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 ) 45 cm , b ) 18 cm , c ) 90 cm , d ) 180 cm , e ) none of these | e | divide(multiply(const_4, divide(power(12, const_3), power(16, const_2))), const_3) | a metallic sphere of radius 12 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ? | volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . Ο ( 16 ) 2 * h = ( 4 / 3 ) Ο ( 12 ) 3 = > h = 9 cm answer : e | a = 12 ** 3
b = 16 ** 2
c = a / b
d = 4 * c
e = d / 3
|
a ) 1 / 6 , b ) 2 / 55 , c ) 14 / 55 , d ) 12 / 55 , e ) 3 / 4 | c | multiply(divide(subtract(12, 4), 12), divide(subtract(subtract(12, 4), const_1), subtract(12, const_1))) | in a box of 12 pens , a total of 4 are defective . if a customer buys 3 pens selected at random from the box , what is the probability that neither pen will be defective ? | "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) i . e . probability of third pen not being defective = ( 6 / 10 ) probability of both pen being non - defect... | a = 12 - 4
b = a / 12
c = 12 - 4
d = c - 1
e = 12 - 1
f = d / e
g = b * f
|
a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19 | d | multiply(divide(33, add(add(divide(20, const_100), const_1), const_1)), add(divide(20, const_100), const_1)) | two friends plan to walk along a 33 - km trail , starting at opposite ends of the trail at the same time . if friend p ' s rate is 20 % faster than friend q ' s , how many kilometers will friend p have walked when they pass each other ? | "if q complete x kilometers , then p completes 1.2 x kilometers . x + 1.2 x = 33 2.2 x = 33 x = 15 then p will have have walked 1.2 * 15 = 18 km . the answer is d ." | a = 20 / 100
b = a + 1
c = b + 1
d = 33 / c
e = 20 / 100
f = e + 1
g = d * f
|
a ) 720 , b ) 180 , c ) 75 , d ) 65 , e ) none of these | c | multiply(multiply(add(floor(2.30), multiply(divide(subtract(2.30, floor(2.30)), const_60), const_100)), const_3), const_10) | the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is | "explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c" | a = math.floor(2, 30)
b = math.floor(2, 30)
c = 2 - 30
d = c / const_60
e = d * 100
f = a + e
g = f * 3
h = g * 10
|
a ) 325 , b ) 350 , c ) 375 , d ) 400 , e ) 425 | c | multiply(divide(multiply(90, const_1000), const_3600), 15) | a train running at the speed of 90 km / hr crosses a pole in 15 seconds . what is the length of the train ? | "speed = ( 90 x ( 5 / 18 ) m / sec = ( 25 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 ) x 15 ) m = 375 m c" | a = 90 * 1000
b = a / 3600
c = b * 15
|
a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 2 hours , e ) 2 hours 10 minutes | d | add(multiply(sqrt(divide(60, 90)), 90), 60) | two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 60 minute... | "both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the rat... | a = 60 / 90
b = math.sqrt(a)
c = b * 90
d = c + 60
|
a ) 480 , b ) 239 , c ) 270 , d ) 282 , e ) 112 | a | add(multiply(multiply(2, 4), const_100), multiply(3, 4)) | four numbers are in the ratio 2 : 3 : 4 : 5 add up to give a sum of 1344 . find the biggest number . | answer : a | a = 2 * 4
b = a * 100
c = 3 * 4
d = b + c
|
a ) 4 , b ) 6 , c ) 8 , d ) 5 , e ) 10 | d | subtract(divide(multiply(20, add(const_4, const_1)), 10), add(const_4, const_1)) | five machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ? | rate of one machine = 1 job / ( 20 * 5 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 5 * 20 ) * 10 * x = 1 job x = 10 10 - 5 = 5 answer : d | a = 4 + 1
b = 20 * a
c = b / 10
d = 4 + 1
e = c - d
|
a ) 13 , b ) 25 , c ) 26 , d ) 27 , e ) 29 | a | divide(add(multiply(multiply(divide(5, 2), 2), 7), 4), subtract(multiply(divide(5, 2), 2), 2)) | find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 5 / 2 ? | "x / 2 y = 3 / 2 = > x = 10 y / 2 = 5 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 5 y ) ) + 4 y ) / ( 5 y - 2 y ) = > 39 y / 3 y = 13 answer : a" | a = 5 / 2
b = a * 2
c = b * 7
d = c + 4
e = 5 / 2
f = e * 2
g = f - 2
h = d / g
|
a ) 3641 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972 | a | subtract(multiply(add(multiply(const_100, const_100), multiply(multiply(const_100, divide(60, 6)), 3)), multiply(multiply(add(const_1, divide(divide(60, 6), const_100)), add(const_1, divide(divide(60, 6), const_100))), add(const_1, divide(divide(60, 6), const_100)))), add(multiply(const_100, const_100), multiply(multip... | there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 11,000 after 3 years at the same rate ? | "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 11000 . t = 3 years and r = 10 % p . a . c . i . = rs . 11000 x 1 + 10 3 - 1 100 = rs . 11000 x 331 1000 = 3641 . a" | a = 100 * 100
b = 60 / 6
c = 100 * b
d = c * 3
e = a + d
f = 60 / 6
g = f / 100
h = 1 + g
i = 60 / 6
j = i / 100
k = 1 + j
l = h * k
m = 60 / 6
n = m / 100
o = 1 + n
p = l * o
q = e * p
r = 100 * 100
s = 60 / 6
t = 100 * s
u = t * 3
v = r + u
w = q - v
|
a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 3 : 2 , e ) 9 : 5 | e | divide(add(multiply(4, divide(add(4, 4), subtract(4, 3))), 4), subtract(multiply(3, divide(add(4, 4), subtract(4, 3))), 4)) | the ratio between the present ages of a and b is 4 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ? | let the present ages of a and b be 4 x and 3 x years respectively . then , ( 4 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1 x = 8 = > x = 8 required ratio = ( 4 x + 4 ) : ( 3 x - 4 ) = 36 : 20 = 9 : 5 . answer : e | a = 4 + 4
b = 4 - 3
c = a / b
d = 4 * c
e = d + 4
f = 4 + 4
g = 4 - 3
h = f / g
i = 3 * h
j = i - 4
k = e / j
|
a ) 1200 , b ) 1340 , c ) 1234 , d ) 1203 , e ) 2485 | e | subtract(divide(multiply(multiply(20, add(20, const_1)), add(multiply(2, 20), const_1)), multiply(const_2, const_3)), divide(multiply(multiply(const_10, add(const_10, const_1)), add(multiply(2, const_10), const_1)), multiply(const_2, const_3))) | find value of x ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = x | ( 11 ^ 2 + 12 ^ 2 + 13 ^ 2 + . . . + 20 ^ 2 ) = ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 20 ^ 2 ) - ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 10 ^ 2 ) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = ( 2870 - 385 ) = 2485 e | a = 20 + 1
