regisss/math_qa huggingface dataset:
Problem: a small pool filled only with water will require an additional 800 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 800 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 ) 1300 , d ) 2000 , e ) 2250
Rationale: "since pumping in additional 800 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 800 = 0.8 * { total } - - > { total } = 2,250 . answer : e ."
Answer: e
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 2500 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 4500 , d ) d ) 2393 , e ) e ) 5000
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 2500 = > x = 2500 . b ' s share = rs . 2 x = 2 * 2500 = rs . 5000 . answer : e"
Answer: e
Problem: the average height of 35 boys in a class was calculated as 184 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ) . ?
Options: a ) 178.27 cm , b ) 182.29 cm , c ) 978.29 cm , d ) 178.89 cm , e ) 176.29 cm
Rationale: "calculated average height of 35 boys = 184 cm . wrong total height of 35 boys = 184 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 184 cm - ( 166 cm - 106 cm ) / 35 = 184 cm - 60 / 35 cm = 184 cm - 1.71 cm = 182.29 cm . answer : b"
Answer: b
Problem: all the students of class are told to sit in circle shape . here the boy at the 7 th position is exactly opposite to 27 th boy . total number of boys in the class ?
Options: a ) 25 , b ) 40 , c ) 35 , d ) 30 , e ) 28
Rationale: "as half the circle shape consist of 27 - 7 = 20 boys , so total number of boys in full circle = 2 * 20 = 40 answer : b"
Answer: b
Problem: on my sister ' s birthday , she was 132 cm in height , having grown 10 % since the year before . how tall was she the previous year ?
Options: a ) 130 cm , b ) 126 cm , c ) 120 cm , d ) 116 cm , e ) 112 cm
Rationale: "let the previous year ' s height be x . 1.1 x = 132 x = 120 the answer is c ."
Answer: c
Problem: a $ 72.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 18 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: listed selling price of chair = 72.95 $ discounted selling price of chair = 59.95 $ discount = 72.95 - 59.95 = 13 $ % decrease in price of chair = ( 13 / 72.95 ) * 100 % = 18 % approx answer a
Answer: a
Problem: if shares of two persons in profits are rs . 400 and rs . 800 then ratio of their capitals is
Options: a ) 3 : 4 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 400 : 800 = 1 : 2 answer : e"
Answer: e
Problem: if an investor puts $ 1000 in a savings account that earns 10 percent annual interest compounded semiannually , how much money will be in the account after one year ?
Options: a ) $ 1100.25 , b ) $ 1100.75 , c ) $ 1101.25 , d ) $ 1101.75 , e ) $ 1102.50
Rationale: "1.05 * 1.05 * 1000 = $ 1102.50 the answer is e ."
Answer: e
Problem: at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 7 : 3 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
Options: a ) 45 / 21 , b ) 46 / 2 , c ) 13 / 30 , d ) 23 / 6 , e ) 4 / 6
Rationale: "red : blue = 7 : 3 let red = 7 x and blue = 3 x 1 / 3 of red are left handed = > 1 / 3 * 7 x = 7 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 3 x = 6 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 7 x / 3 + 6 x / 3 ) / ( 7 x + 3 x ) = 13 / 30 answer : c"
Answer: c
Problem: a reduction of 23 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) s . 2.99 , b ) s . 2.4 , c ) s . 2.5 , d ) s . 2.2 , e ) s . 2.1
Rationale: "100 * ( 23 / 100 ) = 23 - - - 10 ? - - - 1 = > rs . 2.3 100 - - - 77 ? - - - 2.3 = > rs . 2.99 answer : a"
Answer: a
Problem: if 60 % of a number is greater than 30 % of 10 by 27 , what is the number ?
Options: a ) 50 , b ) 100 , c ) 30 , d ) 75 , e ) 5
Rationale: explanation : 60 / 100 * x - 30 / 100 * 10 = 27 60 / 100 * x - 3 = 27 60 / 100 * x = 30 x = 30 * 100 / 60 x = 50 answer : option a
Answer: a
Problem: how many integers from 0 to 53 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 52 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 52 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 51 or , n - 1 = 17 or , n = 18 d"
Answer: d
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 4 : 3 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: "originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 3 / 9 ) * 1350 = 450 acres were planted with tobacco . the answer is b ."
Answer: b
Problem: ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + 0.096 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.68 , b ) 0.086 , c ) 0.86 , d ) 0.068 , e ) none of them
Rationale: "given expression = ( 0.96 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.96 ) ( power 2 ) + ( 0.96 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.96 - 0.1 ) = 0.86 answer is c ."
