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 ) 90 , b ) 110 , c ) 120 , d ) 140 , e ) 220 | d | subtract(divide(subtract(multiply(12, 360), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(360, divide(subtract(multiply(12, 360), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtrac... | a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 360 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ? | "orchestra seats - a balcony seats - b a + b = 360 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 360 = 3320 - 2880 = 440 i . e . a = 110 and b = 360 - 110 = 250 more seats in balcony than orchestra = b - a = 250 - 110 = 140 answe... | a = 12 * 360
b = 3 * 1000
c = 3 * 100
d = b + c
e = 2 * 10
f = d + e
g = a - f
h = 12 - 8
i = g / h
j = 12 * 360
k = 3 * 1000
l = 3 * 100
m = k + l
n = 2 * 10
o = m + n
p = j - o
q = 12 - 8
r = p / q
s = 360 - r
t = i - s
|
a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 90 metres , e ) 100 meters | d | multiply(divide(multiply(36, const_1000), const_3600), 9) | a train running at the speed of 36 km / hr crosses a pole in 9 seconds . what is the length of the train ? | "speed = 36 x 5 / 18 m / sec = 30 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 30 / 3 x 9 m = 90 m . answer : d" | a = 36 * 1000
b = a / 3600
c = b * 9
|
a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116 | d | divide(add(power(56, 2), power(56, 2)), power(28, 2)) | tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = | ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d | a = 56 ** 2
b = 56 ** 2
c = a + b
d = 28 ** 2
e = c / d
|
a ) 90 , b ) 110 , c ) 140 , d ) 130 , e ) 120 | a | multiply(divide(480, multiply(const_4, const_4)), const_3) | a boy has rs . 480 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ? | let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . a | a = 4 * 4
b = 480 / a
c = b * 3
|
a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16 | d | subtract(divide(multiply(130, const_2), subtract(11, 6)), 37) | glen and hannah drive at constant speeds toward each other on a highway . glen drives at a constant speed of 37 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if glen is 130 km away from hannah at 6 am , and also 130 km away fro... | glen and hannah complete 260 km / 5 hours = 52 km / hour hannah ' s speed is 52 - 37 = 15 km / hour the answer is d . | a = 130 * 2
b = 11 - 6
c = a / b
d = c - 37
|
a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 % | b | divide(multiply(subtract(add(add(const_100, 10), multiply(add(const_100, 10), divide(20, const_100))), const_100), const_100), add(add(const_100, 10), multiply(add(const_100, 10), divide(20, const_100)))) | the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ? | "let initial output is o then after 10 % increase it will be 1.1 o and after 20 % increase on this new output the latest output will be 1.1 o * 1.20 = 1.32 o now we have to decrease the output by some percentage so that the new output is same as the starting output ( o ) so , 1.32 o * ( 1 - x / 100 ) = o = > x = 24.24 ... | a = 100 + 10
b = 100 + 10
c = 20 / 100
d = b * c
e = a + d
f = e - 100
g = f * 100
h = 100 + 10
i = 100 + 10
j = 20 / 100
k = i * j
l = h + k
m = g / l
|
a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18 | c | add(const_2, divide(divide(subtract(233, 79), const_2), add(const_3, const_4))) | integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ? | 79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a n... | a = 233 - 79
b = a / 2
c = 3 + 4
d = b / c
e = 2 + d
|
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | b | divide(subtract(add(multiply(10, divide(subtract(multiply(20, 20), multiply(20, 18)), subtract(20, 10))), multiply(20, subtract(20, divide(subtract(multiply(20, 20), multiply(20, 18)), subtract(20, 10))))), multiply(20, 15)), subtract(20, 15)) | each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes m... | "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the ... | a = 20 * 20
b = 20 * 18
c = a - b
d = 20 - 10
e = c / d
f = 10 * e
g = 20 * 20
h = 20 * 18
i = g - h
j = 20 - 10
k = i / j
l = 20 - k
m = 20 * l
n = f + m
o = 20 * 15
p = n - o
q = 20 - 15
r = p / q
|
a ) 120 , b ) 56 , c ) 68 , d ) 87 , e ) 92 | a | multiply(add(const_10, const_2), divide(3600, rectangle_area(18, 20))) | the monthly rent of a shop of dimension 18 feet Γ 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ? | "sol . monthly rent per square feet = 3600 / ( 18 * 20 ) = 10 & annual rent per square feet = 12 * 10 = 120 answer : a" | a = 10 + 2
b = 3600 / rectangle_area
c = a * b
|
a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 42 kmph , e ) 90 kmph | d | divide(378, multiply(divide(3, 2), 6)) | a van takes 6 hours to cover a distance of 378 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 distence = 378 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 378 / 9 = 42 kmph d" | a = 3 / 2
b = a * 6
c = 378 / b
|
a ) $ 40,000 , b ) $ 52,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000 | b | add(multiply(multiply(const_4, const_10), const_1000), divide(subtract(multiply(multiply(const_4, const_2), const_1000), multiply(divide(14, const_100), multiply(multiply(const_4, const_10), const_1000))), divide(20, const_100))) | country x taxes each of its citizens an amount equal to 14 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ? | "equation is correct , so math must be a problem . 0.14 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,600 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,400 - - > x = 52,000 . answer : b ." | a = 4 * 10
b = a * 1000
c = 4 * 2
d = c * 1000
e = 14 / 100
f = 4 * 10
g = f * 1000
h = e * g
i = d - h
j = 20 / 100
k = i / j
l = b + k
|
a ) 60 % , b ) 23 % , c ) 25 % , d ) 56 % , e ) 73 % | c | subtract(divide(multiply(add(const_100, 18.75), const_100), subtract(const_100, 5)), const_100) | a shopkeeper sold an article offering a discount of 5 % and earned a profit of 18.75 % . what would have been the percentage of profit earned if no discount was offered ? | "let c . p . be rs . 100 . then , s . p . = rs . 118.75 let marked price be rs . x . then , 95 / 100 x = 118.75 x = 11875 / 95 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : c" | a = 100 + 18
b = a * 100
c = 100 - 5
d = b / c
e = d - 100
|
a ) 2 % , b ) 1 % , c ) 7 % , d ) 5 % , e ) 8 % | c | multiply(divide(divide(const_3, const_4.0), add(multiply(const_3, const_4), add(const_0_25, const_0_25))), const_100) | a sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest . what is the rate of interest ? | "c 7 % s . i . = ( 21200 - 15600 ) = 5600 . rate = ( 100 x 5600 ) / ( 15600 x 5 ) % = 7 %" | a = 3 / 4