b = 20 * a
c = 2 * 20
d = c + 1
e = b * d
f = 2 * 3
g = e / f
h = 10 + 1
i = 10 * h
j = 2 * 10
k = j + 1
l = i * k
m = 2 * 3
n = l / m
o = g - n
|
a ) 20 liters , b ) 30 liters , c ) 50 liters , d ) 60 liters , e ) none of these | d | subtract(multiply(subtract(60, divide(60, add(2, 1))), 2), divide(60, add(2, 1))) | in a mixture 60 litres , the ratio of milk and water 2 : 1 . if the this ratio is to be 1 : 2 , then the quanity of water to be further added is | "explanation : quantity of milk = 60 * ( 2 / 3 ) = 40 liters quantity of water = 60 - 40 = 20 liters as per question we need to add water to get quantity 2 : 1 = > 40 / ( 20 + x ) = 1 / 2 = > 20 + x = 80 = > x = 60 liters option d" | a = 2 + 1
b = 60 / a
c = 60 - b
d = c * 2
e = 2 + 1
f = 60 / e
g = d - f
|
a ) 38,000 , b ) 40,000 , c ) 42,600 , d ) 45,600 , e ) 48,500 | d | multiply(multiply(const_100, const_100), const_4) | of the 13 employees in a certain department , 1 has an annual salary of 38,000 , 2 have an annual salary of 45,600 each , 2 have an annual salary of 42,500 each , 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each . what is the median annual salary for the 13 employees ? | "median is just the value in the middle when you arrange all values in the ascending order in this question , the 7 th value would be the median ( since there are 13 employees ) 38 , 40 , 40 , 40 , 42.5 , 42.5 , 45.6 so , answer is d ." | a = 100 * 100
b = a * 4
|
a ) 72 , b ) 224 , c ) 370 , d ) 512 , e ) 1,600 | c | gcd(58, const_4) | if m and n are positive integers and m ^ 2 + n ^ 2 = 58 , what is the value of m ^ 3 + n ^ 3 ? | "you need to integers which squared are equal 58 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 stop . the integers ca n ' t be greater than 7 or we will score above 58 . the second integer need to be picked up the same way . 1 ^ 2 ... | a = math.gcd(58, 4)
|
['a ) 118.67', 'b ) 116.67', 'c ) 117.67', 'd ) 120.56', 'e ) 120.57'] | c | subtract(circle_area(add(15, 1.2)), circle_area(15)) | a circular ground whose radius is 15 metres , has a 1.2 metre - broad garden around it . what is the area of the garden in square metres ? | req . area = Γ― β¬ [ ( 16.2 ) 2 Γ’ β¬ β ( 15 ) 2 ] = 22 Γ’ Β β 7 Γ£ β ( 31.2 Γ£ β 1.2 ) [ since a 2 - b 2 = ( a + b ) ( a - b ) ] = ( 22 Γ£ β 31.2 Γ£ β 1.2 ) / 7 = 117.67 sq m answer c | a = 15 + 1
b = circle_area - (
|
a ) rs . 18.28 , b ) rs . 20 , c ) rs . 18.08 , d ) rs . 28.08 , e ) rs . 38.08 | c | divide(add(1160, 920), add(65, 50)) | rahim bought 65 books for rs . 1160 from one shop and 50 books for rs . 920 from another . what is the average price he paid per book ? | average price per book = ( 1160 + 920 ) / ( 65 + 50 ) = 2080 / 115 = rs . 18.08 answer : c | a = 1160 + 920
b = 65 + 50
c = a / b
|
a ) 1 : 22 , b ) 81 : 12 , c ) 41 : 46 , d ) 41 : 19 , e ) 84 : 12 | c | power(divide(512, 729), divide(const_1, const_3)) | the ratio of the volumes of two cubes is 512 : 729 . what is the ratio of their total surface areas ? | "ratio of the sides = Β³ β 512 : Β³ β 729 = 8 : 9 ratio of surface areas = 82 : 92 = 41 : 46 answer : c" | a = 512 / 729
b = 1 / 3
c = a ** b
|
a ) 1 : 2 , b ) 18 : 5 , c ) 1 : 5 , d ) 3 : 1 , e ) 1 : 1 | b | divide(multiply(45000, const_12), multiply(30000, add(const_4, const_3))) | x starts a business with rs . 45000 . y joins in the business after 7 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ? | "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 Γ£ β 12 : 30000 Γ£ β 5 = 45 Γ£ β 12 : 30 Γ£ β 5 = 3 Γ£ β 12 : 2 Γ£ β 5 = 18 : 5 answer : option b" | a = 45000 * 12
b = 4 + 3
c = 30000 * b
d = a / c
|
a ) a ) 426 , b ) b ) 526 , c ) c ) 247 , d ) d ) 204 , e ) e ) 297 | c | multiply(divide(divide(1, 2), add(add(divide(1, 2), divide(1, 3)), divide(3, 4))), 782) | if rs . 782 be divided into 3 parts , proportional to 1 / 2 : 1 / 3 : 3 / 4 , then the first part is ? | given ratio = 1 / 2 : 2 / 3 : 3 / 4 = 6 : 4 : 9 1 st part = 782 * 6 / 19 = rs . 247 answer : c | a = 1 / 2
b = 1 / 2
c = 1 / 3
d = b + c
e = 3 / 4
f = d + e
g = a / f
h = g * 782
|
a ) 35 , b ) 49 , c ) 105 , d ) 255 , e ) 343 | e | power(5, 3) | a palindrome is a word or a number that reads the same forward and backward . for example , 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits 1 , 2 , 3 , 4 , 5 , 6 , and 7 , how many palindromes are possible ? | "there are 7 choices for each of the first three digits . the number of possible palindromes is 7 ^ 3 = 343 . the answer is e ." | a = 5 ** 3
|
a ) 24,602 , b ) 28,888 , c ) 24,600 , d ) 24,628 , e ) 24,400 | e | divide(63.50, divide(const_4, 4)) | a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 63.50 , his capital is ? | "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 63.50 32 x - 31 x = 6350 * 4 x = 25,400 . answer : e" | a = 4 / 4
b = 63 / 50
|
a ) 10 , b ) 20 , c ) 30 , d ) 35 , e ) 43 | b | multiply(divide(subtract(add(25, add(const_0_25, const_0_25)), 5), add(const_100, subtract(add(25, add(const_0_25, const_0_25)), 5))), const_100) | in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ? | "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.25 - 1 ) * 100 = 20 b" | a = const_0_25 + const_0_25
b = 25 + a
c = b - 5
d = const_0_25 + const_0_25
e = 25 + d
f = e - 5
g = 100 + f
h = c / g
i = h * 100
|
a ) l , b ) 3 l , c ) 5 l , d ) 7 l , e ) 9 l | c | subtract(6, const_1) | a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 6 t seconds , then what is the length of the platform ? | "the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 6 t ( l + p ) / ( l / t ) = 6 t p = 5 l the answer is c ." | a = 6 - 1
