 + 5 = 95 % remaining = 100 - 95 = 5 % 5 % = 60000 100 % = 60000 * 100 / 5 = $ 1200000 answer is a" | a = 20 * 3
b = a + 30
c = b + 5
d = 100 - c
e = 60000 / d
f = e * 100
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a ) none , b ) one , c ) two , d ) three , e ) four | c | subtract(15, multiply(3, const_4)) | a = 5 ^ 15 - 625 ^ 3 and a / x is an integer , where x is a positive integer greater than 1 , such that it does not have a factor p such that 1 < p < x , then how many different values for x are possible ? | "a = 5 ^ 15 - 625 ^ 3 = > 5 ^ 15 - ( 5 ^ 4 ) ^ 3 = > 5 ^ 15 - 5 ^ 12 = 5 ^ 12 ( 5 ^ 3 - 1 ) = 5 ^ 12 * 124 124 = 31 * 4 a / x is integer for condition of 2 < p < x only 5 and 31 satisfies this hence answer is c" | a = 3 * 4
b = 15 - a
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a ) 60 , b ) 50 , c ) 40 , d ) 70 , e ) 65 | c | divide(360, divide(multiply(6, 3), 2)) | a car takes 6 hours to cover a distance of 360 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ? | "time = 6 distance = 360 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 360 / 9 = 40 kmph answer c ." | a = 6 * 3
b = a / 2
c = 360 / b
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a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 47 / 84 | e | multiply(multiply(multiply(divide(multiply(7, const_2), multiply(7, const_2)), divide(multiply(4, 4), subtract(multiply(7, const_2), const_1))), divide(subtract(multiply(4, 4), const_2), multiply(4, 4))), divide(subtract(subtract(multiply(4, 4), const_2), const_2), subtract(multiply(4, 4), const_1))) | if 4 people are selected from a group of 7 married couples , what is the probability that none of them would be married to each other ? | "if we are to select 4 people from 7 couples without any restriction , how many ways can we make the selection ? 14 ! / 4 ! 10 ! = 1001 if we are to select 4 people from 7 couples with restriction that no married couple can both make it to the group , only a representative ? 7 ! / 4 ! 3 ! = 35 but we know that to selec... | a = 7 * 2
b = 7 * 2
c = a / b
d = 4 * 4
e = 7 * 2
f = e - 1
g = d / f
h = c * g
i = 4 * 4
j = i - 2
k = 4 * 4
l = j / k
m = h * l
n = 4 * 4
o = n - 2
p = o - 2
q = 4 * 4
r = q - 1
s = p / r
t = m * s
|
a ) 27.5 % , b ) 25.6 % , c ) 31.5 % , d ) 35.9 % , e ) 29.5 % | a | divide(multiply(subtract(add(multiply(divide(multiply(100, 50), const_100), divide(add(const_100, 25), const_100)), multiply(divide(multiply(100, 50), const_100), divide(add(const_100, 30), const_100))), 100), const_100), 100) | a shopkeeper has 100 kg of apples . he sells 50 % of these at 25 % profit and remaining 50 % at 30 % profit . find his % profit on total . | "total number of apples = 100 let the cost price be x selling price at 25 % profit = 1.25 x selling price at 30 % profit = 1.3 x profit % = ( ( sp - cp ) / cp ) * 100 profit % = ( ( 1 / 2 ) * 100 * 1.25 x + ( 1 / 2 ) * 100 * 1.3 x - 100 x ) / 100 x * 100 = ( 255 - 200 ) / 2 = 27.5 % answer is a" | a = 100 * 50
b = a / 100
c = 100 + 25
d = c / 100
e = b * d
f = 100 * 50
g = f / 100
h = 100 + 30
i = h / 100
j = g * i
k = e + j
l = k - 100
m = l * 100
n = m / 100
