regisss/math_qa huggingface dataset:
Problem: a number when divided by a divisor leaves a remainder of 21 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 34 , d ) 37 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 21 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 34 as d is also integer and 34 is a prime number , the d should be 34 to satisfy the above equation . hence answer is ' d '"
Answer: d
Problem: last year a certain bond price with a face value of 5000 yielded 7 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5385 , d ) 6000 , e ) 6154
Rationale: "interest = 0.07 * 5000 = 0.065 * selling price - - > selling price = 0.07 * 5000 / 0.065 - - > selling price = ~ 5,385 answer : c ."
Answer: c
Problem: the length and the breadth of a rectangle are in the ratio of 3 : 2 respectively . if the sides of the rectangle are extended on each side by 1 metre , the ratio of length to breadth becomes 10 : 7 . find the area of the original rectangle in square metres .
Options: a ) 256
b ) 150
c ) 280
d ) data inadequate
e ) none of these
Rationale: let the length and breadth be l and b respectively . l ⁄ b = 3 ⁄ 2 or l = 3 ⁄ 2 b . . . . . ( i ) l + 1 / b + 1 = 10 / 7 or 7 l - 10 b = 3 . . . . . ( ii ) from eq . ( i ) 10.5 b – l 0 b = 6 or , 0.5 b = 3 or , b = 6 and l = 9 area = l × b = 6 × 9 = 54 m 2 answer e
Answer: e
Problem: 32 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2
b ) 2 √ 5
c ) 5
d ) 4 √ 2
e ) 8
Rationale: area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 32 = > x / 360 * 2 * pi * r + 2 r = 32 = > 2 a / r + 2 r = 32 = > a = r 16 - r ^ 2 = r 16 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 16 - 2 r = 0 r = 8 e
Answer: e
Problem: a 300 m long train crosses a platform in 54 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 600 , d ) 277 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 54 = 50 / 3 3 x + 900 = 2700 = > x = 600 m . answer : c"
Answer: c
Problem: compute the perimeter of a square with area 36 .
Options: a ) 24
b ) 27
c ) 25
d ) 26
e ) 29
Rationale: if the length of the square is s , then s 2 = 36 so s = 6 . the perimeter is therefore 4 s = 24 . correct answer a
Answer: a
Problem: a can run 4 times as fast as b and gives b a start of 72 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 96 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 72 m he gains 72 * ( 4 / 3 ) i . e 96 m answer : e"
Answer: e
Problem: evaluate : 30 - 12 ÷ 3 × 2 = ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "according to order of operations , 12 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 3 × 2 = 4 × 2 = 8 hence 30 - 12 ÷ 3 × 2 = 30 - 8 = 22 correct answer b ) 22"
Answer: b
Problem: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 5 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 5 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 5 ) = 0.08 t - - > 60 + 6 ( t - 5 ) = 8 t - - > t = 15 . answer : c ."
Answer: c
Problem: an employer pays rs . 30 for each day a worker works , and forfeits rs . 5 for each day he is idle . at the end of 60 days , a worker gets rs . 500 . for how many days did the worker remain idle ?
Options: a ) 52 , b ) 27 , c ) 99 , d ) 61 , e ) 11
Rationale: explanation : suppose the worker remained idle for m days . then , he worked for ( 60 - m ) days . 30 ( 60 - m ) – 5 m = 500 1800 – 25 m = 500 25 m = 1300 m = 52 so , the worker remained idle for 52 days . answer : a
Answer: a
Problem: a can finish a piece of work in 5 days . b can do it in 15 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 3 days , b ) 5 days , c ) 4 days , d ) 6 days , e ) 7 days
Rationale: "2 / 5 + ( 2 + x ) / 15 = 1 = > x = 7 days answer : e"
Answer: e
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 16 cm
Options: a ) 304 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 16 ) = 304 cm 2 answer : a"
Answer: a
Problem: a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 5 minutes ?
Options: a ) 96.7 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 5 / 60 ) km = 1 / 12 km = 83.3 m . . ' . distance between the criminal and policeman = ( 180 - 83.3 ) m = 96.7 m . answer : a"
Answer: a
Problem: 8269 ã — 9998 = ?
Options: a ) 85432864 , b ) 82673462 , c ) 86985434 , d ) 68954365 , e ) 65486954
Rationale: "8269 ã — ( 10000 - 2 ) 82690000 - 16538 = 82673462 answer b"
Answer: b
Problem: let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 8 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 8 , b ) - 1 , c ) 0 , d ) 1 , e ) 8
Rationale: "when x = 1 and when x = - 8 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 8 ) f ( 0 ) = - 8 the answer is a ."