|
a ) 1.125 , b ) 1.5 , c ) 1.75 , d ) 1.25 , e ) 1 | a | divide(divide(multiply(15, const_3600), add(40, 8)), const_1000) | a bus 15 m long is running with a speed of 40 km / hr . in what time will it pass a man who is skateboarding at 8 km / hr in the direction opposite to that in which the car is going ? | speed of bus relative to man = 40 + 8 = 48 km / hr . = 48 * 5 / 18 = 40 / 3 m / sec . time taken to pass the man = 5 * 3 / 40 = 1.125 sec . answer : a | a = 15 * 3600
b = 40 + 8
c = a / b
d = c / 1000
|
a ) 150 Ο , b ) 240 Ο , c ) 300 Ο , d ) 480 Ο , e ) 1,200 Ο | a | multiply(multiply(multiply(multiply(divide(10, add(multiply(const_2, const_100), multiply(add(const_2, const_3), const_1000))), const_2), divide(add(const_2, multiply(const_2, const_10)), add(const_3, const_4))), 660), const_60) | the end of a blade on an airplane propeller is 10 feet from the center . if the propeller spins at the rate of 660 revolutions per second , how many miles will the tip of the blade travel in one minute ? ( 1 mile = 5,280 feet ) | distance traveled in 1 revolution = 2 Ο r = 2 Ο 10 / 5280 revolutions in one second = 660 revolutions in 60 seconds ( one minute ) = 660 * 60 total distance traveled = total revolutions * distance traveled in one revolution 660 * 60 * 2 Ο 10 / 5280 = 150 Ο a is the answer | a = 2 * 100
b = 2 + 3
c = b * 1000
d = a + c
e = 10 / d
f = e * 2
g = 2 * 10
h = 2 + g
i = 3 + 4
j = h / i
k = f * j
l = k * 660
m = l * const_60
|
a ) 334 , b ) 500 , c ) 400 , d ) 288 , e ) 271 | c | divide(368, divide(92, const_100)) | victor gets 92 % marks in examinations . if these are 368 marks , find the maximum marks . | "let the maximum marks be m then 92 % of m = 368 β 92 / 100 Γ m = 368 β m = ( 368 Γ 100 ) / 92 β m = 36800 / 92 β m = 400 therefore , maximum marks in the examinations are 400 . answer : c" | a = 92 / 100
b = 368 / a
|
a ) 1200 m , b ) 1250 m , c ) 1300 m , d ) 1350 m , e ) 1450 m | b | multiply(divide(multiply(300, const_1000), const_3600), 15) | a train running at the speed of 300 km / hr crosses a pole in 15 seconds . what is the length of the train ? | "speed = ( 300 * 5 / 18 ) m / sec = ( 250 / 3 ) m / sec length of the train = ( speed x time ) = ( 250 / 3 * 15 ) m = 1250 m . answer : b" | a = 300 * 1000
b = a / 3600
c = b * 15
|
a ) 24887 , b ) 20778 , c ) 23788 , d ) 10500 , e ) 2811 | d | divide(multiply(multiply(3500, const_12), 3), multiply(subtract(const_12, 6), 2)) | a starts business with rs . 3500 and after 6 months , b joins with a as his partner . after a year , the profit is divided in the ratio 2 : 3 . what is b Γ’ β¬ β’ s contribution in the capital ? | "explanation : a invested rs . 3500 for 12 months . let b joined with investment x . and he invested for 12 - 6 = 6 months . so there profit ratio = ( 3500 Γ£ β 12 ) : ( 6 x ) = 2 : 3 Γ’ β‘ β x = 10500 answer : d" | a = 3500 * 12
b = a * 3
c = 12 - 6
d = c * 2
e = b / d
|
a ) 10000 , b ) 12000 , c ) 13000 , d ) 14000 , e ) 14400 | e | multiply(10000, power(add(const_1, divide(20, const_100)), 2)) | the population of a village is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 2 years ? | "formula : ( after = 100 denominator ago = 100 numerator ) 10000 Γ 120 / 100 Γ 120 / 100 = 14400 e" | a = 20 / 100
b = 1 + a
c = b ** 2
d = 10000 * c
|
a ) 5 , b ) 8 , c ) 15 , d ) 18 , e ) 20 | e | add(subtract(multiply(30, 2), add(add(12, multiply(8, 2)), multiply(5, 3))), 3) | in a class of 30 students , 5 students did not borrow any books from the library , 12 students each borrowed 1 book , 8 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum numbe... | the average number of books per student was 2 means that total of 2 * 30 = 60 books were borrowed ; 5 + 12 + 8 = 25 students borrowed total of 5 * 0 + 12 * 1 + 8 * 2 = 28 books ; so 60 - 28 = 32 books are left to distribute among 30 - 25 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe n... | a = 30 * 2
b = 8 * 2
c = 12 + b
d = 5 * 3
e = c + d
f = a - e
g = f + 3
|
a ) 2.4 . , b ) 3.6 . , c ) 4.8 . , d ) 5.5 . , e ) 6.4 | c | multiply(multiply(divide(divide(2, divide(3, 2)), 2), 4), 3) | two carpenters , working in the same pace , can build 2 desks in two hours and a half . how many desks can 4 carpenters build in 3 hours ? | "w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 Γ r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 3 hrs = 4 Γ rate of each carpenter x time = 4 Γ 2 / 5 Γ 3 = 4.8 desks c is the correct answer ." | a = 3 / 2
b = 2 / a
c = b / 2
d = c * 4
e = d * 3
|
a ) 2 : 1 , b ) 1 : 2 , c ) 6 : 13 , d ) 13 : 6 , e ) none of these | d | divide(subtract(38, divide(subtract(100, multiply(38, const_2)), const_2)), divide(subtract(100, multiply(38, const_2)), const_2)) | mr . kutty has only hens and sheep . if the total number of their heads is 38 and the total number of legs is 100 then what is the ratio between the numbers of hens and sheep ? | let the total number of hens and sheep be x and y respectively . i . e . , x + y = 38 and 2 x + 4 y = 100 β΄ ratio = 13 : 6 answer d | a = 38 * 2
b = 100 - a
c = b / 2
d = 38 - c
e = 38 * 2
f = 100 - e
g = f / 2
h = d / g
|
a ) 10 , b ) 13 , c ) 11 , d ) 08 , e ) 15 | e | divide(add(multiply(divide(3, const_2), 3), 3), subtract(divide(3, const_2), 1)) | a boat covers a certain distance downstream in 1 hour , while it comes back in 1.30 hours . if the speed of the stream be 3 kmph , what is the speed of the boat in still water ? | "let the speed of the water in still water = x given that speed of the stream = 3 kmph speed downstream = ( x + 3 ) kmph speed upstream = ( x β 3 ) kmph he travels a certain distance downstream in 1 hour and come back in 1 1 β 2 hour . i . e . , distance travelled downstream in 1 hour = distance travelled upstream in 1... | a = 3 / 2
b = a * 3
c = b + 3
d = 3 / 2
e = d - 1
f = c / e
|