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | e | divide(multiply(multiply(multiply(const_4, 4), 2), 1), multiply(multiply(4, 2), 1)) | a card game called β high - low β divides a deck of 52 playing cards into 2 types , β high β cards and β low β cards . there are an equal number of β high β cards and β low β cards in the deck and β high β cards are worth 2 points , while β low β cards are worth 1 point . if you draw cards one at a time , how many ways... | "great question ravih . this is a permutations problem ( order matters ) with repeating elements . given thatlowcards are worth 1 pt andhigh cards 2 pts , and you must draw 3 low cards , we know that you must also draw 1 high card . the formula for permutations problems with repeating elements isn ! / a ! b ! . . . whe... | a = 4 * 4
b = a * 2
c = b * 1
d = 4 * 2
e = d * 1
f = c / e
|
a ) 3.09 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 % | a | multiply(subtract(inverse(divide(970, multiply(multiply(add(const_4, const_1), const_2), const_100))), const_1), const_100) | a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 970 gm . for a kg . his gain is β¦ % . | "his percentage gain is 100 * 30 / 970 as he is gaining 30 units for his purchase of 970 units . so 3.09 % . answer : a" | a = 4 + 1
b = a * 2
c = b * 100
d = 970 / c
e = 1/(d)
f = e - 1
g = f * 100
|
a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24 | c | divide(multiply(const_12, log(2)), log(2)) | if 2 ^ ( 2 w ) = 8 ^ ( w β 6 ) , what is the value of w ? | "2 ^ ( 2 w ) = 8 ^ ( w β 6 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w β 6 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 18 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 18 w = 18 the answer is c ." | a = math.log(2)
b = 12 * a
c = math.log(2)
d = b / c
|
a ) 12.45 mph , b ) 11.25 mph , c ) 10.95 mph , d ) 10.91 mph , e ) 10.56 mph | d | divide(20, add(divide(10, subtract(20, 10)), divide(10, 12))) | tom traveled the entire 20 miles trip . if he did the first 10 miles of at a constant rate 12 miles per hour and the remaining trip of at a constant rate 10 miles per hour , what is the his average speed , in miles per hour ? | avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 10 + 10 ) / ( ( 10 / 12 ) + ( 10 / 10 ) = 120 / 11 = 10.91 mph d | a = 20 - 10
b = 10 / a
c = 10 / 12
d = b + c
e = 20 / d
|
a ) a ) 2 , b ) b ) 6 , c ) c ) 8 , d ) d ) 15 , e ) e ) 20 | d | multiply(3, 5) | a , b are positive integers . the remainder of a to be divided by 8 is 3 and the remainder of b to be divided by 6 is 5 . which is possible to be the remainder of a * b to be divided by 48 | two ways to do it . . . a = 8 x + 3 . . b = 6 y + 5 . . 1 ) convenient way . . take x and y as 0 , and you will get a * b as 3 * 5 = 15 answer : d | a = 3 * 5
|
a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 7.2 , e ) 9 | e | divide(inverse(divide(inverse(add(const_3, const_2)), add(const_1, 1.25))), 1.25) | one pipe can fill a pool 1.25 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the faster pipe is used ? | say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.25 r = 5 r / 4 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 5 r / 4 = 1 / 5 - - > r = 4 / 45 pool / hour , faster pipe fills at ... | a = 3 + 2
b = 1/(a)
c = 1 + 1
d = b / c
e = 1/(d)
f = e / 1
|
a ) 10 , b ) 15 , c ) 20 , d ) 30 , e ) 35 | c | sqrt(multiply(4, const_100)) | the revenue from sales items in 1996 increases by x percent , compared in 1995 and the revenue in 1997 decreases by x percent , compared in 1996 . if the revenue from sales items in 1997 decreases by 4 percent , compared in 1995 , what is the value of x ? | 1995 - let the value be z 1996 - x % increase - z ( 1 + x / 100 ) 1997 - x % decrease - z ( 1 + x / 100 ) ( 1 - x / 100 ) from 95 to 97 decrease is 4 % hence , [ z - { z ( 1 + x / 100 ) ( 1 - x / 100 ) } ] / z = 4 / 100 solving x = 20 % c is the answer | a = 4 * 100
b = math.sqrt(a)
|