Answer: c
Problem: a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 450 bolts ?
Options: a ) 36 , b ) 72 , c ) 120 , d ) 144 , e ) 108
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 450 bolts 450 * 6 / 25 = 108 mins ans e"
Answer: e
Problem: a man ' s speed with the current is 21 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 16 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 21 km / hr = > speed of the man + speed of the current = 21 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 21 - 2.5 = 18.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 18.5 - 2.5 = 16 km / hr answer is c ."
Answer: c
Problem: a train 275 m long , running with a speed of 90 km / hr will pass a tree in
Options: a ) 11 sec , b ) 15 sec , c ) 16 sec , d ) 20 sec , e ) none
Rationale: "sol . speed = ( 90 x 5 / 18 ) m / sec . = 25 m / sec . time taken = ( 275 x 1 / 25 ) sec = 11 sec answer a"
Answer: a
Problem: the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if steve and danny have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if steve and danny submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Problem: 28 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 70
Rationale: "i came up with ( e ) 70 think of 100 people total : from the first fact , 28 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 28 equals the number of fair haired men , which is 42 men with fair hair . add this 42 to the 28 women and get 70 fair haired men and women out of 100 total men and women . 70 % e"
Answer: e
Problem: a jogger running at 9 km / hr along side a railway track is 150 m ahead of the engine of a 100 m long train running at 45 km / hr in the same direction . in how much time will the train pass the jogger ?
Options: a ) 88 , b ) 27 , c ) 36 , d ) 80 , e ) 25
Rationale: "speed of train relative to jogger = 45 - 9 = 36 km / hr . = 36 * 5 / 18 = 10 m / sec . distance to be covered = 150 + 100 = 250 m . time taken = 250 / 10 = 25 sec . answer : e"
Answer: e
Problem: a train running at the speed of 60 km / hr crosses a pole in 12 sec . what is the length of the train ?
Options: a ) 200 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 150 m
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 200 m answer : a"
Answer: a
Problem: if x + 1 / x = 5 then find out the value of x ^ 5 + 1 / x ^ 5 = ?
Options: a ) 2515 , b ) 2525 , c ) 2535 , d ) 2545 , e ) 2555
Rationale: "given , ( x + 1 / x ) = 5 x ^ 2 + 1 / x ^ 2 = ( x + 1 / x ) ^ 2 - 2 * x * 1 / x = 5 ^ 2 - 2 = 23 - - - - - - - ( 1 ) x ^ 3 + 1 / x ^ 3 = ( x + 1 / x ) ^ 3 - 3 * x * 1 / x * ( x + 1 / x ) = 5 ^ 3 - 3 * 5 = 110 - - - - - - - ( 2 ) multiplying ( 1 ) & ( 2 ) , we get = > ( x ^ 2 + 1 / x ^ 2 ) * ( x ^ 3 + 1 / x ^ 3 ) = 23 * 110 = > x ^ 5 + 1 / x + x + 1 / x ^ 5 = 2530 = > x ^ 5 + 1 / x ^ 5 + ( x + 1 / x ) = 2530 = > x ^ 5 + 1 / x ^ 5 + 5 = 2530 = > ( x ^ 5 + 1 / x ^ 5 ) = 2525 answer : b"
Answer: b
Problem: a student traveled 30 percent of the distance of the trip alone , continued another 40 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
Rationale: "let x be the total length of the trip . 0.3 x + 40 miles + 0.5 x = x 40 miles = 0.2 x x = 200 miles the answer is e ."
Answer: e
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 10 : 00 am and pipe b at 11 : 00 am , at what time will the pool be full ?
Options: a ) 22 : 00 , b ) 20 : 00 , c ) 21 : 00 , d ) 18 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 10 : 00 a . m and pipe b at 11 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 11 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 10 : 00 a . m , pool is full at 20 : 00 hrs answer : b"
Answer: b
Problem: calculate the circumference of a circular field whose radius is 12 centimeters .
Options: a ) 2 , b ) 4 , c ) 26 , d ) 24 , e ) 10
Rationale: "circumference c is given by c = 2 ï € r = 2 ï € * 12 = 24 ï € cm correct answer d"
Answer: d
Problem: a number , x is chosen at random from the set of positive integers less than 20 . what is the probability that ( 18 / x ) > x ?
