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a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10 | b | add(divide(20, 3), const_1) | how many integers are divisible by 3 between 10 ! and 10 ! + 20 inclusive ? | "0 ! is divisible by 3 - the way i look factorials is that any number included will also be divisible by the product . 10,9 , 8,7 , 6,5 , 4,3 , 2,1 are all divisors of 10 ! there are 6 numbers between 10 ! and 10 ! + 20 that are divisible by 3 . hence b : 7" | a = 20 / 3
b = a + 1
|
a ) 24 % , b ) 25 % , c ) 32 % , d ) 36 % , e ) 40 % | c | multiply(divide(205, subtract(850, 205)), const_100) | a cricket bat is sold for $ 850 , making a profit of $ 205 . the profit percentage would be | "205 / ( 850 - 205 ) = 205 / 645 = 41 / 129 = 32 % . answer : c ." | a = 850 - 205
b = 205 / a
c = b * 100
|
a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0 | a | subtract(power(3, 2), 4) | for the symbol , m β n = n ^ 2 β m for all values of m and n . what is the value of 4 β 3 ? | "4 β 3 = 9 - 4 = 5 answer : a" | a = 3 ** 2
b = a - 4
|
a ) 25 % , b ) 50 % , c ) 20 % , d ) 150 % , e ) 300 % | d | subtract(divide(25, divide(10, const_100)), const_100) | a man buys an article for $ 10 . and sells it for $ 25 . find the gain percent ? | "c . p . = $ 10 s . p . = $ 25 gain = $ 15 gain % = 15 / 10 * 100 = 150 % answer is d" | a = 10 / 100
b = 25 / a
c = b - 100
|
a ) 28 days , b ) 76 days , c ) 16 days , d ) 18 days , e ) 19 days | a | subtract(inverse(subtract(multiply(divide(const_1, 8), subtract(const_1, multiply(2, divide(const_1, 12)))), divide(const_1, 12))), add(12, 8)) | a can do a piece of work in 12 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ? | 8 / 12 + 6 / x = 1 x = 18 days answer : a | a = 1 / 8
b = 1 / 12
c = 2 * b
d = 1 - c
e = a * d
f = 1 / 12
g = e - f
h = 1/(g)
i = 12 + 8
j = h - i
|
a ) 32 , b ) 39 , c ) 30 , d ) 40 , e ) 28 | b | subtract(multiply(multiply(4, 6), 4), divide(subtract(14, const_1), const_2)) | if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 6 x years from now ? | "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 6 x years from now , age will be 15 + 6 * 4 = 39 option b" | a = 4 * 6
b = a * 4
c = 14 - 1
d = c / 2
e = b - d
|
a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 % | c | multiply(divide(70, multiply(const_100, const_2)), const_100) | sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 48 % nuts , what percent of the combined mixture is dried fruit ? | "48 % is 18 % - points above 30 % and 12 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 3 . 2 / 5 * 70 % = 28 % the answer is c ." | a = 100 * 2
b = 70 / a
c = b * 100
|
a ) 3 , b ) 10 , c ) 6 , d ) 8 , e ) 9 | b | divide(subtract(const_1, multiply(10, divide(const_1, 15))), divide(const_1, 30)) | x can finish a work in 30 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ? | "work done by x in 1 day = 1 / 30 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 β 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 30 ) = 10 b" | a = 1 / 15
b = 10 * a
c = 1 - b
d = 1 / 30
e = c / d
|
a ) 85 , b ) 95 , c ) 100 , d ) 105 , e ) 55 | e | divide(multiply(1, 10), const_4) | what is the sum of the numbers between 1 and 10 , inclusive ? | "sol . add all the numbers between 1 and 10 . final answer = e , 55 ." | a = 1 * 10
b = a / 4
|
a ) 28 days . , b ) 14 days . , c ) 12 days . , d ) 16 days . , e ) 18 days . | d | multiply(add(const_3, const_1), divide(12, const_3)) | a is thrice as good a work man as b and together they finish a piece of work in 12 days . the number of days taken by a alone to finish the work is : | solution ( a β s 1 day β s work ) : ( b β s 1 day β s work ) = 3 : 1 . ( a + b ) ' s 1 day β s work = 1 / 12 divide 1 / 14 in the ratio 3 : 1 . β΄ a β s 1 day β s work = ( 1 / 12 x 2 / 3 ) = 1 / 16 hence , a alone can finish the work in 16 days . answer d | a = 3 + 1
b = 12 / 3
c = a * b
|
a ) 7 , b ) 25 , c ) 35 , d ) 45 , e ) 75 | a | multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(55, 100), multiply(300, divide(60, 100)))), 300), 100) | 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 55 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ? | "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 55 % = 99 responded as satisfied , so remaining satisfied are 120 - 99 = 21 so 21 is what percentage of 300 - 7 % so the answer should be a" | a = 40 / 100
b = a * 300
c = 55 / 100
d = 60 / 100
e = 300 * d
f = c * e
g = b - f
h = g / 300
i = h * 100
|
a ) 78 , b ) 26 , c ) 52 , d ) 54 , e ) 56 | c | divide(add(add(36, 32), multiply(9, 4)), const_2) | the average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years . find the average age of the women ? | "explanation : 36 + 32 + 9 * 4 = 104 / 2 = 52 answer : c" | a = 36 + 32
b = 9 * 4
c = a + b
d = c / 2
|
a ) 0.000196 , b ) 0.00196 , c ) 19.6 , d ) 196 , e ) none | a | multiply(divide(0.014, 0.014), const_100) | 0.014 Γ 0.014 = ? | "solution sum of decimals places = 6 . 14 Γ 14 = 196 . = s 0.014 Γ 0.014 = 0.000196 answer a" | a = 0 / 14
b = a * 100
|
a ) 7200 , b ) 6000 , c ) 3500 , d ) 5000 , e ) 6200 | b | divide(540, multiply(divide(subtract(subtract(const_100, 30), 60), const_100), divide(90, const_100))) | of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 30 percent was planted with soybeans and 60 percent of the cleared land was planted with wheat . if the remaining 540 acres of cleared land was planted with corn , how many acres did the farmer own ? | 30 % od 90 % = 27 % , 60 % 0 f 90 % = 54 % so the remaining 90 - 27 - 54 = 9 % = 540 acres or 10 % of 90 % = 9 % - - > 540 / 9 * 100 = 6000 acres answer ( b ) | a = 100 - 30
b = a - 60
c = b / 100
d = 90 / 100
e = c * d
f = 540 / e
|
a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 32.88 % | e | multiply(divide(subtract(add(const_100, 60), add(const_100, 49)), add(const_100, 49)), const_100) | the wages earned by robin is 49 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ? | "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 149 and $ 160 respectively . charles earns $ 49 more than robin who earns $ 149 . therefore , charles ' wage is 49 / 149 * 100 = 32.88 % . the correct choice is ( e )" | a = 100 + 60