a ) $ 642986 , b ) $ 642987 , c ) $ 642988 , d ) $ 642989 , e ) $ 642990 | b | add(642986, divide(9, 9)) | peter has $ 642986 in his savings account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among his 9 children ? | to find the least amount the man should add to his saving account to split the money evenly among his 9 children , he needs to make the total divisible by 9 simply add the individual digits of the total = 6 + 4 + 2 + 9 + 8 + 6 = 35 if you add 1 , the number is divisible by 9 ( 35 + 1 ) correct option : b | a = 9 / 9
b = 642986 + a
|
a ) 11.12 , b ) 10.11 , c ) 72 , d ) 10.66 , e ) 9.2 | d | multiply(divide(const_4, 3), power(3, 3)) | the measurement of a rectangular box with lid is 25 cmx 4 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of Ο cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere ) | "d = 4 , r = 2 ; volume of the largest sphere = 4 / 3 Ο r 3 = 4 / 3 * Ο * 2 * 2 * 2 = 10.66 Ο cm 3 answer : d" | a = 4 / 3
b = 3 ** 3
c = a * b
|
a ) 425 miles , b ) 625 miles , c ) 300 miles , d ) 225 miles , e ) 625 miles | c | multiply(60, 5) | a car travels at a speed of 60 miles per hour . how far will it travel in 5 hours ? | "during each hour , the car travels 65 miles . for 5 hours it will travel 60 + 60 + 60 + 60 + 60 = 5 * 65 = 300 miles correct answer c" | a = 60 * 5
|
a ) 12 km , b ) 3 km , c ) 4 km , d ) 5 km , e ) 6 km | a | divide(multiply(72, divide(multiply(10, const_1000), const_60)), const_1000) | find the distance covered by a man walking for 72 min at a speed of 10 km / hr ? | "distance = 10 * 72 / 60 = 12 km answer is a" | a = 10 * 1000
b = a / const_60
c = 72 * b
d = c / 1000
|
a ) 276 , b ) 299 , c ) 312 , d ) 322 , e ) none | d | multiply(23, 14) | the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is | "solution clearly , the numbers are ( 23 x 13 ) and ( 23 x 14 ) . larger number = ( 23 x 14 ) = 322 . answer d" | a = 23 * 14
|
a ) 0.5 % , b ) 0.2 % , c ) 1.5 % , d ) 2 % , e ) 3 % | b | multiply(divide(2, 1), const_100) | what percent is 2 gm of 1 kg ? | "1 kg = 1000 gm 2 / 1000 Γ 100 = 200 / 1000 = 1 / 5 = 0.2 % b )" | a = 2 / 1
b = a * 100
|
a ) 71.11 , b ) 71.12 , c ) 72.4 , d ) 71.17 , e ) 71.13 | c | multiply(320, divide(const_1, add(divide(160, 75), divide(160, 70)))) | a car travels first 160 km at 75 km / hr and the next 160 km at 70 km / hr . what is the average speed for the first 320 km of the tour ? | "car travels first 160 km at 75 km / hr time taken to travel first 160 km = distancespeed = 160 / 75 car travels next 160 km at 70 km / hr time taken to travel next 160 km = distancespeed = 160 / 70 total distance traveled = 160 + 160 = 2 Γ 160 total time taken = 160 / 75 + 160 / 70 average speed = total distance trave... | a = 160 / 75
b = 160 / 70
c = a + b
d = 1 / c
e = 320 * d
|
a ) 62 m , b ) 54 m , c ) 50 m , d ) 55 m , e ) 56 m | c | multiply(9, subtract(subtract(multiply(divide(multiply(4, const_1000), const_3600), 10), multiply(divide(multiply(2, const_1000), const_3600), 9)), divide(multiply(2, const_1000), const_3600))) | a train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively . what is the length of the train ? | explanation : let x is the length of the train in meter and v is its speed in kmph x / 9 = ( v - 2 ) ( 10 / 36 ) - - - ( 1 ) x / 10 = ( v - 4 ) ( 10 / 36 ) - - - ( 2 ) dividing equation 1 with equation 2 10 / 9 = ( v - 2 ) / ( v - 4 ) = > 10 v - 40 = 9 v - 18 = > v = 22 substituting in equation 1 , x / 9 = 200 / 36 = >... | a = 4 * 1000
b = a / 3600
c = b * 10
d = 2 * 1000
e = d / 3600