Options: a ) 1 / 5 , b ) 2 / 9 , c ) 3 / 19 , d ) 4 / 19 , e ) 7 / 9
Rationale: "number x has to be chosen from numbers 1 - 19 ( 18 / x ) > x = > 18 > x ^ 2 = > x ^ 2 - 18 < 0 x can have 2 values only 1 , 2 , 3 , 4 therefore , probability = 4 / 19 answer d"
Answer: d
Problem: a , b , c hired a car for rs . 520 and used it for 7 , 8 and 11 hours respectively . hire charges paid by b were ?
Options: a ) 127 , b ) 160 , c ) 287 , d ) 237 , e ) 111
Rationale: a : b : c = 7 : 8 : 11 . hire charges paid by b = rs . ( 520 * 8 / 26 ) = rs . 160 . answer : b
Answer: b
Problem: the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 256,000 locusts ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 15 , e ) 11
Rationale: "- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 + 8 hours : 64,000 + 10 hours : 128,000 + 12 hours : 256,000 answer : a"
Answer: a
Problem: there are 2 white plates , 6 green plates , 8 red plates , 4 pink plates , and 10 purple plates in the cabinet . what is the least number of plates that you have to pull out to make sure that you will have a matching pair ? ( assume that all the plates are identical except for the color )
Options: a ) 2 , b ) 4 , c ) 12 , d ) 7 , e ) 6
Rationale: since there are 5 colors , if you take 5 plates , you could still have 1 plate per color and not have a match . therefore , upon taking the 6 th plate , you will definitely have a match since the 6 th plate will form at least a pair with the 1 st 5 so 5 + 1 = 6 answer is e
Answer: e
Problem: the smallest number which when diminished by 7 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1015 , c ) 1022 , d ) 1032 , e ) none
Rationale: "solution required numbers = ( l . c . m of 12 , 16,18 , 21,28 ) + 7 ‹ = › 1008 + 7 = 1015 . answer b"
Answer: b
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 15 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "soln : - 15 x = 45 - - > 23 / 20 * x = 45 - - > x = 45 * 20 / 23 = 900 / 23 = ~ 39 . answer : b ."
Answer: b
Problem: salesperson a ' s compensation for any week is $ 360 plus 8 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 7,750 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 350 + 0.04 ( x - 1000 ) = 0.08 x x = 7,750 ans : d"
Answer: d
Problem: a train 220 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 12 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 60 + 4 = 64 km / hr . = 64 * 5 / 18 = 160 / 9 m / sec . time taken to pass the men = 220 * 9 / 160 = 12 sec . answer : b"
Answer: b
Problem: what is the dividend . divisor 14 , the quotient is 12 and the remainder is 8
Options: a ) 175 , b ) 176 , c ) 177 , d ) 178 , e ) 179
Rationale: b = d * q + r b = 14 * 12 + 8 b = 168 + 8 b = 176
Answer: b
Problem: jhon works for 60 days . for the day he is present he is paid 7.00 / - and for the day he is absent he is paid 3.00 / - per day . if he is paid 170 / - . how many days he is present .
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: let no . days be = x and no . days he is absent = 60 - x , so 7 x - 3 ( 60 - x ) = 170 x = 35 answer : a
Answer: a
Problem: what is the smallest no . that should be added to 31110 to make it exactly divisible by 9 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
Rationale: "if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 3 + 1 + 1 + 1 + 0 = 6 , the next multiple of 9 is 9 . 3 must be added to 31110 to make it divisible by 9 b"
Answer: b
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 140 kg . in the first week 60 percent is cut away . in the second week 40 percent of the remainder is cut away . in the third week the statue is completed when 30 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 24 kg , b ) 23 kg , c ) 28 kg , d ) 25 kg , e ) 27 kg
Rationale: a 24 kg 140 ã — 0.4 ã — 0.6 ã — 0.7 = 24 kg .
Answer: a
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . what is the number of participants ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let n be the number of participants . the number of games is nc 2 = n * ( n - 1 ) / 2 = 171 n * ( n - 1 ) = 342 = 19 * 18 ( trial and error ) the answer is e ."
Answer: e
Problem: a circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it . as a result the plate lost 1 / 6 th its original weight . the radius of the circular plate is
Options: a ) 16 sqrt 2
b ) 8 sqrt 2
c ) 32 sqrt 2
d ) sqrt 72
e ) sqrt 82
Rationale: area of 12 holes = 12 * pi * 1 ^ 2 = 12 * pi as 12 * pi = ( 1 / 6 ) th weight , so total area of plate = 12 * pi / ( 1 / 6 ) = 72 * pi if r = radius of the plate , then its area = pi * r ^ 2 = 72 * pi , so r = sqrt 72 answer : d
Answer: d
Problem: what is the ratio g of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled ?