Answer: a
Problem: two numbers are in the ratio of 5 : 7 . if 12 is subtracted from each number , they are in the ratio of 11 : 17 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 12 ) : ( 7 x - 12 ) = 11 y : 17 y 5 x - 12 = 11 y 7 x - 12 = 17 y 84 - 60 = 85 y - 77 y 24 = 8 y y = 3 5 x - 12 = 33 x = 9 the two numbers are 5 x and 7 x which are 45 and 63 . the answer is a ."
Answer: a
Problem: the sale price sarees listed for rs . 600 after successive discount is 10 % and 5 % is ?
Options: a ) 227 , b ) 513 , c ) 342 , d ) 787 , e ) 191
Rationale: "600 * ( 90 / 100 ) * ( 95 / 100 ) = 513 answer : b"
Answer: b
Problem: in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 6720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2184
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 6720 32.5 k = 32.5 k / 100 k * 6720 = 2184 the number of valid votes polled in favour of b is 2184 . answer : e"
Answer: e
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 5 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 11
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 5 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 5 x = 11 x august tips as a fraction of total tips = 5 x / 11 x = 5 / 11 . so e"
Answer: e
Problem: a clock store sold a certain clock to a collector for 45 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 25 percent of what the collector had paid . the shop then sold the clock again at a profit of 55 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 180 , for how much did the shop sell the clock the second time ?
Options: a ) $ 149.55 , b ) $ 134.56 , c ) $ 175.43 , d ) $ 158.65 , e ) $ 255.45
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 45 % profit . this means the clocks ' selling price was c ( 1.45 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 25 % the price at which the collector bought it . thus , you get = 1.45 * 0.25 * c = 0.3625 c furthermore , the store sells the clock for the second time for 55 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.55 = 1.55 * 0.3625 c finally given that c - 0.3625 c = 180 - - - - > c = 282.35 $ thus , the cost of the clock the second time around = 1.55 * 0.3625 c = 1.55 * 0.3625 * 282.35 = 158.65 $ . hence d is the correct answer ."
Answer: d
Problem: in a hostel there were 100 students . to accommodate some more students the average budget is decreased by rupees 10 . but total expenditure increased by rs . 400 . if the total expenditure of the hostel now 5400 , find the number of student joined ?
Options: a ) 30 , b ) 20 , c ) 35 , d ) 32 , e ) 40
Rationale: let average is x 100 x + 400 = 5400 x = 50 let the number of student joined is y ( 100 + y ) * ( 50 - 10 ) = 5400 y = 35 answer : d
Answer: d
Problem: 54 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 33 , b ) 66 , c ) 18 , d ) 100 , e ) 281
Rationale: "( 54 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 120 120 – 54 = 66 answer : b"
Answer: b
Problem: what is the probability of getting sum 10 with the help of three dice ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 24 , e ) 1 / 32
Rationale: "( 1 , 3,6 ) 3 ! = 6 ( 2 , 2,6 ) = 3 ! / 2 = 3 ( 1 , 4,5 ) 3 ! = 6 ( 2 , 4,4 ) = 3 ( 2 , 3,5 ) 3 ! = 6 ( 3 , 3,4 ) = 3 prob . of getting sum 10 = ( 6 + 6 + 6 + 3 + 3 + 3 ) / 216 = 1 / 8 ans answer : b"
Answer: b
Problem: a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 7 / 9 . what is this certain fraction ?
Options: a ) 1 / 20 , b ) 1 / 25 , c ) 1 / 30 , d ) 1 / 35 , e ) 1 / 40
Rationale: "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 7 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 7 = 1 / 35 the answer is d ."
Answer: d
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 4 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 23 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 4 ) . ∴ 16 ( x – 4 ) + 87 = 17 x or x = ( 87 – 64 ) = 23 . answer c"
Answer: c
Problem: . if the sides of two cubes are in the ratio 3 : 1 the ratio of their total surface area is ?
Options: a ) 3 : 1
b ) 8 : 1
c ) 9 : 1
d ) 12 : 1
e ) 9 : 1
Rationale: a 1 : a 2 = 3 : 1 6 a 12 : 6 a 22 = 9 : 1 answer : c
Answer: c
Problem: the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 16 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,496
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 16 and c = 1 / 2 into the equation and simplify to get the answer 1496 option e ."
Answer: e
Problem: when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 6 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 6 x = 84 6 x / 9 = 9 * 9 + 3 remainder is 3 . answer is c ."