f = e * 9
g = c - f
h = 2 * 1000
i = h / 3600
j = g - i
k = 9 * j
|
a ) 7.6 , b ) 8.7 , c ) 9.1 , d ) 10.2 , e ) 11.6 | d | divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | what is 15 percent of 68 ? | "( 15 / 100 ) * 68 = 10.2 the answer is d ." | a = 3 + 2
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4
g = 3 + 2
h = f * g
i = 3 + 2
j = i * 2
k = h * j
l = e + k
m = 3 + 3
n = l + m
o = 15 * n
p = o / 100
|
a ) a ) 10.5 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20 | a | divide(subtract(25, power(2, 2)), 2) | if a - b = 2 and a 2 + b 2 = 25 , find the value of ab . | "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 25 - 4 = 21 ab = 10.5 answer : a" | a = 2 ** 2
b = 25 - a
c = b / 2
|
a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5 | c | sqrt(divide(98, const_2)) | the area of a parallelogram is 98 sq m and its altitude is twice the corresponding base . then the length of the base is ? | "2 x * x = 98 = > x = 7 answer : c" | a = 98 / 2
b = math.sqrt(a)
|
a ) 40 , b ) 72 , c ) 84 , d ) 90 , e ) 108 | a | multiply(subtract(divide(multiply(const_2, const_2), subtract(8, multiply(const_2, 2))), divide(const_2, subtract(8, 2))), const_60) | tom and linda stand at point a . linda begins to walk in a straight line away from tom at a constant rate of 2 miles per hour . one hour later , tom begins to jog in a straight line in the exact opposite direction at a constant rate of 8 miles per hour . if both tom and linda travel indefinitely , what is the positive ... | "a is the answer . . . . d = ts where d = distance , t = time and s = speed to travel half distance , ( 2 + 2 t ) = 8 t = = > t = 1 / 3 = = > 20 minutes to travel double distance , 2 ( 2 + 2 t ) = 8 t = = > 1 = = > 60 minutes difference , 40 minutes a" | a = 2 * 2
b = 2 * 2
c = 8 - b
d = a / c
e = 8 - 2
f = 2 / e
g = d - f
h = g * const_60
|
a ) 240 , b ) 388 , c ) 379 , d ) 277 , e ) 320 | e | multiply(divide(840, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8)))) | a and b began business with rs . 3000 and rs . 4000 after 8 months , a withdraws rs . 1000 and b advances rs . 1000 more . at the end of the year , their profits amounted to rs . 840 find the share of a . | "explanation : ( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 840 = 320 answer : e" | a = 3000 * 8
b = 3000 - 1000
c = 12 - 8
d = b * c
e = a + d
f = 4000 * 8
g = 4000 + 1000
h = 12 - 8
i = g * h
j = f + i
k = e + j
l = 840 / k
m = 3000 * 8
n = 3000 - 1000
o = 12 - 8
p = n * o
q = m + p
r = l * q
|
a ) 1 / 6 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 3 , e ) 2 / 3 | e | subtract(1, multiply(divide(const_2, add(const_2, const_3)), divide(add(const_2, const_3), add(add(const_2, const_3), const_1)))) | set # 1 = { a , b , o , d , e } set # 2 = { k , l , m , n , u , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ? | at least questions are best solved by taking the opposite scenario and subtracting it from 1 . probability of choosing no vowel from set 1 is 2 / 5 and set 2 is 5 / 6 . multiply these to get 1 / 3 . therefore , probability of picking at least one vowel = 1 - 1 / 3 = 2 / 3 . answer = e | a = 2 + 3
b = 2 / a
c = 2 + 3
d = 2 + 3
e = d + 1
f = c / e
g = b * f
h = 1 - g
|
a ) a ) 36 , b ) b ) 12 , c ) c ) 18 , d ) d ) 64 , e ) e ) 10 | b | add(multiply(3, 3), 3) | the value of x + ( xx ) when x = 3 is : | x + ( xx ) put the value of x = 2 in the above expression we get , 3 + ( 33 ) = 3 + ( 3 Γ 3 ) = 3 + ( 9 ) = 3 + 9 = 12 b | a = 3 * 3
b = a + 3
|
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