a ) 1 / 16 , b ) 12 , c ) 1 / 12 , d ) 144 , e ) 1 / 144 | e | power(4, multiply(4, const_3)) | if x is a positive number and 1 / 4 the square root of x is equal to 3 x , then x = | "1 / 4 of sqrt ( x ) = 3 x , which means that sqrt ( x ) = 12 x or x = 144 x ^ 2 - > divide by x 1 = 144 x x = 1 / 144 e ." | a = 4 * 3
b = 4 ** a
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a ) 280 , b ) 285 , c ) 290 , d ) 295 , e ) 570 | e | divide(add(multiply(add(floor(divide(15, add(const_3, const_4))), const_1), 510), multiply(subtract(15, add(floor(divide(15, add(const_3, const_4))), const_1)), 240)), 15) | a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 15 days starting with sunday is | "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 Γ 5 + 240 Γ 25 / 15 ) = ( 8550 / 15 ) = 570 answer : option e" | a = 3 + 4
b = 15 / a
c = math.floor(b)
d = c + 1
e = d * 510
f = 3 + 4
g = 15 / f
h = math.floor(g)
i = h + 1
j = 15 - i
k = j * 240
l = e + k
m = l / 15
|
a ) 200 , b ) 350 , c ) 700 , d ) 900 , e ) 1,400 | c | divide(multiply(35, 400), 20) | if 35 percent of 400 is 20 percent of x , then x = | "5 / 100 ( 400 ) = 2 / 10 ( x ) x = 700 . . answer : c" | a = 35 * 400
b = a / 20
|
['a ) 488', 'b ) 429', 'c ) 418', 'd ) 480', 'e ) 410'] | d | divide(multiply(20, sqrt(subtract(power(multiply(const_2, 26), const_2), power(20, const_2)))), const_2) | the side of a rhombus is 26 m and length of one of its diagonals is 20 m . the area of the rhombus is ? | 262 β 102 = 242 d 1 = 20 d 2 = 48 1 / 2 * 20 * 48 = 480 answer : d | a = 2 * 26
b = a ** 2
c = 20 ** 2
d = b - c
e = math.sqrt(d)
f = 20 * e
g = f / 2
|
a ) 900 , b ) 840 , c ) 750 , d ) 860 , e ) 960 | d | divide(multiply(add(80, divide(370, 1550)), 2440), const_100) | 80 370 ? 1550 2440 3530 | "10 ^ 2 - 20 = 80 20 ^ 2 - 30 = 370 30 ^ 2 - 40 = 860 40 ^ 2 - 50 = 1550 50 ^ 2 - 60 = 2440 60 ^ 2 - 70 = 3530 . answer : d" | a = 370 / 1550
b = 80 + a
c = b * 2440
d = c / 100
|
a ) 35 , b ) 33 1 / 3 , c ) 21 , d ) 16 2 / 3 , e ) 15 | c | subtract(50, multiply(divide(50, const_100), 4)) | how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ? | "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 4 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 4 % of the solution . set up an inequality and solve for x : 1.5 ... | a = 50 / 100
b = a * 4
c = 50 - b
|
a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 4 , d ) 7 / 8 , e ) 1 / 8 | c | multiply(const_4, multiply(divide(const_1, 1), divide(const_1, 1))) | three coins are tossed . find the probability of at least 1 head and 1 tail ? | "n ( s ) = 2 ^ 3 = 8 . . . . ( 3 coins tossed ) let e is the event of getting at least 1 head and 1 tail n ( e ) = tth , htt , tht , hht , hth , thh = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 8 = 3 / 4 ans - c" | a = 1 / 1
b = 1 / 1
c = a * b
d = 4 * c
|
a ) 90 , b ) 98 , c ) 35 , d ) 99 , e ) 80 | a | multiply(10, subtract(10, const_1)) | 10 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ? | "though 2 * ( 10 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 9 , so he ' ll play 18 matches . similarly , second guy has to play with the rest of 8 as his 2 games with the ... | a = 10 - 1
b = 10 * a
|
['a ) between 18 and 19', 'b ) between 19 and 20', 'c ) between 20 and 21', 'd ) between 21 and 22', 'e ) between 22 and 23'] | b | sqrt(add(power(add(const_10, const_1), const_2), power(add(const_10, add(5, const_1)), const_2))) | john is building a rectangular fence around a garden . the length will be 5 feet shorter than its width . if the total area of the garden is 176 square feet , what is the length of the diagonal ( in feet ) ? | to solve this , we first need to set up an equation for the area of the garden . if x is the width , then we have x ( x - 5 ) = 176 . by putting the equation in standard form , we get x ^ 2 - 5 x - 176 = 0 . by using the quadratic formula , we get roots of - 11 and 16 . we know that x is the width , and x - 5 is the le... | a = 10 + 1
b = a ** 2
c = 5 + 1
d = 10 + c
e = d ** 2
f = b + e
g = math.sqrt(f)
|
a ) $ 90 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600 | a | divide(450, 1) | divide $ 450 among a , b in the ratio 1 : 4 . how many $ that a get ? | "sum of ratio terms = 1 + 4 = 5 a = 450 * 1 / 5 = $ 90 answer is a" | a = 450 / 1
|
a ) 256 , b ) 258 , c ) 268 , d ) 358 , e ) none of these | b | divide(multiply(88, 370), 24) | 88 % of 370 + 24 % of 210 - ? = 118 | "let 88 % of 370 + 240 % of 210 - x = 118 then , x = ( 88 / 100 * 370 ) + ( 24 / 100 * 210 ) - 118 - 325.60 + 50.40 - 118 = 376 - 118 = 258 correct option : b" | a = 88 * 370
b = a / 24
|
a ) 40 , b ) 50 , c ) 60 , d ) 30 , e ) 20 | d | multiply(multiply(const_0_2778, 54), subtract(22, 20)) | a train passes a platform in 22 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is | "speed of the train = 54 km / hr = ( 54 Γ 10 ) / 36 m / s = 15 m / s length of the train = speed Γ time taken to cross the man = 15 Γ 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 12 = > 300 + l = 15 Γ 22 = 330 = > l = 330 - 300 = 30 meter answe... | a = const_0_2778 * 54
b = 22 - 20
c = a * b
|
a ) 430 , b ) 438 , c ) 436 , d ) 434 , e ) 460 | e | divide(184, divide(subtract(70, subtract(const_100, 70)), const_100)) | in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 184 votes . find the total number of valid votes ? | "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 184 = > 4 x / 10 = 184 = > 4 x = 1840 = > x = 460 . answer : e" | a = 100 - 70
b = 70 - a
c = b / 100
d = 184 / c
|
a ) 3 , b ) 4.5 , c ) 8 , d ) d ) 5.5 , e ) e ) 5 | c | subtract(40, 30) | a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 60 km / hr respectively . b starts four hours after a . if b and k overtake a at the same instant , how many hours after a did k start ? | "the table you made does n ' t make sense to me . all three meet at the same point means the distance they cover is the same . we know their rates are 30 , 40 and 60 . say the time taken by b is t hrs . then a takes 4 + t hrs . and we need to find the time taken by k . distance covered by a = distance covered by b 30 *... | a = 40 - 30