Answer: c
Problem: set a : 3 , r , 8 , 10 set b : 4 , g , 9 , 11 the terms of each set above are given in ascending order . if the median of set a is equal to the median of set b , what is the value of g – r ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: so we have even no . of elements in the set so median is the average of middle two numbers ( r + 8 ) / 2 = ( g + 9 ) / 2 g - r = - 1 answer b
Answer: b
Problem: how many integers from 40 to 200 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 20 , b ) 31 , c ) 35 , d ) 40 , e ) 45
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 40 to 200 , inclusive is ( 189 - 42 ) / 21 + 1 = 8 ; 53 - 8 = 45 . answer : e ."
Answer: e
Problem: water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 45 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 92 ° f , b ) 97 ° f , c ) 104 ° f , d ) 113 ° f , e ) 118 ° f
Rationale: "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 ( 45 ) / 5 + 32 = 113 ° f the answer is d ."
Answer: d
Problem: a sum of money at simple interest amounts to rs . 415 in 2 years and to rs . 514 in 4 years . the sum is ?
Options: a ) rs . 316 , b ) rs . 251 , c ) rs . 154 , d ) rs . 294 , e ) rs . 200
Rationale: "explanation : s . i . for 2 years = ( 514 - 415 ) = rs . 99 s . i . for 1 year = 99 / 2 principal = ( 415 - 99 ) = rs . 316 . answer is a"
Answer: a
Problem: a man can row his boat with the stream at 26 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 11 kmph , e ) 4 kmph
Rationale: "ds = 26 us = 4 s = ? s = ( 26 - 4 ) / 2 = 11 kmph answer : d"
Answer: d
Problem: a and b can complete a work in 30 days and 15 day . they started doing the work together but after 5 days b had to leave and a alone completed the remaining work . the whole work was completed in ?
Options: a ) 10 days , b ) 12 days , c ) 20 days , d ) 18 days , e ) 25 days
Rationale: a + b 1 day work = 1 / 30 + 1 / 15 = 1 / 10 work done by a and b in 10 days = 1 / 10 * 5 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 now 1 / 30 work is done by a in 1 day 1 / 2 work will be done by a in 30 * 1 / 2 = 15 days total time taken = 15 + 5 = 20 days answer is c
Answer: c
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many e miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him e : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer .
Answer: d
Problem: the sum of two numbers is 73 and their difference is 28 . find the difference between their squares .
Options: a ) 101 , b ) 45 , c ) 2044 , d ) 2048 , e ) 2064
Rationale: "explanation : let x and y be the two given numbers ( x + y ) = 73 ; ( x – y ) = 28 ( x 2 – y 2 ) = ( x + y ) ( x – y ) = 73 * 28 = 2044 answer : c"
Answer: c
Problem: a large tank can filled by a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 10 min , b ) 15 min , c ) 30 min , d ) 25 min , e ) 42 min
Rationale: part filled by a + b in 1 minute = 1 / 60 + 1 / 40 = 1 / 24 suppose the tank is filled in x minutes then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 x = 30 min answer is c
Answer: c
Problem: in order to fence a square manish fixed 48 poles . if the distance between two poles , is 1 metres then what will be the area of the square so formed ?
Options: a ) 144 cm 2 , b ) 260 cm 2 , c ) 2500 cm 2 , d ) 302 cm 2 , e ) none of these
Rationale: "let the side of the square be x m . ∴ perimeter of the square = 48 × 1 = 4 x ∴ x = 12 m ∴ area = ( 12 ) 2 = 144 cm 2 answer a"
Answer: a
Problem: the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 80
b ) 70
c ) 60
d ) 40
e ) 50
Rationale: b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c
Answer: c
Problem: two vessels contains equal number of mixtures milk and water in the ratio 8 : 2 and 9 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 17 : 3
Rationale: "the ratio of milk and water in the new vessel is = ( 8 / 10 + 9 / 10 ) : ( 2 / 10 + 1 / 10 ) = 17 / 10 : 3 / 10 = 17 : 3 answer is e"
Answer: e
Problem: for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Problem: tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 3 / 20 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 3
Rationale: s = { 1 , 23 , … . 20 } e = { 3 , 6 , 912 , 1518 } p ( e ) = 6 / 20 = 3 / 10 option a
Answer: a
Problem: find the ratio between whole surfaces of a sphere and a hemisphere ?