b = 100 + 49
c = a - b
d = 100 + 49
e = c / d
f = e * 100
|
a ) 2 , b ) 4 , c ) 8 , d ) 29 , e ) 32 | d | add(subtract(59, add(add(add(15, 10), 5), 3)), 3) | there are 59 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ? | "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 59 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 59 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 29 answer : d" | a = 15 + 10
b = a + 5
c = b + 3
d = 59 - c
e = d + 3
|
a ) $ 1050 , b ) $ 2500 , c ) $ 3000 , d ) $ 3400 , e ) $ 8000 | a | multiply(3, divide(700, subtract(6, 4))) | a sum of salary is distributed among a , b , c , d in the proportion of 2 : 3 : 4 : 6 . if d gets $ 700 more than c , what is the b ' s share ? | let the shares of a , b , c , d are 2 x , 3 x , 4 x , 6 x 6 x - 4 x = 700 x = 350 b ' s share = 3 x = $ 1050 answer is a | a = 6 - 4
b = 700 / a
c = 3 * b
|
a ) 1 / 32 , b ) 1 / 6 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34 | b | multiply(multiply(multiply(divide(const_1, 6), divide(const_1, 6)), divide(const_1, 6)), divide(const_1, 6)) | two 6 faced dice are thrown together . the probability that all the three show the same number on them is ? | "the three dice can fall in 6 * 6 = 36 ways . hence the probability is 6 / 36 = 1 / 6 answer : b" | a = 1 / 6
b = 1 / 6
c = a * b
d = 1 / 6
e = c * d
f = 1 / 6
g = e * f
|
a ) 18 , b ) 16 , c ) 5 , d ) 15 , e ) 4 | d | subtract(const_100, multiply(multiply(add(const_1, divide(16, const_100)), subtract(const_1, divide(27, const_100))), const_100)) | the tax on a commodity is diminished by 27 % and its consumption increased by 16 % . the effect on revenue is ? | "100 * 100 = 10000 73 * 116 = 8468 - - - - - - - - - - - 10000 - - - - - - - - - - - 1532 100 - - - - - - - - - - - ? = > 15 % decrease answer : d" | a = 16 / 100
b = 1 + a
c = 27 / 100
d = 1 - c
e = b * d
f = e * 100
g = 100 - f
|
a ) 128 , b ) 64 , c ) 122 , d ) 125 , e ) 130 | c | subtract(negate(26), multiply(subtract(10, 13), divide(subtract(10, 13), subtract(5, 10)))) | 5 , 10 , 13 , 26 , 29 , 58 , 61 , ( . . . . ) | "numbers are alternatively multiplied by 2 and increased by 3 5 Γ£ β 2 = 10 10 + 3 = 13 13 Γ£ β 2 = 26 26 + 3 = 29 29 Γ£ β 2 = 58 58 + 3 = 61 61 Γ£ β 2 = 122 answer c" | a = negate - (
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a ) 10 , b ) 15 , c ) 16 , d ) 18 , e ) 22 | a | subtract(add(7, 8), 5) | in a class , 7 students like to play basketball and 8 like to play cricket . 5 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ? | draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 5 = 10 a ) | a = 7 + 8
b = a - 5
|
a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120 | b | divide(add(multiply(add(floor(divide(30, add(const_3, const_4))), const_1), 175), multiply(subtract(30, add(floor(divide(30, add(const_3, const_4))), const_1)), 75)), 30) | a library has an average of 175 visitors on sundays and 75 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is : | "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 165 * 5 + 75 * 25 ) / 30 = 2700 / 30 = 90 answer : b ) 90" | a = 3 + 4
b = 30 / a
c = math.floor(b)
d = c + 1
e = d * 175
f = 3 + 4
g = 30 / f
h = math.floor(g)
i = h + 1
j = 30 - i
k = j * 75
l = e + k
m = l / 30
|
a ) 23 , b ) 20 , c ) 27 , d ) 5 , e ) 2 | c | add(divide(add(26, 24), const_2), multiply(1, const_2)) | if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 26 } + { 24 } ? | "soln : { 26 } + { 24 } = 26 * { 24 } + { 24 } = 27 * { 24 } answer : c" | a = 26 + 24
b = a / 2
c = 1 * 2
d = b + c
|
a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 100 , e ) e ) 140 | d | multiply(divide(160, 8), const_3) | in a mixed college 160 students are there in one class . out of this 160 students 3 / 8 students are girls . how many boys are there ? | "total number of students : 160 total girls : 160 * 3 / 8 = 60 total boys : 160 - 60 = 100 answer is d" | a = 160 / 8
b = a * 3
|
a ) 55 m , b ) 56 m , c ) 57 m , d ) 58 m , e ) 59 m | d | subtract(400, multiply(divide(multiply(divide(subtract(500, 25), 500), subtract(500, 50)), 500), 400)) | a beats b by 50 m in a race of 500 m , then b beats by c by 25 m in a race of 500 m . find the distance by which a beats c in a race of 400 ? | a beats b in 500 m race by 50 m so , for every 10 m race a beat b by 1 m . . so , in 400 m race a beat b by 40 m in a case of b & c , b beats c by 25 m in 500 m race . . so , b beats c by 1 m in 20 m race now , in a 400 m race b beats c by 18 m . . in a 400 m race , a beats b by 40 m & b beats c by 18 m . . so , a beats c by 58 m answer : d | a = 500 - 25
b = a / 500
c = 500 - 50
d = b * c
e = d / 500
f = e * 400
g = 400 - f
|
a ) 1050 , b ) 1220 , c ) 1500 , d ) 1060 , e ) 1110 | c | divide(1260, subtract(const_1, divide(multiply(4, 4), const_100))) | a fellow borrowed a certain sum of money at 4 % per annum at simple interest and in 4 years the interest amounted to rs . 1260 less than the sum lent . what was the sum lent ? | "p - 1260 = ( p * 4 * 4 ) / 100 p = 1500 answer : c" | a = 4 * 4
b = a / 100
c = 1 - b
d = 1260 / c
|
a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18 | e | subtract(power(2, 2), 2) | if x ^ 2 + 1 / x ^ 2 = β 20 what is the value of x ^ 4 + 1 / x ^ 4 ? | "important : i notice that if we square x Β² , we get x β΄ , and if we square 1 / x Β² , we get 1 / x β΄ , so let ' s see what happens if we take the equation x Β² + 1 / x Β² = β 20 andsquareboth sides : ( x Β² + 1 / x Β² ) Β² = 20 so , ( x Β² + 1 / x Β² ) ( x Β² + 1 / x Β² ) = 20 expand to get : x β΄ + 1 + 1 + 1 / x β΄ = 20 simplify : x β΄ + 1 / x β΄ = 18 answer : e" | a = 2 ** 2
b = a - 2
|