|
a ) 4 , b ) 8 , c ) 15 , d ) 6 , e ) 7 | c | multiply(5, divide(3, 5)) | a and b together can complete work in 5 days . a alone starts working and leaves it after working for 3 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ? | "explanation : ( a + b ) one day work = 1 / 5 now a does half of the work in 3 days so a can complete the whole work in 6 days a β s one day work = 1 / 6 b β s one day work = 1 / 5 - 1 / 6 = 1 / 30 b alone can complete the work in 30 days so half of the work in 15 days answer : option c" | a = 3 / 5
b = 5 * a
|
a ) 46 m , b ) 26 m , c ) 26 m , d ) 56 m , e ) 25 m | b | divide(multiply(add(15, 50), const_2), 5) | a rectangular plot measuring 15 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ? | "perimeter of the plot = 2 ( 15 + 50 ) = 130 m no of poles = 130 / 5 = 26 m answer : b" | a = 15 + 50
b = a * 2
c = b / 5
|
a ) 281 m , b ) 325 m , c ) 117 m , d ) 375 m , e ) 350 m | d | multiply(multiply(270, const_0_2778), 5) | if a train , travelling at a speed of 270 kmph , crosses a pole in 5 sec , then the length of train is ? | "d d = 270 * 5 / 18 * 5 = 375 m" | a = 270 * const_0_2778
b = a * 5
|
a ) 15 % , b ) 20 % , c ) 22.5 % , d ) 25 % , e ) 40 % | e | multiply(divide(subtract(add(multiply(divide(const_1, 20), 4), multiply(4, divide(const_1, 36))), multiply(8, divide(const_1, 36))), multiply(8, divide(const_1, 36))), const_100) | a certain car uses one gallon of gasoline every 36 miles when it travels on highway , and one gallon of gasoline every 20 miles when it travels in the city . when a car travels 4 miles on highway and 4 additional miles in the city , it uses what percent more gasoline than if it travels 8 miles on the highway ? | "4 miles on the highway = 4 / 36 gallons ; 4 miles in the city = 4 / 20 gallons ; total = 4 / 36 + 4 / 20 = 14 / 45 gallons . 8 miles on the highway = 8 / 30 gallons . the % change = ( 14 / 45 - 8 / 36 ) / ( 8 / 36 ) = 0.40 . answer : e ." | a = 1 / 20
b = a * 4
c = 1 / 36
d = 4 * c
e = b + d
f = 1 / 36
g = 8 * f
h = e - g
i = 1 / 36
j = 8 * i
k = h / j
l = k * 100
|
a ) 2081 , b ) 2083 , c ) 2088 , d ) 1971 , e ) 1973 | c | add(multiply(subtract(multiply(const_4, const_4), const_2), const_2), 2060) | the calendar of the year 2060 can be used again in the year ? | "explanation : given year 2060 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2060 + 28 = 2088 answer : c" | a = 4 * 4
b = a - 2
c = b * 2
d = c + 2060
|
a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 2.4 | e | divide(divide(multiply(40, 80), 80), const_2) | mixture a is 40 percent alcohol , and mixture b is 80 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 50 percent alcohol , approximately how many gallons of mixture a are in the mixture ? | "( 80 - 50 ) / ( 50 - 40 ) = qa / qb 30 / 10 = qa / qb 3 / 1 = qa / qb qa = ( 3 / 5 ) * 4 = 12 / 5 = 2.4 approx answer : e" | a = 40 * 80
b = a / 80
c = b / 2
|
a ) 75 % , b ) 80 % , c ) 145 % , d ) 150 % , e ) 180 % | c | multiply(divide(subtract(subtract(square_area(add(add(const_1, divide(100, 100)), divide(multiply(add(const_1, divide(100, 100)), 75), 100))), const_1), const_4), add(const_1, square_area(add(const_1, divide(100, 100))))), 100) | the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 75 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ? | "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 75 percent to make square c length of eac... | a = 100 / 100
b = 1 + a
c = 100 / 100
d = 1 + c
e = d * 75
f = e / 100
g = b + f
h = square_area - (
i = h - 1
j = i / 4
k = 100 / 100
l = 1 + k
m = 1 + square_area
n = j * m
|
a ) 65 , b ) 75 , c ) 80 , d ) 85 , e ) 90 | e | add(multiply(power(2, multiply(divide(60, 15), subtract(const_1, 2))), 120), 60) | the temperature of a certain cup of coffee 15 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee... | "first , we have to find a . we know that after t = 15 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 15 a ) + 60 60 = 120 * ( 2 ^ - 15 a ) 60 / 120 = 2 ^ - 15 a 1 / 2 = 2 ^ - 15 a 2 ^ - 1 = 2 ^ - 15 a - 1 = - 15 a 1 / 15 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 15 *... | a = 60 / 15
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
|
a ) $ 5 , b ) $ 8 , c ) $ 11 , d ) $ 14 , e ) $ 17 | b | subtract(divide(480, divide(10, subtract(divide(const_3, const_2), const_1))), divide(480, add(divide(10, subtract(divide(const_3, const_2), const_1)), 10))) | p and q are the only two applicants qualified for a short - term research project that pays 480 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job ... | "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - ... | a = 3 / 2
b = a - 1
c = 10 / b
d = 480 / c
e = 3 / 2
f = e - 1
g = 10 / f
h = g + 10
i = 480 / h
j = d - i
|
a ) 140 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 % | a | subtract(divide(subtract(const_100, 20), divide(1, 3)), const_100) | what profit percent is made by selling an article at a certain price , if by selling at 1 / 3 rd of that price , there would be a loss of 20 % ? | "sp 2 = 1 / 3 sp 1 cp = 100 sp 2 = 80 1 / 3 sp 1 = 80 sp 1 = 240 100 - - - 240 = > 140 % answer : a" | a = 100 - 20
b = 1 / 3
c = a / b
d = c - 100
|
a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000 | e | multiply(divide(multiply(1.89, multiply(10, 7)), 420), const_100) | a certain company had a total annual expenditure of 1.89 β 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ? | "given : total annual expenditure of 1.89 β 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 4 = 1890 therefore try to bring the numerator in terms of 1890 average salary = ( 1890 * 10 ^ 4 ) / 420 = 4.5 * 10 ^ 4 = 45,000 option e" | a = 10 * 7
b = 1 * 89
c = b / 420
d = c * 100
|