Options: a ) 4 : 3
b ) 3 : 4
c ) 3 : 2
d ) 5 : 2
e ) 4 : 6
Rationale: 4 ï € r 2 : 3 ï € r 2 = > 4 : 3 answer a
Answer: a
Problem: some of 10 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 15 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 5
Rationale: "let total paint = 1 let amount replaced = x 10 ( 1 - x ) + 20 x = 15 x = 1 / 2 answer : c"
Answer: c
Problem: a person walks from one end to the other of a 100 - meter long moving walkway at a constant rate in 25 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 150 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 37 , b ) 39 , c ) 41 , d ) 43 , e ) 45
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 25 ( v + x ) = 100 then 150 ( v + x ) = 600 150 ( v - x ) = 100 when we add the two equations : 300 v = 700 v = 7 / 3 time = 100 / ( 7 / 3 ) = ( 300 / 7 ) seconds which is about 43 seconds the answer is d ."
Answer: d
Problem: a certain number of workers can do a work in 65 days . if there were 10 workers more it could be finished in 10 days less . how many workers are there ?
Options: a ) 55 , b ) 30 , c ) 28 , d ) 24 , e ) 32
Rationale: "number of workers = 10 * ( 65 - 10 ) / 10 = 55 answer is a"
Answer: a
Problem: a bag contains 6 black and 9 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 4 , b ) 4 / 3 , c ) 4 / 5 , d ) 4 / 9 , e ) 3 / 5
Rationale: "let number of balls = ( 6 + 9 ) = 15 . number of white balls = 9 . p ( drawing a white ball ) = 9 / 15 = 3 / 5 hence answer is e"
Answer: e
Problem: walking at the rate of 8 kmph a man cover certain distance in 4 hr 45 min . running at a speed of 19 kmph the man will cover the same distance in .
Options: a ) 100 min , b ) 110 min , c ) 140 min , d ) 120 min , e ) 150 min
Rationale: "distance = speed * time 8 * 19 / 4 = 38 km new speed = 19 kmph therefore time = d / s = 38 / 19 = 120 min answer : d ."
Answer: d
Problem: a train 420 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 20 , e ) 24
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 420 * 2 / 35 = 24 sec answer : option e"
Answer: e
Problem: every day daniel drives 100 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 28 % , c ) 33 % , d ) 42 % , e ) 52 %
Rationale: "let ' s test x = 4 . . . . on sunday , daniel drove 100 miles at 4 miles / hour . d = ( r ) ( t ) 100 = ( 4 ) ( t ) 100 / 4 = 25 = t it takes 25 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 68 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 68 = ( 2 ) ( t ) 68 / 2 = 34 = t it takes 34 hours for the second part total time to drive home on monday = 4 + 34 = 38 hours we ' re asked by what percent 38 hours is greater than 25 hours . 38 / 25 = 1.52 , so it is 52 % greater . e"
Answer: e
Problem: in what ratio must tea of rs . 42 per kg be mixed with tea of rs . 50 per kg so that cost of mixture is rs . 45 per kg ?
Options: a ) 5 : 3 , b ) 3 : 5 , c ) 2 : 3 , d ) 3 : 4 , e ) 1 : 2
Rationale: 50 - 45 : 45 - 42 = 5 : 3 answer : a
Answer: a
Problem: in the biotechnology class of 2000 , there were x graduates . 32 of the graduates found a job , 45 continued on to their second degree and 13 did both . if only 9 people did n ' t do both , what is x equal to ?
Options: a ) 69 . , b ) 71 , c ) 73 , d ) 75 , e ) 76
Rationale: graduates got job = 32 graduates continued to second degree = 45 graduates got job and continued to second degree = 13 graduates did n ' t get job and did n ' t continue to second degree = 9 job no job total second degree 13 32 45 no second degree 19 9 28 total 32 41 x therefore x = 73 answer c
Answer: c
Problem: the number 61 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 61 : 1 , 4 , 9 , 16 , 25 , 36 , 49 . now , 61 should be the sum of 3 of those 7 numbers . also to simplify a little bit trial and error , we can notice that as 61 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 61 equals to 9 + 16 + 36 = 3 ^ 2 + 4 ^ 2 + 6 ^ 2 = 61 - - > 3 + 4 + 6 = 13 . answer : e ."
Answer: e
Problem: the average weight of 6 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
Options: a ) 74 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
Rationale: "total weight increases = 6 × 1.5 = 9 kg so the weight of new person = 65 + 9 = 74 kg answer a"
Answer: a
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 54 , what is the total amount ?
Options: a ) 234 , b ) 116 , c ) 117 , d ) 118 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 54 39 - - - ? = > 234 answer : a"
Answer: a
Problem: from the sale of sleeping bags , a retailer made a gross profit of 14 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.56 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.14 = selling price - - > cost price * 1.14 = $ 28 - - > cost price = $ 24.56 . answer : c ."