Options: a ) 1 / 4
b ) 3 / 8
c ) 1 / 2
d ) 3 / 5
e ) 2
Rationale: one side surface area of a cube = x * x = x ^ 2 total 6 sides = 6 x ^ 2 as for the rectangular , height ( h ) and width ( w ) are same as cube , x . only length = 2 x . l x h = 2 x * x = 2 x ^ 2 - - - - > 4 sides = 2 x ^ 2 * 4 = 8 x ^ 2 w * h = x * x = x ^ 2 - - - - - - > 2 sides = x ^ 2 * 2 = 2 x ^ 2 total 6 sides = 8 x ^ 2 + 2 x ^ 2 = 10 x ^ 2 ratio of cube area to rectangular area g = 6 x ^ 2 / 10 x ^ 2 - - - - > 6 / 10 - - - - > 3 / 5 ( d )
Answer: d
Problem: if the mean of numbers 28 , x , 50 , 78 and 104 is 62 , what is the mean of 48 , 62 , 98 , 124 and x ?
Options: a ) 76.5 , b ) 58 , c ) 39.8 , d ) 90.3 , e ) 66.67
Rationale: "mean = ( sum of all no . in series ) / ( no . in series ) m 1 = 62 = ( x + 28 + 50 + 78 + 104 ) / ( 5 ) 62 x 5 = 260 + x x = 50 therefore mean of 2 nd series m 2 = ( x + 48 + 62 + 98 + 124 ) / 5 m 2 = 76.5 answer = a"
Answer: a
Problem: john makes $ 60 a week from his job . he earns a raise andnow makes $ 68 a week . what is the % increase ?
Options: a ) 16.12 % , b ) 16.66 % , c ) 16.56 % , d ) 17.66 % , e ) 13.33 %
Rationale: "increase = ( 8 / 60 ) * 100 = ( 2 / 15 ) * 100 = 13.33 % . e"
Answer: e
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) rs . 128
b ) rs . 129
c ) rs . 125
d ) rs . 198
e ) rs . 120
Rationale: 3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 1 / 2 = rs . 125 answer : c
Answer: c
Problem: what will be the compound interest on a sum of rs . 24,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 9718.27 , b ) rs . 9750 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 24000 * ( 1 + 12 / 100 ) 3 ] = 24000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 33718.27 c . i . = ( 33718.27 - 24000 ) = rs . 9718.27 answer : a"
Answer: a
Problem: a man can row 36 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?
Options: a ) 14 kmph , b ) 12 kmph , c ) 18 kmph , d ) 1 kmph , e ) none of these
Rationale: explanation : let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 36 x = 18 rate of upstream = 18 rate of downstream = 54 rate of stream 1 / 2 ( 54 - 18 ) = 18 kmph answer : option c
Answer: c
Problem: the units digit of ( 35 ) ^ ( 87 ) + ( 93 ) ^ ( 51 ) is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 0
Rationale: "the units digit of powers of 3 , cycles in a group of 4 : { 3 , 9 , 7 , 1 } 51 has the form 4 k + 3 , so the units digit of 93 ^ 51 is 7 . the units digit of powers of 5 is always 5 . 7 + 5 = 12 , so the units digit is 2 . the answer is a ."
Answer: a
Problem: how many multiples of 5 are there between 5 to 75 ?
Options: a ) 9 , b ) 18 , c ) 17 , d ) 13 , e ) can not be determined
Rationale: "explanation : as you know , multiples of 5 are integers having 0 or 5 in the digit to the extreme right ( i . e . the units place ) . so the numbers are 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 . answer : d"
Answer: d
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 765 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 192 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 765 . as per question we need to take 1 / 4 of 765 to be considered for top 10 movies = 191.25 approximate the value we 192 . answer : option b is the correct answer . ."
Answer: b
Problem: a box measuring 24 inches long by 40 inches wide by 16 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 35 , e ) 37
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 8 is the biggest number that could divide all three , 24 , 40 and 16 . thus side of cube must be 8 , and total number of cubes = 24 / 8 * 40 / 8 * 16 / 8 = 30 ans b"
Answer: b
Problem: there are 11 baskets numbered from 1 to 11 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 180 , b ) 220 , c ) 260 , d ) 300 , e ) 340
Rationale: each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 11 * 12 / 2 = 66 apples . the total number of apples taken by 10 children is 10 * 66 = 660 the number of apples left in the end is 1000 - 660 = 340 apples . the answer is e .