a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 7 | e | subtract(divide(480, 40), 5) | the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 5 miles per gallon , will not get him there . by how many miles per gallon must the aircraft β s fuel efficiency be improved to make the flight to cleveland possible ? | actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 5 miles / gallon . additional 7 miles / gallon is required to match the actual mileage . imo option e . | a = 480 / 40
b = a - 5
|
a ) 9 : 30 , b ) 9 : 00 , c ) 8 : 40 , d ) 7 : 50 , e ) 7 : 00 | d | divide(add(5, divide(multiply(add(subtract(5, 4), divide(subtract(20, 30), const_60)), 30), subtract(40, 30))), 20) | tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 40 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 20 , at what time will they be reading the same page ? | "relative speed = jan - tom = 10 pages per hour = 1 / 6 page per minute time diff = 50 minutes by the time jan started tom already finished ( 30 / 60 ) * 50 = 25 pages time taken = 25 / ( 1 / 6 ) = 25 * 6 = 150 minutes = 7 : 50 answer : d" | a = 5 - 4
b = 20 - 30
c = b / const_60
d = a + c
e = d * 30
f = 40 - 30
g = e / f
h = 5 + g
i = h / 20
|
['a ) 0 %', 'b ) 20 % increase', 'c ) 20 % decrease', 'd ) 12 % decrease', 'e ) insufficient data'] | d | subtract(const_100, divide(multiply(add(const_100, 35), subtract(const_100, 35)), const_100)) | what is the % change in the area of a rectangle when its length increases by 35 % and its width decreases by 35 % ? | ( 135 / 10 ) * ( 65 / 10 ) = 8775 / 100 ~ 88 of original area 0.88 is a 12 % decrease from 100 / 100 - > d | a = 100 + 35
b = 100 - 35
c = a * b
d = c / 100
e = 100 - d
|
a ) 0.16 , b ) 0.64 , c ) 80.08 , d ) 64 , e ) 6.4 | e | multiply(floor(subtract(780.38, multiply(floor(divide(780.38, const_100)), const_100))), divide(subtract(multiply(780.38, const_10), floor(multiply(780.38, const_10))), const_10)) | what is the product between the place values of two 8 ' s in the numeral 780.38 | required product = 80 x 0.08 = 6.4 answer is e | a = 780 / 38
b = math.floor(a)
c = b * 100
d = 780 - 38
e = math.floor(d)
f = 780 * 38
g = 780 * 38
h = math.floor(g)
i = f - h
j = i / 10
k = e * j
|
a ) 19 % , b ) 80 % , c ) 10 % , d ) 90 % , e ) 15 % | c | multiply(divide(subtract(subtract(const_100, 30), subtract(const_100, 37)), subtract(const_100, 30)), const_100) | two numbers are 30 % and 37 % are less than a third number . how much percent is the second number less than the first ? | i ii iii 70 63 100 70 - - - - - - - - 7 100 - - - - - - ? = > 10 % answer : c | a = 100 - 30
b = 100 - 37
c = a - b
d = 100 - 30
e = c / d
f = e * 100
|
a ) 87 , b ) 69 , c ) 60 , d ) 72 , e ) 21 | c | divide(add(360, 140), divide(multiply(30, const_1000), const_3600)) | a train is 360 meter long is running at a speed of 30 km / hour . in what time will it pass a bridge of 140 meter length ? | "speed = 30 km / hr = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 25 ) = 60 seconds answer : c" | a = 360 + 140
b = 30 * 1000
c = b / 3600
d = a / c
|
a ) 22.5 % , b ) 21.5 % , c ) 20.5 % , d ) 12.5 % , e ) 10.5 % | a | subtract(add(const_12, const_12), divide(subtract(add(multiply(90, const_1), const_3), multiply(90, const_1)), const_2)) | the total car population in a chennai is 9000 out of which 5000 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red | total honda brand red cars = 90 / 100 * 5000 = 4500 total red cars = 60 / 100 * 9000 = 5400 no . of non - honda cars = 9000 - 5000 = 4000 no . of non - honda red cars = 5400 - 4500 = 900 % of non - honda red cars = 900 / 4000 * 100 = 22.5 % answer : a | a = 12 + 12
b = 90 * 1
c = b + 3
d = 90 * 1
e = c - d
f = e / 2
g = a - f
|
a ) 14.5 minutes , b ) 29 minutes , c ) 35 minutes , d ) 58 minutes , e ) 87 minutes | a | divide(29, const_2) | danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 29 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ? | danny ' s time is 29 minutes . the time to reach halfway is 14.5 minutes . steve ' s time is 58 minutes . the time to reach halfway is 29 minutes . the time difference is 29 - 14.5 = 14.5 minutes the answer is a . | a = 29 / 2
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a ) 1 / 2 , b ) 2 / 12 , c ) 14 / 30 , d ) 3 / 8 , e ) 7 / 9 | c | multiply(divide(divide(2, 5), divide(3, 7)), divide(1, 2)) | find the fraction which has the same ratio to 1 / 2 that 2 / 5 has to 3 / 7 | "a : 1 / 2 = 2 / 5 : 3 / 7 as the product of the means is equal to the product of the extremes . a * 3 / 7 = 1 / 2 * 2 / 5 a * 3 / 7 = 2 / 10 a = 14 / 30 = > a = 14 / 30 answer : c" | a = 2 / 5
b = 3 / 7
c = a / b
d = 1 / 2
e = c * d
|
a ) 42.0 , b ) 48.0 , c ) 50.0 , d ) 52.2 , e ) 54.0 | c | multiply(divide(subtract(add(9, floor(divide(7, const_2))), subtract(9, floor(divide(7, const_2)))), add(9, floor(divide(7, const_2)))), const_100) | the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ? | explanation : in such a case the middle number ( d ) is the average β΄ d = 9 and a = 6 and g = 12 required percentage = 6 / 12 x 100 = 50.0 answer : option c | a = 7 / 2
b = math.floor(a)
c = 9 + b
d = 7 / 2
e = math.floor(d)
f = 9 - e
g = c - f
h = 7 / 2
i = math.floor(h)
j = 9 + i
k = g / j
l = k * 100
|
a ) 1 : 1 , b ) 3 : 8 , c ) 4 : 3 , d ) 8 : 9 , e ) 1 : 3 | a | divide(divide(6, 8), divide(3, 4)) | a hen leaps 6 leaps for every 8 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ? | given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 6 / 3 * 8 = 1 : 1 ' ' answer : 1 : 1 ; | a = 6 / 8
b = 3 / 4
c = a / b
|
a ) 700 m , b ) 500 m , c ) 870 m , d ) 880 m , e ) 840 m | d | divide(multiply(24, multiply(2.2, const_1000)), 60) | amar takes as much time in running 24 meters as a car takes in covering 60 meters . what will be the distance covered by amar during the time the car covers 2.2 km ? | "distance covered by amar = 24 / 60 ( 2.2 km ) = 2 / 5 ( 2200 ) = 880 m answer : d" | a = 2 * 2
b = 24 * a
c = b / 60
|