Answer: c
Problem: in 150 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 9 m , e ) 30 m
Rationale: "distance covered by b in 9 sec . = 150 / 45 x 9 m = 30 m . a beats b by 30 metres . answer : option e"
Answer: e
Problem: the value of ( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) is close to
Options: a ) 2 , b ) 1.15 , c ) 2.05 , d ) 0.29 , e ) 2.35
Rationale: "( 34.31 * 0.473 * 1.567 ) / ( 0.5 * 23.25 * 7.57 ) = 25.4303 / 88.00125 = 0.29 answer : d"
Answer: d
Problem: if x is 12 percent greater than 70 , then x =
Options: a ) 78.4 , b ) 91.0 , c ) 88.0 , d ) 70.4 , e ) 71.2
Rationale: "12 % of 70 = ( 70 * 0.11 ) = 8.4 12 % greater than 70 = 70 + 8.4 = 78.4 answer is clearly a ."
Answer: a
Problem: a man is 28 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is
Options: a ) 26 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 28 ) years . then â € ¹ = â € º ( x + 28 ) + 2 = 2 ( x + 2 ) â € ¹ = â € º x + 30 = 2 x + 4 x = 26 . answer a"
Answer: a
Problem: a and b invests rs . 3000 and rs . 10000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 9 : 6 , b ) 9 : 8 , c ) 9 : 20 , d ) 9 : 9 , e ) 9 : 5
Rationale: "( 3 * 6 + 6 * 6 ) : ( 10 * 12 ) 54 : 120 = > 9 : 20 . answer : c"
Answer: c
Problem: what is the smallest integer that is multiple of 3 , 5,7
Options: a ) a ) 105 , b ) b ) 35 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 3 , 5 and 7 which is 105 . the answer is a ."
Answer: a
Problem: a call center has two teams . each member of team a was able to process 7 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
Options: a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 15 , d ) 1 / 2 , e ) 1 / 5
Rationale: "let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 7 calls , so total calls for team a = 35 fraction for team b = 40 / ( 40 + 35 ) = 8 / 15 = answer = c"
Answer: c
Problem: the speed at which a man can row a boat in still water is 10 kmph . if he rows downstream , where the speed of current is 2 kmph , what time will he take to cover 60 metres ?
Options: a ) 18 seconds , b ) 34 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 10 + 2 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : a"
Answer: a
Problem: what is the value of 4 ^ 5 + 4 ^ 4 ?
Options: a ) 4 ^ 12 , b ) 5 ( 4 ^ 4 ) , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 7 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 4 = 4 ^ 4 ( 4 + 1 ) = 4 ^ 4 * 5 answer b"
Answer: b
Problem: the positive numbers w , x , y , and z are such that x is 10 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 16 - answer b"
Answer: b
Problem: a man misses a bus by 40 minutes if he travels at 30 kmph . if he travels at 40 kmph , then also he misses the bus by 10 minutes . what is the minimum speed required to catch the bus on time ?
Options: a ) 22 , b ) 45 , c ) 66 , d ) 88 , e ) 12
Rationale: let the distance to be travelled to catch the bus be x km x / 30 - x / 40 = 30 / 60 = > ( 4 x - 3 x ) / 120 = 1 / 2 = > x = 60 km by traavelling 30 kmph time taken = 60 / 30 = 2 hours by taking 2 hours , he is late by 40 min . so , he has to cover 60 km in at most speed = 60 / ( 4 / 3 ) = 45 kmph . answer : b
Answer: b
Problem: 5 n + 2 > 12 and 7 n + 2 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 2 and 7 , e ) 2 and 9
Rationale: "5 n + 2 > 12 5 n > 10 n > 2 7 n + 2 < 44 7 n < 42 n < 6 so n must be between 2 and 6 2 < n < 6 correct answer b"
Answer: b
Problem: a committee is reviewing a total of 20 x black - and - white films and 4 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction of the selected films are in color ?
Options: a ) 26 / 21 , b ) 28 / 21 , c ) 20 / 21 , d ) 40 / 21 , e ) 60 / 21
Rationale: "say x = y = 10 . in this case we would have : 20 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 2 black - and - white films and all 40 color films , thus total of 42 films were selected . color films thus compose 40 / 42 = 20 / 21 of the selected films . answer : c"
Answer: c
Problem: a jogger running at 9 kmph along side a railway track is 250 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 37 sec , c ) 36 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 250 + 120 ) m = 370 m . ∴ time taken = ( 370 ⁄ 10 ) sec = 37 sec . answer b"
Answer: b
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 11 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 63
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 11 = 63 answer e"
Answer: e
Problem: a train traveling at 42 kms / hr passes a cyclist going in the same direction in 9 secs . if the cyclist had been going in the opposite direction , the train would have passed him in 5 secs . find the length of the train .