a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes | e | divide(multiply(4.00, const_60), 5) | the timing of a college is from 12 p . m to 4.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture . | "explanation : total time a student spends in college = 4 hours 00 minutes = 240 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 240 Γ’ β¬ β 20 ) / 5 = 44 minutes answer e" | a = 4 * 0
b = a / 5
|
a ) 2 , b ) 9 , c ) 15 , d ) 18 , e ) 30 | d | divide(subtract(0.60, multiply(0.06, 4)), subtract(0.08, 0.06)) | a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 4 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company ch... | "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = ... | a = 0 * 6
b = 0 - 60
c = 0 - 8
d = b / c
|
['a ) 486', 'b ) 366', 'c ) 299', 'd ) 278', 'e ) 1888'] | a | multiply(multiply(const_3, power(power(add(add(power(1, const_3), power(6, const_3)), power(8, const_3)), const_0_33), const_2)), const_2) | three solid cubes of sides 1 cm , 6 cm and 8 cm are melted to form a new cube . find the surface area of the cube so formed | explanation : volume of new cube = = edge of new cube = = 9 cm surface area of the new cube = ( 6 x 9 x 9 ) = 486 answer : a ) 486 | a = 1 ** 3
b = 6 ** 3
c = a + b
d = 8 ** 3
e = c + d
f = e ** const_0_33
g = f ** 2
h = 3 * g
i = h * 2
|
a ) 19.81 % , b ) 21 % , c ) 37.5 % , d ) 25 % , e ) 37.5 % | b | multiply(subtract(add(const_100, 10), add(12, subtract(const_100, 20))), const_2) | a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 12 % below the cost price of the claimed weight . | "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while ... | a = 100 + 10
b = 100 - 20
c = 12 + b
d = a - c
e = d * 2
|
a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000 | b | multiply(divide(divide(subtract(subtract(multiply(multiply(const_3, const_4), const_1000), multiply(multiply(multiply(1, const_4), const_1000), divide(1, 2))), multiply(subtract(multiply(multiply(1, const_4), const_1000), multiply(multiply(multiply(1, const_4), const_1000), divide(1, 2))), divide(1, 2))), const_1000), ... | in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 2 of the absentee ballets were thrown out and 1 / 2 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ? | "1 / 2 * 1 / 2 ( total absentee votes ) = 1 / 4 ( total votes ) = 1 / 4 * 12000 = 3000 answer is b" | a = 3 * 4
b = a * 1000
c = 1 * 4
d = c * 1000
e = 1 / 2
f = d * e
g = b - f
h = 1 * 4
i = h * 1000
j = 1 * 4
k = j * 1000
l = 1 / 2
m = k * l
n = i - m
o = 1 / 2
p = n * o
q = g - p
r = q / 1000
s = r / 4
t = s * 1
|
a ) rs . 500 , b ) rs . 515 , c ) rs . 550 , d ) rs . 600 , e ) none | a | divide(multiply(divide(multiply(616, const_100), add(const_100, 10)), add(const_100, 10)), add(const_100, 12)) | the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is | "solution 110 % of s . p . = 616 βΉ = βΊ s . p . = ( 616 x 100 / 110 ) . βΉ = βΊ rs . 560 . c . p . βΉ = βΊ rs . ( 100 / 112 x 560 ) βΉ = βΊ rs . 500 . answer a" | a = 616 * 100
b = 100 + 10
c = a / b
d = 100 + 10
e = c * d
f = 100 + 12
g = e / f
|
a ) 17 , b ) 24 , c ) 7 , d ) 24 , e ) 20 | c | divide(add(divide(25, 5), divide(45, 5)), const_2) | a man swims downstream 45 km and upstream 25 km taking 5 hours each time , what is the speed of the man in still water ? | "45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = ( 9 + 5 ) / 2 = 14 / 2 = 7 answer : c" | a = 25 / 5
b = 45 / 5
c = a + b
d = c / 2
|
a ) 145 , b ) 215 , c ) 265 , d ) 285 , e ) 375 | d | subtract(multiply(divide(multiply(45, const_1000), const_3600), 30), 90) | the length of a bridge in meters , which a train 90 - meters long and traveling at 45 km / hr can cross in 30 seconds is ? | 45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 90 = 375 meters x = 285 meters the answer is d . | a = 45 * 1000
b = a / 3600
c = b * 30
d = c - 90
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | b | subtract(subtract(8, 3), const_1) | if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ? | 3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b . | a = 8 - 3
b = a - 1
|
a ) 3 / 8 , b ) 1 / 4 , c ) 3 / 16 , d ) 1 / 8 , e ) 1 / 16 | a | subtract(2, multiply(divide(factorial(4), factorial(2)), power(divide(2, 2), 4))) | a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 2 boys ? | "no of ways of getting p ( ggbb ) is 4 ! / 2 ! * 2 ! ; total no of ways is 2 ^ n = 2 ^ 4 = 16 ; 6 / 16 = 3 / 8 ; we can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads . p ( all out comes ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ; p ( favorable outco... | a = math.factorial(4)
b = math.factorial(2)
c = a / b
d = 2 / 2
e = d ** 4
f = c * e
g = 2 - f
|
a ) 9 days , b ) 9 ( 3 / 5 ) days , c ) 11 1 / 5 days , d ) 13 days , e ) 13 1 / 7 | b | inverse(subtract(subtract(divide(const_1, 4), divide(const_1, 12)), divide(const_1, 16))) | p can lay railway track between two stations in 16 days . q can do the same job in 12 days . with the help of r , they completes the job in 4 days . how much days does it take for r alone to complete the work ? | amount of work p can do in 1 day = 1 / 16 amount of work q can do in 1 day = 1 / 12 amount of work p , q and r can together do in 1 day = 1 / 4 amount of work r can do in 1 day = 1 / 4 - ( 1 / 16 + 1 / 12 ) = 3 / 16 β 1 / 12 = 5 / 48 = > hence r can do the job on 48 / 5 days = 9 ( 3 / 5 ) days b ) | a = 1 / 4
b = 1 / 12
c = a - b
d = 1 / 16
e = c - d
f = 1/(e)
|
a ) 5 hours , b ) 10 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours | b | divide(subtract(12, 10), 20) | two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 20 km apart , if they walk in the same direction ? | "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 20 = 10 hours answer is b" | a = 12 - 10
b = a / 20
|
a ) 70 , b ) 52 , c ) 62 , d ) 59 , e ) 50 | d | add(add(16, 12), add(18, 13)) | in a games hour 4 different types of players came to the ground ? cricket 16 , hokey 12 , football 18 , softball 13 . how many players are present in the ground ? | "total number of players = 16 + 12 + 18 + 13 = 59 answer is d" | a = 16 + 12