a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21 | d | divide(subtract(subtract(add(add(multiply(600, divide(40, const_100)), multiply(600, divide(50, const_100))), multiply(600, divide(35, const_100))), 600), multiply(600, divide(18, const_100))), 2) | of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents b watch all of the shows ? | oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , b is 21 . d is the correct answer | a = 40 / 100
b = 600 * a
c = 50 / 100
d = 600 * c
e = b + d
f = 35 / 100
g = 600 * f
h = e + g
i = h - 600
j = 18 / 100
k = 600 * j
l = i - k
m = l / 2
|
a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35 | d | sqrt(add(power(sqrt(subtract(289, multiply(const_2, 336))), const_2), multiply(const_4, 336))) | the product of two numbers is 336 and the sum of their squares is 289 . the sum of the number is ? | "let the numbers be x and y . then , xy = 336 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 336 ) = 961 x + y = 31 . option d" | a = 2 * 336
b = 289 - a
c = math.sqrt(b)
d = c ** 2
e = 4 * 336
f = d + e
g = math.sqrt(f)
|
a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 12,375 , d ) rs . 16,500 , e ) none | c | multiply(600, multiply(5.5, 3.75)) | the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre . | "solution area of the floor = ( 5.5 x 3.75 ) m Β² = 20.635 m Β² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c" | a = 5 * 5
b = 600 * a
|
a ) 15 days . , b ) 12 days . , c ) 24 days . , d ) 13 days . , e ) 16 days . | c | inverse(subtract(inverse(12), inverse(24))) | x and y together can completes a work in 12 days and y complete the same work in 24 days . then the number of days x required to complete the work will be ? | x and y complete in one day = 1 / 12 part , y completes in one day = 1 / 24 parts . therefore x alone can do in one day = 1 / 24 part . therefore the work can be finished by x = 24 days . ans : c | a = 1/(12)
b = 1/(24)
c = a - b
d = 1/(c)
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a ) 16 , b ) 1.6 , c ) 0.16 , d ) 0.016 , e ) none of these | b | divide(2.04, 1.275) | if 204 Γ· 12.75 = 16 , then 2.04 Γ· 1.275 = ? | explanation : ( 204 / 12.75 ) = 16 β ( 20.4 ) / ( 1.275 ) = 16 ( β΅ divided numerator and denominator by 10 ) β 2.04 / 1.275 = 1.6 ( β΅ divided lhs and rhs by 10 ) answer : option b | a = 2 / 4
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a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11 | b | floor(sqrt(divide(3600, 101))) | if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ? | "101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b" | a = 3600 / 101
b = math.sqrt(a)
c = math.floor(b)
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a ) 7 : 3 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3 | a | divide(3, 7) | the simple form of the ratio 4 / 3 : 3 / 7 is ? | "4 / 3 : 3 / 7 = 21 : 9 = 7 : 3 answer : a" | a = 3 / 7
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a ) $ 2400 , b ) $ 3200 , c ) $ 3500 , d ) $ 6400 , e ) $ 9600 | c | multiply(multiply(const_100, add(const_3, const_2)), divide(105, subtract(const_100, add(add(30, 20), 35)))) | each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 105 dollar , which she typically uses for gifts and charitable causes . what is jill β s net monthly salary ? | let x be the monthly salary 15 % of 1 / 5 * x = 105 x = 3500 answer c | a = 3 + 2
b = 100 * a
c = 30 + 20
d = c + 35
e = 100 - d
f = 105 / e
g = b * f
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a ) 11.21 , b ) 9.6 , c ) 8.66 , d ) 12.23 , e ) 13.1 | b | divide(multiply(12, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100) | what is 12 percent of 80 ? | "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x = 12 % therefore , 80 / x = 100 % / 12 % 80 / x = 8.33 x = 9.6 b" | a = 3 + 2
b = a * 2
c = 3 * 4
d = c * 100
e = b * d
f = 3 + 4
g = 3 + 2
h = f * g
i = 3 + 2
j = i * 2
k = h * j
l = e + k
m = 3 + 3
n = l + m
o = 12 * n
p = o / 100
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a ) 20 , b ) 22 , c ) 25 , d ) 30 , e ) 48 | c | add(divide(140, 6), 2) | if the average ( arithmetic mean ) of 5 b , 6 b + 47 b , 8 b - 4 and 2 b is 140 , what is the value of b ? | am of 5 b , 6 b + 47 b , 8 b - 4 and 2 b = 5 b + 6 b + 4 + 7 b + 8 b - 4 + 2 b = 28 b / 5 given that 28 b / 5 = 140 b = 25 answer is c | a = 140 / 6
b = a + 2
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a ) 28 , b ) 29 , c ) 30 , d ) 20 , e ) 32 | d | sqrt(400) | you buy a piece of land with an area of Γ’ Λ Ε‘ 400 , how long is one side of the land plot ? | "try filling the numbers into the answer y x y = find the closest to 400 . answer d" | a = math.sqrt(400)
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a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156 | d | multiply(divide(62, const_2), 5) | find the number , difference between number and its 3 / 5 is 62 . | "explanation : let the number = x , then , x - ( 3 / 5 ) x = 62 , = > ( 2 / 5 ) x = 62 = > 2 x = 62 * 5 , = > x = 155 answer : option d" | a = 62 / 2
b = a * 5
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a ) 66 % , b ) 75 % , c ) 86 % , d ) 97 % , e ) 150 % | d | multiply(divide(add(100, 90), add(100, divide(add(100, 90), const_2))), 100) | company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 90 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ? | "let the price of company a ' s assets be 100 price of assets of kw is 90 % more than company a ' s assets which is 190 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 95 a + b = 195 kw = 190 kw / ( a + b ) * 100 = 190 / 195 * 100 = 97.43 % or 97 % d" | a = 100 + 90
b = 100 + 90
c = b / 2
d = 100 + c
e = a / d
f = e * 100
|
a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 210 | e | add(150, divide(multiply(multiply(150, 6), divide(divide(multiply(subtract(240, 200), 200), 200), 3)), 200)) | if $ 200 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ? | "200 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 200 + 200 * ( r / 100 ) * ( 3 ) = 240 = > r = 20 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 210 answer is e ." | a = 150 * 6
b = 240 - 200
c = b * 200
d = c / 200
e = d / 3
f = a * e
g = f / 200
h = 150 + g