Options: a ) 75 meters , b ) 60 meters , c ) 90 meters , d ) 80 meters , e ) 70 meters
Rationale: let the length of the train be x meter and the speed of the cyclist is y m / s now when the train and the cyclist are in the same direction , the relative speed is : ( 35 / 3 - y ) m / s [ converting 42 km / h to m / s - 35 / 3 m / s ] now distance / relative speed = 9 seconds substituting the values , we get x + 9 y . . . . . . . . . . . . . . . . . . . . . ( 1 ) similarly calculate the relative speed when they are in the opposite direction the relative speed is ( 35 / 3 + y ) now distance / relative speed is equivalent to 5 seconds substituting the values , we get the equation 3 x - 15 y = 175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 2 ) solving ( 1 ) and ( 2 ) , we get x = 75 meters answer : a
Answer: a
Problem: the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 245 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 455 , e ) none of these
Rationale: "average would be : 350 = ( 245 + x ) / 2 on solving , x = 455 . answer : d"
Answer: d
Problem: in what ratio should a variety of rice costing rs . 5.5 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 8 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 5.5 ) = 5 / 8 answer : d"
Answer: d
Problem: john can complete a given task in 16 days . jane will take only 12 days to complete the same task . john and jane set out to complete the task by beginning to work together . however , jane was indisposed 5 days before the work got over . in how many days did the work get over from the time john and jane started to work on it together ?
Options: a ) 62 , b ) 64 , c ) 66 / 7 , d ) 10 , e ) 68 / 7
Rationale: "in such questions , you need to start from the end . last 5 days john works alone and completes 5 * ( 1 / 16 ) = 5 / 16 of the work . so 11 / 16 of the work should have been completed by the two of them together before jane left . their combined rate of work is 1 / 16 + 1 / 12 = 7 / 48 time taken to complete 11 / 16 of the work = ( 11 / 16 ) / ( 7 / 48 ) = 33 / 7 days . so total number of days taken to complete the work = 33 / 7 + 5 = 68 / 7 days . e"
Answer: e
Problem: what is the least positive integer that is not a factor of 30 ! and is not a prime number ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 62 , e ) 64
Rationale: a ) 31 is prime and per the question stem we can not use this b ) 32 = 2 * 16 - within 30 ! we have a 2 and 16 so 32 will be a factor of 30 ! c ) 33 = 3 * 11 - again within 30 ! we have a 3 and an 11 so 33 will be a factor of 30 ! d ) 62 = 31 * 2 - bingo 31 is not included in 30 ! e ) 64 = 16 * 4 - both 16 and 4 are multiplied in 30 ! answer is d !
Answer: d
Problem: if the true discount on a sum due 3 years hence at 14 % per annum be rs . 168 , the sum due is :
Options: a ) 698 , b ) 768 , c ) 1430 , d ) 1980 , e ) none
Rationale: "sol . p . w . = 100 * t . d . / r * t = 100 * 168 / 14 * 2 = 600 . ∴ sum = ( p . w . + t . d . ) = rs . ( 600 + 168 ) = rs . 768 . answer b"
Answer: b
Problem: find the slope of the line perpendicular to the line y = ( 1 / 5 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 5 , d ) 4 , e ) 5
Rationale: two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 5 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 5 ) = - 1 solve for m m = - 5 correct answer c ) - 5
Answer: c
Problem: each child has 2 pencils and 13 skittles . if there are 9 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
Rationale: 2 * 9 = 18 . answer is c .
Answer: c
Problem: a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 400 m long ?
Options: a ) 176 sec , b ) 190 sec , c ) 178 sec , d ) 160 sec , e ) 276 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1600 m t = d / s t = 1600 / 10 t = 160 sec answer : d"
Answer: d
Problem: chris age after 14 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 11
Rationale: "chris present age = x after 14 years = x + 14 5 years back = x - 5 x + 14 = 5 ( x - 5 ) x = 11 answer is e"
Answer: e
Problem: the average of 13 numbers is 59 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 59 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 59 = 767 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 767 = 59 . answer : a"
Answer: a
Problem: x is a positive integer less than 400 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 400 n = 23.42 or n = 23 answer : - c
Answer: c
Problem: a 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec . what is the length of the platform ?