b = 18 + 13
c = a + b
|
a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54 | b | subtract(69, subtract(add(41, 22), 9)) | in a class of 69 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ? | "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b" | a = 41 + 22
b = a - 9
c = 69 - b
|
a ) 50 % , b ) 60 % , c ) 75 % , d ) 80 % , e ) 90 % | b | multiply(divide(subtract(const_100, multiply(divide(subtract(const_100, 50), subtract(const_100, 20)), const_100)), multiply(divide(subtract(const_100, 50), subtract(const_100, 20)), const_100)), const_100) | the charge for a single room at hotel p is 50 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ? | "p = 0.5 r = 0.8 g r = 0.8 g / 0.5 = 1.6 * g thus r is 60 % greater than g . the answer is b ." | a = 100 - 50
b = 100 - 20
c = a / b
d = c * 100
e = 100 - d
f = 100 - 50
g = 100 - 20
h = f / g
i = h * 100
j = e / i
k = j * 100
|
a ) 11 , b ) 50 , c ) 28 , d ) 45 , e ) 18 | d | add(18, 27) | laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 18 kmph and prasanna moves southward at a speed of 27 kmph . how far will be prasanna from laxmi after 60 minutes ? | "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 18 kmph x 1 hr = 18 km total southward prasanna ' s distance = 27 kmph x 1 hr = 27 km total distance between prasanna and laxmi is = 18 + 27 = 45 km . answer : d" | a = 18 + 27
|
a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 578 | e | subtract(815, divide(multiply(subtract(894, 815), 3), 4)) | a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 894 in 4 years . the sum is : | "s . i . for 1 year = rs . ( 894 - 815 ) = rs . 79 . s . i . for 3 years = rs . ( 79 x 3 ) = rs . 237 . principal = rs . ( 815 - 237 ) = rs . 578 . answer : option e" | a = 894 - 815
b = a * 3
c = b / 4
d = 815 - c
|
a ) 55 mph , b ) 50 mph , c ) 40 mph , d ) 60 mph , e ) 70 mph | c | divide(80, add(divide(50, subtract(80, 30)), divide(30, 30))) | tom traveled the entire 80 miles trip . if he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 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 ) = ( 30 + 50 ) / ( ( 30 / 30 ) + ( 50 / 50 ) ) = 80 / 2 = 40 mph c" | a = 80 - 30
b = 50 / a
c = 30 / 30
d = b + c
e = 80 / d
|
a ) 6 , b ) 7 , c ) 8 , d ) 2 , e ) 9 | a | divide(subtract(multiply(3, 24), 24), subtract(multiply(3, 3), 1)) | there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches and roses were planted ? | let xx be the number of roses . then the number of birches is 24 β x 24 β x , and the number of boys is 3 Γ ( 24 β x ) 3 Γ ( 24 β x ) . if each girl planted 3 roses , there are x 3 x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 β x ) = 24 x 3 + 3 ( 24 β x ) = 24 x + 9 ... | a = 3 * 24
b = a - 24
c = 3 * 3
d = c - 1
e = b / d
|
a ) $ 1.20 , b ) $ 1.50 , c ) $ 1.80 , d ) $ 2.00 , e ) $ 2.50 | b | divide(multiply(multiply(3, 5), 0.40), 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 $ 0.40 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 = 40 cents ( 4 / 15 ) x = 40 x = $ 1.50 the answer is b ." | a = 3 * 5
b = a * 0
c = b / 4
|
a ) 32 , b ) 78 , c ) 92 , d ) 84 , e ) 96 | d | divide(divide(26, subtract(multiply(divide(3, 4), divide(5, 7)), multiply(divide(4, 5), divide(3, 3)))), 4) | 3 / 4 of 5 / 7 of a number is greater than 2 / 3 of 4 / 7 of the same number by 26 . what is half of that number ? | "let no . be x 3 / 4 * 5 / 7 * x - 2 / 3 * 4 / 7 * x = 26 by further solving 15 x / 28 - 8 x / 21 = 26 13 x / 84 = 26 x = 168 we have to find x / 2 = 168 / 2 = 84 answer : d" | a = 3 / 4
b = 5 / 7
c = a * b
d = 4 / 5
e = 3 / 3
f = d * e
g = c - f
h = 26 / g
i = h / 4
|
a ) a ) 9500 , b ) b ) 12500 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600 | c | subtract(18500, 7280) | robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert earned a performance incentive rs . 7280 / - from company . but robert forgot that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the bonus amount given to robert ? | total salary = rs . 15000 / - incentive earned earlier = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - bonus = 18500 - 7720 = 10780 / - answer is c | a = 18500 - 7280
|
a ) 2300 mtrs , b ) 2400 mtrs , c ) 2500 mtrs , d ) 2600 mtrs , e ) 2700 mtrs | a | add(multiply(800, const_2), 700) | if a and b run on a circular path in opposite directions of constant speeds with different velocities from p and q . first time they meet 800 mts away from p and second time they meet 700 mts away from p , what is the lenght of the circular path . | 800 + 800 + 700 = 2300 mtrs answer : a | a = 800 * 2
b = a + 700
|
a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 % | d | divide(multiply(11, const_100), add(11, const_100)) | the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 11 percent , what was the annual interest rate last year ? | "let us suppose the interest rate last year is x , this year the interest rate is increased by 10 % . hence this year interest rate would be 1.1 * x . setting up the equation - - - - - > 11 = 1.1 * x x = 10 % answer : d" | a = 11 * 100
b = 11 + 100
c = a / b
|
a ) rs . 692 , b ) rs . 768 , c ) rs . 876 , d ) rs . 972 , e ) none | c | multiply(divide(surface_cube(8), 16), 36.50) | the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ? | "solution surface area of the cube = ( 6 Γ 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg βΉ = βΊ 24 kg . cost of painting = rs . ( 36.50 Γ 24 ) = rs . 876 . answer c" | a = surface_cube / (
b = a * 16
|
a ) 13.33 mps , b ) 23.33 mps , c ) 33.33 mps , d ) 25.33 mps , e ) 43.33 mps | b | multiply(const_0_2778, 84) | express a speed of 84 kmph in meters per second ? | "84 * 5 / 18 = 23.33 mps answer : b" | a = const_0_2778 * 84
|