Answer: e
Problem: two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 3 : 1 and 6 : 4 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 26 : 11 , b ) 23 : 11 , c ) 21 : 11 , d ) 24 : 11 , e ) 25 : 11
Rationale: "vessel a = 300 gallons - - > milk = 225 , water = 75 ; vessel b = 500 gallons - - > milk = 300 , water = 200 ; vessel a + b = 800 gallons - - > milk = 525 , water 275 the ratio = 525 / 275 - - > 21 : 11 answer : c"
Answer: c
Problem: suzie ’ s discount footwear sells all pairs of shoes for one price and all pairs of boots for another price . on monday the store sold 22 pairs of shoes and 16 pairs of boots for $ 508 . on tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $ 656 . how much more do pairs of boots cost than pairs of shoes at suzie ’ s discount footwear ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 8
Rationale: "let x be pair of shoes and y be pair of boots . 22 x + 16 y = 508 . . . eq 1 8 x + 32 y = 656 . . . . eq 2 . now multiply eq 1 by 2 and sub eq 2 . 44 x = 1016 8 x = 656 . 36 x = 360 = > x = 10 . sub x in eq 2 . . . . we get 80 + 32 y = 656 . . . then we get 32 y = 576 then y = 18 differenece between x and y is 8 answer : e"
Answer: e
Problem: a rectangular block 10 cm by 20 cm by 35 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 56 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 10 * 20 * 35 = 7000 cm ^ 3 side of the largest cube = h . c . f of 10 , 20,35 = 5 cm volume of the cube = 5 * 5 * 5 = 125 cm ^ 3 number of cubes = 7000 / 125 = 56 answer is b"
Answer: b
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 5 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to get 40 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
Answer: e
Problem: if a lends rs . 2000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 90 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 212.5
Rationale: "( 2000 * 1.5 * 3 ) / 100 = > 90 answer : a"
Answer: a
Problem: a swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side . its volume is :
Options: a ) 260
b ) 262
c ) 270
d ) 272
e ) none of these
Rationale: explanation : volume will be length * breadth * height , but in this case two heights are given so we will take average , volume = ( 12 ∗ 9 ∗ ( 1 + 4 / 2 ) ) m 312 ∗ 9 ∗ 2.5 m 3 = 270 m 3 option c
Answer: c
Problem: the time taken by mr . dhoni to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 72 kmph , find the speed of the stream ?
Options: a ) 24 kmph , b ) 25 kmph , c ) 26 kmph , d ) 30 kmph , e ) 28 kmph
Rationale: the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 72 / 3 = 24 kmph . answer : a
Answer: a
Problem: a math teacher has 24 cards , each of which is in the shape of a geometric figure . half of the cards are rectangles , and a third of the cards are rhombuses . if 8 cards are squares , what is the maximum possible number of cards that re circles .
Options: a ) 7 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "a square is a special kind of rhombus ( sides are perpendicular ) a square is a special kind of rectangles ( sides with same length ) among the 24 cards with have : 15 rectangles 10 rhombus 8 squares among the 15 rectangles , there could be 8 special ones ( with sides of same length ) that are squares . that lets at least 7 rectangles that are not square . among the 10 rectangles , there could be 8 special ones ( with sides perpendicular ) that are squares . that lets at least 2 rhombus that are not square . we have 8 squares . so the minimum different cards that represent a square , a rhombus or a rectangle is 2 + 7 + 8 = 17 which means that the maximum number of circles that you could have is 24 - 17 = 7 answer ( a )"
Answer: a
Problem: increasing the original price of a certain item by 15 percent and then increasing the new price by 15 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 30.0 , d ) 32.75 , e ) 32.25
Rationale: "we ' re told that the original price of an item is increased by 15 % and then that price is increased by 15 % . . . . if . . . . starting value = $ 100 + 15 % = 100 + . 15 ( 100 ) = 115 + 15 % = 115 + . 15 ( 115 ) = 115 + 17.25 = 132.25 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 32.25 / 100 = 32.25 % final answer : e"
Answer: e
Problem: if a number n is chosen at random from the set of two - digit integers whose digits are both prime numbers , what is the probability t that n is divisible by 3 ?
Options: a ) 1 / 3 , b ) ¼ , c ) 9 / 25 , d ) 5 / 16 , e ) 0
Rationale: "prime digits are : 2 , 3 , 5 , 7 total number of 2 digit # s with both digits prime are : 4 * 4 = 16 out of these numbers divisible by 3 = 33 , 27 , 57 , 72 and 75 . i had to find the numbers manually using the 4 numbers above . = > prob = 5 / 16 . ans d . took me 3 : 20 mins ."