b = 3 * 4
c = const_0_25 + const_0_25
d = b + c
e = a / d
f = e * 100
|
a ) 120 , b ) 75 , c ) 100 , d ) 150 , e ) 175 | a | divide(subtract(multiply(16, const_2), 8), subtract(subtract(subtract(1, divide(20, const_100)), multiply(subtract(1, divide(20, const_100)), divide(1, const_4))), multiply(const_2, divide(20, const_100)))) | a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 8 gallons of water and 16 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ? | "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 16 gallons salt is add... | a = 16 * 2
b = a - 8
c = 20 / 100
d = 1 - c
e = 20 / 100
f = 1 - e
g = 1 / 4
h = f * g
i = d - h
j = 20 / 100
k = 2 * j
l = i - k
m = b / l
|
a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2 | b | divide(divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(8, 7)), divide(subtract(multiply(450, const_100), multiply(6000, 7)), subtract(8, 7))) | rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 8 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ? | "let the amount lent at 7 % be rs . x amount lent at 8 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 8 / 100 ( 6000 - x ) = 480 - x / 100 = > 480 - 1 / 100 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b" | a = 450 * 100
b = 6000 * 7
c = a - b
d = 8 - 7
e = c / d
f = 450 * 100
g = 6000 * 7
h = f - g
i = 8 - 7
j = h / i
k = e / j
|
a ) $ 600 , b ) $ 650 , c ) $ 700 , d ) $ 750 , e ) $ 800 | c | divide(subtract(multiply(multiply(const_100, multiply(add(const_2, const_3), const_2)), add(divide(6, const_100), const_1)), add(add(multiply(const_100, multiply(add(const_2, const_3), const_2)), multiply(multiply(add(const_2, const_3), const_2), const_4)), multiply(const_2, const_3))), subtract(add(divide(6, const_100... | we invested a total of $ 1,000 . we invested one part of the money at 4 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 4 % ? | let x be the money invested at 4 % . 1.04 x + 1.06 ( 1000 - x ) = 1046 . 0.02 x = 1060 - 1046 . 0.02 x = 14 . 2 x = 1400 . x = 700 . the answer is c . | a = 2 + 3
b = a * 2
c = 100 * b
d = 6 / 100
e = d + 1
f = c * e
g = 2 + 3
h = g * 2
i = 100 * h
j = 2 + 3
k = j * 2
l = k * 4
m = i + l
n = 2 * 3
o = m + n
p = f - o
q = 6 / 100
r = q + 1
s = 4 / 100
t = s + 1
u = r - t
v = p / u
|
a ) 52 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph | a | add(divide(add(multiply(60, 3), multiply(40, 2)), add(3, 2)), subtract(divide(const_100, 3), const_0_33)) | steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 60 mph . what is his average speed of travel for the entire journey ? | "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time =... | a = 60 * 3
b = 40 * 2
c = a + b
d = 3 + 2
e = c / d
f = 100 / 3
g = f - const_0_33
h = e + g
|
['a ) 4 cm', 'b ) 8 cm', 'c ) 16 cm', 'd ) 24 cm', 'e ) none of the above'] | a | sqrt(divide(add(8, sqrt(add(multiply(const_4, 128), power(8, const_2)))), const_2)) | the volume of a box with a square base is 128 cubic cm . the area of the base of the box is 8 inches more than the height . what is the length of the base of the box ? | l x w x h = 64 l x w - 8 = h l = w solving the 3 equations we get area of base = 16 square cm and height = 8 cm , which means length = 4 cm and width = 4 cm correct answer : a | a = 4 * 128
b = 8 ** 2
c = a + b
d = math.sqrt(c)
e = 8 + d
f = e / 2
g = math.sqrt(f)
|
a ) 0.94 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none | a | divide(subtract(const_100, 6), const_100) | subtracting 6 % of a from a is equivalent to multiplying a by how much ? | "answer let a - 6 % of a = ab . β ( 94 x a ) / 100 = ab β΄ b = 0.94 correct option : a" | a = 100 - 6
b = a / 100
|
a ) 146 , b ) 148 , c ) 150 , d ) 152 , e ) none of these | c | add(subtract(subtract(const_1000, const_10), multiply(multiply(const_10, multiply(3, 3)), multiply(const_4, const_2))), const_10) | how many 3 digit numbers are completely divisible 6 ? | "explanation : 100 / 6 = 16 , remainder = 4 . hence 2 more should be added to 100 to get the minimum 3 digit number divisible by 6 . = > minimum 3 digit number divisible by 6 = 100 + 2 = 102 999 / 6 = 166 , remainder = 3 . hence 3 should be decreased from 999 to get the maximum 3 digit number divisible by 6 . = > maxim... | a = 1000 - 10
b = 3 * 3
c = 10 * b
d = 4 * 2
e = c * d
f = a - e
g = f + 10
|
a ) 52 , b ) 35 , c ) 42 , d ) 41 , e ) 43 | e | subtract(divide(100, const_2), multiply(7, 7)) | what is the remainder if 7 ^ 3 is divided by 100 ? | "7 * 7 * 7 / 100 = 343 / 100 remainder 43 answer : e" | a = 100 / 2
b = 7 * 7
c = a - b
|
a ) 20 m , b ) 28 m , c ) 22.5 m , d ) 9 m , e ) 12 m | b | multiply(divide(140, 45), subtract(45, 36)) | in 140 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by : | "distance covered by b in 9 sec . = 140 / 45 x 9 m = 28 m . a beats b by 28 metres . answer : option b" | a = 140 / 45
b = 45 - 36
c = a * b
|
a ) 22 , b ) 24 , c ) 44 , d ) 48 , e ) 52 | c | divide(subtract(multiply(const_2, multiply(const_2, const_12)), const_4), const_2) | how many times in a day , the hands of a clock are straight ? | "in 12 hours , the hands coincide or are in opposite direction 22 times . in 24 hours , the hands coincide or are in opposite direction 44 times a day . answer : option c" | a = 2 * 12
b = 2 * a
c = b - 4
d = c / 2
|
['a ) 500 ( Ο β 3 )', 'b ) 500 ( Ο β 2.5 )', 'c ) 500 ( Ο β 2 )', 'd ) 550 ( Ο β 1.5 )', 'e ) 500 ( Ο β 1 )'] | d | divide(volume_cylinder(5, 22), const_2) | a right circular cylinder has a height of 22 and a radius of 5 . a rectangular solid with a height of 15 and a square base , is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall . liquid is then poured into the cylinder such that it reaches the rim . what is the volume of... | [ quote = bunuel ] a right circular cylinder has a height of 20 and a radius of 5 . a rectangular solid with a height of 15 and a square base , is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall . liquid is then poured into the cylinder such that it reaches the rim . wh... | a = volume_cylinder / (
|
a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 560 | e | divide(140, subtract(const_1, divide(3, 4))) | the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 140 visitors who did not enjoy the painting also d... | "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 120 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 560 n = 480 answer = ( e )" | a = 3 / 4