Options: a ) 287 m , b ) 350 m , c ) 1267 m , d ) 1287 m , e ) 1162.5 m
Rationale: "speed = 300 / 8 = 75 / 2 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 75 / 2 = > x = 1162.5 m . answer : e"
Answer: e
Problem: the rate of increase of the price of sugar is observed to be 3 percent more than the inflation rate expressed in percentage . the price of sugar , on january 1 , 1994 , is rs . 25 per kg . the inflation rate for the years 1994 and 1995 are expected to be 12 % each . the expected price of sugar on january 1 , 1996 would be
Options: a ) 33.06 , b ) 34.1 , c ) 34.2 , d ) 24.6 , e ) none of these
Rationale: explanation : increase in the price of sugar = ( 12 + 3 ) = 15 % hence , price of the sugar on jan 1 , 1996 = > ( 25 * 115 * 115 ) / ( 100 * 100 ) = rs 33.06 . answer : a
Answer: a
Problem: a metallic sheet is of rectangular shape with dimensions 30 m x 25 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 6 m , the volume of the box ( in m cube ) is :
Options: a ) 920 m cube , b ) 840 m cube , c ) 1000 m cube , d ) 120 m cube , e ) none of these
Rationale: "explanation : l = ( 30 - 12 ) m = 20 m , [ because 6 + 6 = 12 ] b = ( 25 - 12 ) m = 13 m , h = 6 m . volume of the box = ( 12 x 13 x 6 ) m cube = 936 m cube . option e"
Answer: e
Problem: average weight of 10 people increased by 3 kg when one person of 45 kg is replaced by a new man . then weight of the new man is
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 75
Rationale: explanation : total weight increased is 3 * 10 = 30 . so weight of new person is 45 + 30 = 75 answer : option e
Answer: e
Problem: find the average of all numbers between 4 and 41 which are divisible by 5
Options: a ) 22.5 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 ) / 8 = 180 / 8 = 22.5 answer : option a"
Answer: a
Problem: the value of log 5 ( 1 / 125 ) is
Options: a ) 3 , b ) - 3 , c ) 1 / 3 , d ) - 1 / 3 , e ) none
Rationale: "solution let log 5 ( 1 / 125 ) = n . then , 5 n = 1 / 125 ‹ = › 5 n = 5 - 3 n = - 3 . answer b"
Answer: b
Problem: a train 280 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 65 sec , b ) 16 sec , c ) 18 sec , d ) 13 sec , e ) 76 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 280 * 2 / 35 = 16 sec answer : b"
Answer: b
Problem: at a certain bowling alley , it costs $ 1 to rent bowling shoes for the day and $ 1.25 to bowl 1 game . if a person has $ 12.80 and must rent shoes , what is the greatest number of complete games that person can bowl in one day ?
Options: a ) 7 , b ) 8 , c ) 5 , d ) 10 , e ) 9
Rationale: "after renting bowling shoes the person is left with $ 12.80 - $ 1 = $ 11.80 , which is enough for 11.8 / 1.25 < 10 = ~ 9 . answer : e ."
Answer: e
Problem: sales price is $ 54 , gross profit is 125 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 30 , c ) 39 , d ) 40 , e ) 42
Rationale: "cost + profit = sales cost + ( 125 / 100 ) cost = 54 cost = 24 profit = 54 - 24 = 30 answer ( b )"
Answer: b
Problem: two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 22 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 288 , b ) 516 , c ) 877 , d ) 278 , e ) 178
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 22 + 21 = 43 t = 12 d = 43 * 12 = 516 answer : b"
Answer: b
Problem: marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 10 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: "last year revenue = 100 ( assume ) ; this year revenue = 90 ; projected revenue = 120 . actual / projected * 100 = 90 / 120 * 100 = 75 % . answer : e ."
Answer: e
Problem: if the l . c . m of two numbers is 750 and their product is 18750 , find the h . c . f of the numbers
Options: a ) 23 , b ) 28 , c ) 48 , d ) 25 , e ) 99
Rationale: "explanation : h . c . f = ( product of the numbers ) / ( their l . c . m ) = 18750 / 750 = 25 . answer : d"
Answer: d
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 12 . if the shop carries 375 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 75 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 12 x total dogs and bunnies = 15 x . and we are given that 15 x = 375 . hence x = 25 . dogs = 3 x = 3 * 25 = 75 ( option c )"
Answer: c
Problem: 30 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 120 , c ) 50.4 , d ) 60 , e ) 90
Rationale: "30 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 30 ) * 100 = 120 square feet answer : option b"
Answer: b
Problem: a sum of money at simple interest amounts to rs . 830 in 3 years and to rs . 854 in 4 years . the sum is :
Options: a ) 647 , b ) 698 , c ) 758 , d ) 847 , e ) 976
Rationale: "s . i . for 1 year = rs . ( 854 - 830 ) = rs . 24 . s . i . for 3 years = rs . ( 24 x 3 ) = rs . 72 . principal = rs . ( 830 - 72 ) = rs . 758 . answer : c"
Answer: c
Problem: a person p takes 4 hrs time to complete a job and q takes 6 hrs to complete the same job if they work together how much time will they require to complete the job ?