Answer: d
Problem: raj invests a part of rs . 12000 in 12 % stock at rs . 120 and the remainder in 15 % stock at rs . 125 . if his total dividend per annum is rs . 1360 , how much does he invest in 12 % stock at rs . 120 ?
Options: a ) 3000 , b ) 4000 , c ) 5000 , d ) 5500 , e ) 6000
Rationale: investment in 12 % stock be x then investment 15 % stock = ( 12000 - x ) 12 / 120 * x + 15 / 125 * ( 12000 - x ) = 1360 x = 4000 answer b
Answer: b
Problem: if 42.24 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: 42.24 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.24 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.24 = km / 50 . . . . . . 24 / 100 = 3 m / 50 . . . . . . m = 4 k + m = 3 + 4 = 7 answer : b
Answer: b
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 14 - meter platform and caught it after it had traveled 41.7 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 6 division of total diatance travelled will be 14 + 14 + 7 + 3.5 + 1.75 + 0.9 + 0.5 ans b"
Answer: b
Problem: a and b are two partially filled buckets of water . if 2 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 2 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 21 , e ) 22 / 5
Rationale: "let a contains a , b contains b liters so , ( a - 2 ) / ( b + 2 ) = 1 / 3 . . . . . . . ( 1 ) or 3 a - 6 = b + 2 or 3 a - b = 8 again , ( b - 2 ) / ( a + 2 ) = 1 / 2 . . ( 2 ) or 2 b - 4 = a + 2 or 2 b - a = 6 from ( 1 ) ( 2 ) we find a = 22 / 5 ans : e"
Answer: e
Problem: the reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 182
Rationale: "reciprocal of the hcf and lcm of two are 1 / 14 and 1 / 312 so , hcf = 14 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 14 * 312 / 24 = 182 answer : e"
Answer: e
Problem: the average mark of the students of a class in a particular exam is 80 . if 5 students whose average mark in that exam is 30 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 30 , c ) 35 , d ) 45 , e ) 55
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 5 ) students = 90 ( x - 5 ) 80 x - ( 5 * 30 ) = 90 ( x - 5 ) 300 = 10 x = > x = 30 answer : b"
Answer: b
Problem: a , b and c have rs . 450 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 100 , b ) b ) 110 , c ) c ) 120 , d ) d ) 130 , e ) e ) 140
Rationale: "a + b + c = 450 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 450 - - - - - - - - - - - - - - - - c = 100 answer : a"
Answer: a
Problem: one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of field ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "other side = [ ( 17 x 17 ) - ( 15 x 15 ) ] = ( 289 - 225 ) = 8 m area = 15 x 8 = 120 sq . m answer : b"
Answer: b
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 21 liters of forest green to change it to verdant green ?
Options: a ) 1 / 3 , b ) 7 , c ) 1 / 2 , d ) 1 / 7 , e ) 1 / 8
Rationale: "21 liter of forset green have 12 liter of blue and 9 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 12 / ( 9 + x ) = ¾ 27 + 3 x = 48 = > x = 7 answer : b"
Answer: b
Problem: mr . evans will states that each of his children will receive an equal share of his estate and that his grandchildren will split a portion of the estate that is equal to the share received by each of his children . if mr . evans has 4 children and 6 grandchildren , then approximately what percentage of mr . evans estate will each grandchild receive ?
Options: a ) 20 % , b ) 17 % , c ) 4.0 % , d ) 3.3 % , e ) 2.8 %
Rationale: "20 / 6 = 3.33 answer : d"
Answer: d
Problem: a and b invests rs . 4000 and rs . 6000 in a business . after 4 months , a withdraws three - fourth of his capital and 4 months later , b withdraws half of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 3 : 7 , e ) 5 : 7
Rationale: "a : b ( 4000 * 4 ) + ( 1000 * 8 ) : ( 6000 * 8 ) + ( 3000 * 4 ) 24000 : 60000 2 : 5 answer : a"
Answer: a
Problem: a trader marked the selling price of an article at 10 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 110 * 100 ] % = 10 % answer a"
Answer: a
Problem: a goods train runs at the speed of 72 kmph and crosses a 280 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 270 m , c ) 240 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 280 / 26 = 20 x + 280 = 520 x = 240 . answer : c"
Answer: c
Problem: two cars start at the same time from opposite ends of a highway that is 500 miles long . one car is riding at 40 mph and the second car is riding at 60 mph . how long after they begin will they meet ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: as cars are moving in opposite directions their speeds will be added . so their relative speeds : 60 + 40 = 100 mph total distance to be covered = 500 miles . time taken would be : 500 miles / 100 mph = 5 hours e is the answer .