b = 1 - a
c = 140 / b
|
a ) 870 , b ) 600 , c ) 287 , d ) 771 , e ) 191 | a | subtract(multiply(430, 9), subtract(multiply(430, 9), 870)) | the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 ... | "explanation : total salary of 8 workers and supervisor together = 9 Γ£ β 430 = 3870 now total salary of 8 workers = 3870 Γ’ Λ β 870 = 3000 total salary of 9 workers including the new supervisor = 9 Γ£ β 430 = 3870 salary of the new supervisor = 3870 Γ’ Λ β 3000 = 870 answer : a" | a = 430 * 9
b = 430 * 9
c = b - 870
d = a - c
|
a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24 | a | multiply(factorial(3), factorial(2)) | 3 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other ) | the list should be wmwmw . hence , from women 2 ! and men 3 ! , we get ( 2 ! ) ( 3 ! ) = 12 . therefore , the correct answer is a . | a = math.factorial(3)
b = math.factorial(2)
c = a * b
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11 | c | floor(divide(40, divide(10, const_2))) | what is the greatest integer m for which the number 40 ! / 10 ^ m is an integer ? | "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 40 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 , 35 , 40 . thus 5 ^ 9 will divide 40 ! but 5 ^ 10 will not . clearly 2 ^ 9 will divide 40 ! so m = 9 is the largest possible integer . the answer is c ." | a = 10 / 2
b = 40 / a
c = math.floor(b)
|
a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these | b | divide(multiply(4, 50), multiply(40, 20)) | 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be : | "explanation : total volume of water displaced = ( 4 x 50 ) m 3 = 200 m 3 rise in water level = 200 / 40 Γ 20 = 0.25 m = 25 cm answer : b" | a = 4 * 50
b = 40 * 20
c = a / b
|
a ) 10.5 , b ) 0.5 , c ) 25.5 , d ) 30 , e ) 60 | b | subtract(subtract(divide(const_60, const_2), 25), divide(const_60, divide(20, 1.5))) | darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the ... | "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 25 x = 0.5 minutes answer : b" | a = const_60 / 2
b = a - 25
c = 20 / 1
d = const_60 / c
e = b - d
|
a ) 26 , b ) 24 , c ) 21 , d ) 28 , e ) 20 | c | divide(log(multiply(power(8, 7), power(5, 21))), log(const_10)) | if 5 ^ 21 x 8 ^ 7 = 10 ^ n what is the value of n ? | 5 ^ 21 * ( 2 ^ 3 ) ^ 7 = 10 ^ n or 5 ^ 21 * 2 ^ 21 = 10 ^ n or 10 ^ 21 = 10 ^ n n = 21 c | a = 8 ** 7
b = 5 ** 21
c = a * b
d = math.log(c)
e = math.log(10)
f = d / e
|
a ) $ 10,000 , b ) $ 11,200 , c ) $ 12,000 , d ) $ 12,800 , e ) $ 26,400 | e | multiply(floor(multiply(divide(subtract(add(multiply(divide(20, const_100), 60000), multiply(add(divide(40, const_100), 1), subtract(60000, multiply(divide(20, const_100), 60000)))), add(multiply(multiply(2, 20000), divide(20, const_100)), multiply(subtract(multiply(2, 20000), multiply(multiply(2, 20000), divide(20, co... | at a certain supplier , a machine of type a costs $ 20000 and a machine of type b costs $ 60000 . each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time . if the finance charges are equal to 40 percent of the remainder of th... | total cost of 2 machines of type a = 20 % of ( cost of 2 machine a ) + remainder + 40 % remainder = 20 % of 40000 + ( 40000 - 20 % of 40000 ) + 40 % of ( 40000 - 20 % of 40000 ) = 52800 total cost of 1 machine of type b = 20 % of ( cost of 1 machine b ) + remainder + 40 % remainder = 20 % of 60000 + ( 60000 - 20 % of 6... | a = 20 / 100
b = a * 60000
c = 40 / 100
d = c + 1
e = 20 / 100
f = e * 60000
g = 60000 - f
h = d * g
i = b + h
j = 2 * 20000
k = 20 / 100
l = j * k
m = 2 * 20000
n = 2 * 20000
o = 20 / 100
p = n * o
q = m - p
r = 40 / 100
s = r + 1
t = q * s
u = l + t
v = i - u
w = v / 60000
x = w * 10
y = math.floor(x)
z = y * 3
|
a ) 2378 , b ) 277 , c ) 208 , d ) 270 , e ) 350 | e | divide(subtract(11600, multiply(16, divide(subtract(multiply(11600, const_2), 11600), subtract(multiply(37, const_2), 16)))), 24) | the wages of 24 men and 16 women amounts to rs . 11600 per day . half the number of men and 37 women earn the same amount per day . what is the daily wage of a man ? | let the wage of a man is m and woman be w . 24 m + 16 w = 11600 12 m + 37 w = 11600 solving we get m = 350 answer : e | a = 11600 * 2
b = a - 11600
c = 37 * 2
d = c - 16
e = b / d
f = 16 * e
g = 11600 - f
h = g / 24
|
a ) 2.5 % , b ) 20 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 % | b | multiply(divide(multiply(divide(30, const_100), subtract(1, divide(1, 2))), subtract(1, divide(1, 3))), const_100) | a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 2 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ? | "fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 3,060 non transferred fiction novels = 2,448 percent of the remaining collection was fiction novels = 2,448 / ( 18360 - 6120 ) * 100 = > 20 % hence answer will be ( b )" | a = 30 / 100
b = 1 / 2
c = 1 - b
d = a * c
e = 1 / 3
f = 1 - e
g = d / f
h = g * 100
|
['a ) 2998', 'b ) 2799', 'c ) 1782', 'd ) 1485', 'e ) 2780'] | c | multiply(volume_cylinder(divide(3, const_2), 14), 18) | find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 18 per cubic meter ? | 22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 18 = 1782 answer : c | a = 3 / 2
b = volume_cylinder * (
|
a ) 3616.5 , b ) 3613.5 , c ) 3313.5 , d ) 3616.5 , e ) 3113.5 | b | divide(multiply(multiply(multiply(const_3, const_100), const_100), multiply(5, divide(8.5, multiply(8.5, const_3)))), const_100) | what is the compound interest on rs . 7000 at 8.5 % p . a . compounded half - yearly for 5 years . | "compound interest : a = p ( 1 + r / n ) nt a = 10 , 613.50 c . i . > > 10 , 613.50 - 7000 > > rs . 3613.5 answer : b" | a = 3 * 100
b = a * 100
c = 8 * 5
d = 8 / 5
e = 5 * d
f = b * e
g = f / 100
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a ) 5 : 3 , b ) 8 : 11 , c ) 8 : 7 , d ) 6 : 5 , e ) 3 : 11 | c | divide(add(multiply(4, divide(14, add(4, 3))), 8), add(multiply(3, divide(14, add(4, 3))), 8)) | the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 14 years . the ratio of their ages after 8 years will be | "let mini β s age = 4 x and minakshi β s age = 3 x then 4 x + 3 x = 14 x = 2 mini β s age = 8 years and minakshi β s age = 6 years ratio of their ages after 8 years = ( 8 + 8 ) : ( 6 + 8 ) = 16 : 14 = 8 : 7 answer : c" | a = 4 + 3
b = 14 / a
c = 4 * b
d = c + 8
e = 4 + 3
f = 14 / e
g = 3 * f
h = g + 8
i = d / h