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a ) 30 , b ) 36 , c ) 40 , d ) 50 , e ) 48 | a | divide(original_price_before_loss(20, 60), divide(original_price_before_gain(20, 60), 20)) | a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 60 to incur a loss 20 % ? | "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 60 * ( 100 % + 20 % ) = $ 72 number of articles to be sold for $ 72 to incur a 20 % loss : $ 72 / $ 2.40 = 30 thus , solution a is correct ." | a = original_price_before_loss / (
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a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 36 kmph | e | subtract(multiply(40, multiply(const_60.0, const_0_2778)), 200) | a train 200 m long crosses a platform 200 m long in 40 sec ; find the speed of the train ? | "d = 200 + 200 = 400 t = 40 s = 400 / 40 * 18 / 5 = 36 kmph answer : e" | a = const_60 * 0
b = 40 * a
c = b - 200
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a ) 15 % , b ) 18 % , c ) 20 % loss , d ) 25 % , e ) 30 % | c | multiply(divide(subtract(25, 30), 30), const_100) | a shopkeeper sold 30 articles at the cost price of 25 articles . then find the profit % or lost % | "here 30 articles selling price = 25 articles cost price so the difference = 25 - 30 = - 5 % of loss = 5 * 100 / 25 = 20 % correct option is c" | a = 25 - 30
b = a / 30
c = b * 100
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a ) 14 , b ) 16 , c ) 18 , d ) 25 , e ) 34 | d | add(add(power(add(add(divide(subtract(subtract(30, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(30, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(30, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(30, const_10), const_2), const_4), const_2), const_2))) | the sum of three consecutive even numbers is 30 . find the middle number of the three ? | "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 30 6 p = 30 = > p = 5 . the middle number is : 5 p = 25 . answer : d" | a = 30 - 10
b = a - 2
c = b / 4
d = c + 2
e = d + 2
f = e ** 2
g = 30 - 10
h = g - 2
i = h / 4
j = i + 2
k = j + 2
l = k + 2
m = l ** 2
n = f + m
o = 30 - 10
p = o - 2
q = p / 4
r = q ** 2
s = 30 - 10
t = s - 2
u = t / 4
v = u + 2
w = v ** 2
x = r + w
y = n + x
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a ) 16 / 5 , b ) 17 / 5 , c ) 28 / 7 , d ) 30 / 7 , e ) 31 / 7 | c | add(add(divide(add(add(add(divide(9, 2), divide(10, 3)), divide(27, 9)), divide(21, 5)), const_4), divide(const_10, const_100)), divide(const_10, const_100)) | if x is the median of the set { 9 / 2 , 10 / 3 , 27 / 9 , 21 / 5 , x } , x could be | "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 10 / 3 = 3 . something , 27 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( c )" | a = 9 / 2
b = 10 / 3
c = a + b
d = 27 / 9
e = c + d
f = 21 / 5
g = e + f
h = g / 4
i = 10 / 100
j = h + i
k = 10 / 100
l = j + k
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a ) 1 / 26 , b ) 1 / 36 , c ) 1 / 46 , d ) 1 / 66 , e ) 1 / 56 | d | multiply(const_2, multiply(divide(const_1, 12), divide(const_1, subtract(12, const_1)))) | james and david work at a grocery shop with 12 other workers . for an internal review , 2 of the 12 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ? | probability that james and david will both be chosen out of 12 workers = ( 2 / 12 ) * ( 1 / 11 ) = 1 / 66 answer d | a = 1 / 12
b = 12 - 1
c = 1 / b
d = a * c
e = 2 * d
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a ) 6 , b ) 4 , c ) 8 , d ) 10 , e ) 12 | c | divide(subtract(subtract(add(multiply(subtract(40, 10), 10), multiply(10, 20)), 300), multiply(gcd(40, 10), 20)), 10) | bookman purchased 40 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 300 , how many paperback copies were sold ? | "the bookman had 10 hardback ad 40 - 10 = 30 paperback copies ; 14 copies were sold , hence 40 - 14 = 26 copies were left . let # of paperback copies left be p then 10 p + 20 ( 26 - p ) = 300 - - > 10 p = 220 - - > p = 22 # of paperback copies sold is 30 - 22 = 8 answer : c" | a = 40 - 10
b = a * 10
c = 10 * 20
d = b + c
e = d - 300
f = math.gcd(40, 10)
g = f * 20
h = e - g
i = h / 10
|
a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500 | b | divide(1800, subtract(subtract(const_1, divide(35, const_100)), divide(35, const_100))) | a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ? | "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b" | a = 35 / 100
b = 1 - a
c = 35 / 100
d = b - c
e = 1800 / d
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a ) 46 , b ) 80 , c ) d . 90 , d ) d . 100 , e ) 200 | d | add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2)) | a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x β 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number d of people surveyed by the company ? | 100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d . | a = 100 - 23
b = a + 23
c = b + 20
d = c / 2
e = d - 20
f = 100 - 23
g = f + 23
h = g + 20
i = h / 2
j = e + i
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a ) 82 m , b ) 50 m , c ) 75 m , d ) 80 m , e ) none of these | c | divide(multiply(divide(multiply(subtract(46, 36), const_1000), const_3600), 54), const_2) | two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is : | "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 Γ 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c" | a = 46 - 36
b = a * 1000
c = b / 3600
d = c * 54
e = d / 2
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a ) 22.8 kg , b ) 26.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these | b | divide(multiply(7, 42.75), 11.25) | if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ? | "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b" | a = 7 * 42
b = a / 11