Answer: e
Problem: the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 12 . what is the radius of circle o ?
Options: a ) – 2 / pi
b ) 2
c ) 3
d ) 4
e ) 6
Rationale: pi * r ^ 2 + 2 r - 2 * pi * r = 12 simplifying the equation : pi * r ( r - 2 ) + 2 r = 12 without much algebraic : we can test the answers quickly , then 6 is the only possible answer that will eliminate pi from equation . answer is e
Answer: e
Problem: linda spent 2 / 3 of her savings on furniture and the rest on a tv . if the tv cost her $ 250 , what were her original savings ?
Options: a ) $ 750 , b ) $ 350 , c ) $ 650 , d ) $ 550 , e ) $ 850
Rationale: "if linda spent 2 / 3 of her savings on furniture , the rest 3 / 3 - 2 / 3 = 1 / 3 on a tv but the tv cost her $ 250 . so 1 / 3 of her savings is $ 250 . so her original savings are 3 times $ 250 = $ 750 correct answer a"
Answer: a
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 188 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 470 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 188 = > 4 x / 10 = 188 = > 4 x = 1880 = > x = 470 . answer : d"
Answer: d
Problem: in a classroom , 12 students brought apples and 8 students brought bananas . if exactly 10 students brought only one of the two types of fruits , how many students brought both types of fruits ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: say x students brought both fruits . ( 12 - x ) + ( 8 - x ) = 10 - - > x = 5 . answer : a .
Answer: a
Problem: the average ( arithmetic mean ) of the even integers from 20 to 60 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 10 to 140 inclusive ?
Options: a ) 40 , b ) 15 , c ) 35 , d ) 20 , e ) 25
Rationale: so , according to a mean of a set of even numbers from 20 to 60 = ( 20 + 60 ) / 2 = 40 and mean of a set of even numbers from 10 to 140 = ( 10 + 140 ) / 2 = 75 difference = 75 - 40 = 35 answer : c .
Answer: c
Problem: ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 24
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 option b"
Answer: b
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 38 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 205 , b ) 245 , c ) 285 , d ) 325 , e ) 365
Rationale: after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 8 miles per hour . the time to catch up is 60 / 8 = 7.5 hours . in 7.5 hours , train a travels another 30 * 7.5 = 225 miles for a total of 285 miles . the answer is c .
Answer: c
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 100 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?
Options: a ) 12.25 , b ) 44 , c ) 18 , d ) 16 , e ) 14
Rationale: let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 100 / 2 = 50 sq m l b = 50 i . e . , l * l / 3 = 150 l 2 = 150 = > l = 12.25 answer : a
Answer: a
Problem: if | x + 10 | = 10 what is the sum of all the values of x .
Options: a ) 20 , b ) 40 , c ) - 20 , d ) 0 , e ) - 40
Rationale: "there will be two cases x + 10 = 10 and x + 10 = - 10 solve for x = > x = 10 - 10 = > x = 0 or x = - 10 - 10 = > x = - 20 the sum of both values will be 0 + - 20 = - 20 answer is c"
Answer: c
Problem: anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 12 coconut doughnuts , and 10 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 34 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 12 + 12 + 10 = 34 . answer is b ."
Answer: b
Problem: a bowl was filled with 10 ounces of water , and 0.014 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 7 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 014 * 50 = . 014 * 100 / 2 = 1.4 / 2 = . 7 percent of the original amount of water evaporated during this period = ( . 7 / 10 ) * 100 % = 7 % answer d"
Answer: d
Problem: a and b play a game where each is asked to select a number from 1 to 16 . if the two numbers match , both of them win a prize . find the probability that they will not win a prize in a single trial .
Options: a ) 15 / 16 , b ) 1 / 16 , c ) 7 / 8 , d ) 9 / 8 , e ) none of these
Rationale: explanation : a and b win a prize , only if both a and b select the number . so , if a chooses a number , b has to select the same number . hence , it is problem on dependent event . let a select a number . , then p ( a ) = 1 / 16 = probability of a . now , b selects the same number after a has already selected that number . then , p ( b / a ) = 1 / 1 = dependent probability of b given a has occurred . p ( ab ) = probability of winning a prize by both a and b is : - = > p ( a ) x p ( ab ) . = > ( 1 / 16 ) x 1 = 1 / 16 . hence , the probability of not winning a prize is : - = 1 - ( 1 / 16 ) . = 15 / 16 . answer : a
Answer: a
Problem: a family pays $ 700 per year for an insurance plan that pays 60 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total how much ?