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a ) 400 , b ) 365 , c ) 385 , d ) 315 , e ) 355 | d | divide(subtract(700700, multiply(divide(700700, const_2), divide(const_1, add(const_1, const_4)))), const_2) | a large field of 700700 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ? | "explanation : average of the two areas = 700 / 2 = 350 one - fifth of the average of the two areas = 350 / 5 = 70 β difference of the two areas = 70 = 70 let area of the smaller part = x hectares . then , area of the larger part = x + 70 hectares . x + ( x + 70 ) = 700 β 2 x = 630 β x = 315 answer : option d" | a = 700700 / 2
b = 1 + 4
c = 1 / b
d = a * c
e = 700700 - d
f = e / 2
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a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 55 % | e | add(multiply(divide(12, 48), const_100), 30) | the purchase price of an article is $ 48 . in order to include 30 % of cost for overhead and to provide $ 12 of net profit , the markup should be | "cost price of article = 48 $ % of overhead cost = 30 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 30 = 55 % answer e" | a = 12 / 48
b = a * 100
c = b + 30
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a ) 201 , b ) 159 , c ) 179 , d ) 189 , e ) 209 | e | divide(multiply(subtract(23, const_1), subtract(subtract(23, const_1), const_3)), const_2) | how many diagonals does a polygon with 23 sides have , if one of its vertices does not connect to any diagonal ? | "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 23 - 1 then 22 * ( 22 - 3 ) / 2 = 209 correct option : e" | a = 23 - 1
b = 23 - 1
c = b - 3
d = a * c
e = d / 2
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a ) $ 220 , b ) $ 230 , c ) $ 240 , d ) $ 200 , e ) $ 250 | d | subtract(260, multiply(divide(subtract(350, 260), 3), 2)) | mary invested a certain sum of money in a bank that paid simple interest . the amount grew to $ 260 at the end of 2 years . she waited for another 3 years and got a final amount of $ 350 . what was the principal amount that she invested at the beginning ? | what shall be the rate of interest . ? does that is not required for the calculation ? not really ! keep in mind that the interest earned each year will be the same in simple interest . at the end of 2 years , amount = $ 260 at the end of 5 years , amount = $ 350 this means she earned an interest of $ 90 in 3 years . o... | a = 350 - 260
b = a / 3
c = b * 2
d = 260 - c
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a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 6.25 liters . , e ) 2.1 liters . | d | divide(multiply(divide(subtract(const_100, 90), const_100), 50), divide(subtract(const_100, 20), const_100)) | heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 50 litres of tomato juice ? | "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . Γ’ β‘ β Γ’ β‘ β 10 % ( 50 ) = 80 % ( x ) Γ’ β‘ β Γ’ β‘ β x = 6.25 liters . answer : d" | a = 100 - 90
b = a / 100
c = b * 50
d = 100 - 20
e = d / 100
f = c / e
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a ) 44 , b ) 50 , c ) 28 , d ) 27 , e ) 18 | a | add(22, 24) | laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 22 kmph and prasanna moves southward at a speed of 24 kmph . how far will be prasanna from laxmi after 60 minutes ? | "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 22 kmph x 1 hr = 22 km total southward prasanna ' s distance = 24 kmph x 1 hr = 24 km total distance between prasanna and laxmi is = 22 + 24 = 44 km . answer : a" | a = 22 + 24
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a ) 2 : 1 , b ) 3 : 1 , c ) 5 : 2 , d ) 1 : 1 , e ) none of these | a | divide(1, subtract(divide(60, 40), 1)) | a good train and a passenger train are running on parallel tracks in the same direction . the driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec . whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec .... | explanation : let , the speeds of the two trains be s and 2 s m / s respectively . also , suppose that the lengths of the two trains are p and q metres respectively . then , = > ( p + q ) / ( 2 s β s ) = 60 . - - - - - - - - - - - - - - ( 1 ) and , = > p / ( 2 s β s ) = 40 . - - - - - - - - - - - - - - ( 2 ) on dividin... | a = 60 / 40
b = a - 1
c = 1 / b
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a ) 380 , b ) 350 , c ) 333 , d ) 310 , e ) none of these | c | multiply(3164, power(add(const_4, const_1), const_4)) | ( 3164 + 6160 ) / 28 | "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9324 ) / 28 = 333 option c" | a = 4 + 1
b = a ** 4
c = 3164 * b
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a ) $ 200 , b ) $ 220 , c ) $ 285 , d ) $ 300 , e ) $ 360 | c | subtract(subtract(600, divide(multiply(600, 2), 5)), multiply(subtract(subtract(15, divide(multiply(15, 3), 5)), const_1), 15)) | a prize of $ 600 is to be distributed among 15 winners , each of whom must be awarded at least $ 15 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ? | "total value of the prize = $ 600 number of people = 15 2 / 5 of 600 ( = $ 240 ) should be distributed among 3 / 5 of 15 ( = 9 people ) with each getting $ 15 each . remaining money = 600 - 240 = $ 360 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ ... | a = 600 * 2
b = a / 5
c = 600 - b
d = 15 * 3
e = d / 5
f = 15 - e
g = f - 1
h = g * 15
i = c - h
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a ) 675 , rs . 2025 , b ) 575 , rs . 1350 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875 | a | multiply(subtract(rectangle_area(add(75, multiply(2.5, const_2)), add(55, multiply(2.5, 3))), rectangle_area(75, 55)), 3) | a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 3 per sq m ? | "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 3 = rs . 2025 answer : a" | a = 2 * 5
b = 75 + a
c = 2 * 5
d = 55 + c
e = rectangle_area - (
f = e * rectangle_area
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a ) 10 ΒΊ , b ) 75 ΒΊ , c ) 180 ΒΊ , d ) 270 ΒΊ , e ) 360 ΒΊ | b | divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2) | the angle between the minute hand and the hour hand of a clock when the time is 8.30 , is : | "angle traced by hour hand in 17 / 2 hrs = ( 360 / 12 x 17 / 2 ) ΒΊ = 255 . angle traced by min . hand in 30 min . = ( 360 / 60 x 30 ) ΒΊ = 180 . required angle = ( 255 - 180 ) ΒΊ = 75 ΒΊ . answer b" | a = 3 * 4
b = 3 * 4
c = b - 1
d = a / c
e = 4 + 1
f = 3 * 4
g = f - 1
h = e * g
i = d * h
j = const_60 / 2
k = i - j
l = 3 * 4
m = l - 1
n = k * m
o = n / 2