Options: a ) 1.2 hrs , b ) 1.8 hrs , c ) 2.4 hrs , d ) 3.0 hrs , e ) none of these
Rationale: explanation : p ’ s 1 hr work = 1 / 4 q ’ s 1 hr work = 1 / 6 ( p + q ) ’ s 1 hr work = 1 / 4 + 1 / 6 = 5 / 12 = > time = 12 / 5 = 2.4 hrs answer : option c
Answer: c
Problem: a shopkeeper fixes the marked price of an item 35 % above its cost price . the percentage of discount allowed to gain 8 % is
Options: a ) 20 % , b ) 27 % , c ) 31 % , d ) 43 % , e ) none
Rationale: solution let c . p = rs . 100 then , marked price = rs . 135 , s . p = rs . 108 . discount % = ( 27 / 135 × 100 ) % = 20 % answer a
Answer: a
Problem: if the cost price of 22 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 37.5 % profit , c ) 37.5 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 22 articles = rs . 22 . selling price of 16 articles = rs . 22 therefore , selling price of 22 articles is : - = > 22 / 16 ã — 22 = > 30.25 . therefore , profit = selling price - cost price . = > 30.25 â ˆ ’ 22 = 8.25 hence , the percentage of profit = profit x 100 / c . p . = > 8.25 / 22 ã — 100 . = > 37.5 % profit . answer : b"
Answer: b
Problem: six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 30 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) none
Rationale: "l . c . m . of 2 , 4 , 6 , 8 , 10 , 12 is 120 . so , the bells will toll together after every 120 seconds ( 2 minutes ) . in 30 minutes , they will toll together 30 / 2 + 1 = 16 times answer d"
Answer: d
Problem: at what rate percent per annum will the simple interest on a sum of money be 4 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 7 % , c ) 8 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = 4 x / 5 , time = 10 years . rate = ( 100 * 4 x ) / ( x * 5 * 10 ) = 8 % answer : c"
Answer: c
Problem: the area of a rectangular field is equal to 300 square meters . its perimeter is equal to 70 meters . find the length of this rectangle .
Options: a ) 40 , b ) 70 , c ) 20 , d ) 80 , e ) 60
Rationale: "l * w = 300 : area , l is the length and w is the width . 2 l + 2 w = 70 : perimeter l = 35 - w : solve for l ( 35 - w ) * w = 300 : substitute in the area equation w = 15 and l = 20 : solve for w and find l using l = 35 - w . correct answer c"
Answer: c
Problem: a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 1 km , b ) 1.5 km , c ) 5 km , d ) 3.2 km , e ) 2.4 km
Rationale: speed of down stream = 5 + 1 = 6 kmph speed of upstream = 5 - 1 = 4 kmph let the required distance be xkm x / 6 + x / 4 = 1 2 x + 3 x = 12 x = 2.4 km answer is e
Answer: e
Problem: a sum fetched a total simple interest of $ 4106.25 at the rate of 9 p . c . p . a . in 5 years . what is the sum ?
Options: a ) $ 8829 , b ) $ 2840 , c ) $ 6578 , d ) $ 7782 , e ) $ 8927
Rationale: "e 8927 principal = $ 100 x 4106.25 / 9 x 5 = $ 410625 / 45 = $ 8927 ."
Answer: e
Problem: find the perimeter and area of a square of side 13 cm .
Options: a ) 121
b ) 144
c ) 169
d ) 196
e ) 225
Rationale: we know that the perimeter of square = 4 ã — side side = 13 cm therefore , perimeter = 4 ã — 13 cm = 52 cm now , area of the square = ( side ã — side ) sq . units = 13 ã — 13 cm â ² = 169 cm â ² answer : c
Answer: c
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 75 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1733.33 , d ) 1800 , e ) 2025
Rationale: 300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 75 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 75 = 1733.33 c is the answer
Answer: c
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 45 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 928 , d ) $ 870 , e ) $ 660
Rationale: "let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 145 % of $ 640 = $ 928 . c"
Answer: c