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a ) 600 , b ) 490 , c ) 448 , d ) 435 , e ) 679 | c | multiply(divide(add(40, multiply(2, 85)), subtract(160, 85)), 160) | if a farmer wants to plough a farm field on time , he must plough 160 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ? | "let x be the number of days in the initial plan . therefore , the whole field is 160 Γ’ βΉ β¦ x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 160 x = 85 ( x + 2 ) + 40 75 x = 210 x = 2.8 so the farmer planned to have the work done in 6 days , and the area of the farm field is 160 ( 2.8 ) = 448 hectares correct answer c" | a = 2 * 85
b = 40 + a
c = 160 - 85
d = b / c
e = d * 160
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a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3 | a | divide(10, subtract(60, 10)) | a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ? | "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 10 ) / ( 10 - 0 ) = 5 / 1 1 / x = 5 / 1 x = 1 / 5 answer : a" | a = 60 - 10
b = 10 / a
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a ) 7 : 18 , b ) 7 : 48 , c ) 8 : 18 , d ) 8 : 48 , e ) 9 : 18 | d | divide(add(4, divide(multiply(add(subtract(4, 4), divide(subtract(48, 00), const_60)), 30), subtract(36, 30))), 48) | tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 36 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 48 , at what time will they be reading the same page ? | "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 6 pages per hour , so it will take 4 hours to catch tom . the answer is d ." | a = 4 - 4
b = 48 - 0
c = b / const_60
d = a + c
e = d * 30
f = 36 - 30
g = e / f
h = 4 + g
i = h / 48
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a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 53 | d | subtract(divide(multiply(multiply(70, const_3), 4), add(add(4, 1), 2)), 70) | bhatia , ashtikar and singh begin to play with rs 70 each . at the end the ratio of the amounts left with ashtikar and singh is 1 : 2 and of those with singh and bhatia is 4 : 1 . what is singh ' s gain ( in rs ) ? | we have b + a + s = 210 and s = 2 a , s = 4 b and a = 2 b solving these eqs we got that singh have rs . 120 in the end bhatia have 30 and astikar have 60 . so singh ' s profit is 120 - 70 = 50 answer : d | a = 70 * 3
b = a * 4
c = 4 + 1
d = c + 2
e = b / d
f = e - 70
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a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 47 | e | subtract(power(2, 2), 2) | if x ^ 2 + ( 1 / x ^ 2 ) = 7 , x ^ 4 + ( 1 / x ^ 4 ) = ? | "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 7 ^ 2 - 2 = 47 . thus , the answer is e ." | a = 2 ** 2
b = a - 2
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a ) 144 m 2 , b ) 140 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these | b | subtract(rectangle_area(add(multiply(2, 2), 19), add(12, multiply(2, 2))), rectangle_area(19, 12)) | the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is : | "area of the outer rectangle = 23 Γ£ β 16 = 368 m 2 area of the inner rectangle = 19 Γ£ β 12 = 228 m 2 required area = ( 368 Γ’ β¬ β 228 ) = 140 m 2 answer b" | a = 2 * 2
b = a + 19
c = 2 * 2
d = 12 + c
e = rectangle_area - (
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a ) 50 % , b ) 60 % , c ) 65 % , d ) 56 % , e ) 45 % | d | multiply(subtract(multiply(divide(add(const_100, 30), const_100), divide(add(20, const_100), const_100)), const_1), const_100) | the price of a tv was increased by 30 percent . the new price was then increased by 20 percent . a single increase of what percent is equivalent to these two successive increases ? | consider base price - $ 100 25 % increase = 1.30 * 100 = $ 130 another 20 % increase on new price = 1.2 * 130 = $ 156 so final price of radio - $ 156 therefore a 56 % increase correct option - d | a = 100 + 30
b = a / 100
c = 20 + 100
d = c / 100
e = b * d
f = e - 1
g = f * 100
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a ) 761200 , b ) 761400 , c ) 761800 , d ) 210000 , e ) none of them | d | add(multiply(500, 500), multiply(200, 200)) | simplify : 500 x 500 - 200 x 200 | "( 500 ) ^ 2 - ( 200 ) ^ 2 = ( 500 + 200 ) ( 500 - 200 ) = 700 x 300 = 210000 . answer is d ." | a = 500 * 500
b = 200 * 200
c = a + b
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a ) rs 14000 , b ) rs 15000 , c ) rs 12000 , d ) rs 17000 , e ) none of these | c | divide(multiply(4320, const_100), multiply(12, 3)) | a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 4320 interest . the principal amount borrowed by him was . | "explanation : s . i . = p Γ’ Λ β r Γ’ Λ β t / 100 = > p = s . i . Γ’ Λ β 100 / r Γ’ Λ β t = > p = 4320 Γ’ Λ β 100 / 12 Γ’ Λ β 3 = rs 12000 option c" | a = 4320 * 100
b = 12 * 3
c = a / b
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a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 27 , e ) 8 / 7 | d | divide(divide(divide(10, const_100), divide(30, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(30, const_100))) | a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 10 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ] | "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 10 % are male i . e 10 / 100 * 20 = 2 geese ( males ) and now we know out of the total 20 geese , 2 are male , then 18 have to be female . now the ratio part , male geese ratios = 2 / 30 = 1 / 15 . - a female geese ratios = 18 / 70 = 9 / 35 - b cross multiply equations a and b and you get = 7 / 27 . ans d" | a = 10 / 100
b = 30 / 100
c = a / b
d = 2 * 4
e = d * 10
f = e / 100
g = 30 / 100
h = f / g
i = c / h
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a ) 54 , b ) 55 , c ) 59 , d ) 71 , e ) 92 | b | add(37, multiply(subtract(const_1, divide(const_1, const_3)), subtract(64, 37))) | of 64 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ? | "total = 64 thrower = 37 rest = 64 - 37 = 27 left handed = 27 / 3 = 9 right handed = 18 if all thrower are right handed then total right handed is 37 + 18 = 55 so b . 55 is the right answer" | a = 1 / 3
b = 1 - a
c = 64 - 37
d = b * c
e = 37 + d
|