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a ) 3775 , b ) 3665 , c ) 3456 , d ) 3459 , e ) 3569 | a | multiply(divide(add(100, 51), const_2), subtract(51, const_1)) | evaluate ( 51 + 52 + 53 + . . . + 100 ) | sn = ( 1 + 2 + 3 + . . . + 50 + 51 + 52 + . . . + 100 ) - ( 1 + 2 + 3 + . . . + 50 ) = ( 50 x 101 ) - ( 25 x 51 ) = ( 5050 - 1275 ) = 3775 . option a | a = 100 + 51
b = a / 2
c = 51 - 1
d = b * c
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a ) 18 , b ) 16 , c ) 12 , d ) 10 , e ) 6 | e | subtract(90, add(add(38, const_1), 45)) | 90 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ? | { total } = { writers } + { editors } - { both } + { neither } . { total } = 90 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 90 = 45 + { editors } - x + 2 x - - > x = 45 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 3... | a = 38 + 1
b = a + 45
c = 90 - b
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a ) 23 , b ) 37 , c ) 28 , d ) 44 , e ) 81 | d | subtract(const_100, subtract(add(34, 44), 22)) | in an examination , 34 % of total students failed in hindi , 44 % failed in english and 22 % in both . the percentage of these who passed in both the subjects is : | explanation : formula n ( a Γ’ Λ Βͺ b ) = n ( a ) + n ( b ) Γ’ Λ β n ( a Γ’ Λ Β© b ) fail in hindi or english = 34 + 44 Γ’ β¬ β 22 = 56 therefore students who passed = 100 Γ’ β¬ β 56 = 44 . answer : d | a = 34 + 44
b = a - 22
c = 100 - b
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a ) 50 , b ) 45 , c ) 40 , d ) 35 , e ) 30 | e | add(divide(multiply(3, 12), 3), divide(multiply(3, 12), subtract(5, 3))) | nicky and cristina are running a 500 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ? | "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . e" | a = 3 * 12
b = a / 3
c = 3 * 12
d = 5 - 3
e = c / d
f = b + e
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a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996 | e | add(1990, multiply(10, multiply(const_2, const_3))) | in 1990 the budgets for projects q and v were $ 540,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ? | let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e . | a = 2 * 3
b = 10 * a
c = 1990 + b
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a ) 320 , b ) 340 , c ) 360 , d ) 380 , e ) 400 | d | multiply(divide(multiply(divide(multiply(divide(320, 5), 5), 2), 19), 24), 5) | there is a train and car . the ratio between the speed of a train & a car is 24 : 19 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 2 / 3 rd of the speed of the train . how many kilometers will the car cover in 5 hours ? | "the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 3 ) / 2 = 96 km / hr the speed of the car is 96 / 24 * 19 = 76 km / hr the distance covered by the car in 5 hours is 76 Γ 5 = 380 km the answer is d ." | a = 320 / 5
b = a * 5
c = b / 2
d = c * 19
e = d / 24
f = e * 5
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a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 18 | e | divide(multiply(12, const_3), const_2) | youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 12 minutes more to walk to work than to ride his bike to work , then x equals ? | "please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 720 ( which i... | a = 12 * 3
b = a / 2
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a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5 | c | subtract(4, 2) | buffalo gives 4 liter milk , cow gives ( 1 / 2 ) liter milk and goat gives 1 / 4 liter milk . you have to get 20 liter milk by 20 animals . what is the number of buffalos ? | "assume number of respective animals are x , y , z . x + y + z = 20 - - - ( 1 ) as the total number of animal has to be 20 amt of milk will be 4 x + ( 1 / 2 ) y + ( 1 / 4 ) z = 20 - - - ( 2 ) solving equation 1 and 2 we get 15 x + y = 60 - - - - ( 3 ) since buffalo gives 4 litre and total milk is 20 , x < 5 but from eq... | a = 4 - 2
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a ) 288 , b ) 560 , c ) 155 , d ) 600 , e ) 441 | b | multiply(subtract(divide(12000, 10000), divide(8000, 10000)), 1400) | a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1400 . the difference between the profit shares of a and c is ? | "ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1400 = > 5 parts out of 15 parts is rs . 1400 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1400 ) = rs . 560 answer : b" | a = 12000 / 10000
b = 8000 / 10000
c = a - b
d = c * 1400
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a ) 7 / 15 , b ) 1 / 5 , c ) 4 / 15 , d ) 1 / 3 , e ) 2 / 5 | a | subtract(divide(1, 2), divide(const_1, multiply(3, const_10))) | of all the students in a certain dormitory , 1 / 2 are first - year students and the rest are second - year students . if 4 / 5 of the first - year students have not declared a major and if the fraction of second - year students who have declared a major is 1 / 3 times the fraction of first - year students who have dec... | tot students = x 1 st year student = x / 2 - - - - > non majaor = 4 / 5 ( x / 2 ) - - - - - > maj = 1 / 5 ( x / 2 ) 2 nd year student = x / 2 - - - - > maj = 1 / 3 ( 1 / 5 ( x / 2 ) ) = 1 / 30 ( x ) - - - > non major = x / 2 - 1 / 30 ( x ) = 7 / 15 ( x ) hence 7 / 15 a | a = 1 / 2
b = 3 * 10
c = 1 / b
d = a - c
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a ) 42 , b ) 56 , c ) 76 , d ) 84 , e ) 85 | a | add(multiply(multiply(3, const_4.0), const_100), multiply(4, 72)) | two numbers are in the ratio 3 : 4 . if their l . c . m . is 72 . what is sum of the numbers ? | "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 72 = > 12 x = 72 = > x = 72 / 12 = 6 sum of the numbers = 3 x + 4 x = 7 x = 7 x 6 = 42 answer : option a" | a = 3 * 4
b = a * 100
c = 4 * 72
d = b + c
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a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 13 % | c | multiply(divide(subtract(9990, 9000), 9000), const_100) | a sum of money deposited at c . i . amounts to rs . 9000 in 10 years and to rs . 9990 in 11 years . find the rate percent ? | "9000 - - - 990 100 - - - ? = > 11 % answer : c" | a = 9990 - 9000
b = a / 9000
c = b * 100
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a ) 125 , b ) 280 , c ) 384 , d ) 480 , e ) 500 | d | divide(multiply(multiply(250, 16), 6), subtract(multiply(5, 16), multiply(5, 6))) | in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 250 more than the correct answer . find the number . | "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 250 25 * x / 48 = 250 x = 480 answer d" | a = 250 * 16
b = a * 6
c = 5 * 16
d = 5 * 6
e = c - d
f = b / e