a ) s . 59 , b ) s . 58 , c ) s . 36 , d ) s . 46 , e ) s . 13 | c | add(divide(9000, 300), 6) | a shopkeeper sells 300 metres of cloth for rs . 9000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ? | "sp per metre = 9000 / 300 = rs . 30 loss per metre = rs . 6 cp per metre = 30 + 6 = rs . 36 answer : c" | a = 9000 / 300
b = a + 6
|
a ) 588 , b ) 642 , c ) 567 , d ) 344 , e ) 789 | a | multiply(42, 14) | the h . c . f . of two numbers is 42 and the other two factors of their l . c . m . are 12 and 14 . the larger of the two numbers is : | "explanation : clearly , the numbers are ( 42 x 12 ) and ( 42 x 14 ) . { \ color { blue } \ therefore } larger number = ( 42 x 14 ) = 588 . answer : a ) 588" | a = 42 * 14
|
a ) 1 / 336 , b ) 5 / 336 , c ) 11 / 336 , d ) 1 / 168 , e ) 1 / 84 | a | multiply(multiply(divide(1, 7), divide(1, 8)), subtract(1, divide(1, 6))) | jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that all three will make a basket ? | "the probability that all three will make a basket is 1 / 6 * 1 / 7 * 1 / 8 = 1 / 336 . the answer is a ." | a = 1 / 7
b = 1 / 8
c = a * b
d = 1 / 6
e = 1 - d
f = c * e
|
a ) 22 , b ) 67 , c ) 10 , d ) 12 , e ) 66 | c | subtract(multiply(40, divide(75, const_100)), multiply(divide(4, 5), 25)) | how much is 75 % of 40 is greater than 4 / 5 of 25 ? | "( 75 / 100 ) * 40 β ( 4 / 5 ) * 25 = 10 answer : c" | a = 75 / 100
b = 40 * a
c = 4 / 5
d = c * 25
e = b - d
|
a ) 12 , b ) 29 , c ) 27 , d ) 15 , e ) 99 | d | divide(subtract(105, multiply(const_3, 5)), multiply(const_3, const_2)) | a number is doubled and 5 is added . if the resultant is trebled , it becomes 105 . what is that number ? | "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 105 6 x + 15 = 105 6 x = 90 x = 15 answer : d" | a = 3 * 5
b = 105 - a
c = 3 * 2
d = b / c
|
a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45 | e | subtract(add(10, add(35, 5)), 5) | 10 play kabadi , 35 play kho kho only , 5 play both gmaes . then how many in total ? | "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 35 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 35 + 5 = 40 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 40 - 5 = 45 answer : e" | a = 35 + 5
b = 10 + a
c = b - 5
|
a ) 20 , b ) 30 , c ) 40 , d ) 25 , e ) 35 | d | multiply(12, const_2) | if the average of 12 x and 8 y is greater than 200 , and x is twice y , what is the least integer value of x ? | substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x... | a = 12 * 2
|
a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540 | c | divide(multiply(divide(multiply(150, 10), subtract(15, 10)), const_100), 10) | i sold a book at a profit of 10 % . had i sold it for $ 150 more , 15 % would have been gained . find the cost price ? | "115 % of cost - 110 % of cost = $ 150 5 % of cost = $ 150 cost = 150 * 100 / 5 = $ 3000 answer is c" | a = 150 * 10
b = 15 - 10
c = a / b
d = c * 100
e = d / 10
|
a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30 | b | floor(divide(multiply(24, 8), 7)) | in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers ? | 8 / 7 * 24 = 27.4 the answer is b . | a = 24 * 8
b = a / 7
c = math.floor(b)
|
a ) 9.5 , b ) 10.5 , c ) 5.5 , d ) 5.9 , e ) 8.5 | d | add(divide(multiply(8, 24), const_100), divide(multiply(10, 40), const_100)) | add 8 % of 24 and 10 % of 40 . | "8 % of 24 + 10 % of 40 24 * 8 / 100 + 40 * 10 / 100 1.9 + 4 = 5.9 answer d" | a = 8 * 24
b = a / 100
c = 10 * 40
d = c / 100
e = b + d
|
a ) 13 , b ) 20 , c ) 30 , d ) 43 , e ) 50 | a | multiply(divide(subtract(add(20, add(const_0_25, const_0_25)), 5), add(const_100, subtract(add(20, add(const_0_25, const_0_25)), 5))), const_100) | in a certificate by mistake a candidate gave his height as 20 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ? | "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.20 - 1 ) = 13 a" | a = const_0_25 + const_0_25
b = 20 + a
c = b - 5
d = const_0_25 + const_0_25
e = 20 + d
f = e - 5
g = 100 + f
h = c / g
i = h * 100
|
a ) 12 / 16 , b ) 11 / 36 , c ) 14 / 24 , d ) 18 / 36 , e ) 2 / 24 | b | divide(12, add(multiply(4, divide(12, 2)), multiply(5, divide(12, 3)))) | if 2 men or 3 women can reap a field in 12 days how long will 4 men and 5 women take to reap it ? | "explanation : 2 men reap 1 / 12 field in 1 day 1 man reap 1 / ( 2 x 12 ) 3 women reap 1 / 12 field in 1 day 1 woman reap 1 / ( 12 x 3 ) 4 men and 5 women reap ( 4 / ( 2 x 12 ) + 5 / ( 3 x 12 ) = 11 / 36 in 1 day 4 men and 5 women will reap the field in 11 / 36 days answer : option b" | a = 12 / 2
b = 4 * a
c = 12 / 3
d = 5 * c
e = b + d
f = 12 / e
|
a ) 250 , b ) 260 , c ) 500 , d ) 280 , e ) 240 | e | divide(subtract(500, 20), const_2) | one pack of cake mix is being stirred before being poured into two separate baking trays . the first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first . if the total number of cups poured is 500 , how many cups of batter does the second tray hold ? | tray one as t 1 and tray two as t 2 . t 2 = t 1 - 20 cups as equation a . t 1 + t 2 = 500 cups in total as equation b . substitute equation a into equation b , resulting in t 1 + ( t 1 - 20 ) = 500 transpose like terms , 2 * t 1 = 500 + 20 ( 2 * t 1 ) / 2 = 520 / 2 t 1 = 260 , thus t 2 is t 1 less 20 cups , which is 24... | a = 500 - 20
b = a / 2
|
a ) $ 25 , b ) $ 48 , c ) $ 44 , d ) $ 49 , e ) $ 40 | c | multiply(242, divide(inverse(14), add(inverse(21), add(inverse(7), inverse(14))))) | a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got $ 242 . what is the share of c ? | "c $ 44 the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = $ 44" | a = 1/(14)
b = 1/(21)
c = 1/(7)
d = 1/(14)
e = c + d
f = b + e
g = a / f
h = 242 * g
|
a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9 | d | subtract(subtract(subtract(95, 25), const_4), const_2) | a certain no . when divided by 95 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ? | "explanation : 95 + 25 = 120 / 15 = 8 ( remainder ) d" | a = 95 - 25
b = a - 4
c = b - 2
|
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