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,500 , d ) $ 1,800 , e ) $ 2,200
Rationale: "assuming the medical expenses are $ 1000 or more , the family pays $ 700 + $ 400 = $ 1100 . the total amount paid by insurance plan for the first $ 1000 of expenses is $ 600 . the insurance will pay another $ 500 when the medical expenses are $ 1500 . the answer is c ."
Answer: c
Problem: the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.50 , in which year will commodity x cost 90 cents more than the commodity y ?
Options: a ) 2010 , b ) 2011 , c ) 2012 , d ) 2013 , e ) 2014
Rationale: "the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 30 + 90 = $ 1.20 cents on commodity y , which will take 12 years . the answer is d ."
Answer: d
Problem: there are 20 poles with a constant distance between each pole . a car takes 20 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 34.4543 , b ) 34.5455 , c ) 34.45128 , d ) 34.51288 , e ) 34.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 20 seconds 1 pole ( 20 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 20 / 11 ) seconds = 34.5455 seconds answer : b"
Answer: b
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 301 ?
Options: a ) 10,100 , b ) 20,200 , c ) 22,650 , d ) 40,200 , e ) 45,150
Rationale: firstly calculate the number of even integers between 99 and 301 : no of even integers = ( 300 - 100 ) / 2 + 1 = 101 avg of the even integers is ( 100 + 300 ) / 2 = 200 . the sum would be = no of even integers * avg . = = > 101 * 202 = 20,200 answer b .
Answer: b
Problem: what percent of 500 is 125 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 40 % , e ) 250 %
Rationale: "500 * x / 100 = 125 x = 125 / 5 x = 25 ans : c"
Answer: c
Problem: a number is increased by 40 % and then decreased by 40 % . find the net increase or decrease per cent .
Options: a ) 19 % , b ) 18 % , c ) 17 % , d ) 13 % , e ) 16 %
Rationale: "let the number be 100 . increase in the number = 40 % = 40 % of 100 = ( 40 / 100 × 100 ) = 40 therefore , increased number = 100 + 40 = 140 this number is decreased by 40 % therefore , decrease in number = 40 % of 140 = ( 40 / 100 × 140 ) = 5600 / 100 = 56 therefore , new number = 140 - 56 = 84 thus , net decreases = 100 - 84 = 16 hence , net percentage decrease = ( 16 / 100 × 100 ) % = ( 1600 / 100 ) % = 16 % answer : e"
Answer: e
Problem: a man buys an article for $ 20 . and sells it for $ 25 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 15 % , e ) 30 %
Rationale: "c . p . = $ 20 s . p . = $ 25 gain = $ 5 gain % = 5 / 20 * 100 = 25 % answer is a"
Answer: a
Problem: add 20 % of 40 and 25 % of 60 .
Options: a ) 9.5 , b ) 23 , c ) 25 , d ) 22 , e ) 15
Rationale: "20 % of 40 + 25 % of 60 40 * 20 / 100 + 60 * 25 / 100 8 + 15 = 23 answer b"
Answer: b
Problem: of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 800 , e ) 400
Rationale: we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 40 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 40 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 800 = 20 t 19 t + 800 = 20 t 800 = t there are a total of 800 students in the math class . answer is d .
Answer: d
Problem: the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 8 points after 5 games , what is the least number of the remaining matches it has to win to reach the 40 - point mark by the end of the tournament ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: to get 40 points as end of season we need another 32 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 hence option d - 9
Answer: d
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 12
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : on dividing 427398 by 12 we get the remainder 6 , so 6 should be subtracted answer : option c
Answer: c
Problem: charges made by two companies for the same a / c company xcompany y price $ 575 $ 530 surcharge as a percent of price 4 % 3 % installation charge $ 82.50 $ 93.00 the table above shows the various charges made by two companies for the same air conditioner . what is the total amount that can be saved on the purchase and installation of the air conditioner by dealing with the company that offers the lower total charge ?
Options: a ) $ 41.60 , b ) $ 45.00 , c ) $ 50.75 , d ) $ 55.75 , e ) $ 61.25
Rationale: looking at the values / percentage , its clear that company x costlier than company y just observed the oa ; they have 4 distinct numbers after decimal point total calculation of company x gives . 00 + . 00 + . 50 = . 50 at the decimal total calculation of company y gives . 00 + . 90 + . 00 = . 90 at the decimal there difference provides . 60 at the decimal ; only 41.60 fits in answer = a
Answer: a