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a ) 132 , b ) 39 , c ) 42 , d ) 65 , e ) 156 | a | multiply(multiply(multiply(power(2, 2), 3), divide(11, 2)), 2) | if 2 ^ 5 , 3 ^ 3 , and 11 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ? | "here 156 has three two ' s two three ' s and one 11 rest of them must be in w so w = 11 * 3 * 4 = 132 smash a" | a = 2 ** 2
b = a * 3
c = 11 / 2
d = b * c
e = d * 2
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a ) 132 Β° f , b ) 140 Β° f , c ) 148 Β° f , d ) 156 Β° f , e ) 164 Β° f | b | add(multiply(divide(subtract(212, 32), 100), 60), 32) | water boils at 212 Β° f or 100 Β° c and ice melts at 32 Β° f or 0 Β° c . if the temperature of a pot of water is 60 Β° c , what is the temperature of the pot of water in Β° f ? | "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 60 ) / 5 + 32 = 140 Β° f the answer is b ." | a = 212 - 32
b = a / 100
c = b * 60
d = c + 32
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a ) 2 , b ) 4 , c ) 8 , d ) 256 , e ) 32 | d | power(4, multiply(const_4, 1)) | xy = 1 then what is ( 4 ^ ( x + y ) ^ 2 ) / ( 4 ^ ( x - y ) ^ 2 ) | "( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 4 4 ^ 4 = 256 answer d" | a = 4 * 1
b = 4 ** a
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a ) 150 cm , b ) 140 cm , c ) 142 cm , d ) 148 cm , e ) 146 cm | b | subtract(154, divide(multiply(154, 10), const_100)) | on my sister ' s birthday , she was 154 cm in height , having grown 10 % since the year before . how tall was she the previous year ? | "let the previous year ' s height be x . 1.1 x = 154 x = 140 the answer is b ." | a = 154 * 10
b = a / 100
c = 154 - b
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a ) 3 / 5 , b ) 5 / 9 , c ) 1 / 24 , d ) 4 / 9 , e ) 7 / 15 | e | divide(subtract(divide(16, const_2), const_1), subtract(16, const_1)) | an empty wooden vessel weighs 16 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled . | "an empty wooden vessel weighs 16 % of its total weight when filled with paint : vessel = 0.16 ( vessel + paint ) ; 16 v = v + p ( so the weight of completely filled vessel is 16 v ) p = 15 v ( so the weight of the paint when the vessels is completely filled is 15 v ) . the weight of a partially filled vessel is one ha... | a = 16 / 2
b = a - 1
c = 16 - 1
d = b / c
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a ) 5 seconds , b ) 4.5 seconds , c ) 3 seconds , d ) 2.3 seconds , e ) none of these | d | divide(120, multiply(184, const_0_2778)) | in what time will a train 120 meters long cross an electric pole , if its speed is 184 km / hr | "explanation : first convert speed into m / sec speed = 184 * ( 5 / 18 ) = 51 m / sec time = distance / speed = 120 / 51 = 2.3 seconds option d" | a = 184 * const_0_2778
b = 120 / a
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a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99 | e | divide(subtract(add(multiply(divide(const_100, 4), const_2), multiply(divide(const_100, 5), const_2)), 4), subtract(const_100, 1)) | if x is a positive integer with fewer than 3 digits , what is the probability r that x * ( x + 1 ) is a multiple of either 4 or 5 ? | "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability r that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either... | a = 100 / 4
b = a * 2
c = 100 / 5
d = c * 2
e = b + d
f = e - 4
g = 100 - 1
h = f / g
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a ) 432 , b ) 288 , c ) 376 , d ) 397 , e ) 592 | a | multiply(multiply(divide(96, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(96, add(multiply(const_3, const_2), multiply(const_1, const_2)))) | the length of rectangle is thrice its breadth and its perimeter is 96 m , find the area of the rectangle ? | "2 ( 3 x + x ) = 96 l = 36 b = 12 lb = 36 * 12 = 432 answer : a" | a = 3 * 2
b = 1 * 2
c = a + b
d = 96 / c
e = d * 3
f = 3 * 2
g = 1 * 2
h = f + g
i = 96 / h
j = e * i
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a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6 | b | add(subtract(12, 11), 2) | there are 12 pieces of radioactive metal a that look identical . 11 of the pieces give the same radiation count when measured , the 12 th piece is a counterfeit and gives a different radiation level , which may be more or less than the other 11 . we are given a radiation scale , which can take 2 sets of samples and com... | first of all if you are down to just 3 pieces and you know that if the offending piece is less or more active , then it takes exactly 1 measurement to find out the offending piece . so you know you have to reduce the problem to three . now when you are down to either a or b after measurement 1 , you need the next measu... | a = 12 - 11
b = a + 2
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a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 4 , d ) 5 / 6 , e ) 6 / 7 | b | divide(add(1, add(divide(1, const_2), add(divide(1, add(1, 5)), divide(5, add(1, 5))))), add(1, 5)) | in a bag containing 5 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of the balls that initiallyin the bag wereequally possible ? | "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . β΄ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b" | a = 1 / 2
b = 1 + 5
c = 1 / b
d = 1 + 5
e = 5 / d
f = c + e
g = a + f
h = 1 + g
i = 1 + 5
j = h / i
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a ) 20 cs , b ) cs / 2 , c ) 60 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s | c | multiply(5, const_12) | a certain school implemented a reading program for its students , with the goal of getting each student to read 5 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ? | "ans : c solution : simple multiplication s students , c classes , 5 books / month = 60 books a year total number of books = 60 cs" | a = 5 * 12
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a ) 14 , b ) 17 , c ) 11 , d ) 19 , e ) 99 | b | subtract(divide(44, const_2), 5) | a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 44 now , the son age 5 years back was | "let the son ' s present age be x years . then , ( 44 - x ) = x x = 22 . son ' s age 5 years back = ( 22 - 5 ) = 17 years answer : b" | a = 44 / 2
b = a - 5
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a ) 16 , b ) 32 , c ) 64 , d ) 96 , e ) 128 | c | multiply(16, multiply(16, divide(4, multiply(4, 4)))) | 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 16 weavers in 16 days ? | "1 weaver can weave 1 mat in 4 days . 16 weavers can weave 16 mats in 4 days . 16 weavers can weave 64 mats in 16 days . the answer is c ." | a = 4 * 4
b = 4 / a
c = 16 * b