a ) 4 minutes , b ) 15 / 4 minutes , c ) 192 / 7 minutes , d ) 224 / 7 minutes , e ) 28 minutes | b | inverse(add(divide(const_1, 30), add(divide(const_1, 30), divide(6, 30)))) | pipe a can fill a tank in 30 minutes . pipe b can fill the same tank 6 times faster than pipe a . if both the pipes are connected to the tank so that they fill the tank simultaneously , how long will it take for the empty tank to overflow ? | "pipe a can fill a tank in 30 minutes - - > the rate of a = 1 / 30 tank / minute ; pipe b can fill the same tank 6 times fasterthan pipe a - - > the rate of b = 1 / 30 + 6 / 30 = 7 / 30 tank / minute . their combined rate = 1 / 30 + 7 / 30 = 4 / 15 tank / minute ; therefore , a and b can fill the tank in 15 / 4 minutes . answer : b" | a = 1 / 30
b = 1 / 30
c = 6 / 30
d = b + c
e = a + d
f = 1/(e)
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a ) 11 , b ) 17 , c ) 18 , d ) 19 , e ) 16 | c | divide(const_1, subtract(subtract(const_0_25, divide(const_1, 12)), divide(const_1, 9))) | if a , b and c together can finish a piece of work in 4 days . a alone in 12 days and b in 9 days , then c alone can do it in ? | "c = 1 / 4 - 1 / 12 β 1 / 9 = 1 / 18 = > 18 days ' answer : c" | a = 1 / 12
b = const_0_25 - a
c = 1 / 9
d = b - c
e = 1 / d
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a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 % | a | multiply(power(add(const_1, divide(divide(6.4, const_100), const_2)), add(const_2, const_3)), const_100) | michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6.4 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ? | since michelle earns 6.4 % interest compounded semiannually , then she earns 3.2 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3.2 % * 5 = 16 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 16 % , only answer choice a fits . answer : a | a = 6 / 4
b = a / 2
c = 1 + b
d = 2 + 3
e = c ** d
f = e * 100
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a ) 3 , b ) 3.5 , c ) 2.5 , d ) 4 , e ) 4.5 | c | multiply(divide(50, add(const_100, const_100)), const_10) | a certain maroon paint contains 50 percent blue pigment and 50 percent red pigment by weight . a certain green paint contains 30 percent blue pigment and 70 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ? | 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 5 = 2.5 grams of red pigment | a = 100 + 100
b = 50 / a
c = b * 10
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a ) 20 , b ) 25 , c ) 15 , d ) 22 , e ) 10 | e | subtract(divide(add(multiply(5, 5), 15), subtract(5, const_1)), subtract(divide(add(multiply(5, 5), 15), subtract(5, const_1)), 5)) | chris age after 15 years will be 5 times his age 5 years back . what is the present age of chris ? | "chris present age = x after 15 years = x + 15 5 years back = x - 5 x + 15 = 5 ( x - 5 ) x = 10 answer is e" | a = 5 * 5
b = a + 15
c = 5 - 1
d = b / c
e = 5 * 5
f = e + 15
g = 5 - 1
h = f / g
i = h - 5
j = d - i
|
a ) 25 days , b ) 30 days , c ) 23 days , d ) 35 days , e ) 45 days | d | divide(const_1, subtract(divide(const_1, 10), divide(const_1, 14))) | a can do a work in 14 days and working together a and b can do the same work in 10 days . in what time can b alone do the work ? | work done by b in 1 day = 1 / 10 - 1 / 14 = ( 7 - 5 ) / 70 = 1 / 35 so , b alone can do the work in 35 days . answer : d | a = 1 / 10
b = 1 / 14
c = a - b
d = 1 / c
|
a ) 50 , b ) 53 , c ) 49 , d ) 48 , e ) 44 | b | add(divide(subtract(multiply(45, 5), 10), 5), 10) | if the average of 5 positive integers is 45 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ? | "sum of 5 integer ( a , b , c , d , e ) = 5 * 45 = 225 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 225 i . e . 5 a = 215 i . e . a = 43 i . e . largest e = 43 + 10 = 53 answer : option b" | a = 45 * 5
b = a - 10
c = b / 5
d = c + 10
|
a ) 360 , b ) 420 , c ) 120 , d ) 320 , e ) 280 | c | lcm(lcm(24, 30), 40) | find the lowest common multiple of 24 , 30 and 40 . | "lcm = 2 * 2 * 2 * 3 * 5 = 120 . answer is c" | a = math.lcm(24, 30)
b = math.lcm(a, 40)
|
a ) 5.2 hrs , b ) 13.3 hrs , c ) 1.9 hrs , d ) 7.2 hrs , e ) 1.4 hrs | b | divide(const_1, subtract(divide(const_1, 5), divide(const_1, 8))) | a cistern can be filled by a tap in 5 hours while it can be emptied by another tap in 8 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ? | "net part filled in 1 hour = ( 1 / 5 - 1 / 8 ) = 3 / 40 the cistern will be filled in 40 / 3 hrs i . e . , 13.3 hrs . answer : b" | a = 1 / 5
b = 1 / 8
c = a - b
d = 1 / c
|
a ) 2 / 5 , b ) 1 / 2 , c ) 11 / 16 , d ) 5 / 7 , e ) 3 / 4 | b | divide(add(const_1, divide(subtract(multiply(divide(4, 8), const_2), const_1), divide(const_1, subtract(multiply(divide(3, 4), const_2), const_1)))), const_2) | a , b , and c are integers and a < b < c . s is the set of all integers from a to b , inclusive . q is the set of all integers from b to c , inclusive . the median of set s is ( 3 / 4 ) * b . the median of set q is ( 4 / 8 ) * c . if r is the set of all integers from a to c , inclusive , what fraction of c is the median of set r ? | "the answer isc : 11 / 16 . the key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean . for example , the mean and median of a set consisting of x , x + 1 , x + 2 , . . . , y will always be ( x + y ) / 2 . for set s , consisting of numbers ( a , a + 1 , . . . , b ) , the median is given to be 3 / 4 * b : ( a + b ) / 2 = ( 3 / 4 ) * b a = b / 2 for set q , consisting of numbers ( b , b + 1 , . . . , c ) , the median is given to be 4 / 8 * c : ( b + c ) / 2 = ( 4 / 8 ) * c b = 0 for set r , consisting of numbers ( a , a + 1 , . . . c ) , the median needs to be found : a = b / 2 = ( 0 ) / 2 = 0 median = ( a + c ) / 2 = ( 0 + c ) / 2 = c / 2 = ( 1 / 2 ) * c ( answer b )" | a = 4 / 8
b = a * 2
c = b - 1
d = 3 / 4
e = d * 2
f = e - 1
g = 1 / f
h = c / g
i = 1 + h
j = i / 2
|
a ) 540 , b ) 560 , c ) 580 , d ) 600 , e ) 680 | d | divide(360, subtract(const_1, divide(multiply(5, 8), const_100))) | a person lent a certain sum of money at 5 % per annum at simple interest and in 8 years the interest amounted to $ 360 less than the sum lent . what was the sum lent ? | "p - 360 = ( p * 5 * 8 ) / 100 p = 600 the answer is d ." | a = 5 * 8