d = 16 * c
|
a ) 16 , b ) 20 , c ) 32 , d ) 40 , e ) 48 | d | divide(subtract(15, multiply(divide(20, const_100), 65)), subtract(divide(25, const_100), divide(20, const_100))) | a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 65 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ? | lets say x ounces of p is mixed with q . = > 65 - x ounces of q is present in the mixture ( as the total = 65 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 65 - x ) = 15 = > x = 25 = > 65 - 25 = 40 ounces of q is present in the mixture . answer is d . | a = 20 / 100
b = a * 65
c = 15 - b
d = 25 / 100
e = 20 / 100
f = d - e
g = c / f
|
a ) 1 / 3 , b ) ΒΌ , c ) 9 / 25 , d ) 5 / 16 , e ) 0 | d | divide(add(3, const_2), multiply(const_4, const_4)) | if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability q that n is divisible by 3 ? | "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ." | a = 3 + 2
b = 4 * 4
c = a / b
|
a ) 37 min , b ) 55 min , c ) 47 min , d ) 67 min , e ) 45 min | e | divide(add(330, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36)) | a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 330 m long platform ? | "e 45 min let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 330 ) / 36 * 5 / 18 = 45 min ." | a = const_0_2778 * 36
b = a * 12
c = 330 + b
d = const_0_2778 * 36
e = c / d
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7 | d | subtract(subtract(10, 3), const_1) | if 3 < x < 6 < y < 10 , then what is the greatest possible positive integer difference of x and y ? | "3 < x < 6 < y < 10 ; 3 < x y < 10 3 + y < x + 10 y - x < 7 . positive integer difference is 6 ( for example y = 9.5 and x = 3.5 ) answer : d ." | a = 10 - 3
b = a - 1
|
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) - 2 | e | subtract(6, 8) | what is 10 - 8 + 6 - 4 + . . . + ( - 14 ) ? | the expression considers all even numbers between 10 and - 14 with alternate addition and subtraction of the numbers . the numbers to be used are : 10 , 8 , 6 , 4 , 2 , 0 , - 2 , - 4 , - 6 , - 8 , - 10 , - 12 , and - 14 now , the first term is positive and the next term is subtracted . so , the required expression beco... | a = 6 - 8
|
a ) rs . 16003 , b ) rs . 16029 , c ) rs . 22500 , d ) rs . 16108 , e ) rs . 16011 | c | subtract(multiply(add(1500, 1000), add(20, const_1)), multiply(1500, 20)) | the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 1000 . what is the manager ' s monthly salary ? | "explanation : manager ' s monthly salary rs . ( 2500 * 21 - 1500 * 20 ) = rs . 22500 . answer : c" | a = 1500 + 1000
b = 20 + 1
c = a * b
d = 1500 * 20
e = c - d
|
a ) 15 mile , b ) 14 mile , c ) 11 mile , d ) 10 mile , e ) 12.5 mile | e | multiply(divide(subtract(30, multiply(24, divide(add(1, 5), const_60))), add(5, add(1, 5))), 5) | stacy and heather are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the tw... | "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 30 - 2.4 = 17.6 time taken = distance / speed = 27.6 / 11 = 2.5 hrs heather wi... | a = 1 + 5
b = a / const_60
c = 24 * b
d = 30 - c
e = 1 + 5
f = 5 + e
g = d / f
h = g * 5
|
a ) 672 m , b ) 6738 m , c ) 634 m , d ) 671 m , e ) 636 m | a | subtract(224, multiply(8, speed(224, 32))) | for a race a distance of 224 meters can be covered by p in 8 seconds and q in 32 seconds . by what distance does p defeat q eventually ? | "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 8 = 28 m / s = > speed of q = 224 / 32 = 7 m / s = > difference in time taken = 24 seconds therefore , distance covered by p in that time = 28 m / s x 24 seconds = 672 metres answer : a" | a = 8 * speed
b = 224 - a
|
a ) 1 / 3 , b ) 1 / 4 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7 | a | divide(const_2, add(4, const_2)) | in a single throw of a die , what is the probability of getting a number greater than 4 ? | s = { 1,2 , 3,4 , 5,6 } e = { 5,6 } probability = 2 / 6 = 1 / 3 answer is a | a = 4 + 2
b = 2 / a
|
a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 4 | e | divide(subtract(multiply(12, subtract(40, 6)), multiply(12, 32)), 6) | the average age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasing the average by 6 year . find what was the original average age of the class ? | let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 34 Γ’ β‘ β 40 y + 384 = 34 y + 408 Γ’ β‘ β 6 y = 24 Γ’ Λ Β΄ y = 4 e | a = 40 - 6
b = 12 * a
c = 12 * 32
d = b - c
e = d / 6
|
a ) 10 kmph , b ) 20 kmph , c ) 15 kmph , d ) 30 kmph , e ) 25 kmph | b | divide(180, divide(multiply(6, 3), 2)) | a car takes 6 hours to cover a distance of 180 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 = 280 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 180 / 9 = 20 kmph b )" | a = 6 * 3
b = a / 2
c = 180 / b
|
a ) 1 and 8 , b ) 2 and 6 , c ) 2 and 9 , d ) 2 and 7 , e ) 2 and 9 | c | add(multiply(const_2, const_10), divide(add(44, 19), 7)) | 5 n + 2 > 12 and 7 n - 19 < 44 ; n must be between which numbers ? | 5 n + 2 > 12 5 n > 10 n > 2 7 n - 19 < 44 7 n < 63 n < 9 so n must be between 2 and 9 2 < n < 9 correct answer c | a = 2 * 10
b = 44 + 19
c = b / 7
d = a + c
|
a ) β 2 % , b ) 2 % , c ) 22 % , d ) 25 % , e ) can not be determined | d | multiply(const_100, subtract(divide(add(const_1, divide(const_10, const_100)), subtract(const_1, divide(const_12, const_100))), const_1)) | the price of a consumer good increased by pp % during 20122012 and decreased by 1212 % during 20132013 . if no other change took place in the price of the good and the price of the good at the end of 20132013 was 1010 % higher than the price at the beginning of 20122012 , what was the value of pp ? | as per question = > price was simple 10 percent greater hence x [ 1 + 10 / 100 ] must be the final price . equating the two we get = > x [ 110 / 100 ] = x [ 1 + p / 100 ] [ 88 / 100 ] = > 44 p + 4400 = 5500 = > 44 p = 1100 = > p = 1100 / 44 = > 100 / 4 = > 25 . so p must be 25 answer : d | a = 10 / 100
b = 1 + a
c = 12 / 100
d = 1 - c
e = b / d
f = e - 1
g = 100 * f
|
a ) 4 , b ) 6 , c ) 12 , d ) 24 , e ) 30 | d | multiply(divide(multiply(2, 6), subtract(4, 2)), 4) | two integers are in the ratio of 1 to 4 . if 6 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer . | "assume the integers to be x and y , where x < y given x / y = 1 / 4 - ( i ) or y = 4 x and x + 6 / y = 1 / 2 - ( ii ) or y = 2 x + 12 substituting the value of y from ( i ) , 4 x = 2 x + 12 x = 6 hence y = 4 * 6 = 24 answer d" | a = 2 * 6
b = 4 - 2
c = a / b
d = c * 4
|