b = a / 100
c = 1 - b
d = 360 / c
|
a ) 11 , b ) 40 , c ) 66 , d ) 55 , e ) 44 | b | subtract(divide(multiply(760, subtract(22, const_2)), 19), 760) | there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 19 days more ? | "760 - - - - 22 760 - - - - 20 x - - - - - 19 x * 19 = 760 * 20 x = 800 760 - - - - - - - 40 answer : b" | a = 22 - 2
b = 760 * a
c = b / 19
d = c - 760
|
a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 85 | e | multiply(add(14, const_3), const_3) | if p represents the product of the first 14 positive integers , then p is not a multiple of | "answer is e . since prime factor of 85 is 5 x 17 . 17 is a prime number and not part of the first 14 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 5 x 17" | a = 14 + 3
b = a * 3
|
a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 73 | d | divide(26.5, 0.36) | how many pieces of 0.36 meteres can be cut from a rod 26.5 meteres long | "explanation : we need so simple divide 26.5 / 0.36 , = ( 2650 / 36 ) = 73 option d" | a = 26 / 5
|
a ) 28 % , b ) 30 % , c ) 32 % , d ) 34 % , e ) 36 % | a | multiply(const_100, divide(add(divide(40, const_100), multiply(4, divide(25, const_100))), add(const_1, 4))) | because he β s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 25 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ? | "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.0 x = 1.4 x 1.4 x / 5 x = 0.28 the answer is a ." | a = 40 / 100
b = 25 / 100
c = 4 * b
d = a + c
e = 1 + 4
f = d / e
g = 100 * f
|
a ) 65 , b ) 61.875 , c ) 80 , d ) 85 , e ) 90 | b | add(multiply(power(2, multiply(divide(60, 5), subtract(const_1, 2))), 120), 60) | the temperature of a certain cup of coffee 5 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 30 minutes after it was poured was how many degrees fahrenheit ? | "first , we have to find a . we know that after t = 5 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 5 a ) + 60 60 = 120 * ( 2 ^ - 5 a ) 60 / 120 = 2 ^ - 5 a 1 / 2 = 2 ^ - 5 a 2 ^ - 1 = 2 ^ - 5 a - 1 = - 5 a 1 / 5 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 5 * 30 ) + 60 f = 120 * ( 2 ^ - 6 ) + 60 f = 120 * ( 1 / 2 ^ 6 ) + 60 f = 120 * 1 / 64 + 60 f = 1.875 + 60 = 61.875 answer b !" | a = 60 / 5
b = 1 - 2
c = a * b
d = 2 ** c
e = d * 120
f = e + 60
|
a ) 2 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9 | a | add(multiply(2, const_10), divide(add(44, 12), 7)) | 5 n + 2 > 12 and 7 n - 12 < 44 ; n must be between which numbers ? | "5 n + 2 > 12 5 n > 10 n > 2 7 n - 12 < 44 7 n < 56 n < 8 so n must be between 2 and 8 2 < n < 8 correct answer a" | a = 2 * 10
b = 44 + 12
c = b / 7
d = a + c
|
a ) 56 , b ) 80 , c ) 20 , d ) 25 , e ) 26 | a | multiply(subtract(73, 45), const_2) | a pupil ' s marks were wrongly entered as 73 instead of 45 . due to that the average marks for the class got increased by half . the number of pupils in the class is : | "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 73 - 45 ) = > x / 2 = 28 = > x = 56 . answer : a" | a = 73 - 45
b = a * 2
|
a ) 1 : 25 , b ) 1 : 22 , c ) 1 : 52 , d ) 1 : 64 , e ) none | d | divide(const_4, const_100) | a cube of edge 8 cm is cut into cubes each of edge 1 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to : | "sol . required ratio = 6 * 1 * 1 / 6 * 8 * 8 = 1 / 64 = 1 : 64 . answer d" | a = 4 / 100
|
a ) 3 , b ) 52 , c ) 15 , d ) 19 , e ) 25 | b | add(add(power(2, 2), multiply(2, 2)), 4) | if [ [ x ] ] = x ^ 2 + 2 x + 4 , what is the value of [ [ 6 ] ] ? | "these functions questions might look intimidating , but they just test your knowledge about how well you can substitute values [ [ x ] ] = x ^ 2 + 2 x + 4 [ [ 6 ] ] = 6 ^ 2 + 2 * 6 + 4 = 52 . option b" | a = 2 ** 2
b = 2 * 2
c = a + b
d = c + 4
|
a ) 4004 , b ) 4725 , c ) 4404 , d ) 4044 , e ) 4055 | a | add(2015.98, divide(multiply(1275.087, 175.98), divide(0.95, 988.09))) | 2015.98 + 1275.087 β 175.98 Γ 0.95 + 988.09 = ? | "explanation : = 2016 + 1275 β 275.98 Γ 1 + 988 = 2016 + 1275 - 275 + 988 = 4004 answer : option a" | a = 1275 * 87
b = 0 / 95
c = a / b
d = 2015 + 98
|
a ) 10 , b ) 12 , c ) 16 , d ) 19 , e ) 20 | c | divide(add(add(add(add(3, const_4), add(3, const_4)), add(const_4, const_4)), 50), 5) | the sum of ages of 5 children born 3 years different each is 50 yrs . what is the age of the elder child ? | "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 x = 4 . x + 12 = 4 + 12 = 16 c" | a = 3 + 4
b = 3 + 4
c = a + b
d = 4 + 4
e = c + d
f = e + 50
g = f / 5
|
a ) 5.2 , b ) 2.6 , c ) 3.6 , d ) 4.5 , e ) 4.6 | a | divide(subtract(multiply(6, 5.40), add(multiply(2, 5.2), multiply(2, 5.80))), 2) | the average of 6 no . ' s is 5.40 . the average of 2 of them is 5.2 , while the average of the other 2 is 5.80 . what is the average of the remaining 2 no ' s ? | "sum of the remaining two numbers = ( 5.40 * 6 ) - [ ( 5.2 * 2 ) + ( 5.8 * 2 ) ] = 32.40 - ( 10.4 + 11.6 ) = 32.40 - 22.0 = 10.40 . required average = ( 10.4 / 2 ) = 5.2 answer : a" | a = 6 * 5
b = 2 * 5
c = 2 * 5
d = b + c
e = a - d
f = e / 2
|
a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 60 | b | add(divide(70, add(0.75, 5)), divide(70, add(0.75, 5))) | a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 5 tons ? | the weight of one car and one truck is 5.75 tons . 70 / 5.75 = 12 plus a remainder the ferry could carry 12 cars and 12 trucks for a total of 24 vehicles . the answer is b . | a = 0 + 75
b = 70 / a
c = 0 + 75
d = 70 / c
e = b + d
|
a ) 28 , b ) 35 , c ) 49 , d ) 63 , e ) 55 | e | add(add(subtract(add(multiply(8, 8), multiply(8, 10)), add(multiply(8, 10), 8)), 10), const_3) | x , a , z , and b are single digit positive integers . x = 1 / 8 a . z = 1 / 8 b . ( 10 a + b ) β ( 10 x + z ) could not equal | "a = 8 x , b = 8 z therefore ( 8 x . 10 + 8 z ) - ( 10 x + z ) = ( 8 - 1 ) ( 10 x + z ) = 7 . ( 10 x + z ) number should be divisible by 7 e" | a = 8 * 8
b = 8 * 10
c = a + b
d = 8 * 10
e = d + 8
f = c - e
g = f + 10
h = g + 3
|
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