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9 | b | divide(divide(multiply(multiply(12, 8), 10), 16), 12) | in a garment industry , 12 men working 8 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 16 hours a day , the number of men required is : | "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 16 : 8 : : 12 : x = > 12 x 16 x x = 10 x 8 x 12 = > x = 10 x 8 x 12 / ( 12 x 16 ) = > x = 5 answer : b" | a = 12 * 8
b = a * 10
c = b / 16
d = c / 12
|
['a ) 952 cm ^ 2', 'b ) 957 cm ^ 2', 'c ) 954 cm ^ 2', 'd ) 958 cm ^ 2', 'e ) none of them'] | b | add(multiply(multiply(power(divide(7, const_2), const_2), const_pi), const_2), multiply(multiply(7, const_pi), 40)) | find the volume , curved surface area and the total surface area of a cylinder with diameter of base 7 cm and height 40 cm . | volume = β r 2 h = ( ( 22 / 7 ) x ( 7 / 2 ) x ( 7 / 2 ) x 40 ) = 1540 cm ^ 3 . . curved surface area = 2 β rh = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x 40 ) = 880 cm ^ 2 . total surface area = 2 β rh + 2 β r 2 = 2 β r ( h + r ) = ( 2 x ( 22 / 7 ) x ( 7 / 2 ) x ( 40 + 3.5 ) ) cm 2 = 957 cm ^ 2 answer is b | a = 7 / 2
b = a ** 2
c = b * math.pi
d = c * 2
e = 7 * math.pi
f = e * 40
g = d + f
|
a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349 | c | divide(factorial(subtract(add(const_4, 15), const_1)), multiply(factorial(15), factorial(subtract(const_4, const_1)))) | how many positive integers less than 5,000 are evenly divisible by neither 15 nor 23 ? | "integers less than 5000 divisible by 15 5000 / 15 = 333 . something , so 333 integers less than 5000 divisible by 23 5000 / 23 = 238 . # # , so 238 we have double counted some , so take lcm of 15 and 23 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 15 and 23 = 333 + 238 - 47 = 524 now subtract tha... | a = 4 + 15
b = a - 1
c = math.factorial(b)
d = math.factorial(15)
e = 4 - 1
f = math.factorial(e)
g = d * f
h = c / g
|
a ) 1000 , b ) 6000 , c ) 5000 , d ) 8000 , e ) 1900 | a | multiply(multiply(divide(50, multiply(20, 4)), const_100), multiply(20, 4)) | find the sum the difference between the compound and s . i . on a certain sum of money for 4 years at 20 % per annum is rs . 50 of money ? | "p = 50 ( 100 / 20 ) 4 = > p = 1000 answer : a" | a = 20 * 4
b = 50 / a
c = b * 100
d = 20 * 4
e = c * d
|
a ) rs . 27,000 , b ) rs . 26,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these | b | multiply(add(multiply(multiply(multiply(const_4, 2), multiply(add(2, const_3), 2)), const_100), multiply(multiply(add(2, const_3), const_100), const_100)), divide(divide(multiply(add(2, const_3), 2), 2), multiply(const_4, const_3))) | jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 52,000 after completion of one year . what will be madhu ' s share of profit ? | "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 52,000 i . e . rs . 26,000 answer : b" | a = 4 * 2
b = 2 + 3
c = b * 2
d = a * c
e = d * 100
f = 2 + 3
g = f * 100
h = g * 100
i = e + h
j = 2 + 3
k = j * 2
l = k / 2
m = 4 * 3
n = l / m
o = i * n
|
a ) $ 28,300 , b ) $ 30,400 , c ) $ 31,300 , d ) $ 31,200 , e ) $ 35,100 | d | multiply(divide(234, divide(9, multiply(const_3, const_4))), const_100) | an investment yields an interest payment of $ 234 each month . if the simple annual interest rate is 9 % , what is the amount of the investment ? | let the principal amount = p simple annual interest = 9 % simple monthly interest = ( 9 / 12 ) = ( 3 / 4 ) % ( 3 / 4 ) * ( p / 100 ) = 234 = > p = ( 234 * 4 * 10 ^ 2 ) / 3 = 78 * 4 * 10 ^ 2 = 312 * 10 ^ 2 = 31200 answer d | a = 3 * 4
b = 9 / a
c = 234 / b
d = c * 100
|
a ) 0.8 , b ) 1.25 , c ) 8.0 , d ) 2.5 , e ) 80.0 | d | subtract(divide(power(const_100, const_3), multiply(400, 1,000)), const_2) | the mass of 1 cubic meter of a substance is 400 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters ) | "density is mass divided by volume . so density of the given substance will be mass / volume = 400 kg / 1 m ^ 3 = 400 kg / m ^ 3 or 1 g / 2.5 cm ^ 3 = 0.4 g / cm ^ 3 . next , ask yourself if 400,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 0... | a = 100 ** 3
b = 400 * 1
c = a / b
d = c - 2
|
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | d | divide(80, add(const_4, divide(const_2, const_2))) | a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 80 , how many horses are there ? | "legs 16 * 4 = 64 now half on their horses so remaining on the walk so 8 men 8 men has 16 legs so , 16 + 64 = 80 legs walking answer : d" | a = 2 / 2
b = 4 + a
c = 80 / b
|
a ) 33 , b ) 34 , c ) 26 , d ) 28 , e ) 19 | b | subtract(54, divide(subtract(780, multiply(54, 10)), subtract(22, 10))) | 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is : | "explanation : let the two parts be ( 54 - x ) and x . then , 10 ( 54 - x ) + 22 x = 780 = > 12 x = 240 = > x = 20 . bigger part = ( 54 - x ) = 34 . answer : b ) 34" | a = 54 * 10
b = 780 - a
c = 22 - 10
d = b / c
e = 54 - d
|
a ) 50 hrs , b ) 30 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs | b | divide(const_1, subtract(divide(const_1, 10), divide(const_1, 15))) | a cistern is filled by pipe a in 10 hours and the full cistern can be leaked out by an exhaust pipe b in 15 hours . if both the pipes are opened , in what time the cistern is full ? | "time taken to full the cistern = ( 1 / 10 - 1 / 15 ) hrs = 1 / 30 = 30 hrs answer : b" | a = 1 / 10
b = 1 / 15
c = a - b
d = 1 / c
|
a ) 65 , b ) 68 , c ) 72 , d ) 70 , e ) 58 | d | multiply(subtract(45, 10), const_2) | all the students of class are told to sit in circle shape . here the boy at the 10 th position is exactly opposite to 45 th boy . total number of boys in the class ? | "as half the circle shape consist of 45 - 10 = 35 boys , so total number of boys in full circle = 2 * 35 = 70 answer : d" | a = 45 - 10
b = a * 2
|
a ) 10 , b ) 20 , c ) 60 , d ) 120 , e ) 600 | b | divide(factorial(multiply(divide(2000, const_1000), divide(3000, const_1000))), multiply(factorial(divide(3000, const_1000)), factorial(divide(3000, const_1000)))) | how many integers between 2000 and 3000 that have distinct digits and increase from left to right ? | since the numbers must be distinct and increasing from left to right , the only arrangements we could come - up with are : 245 _ - - > 4 246 _ - - > 3 247 _ - - > 2 248 _ - - > 1 256 _ - - > 3 257 _ - - > 2 258 _ - - > 1 267 _ - - > 2 268 _ - - > 1 number of integers = 20 b | a = 2000 / 1000
b = 3000 / 1000
c = a * b
d = math.factorial(c)
e = 3000 / 1000
f = math.factorial(e)
g = 3000 / 1000
h = math.factorial(g)
i = f * h
j = d / i
|
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