regisss/math_qa huggingface dataset:
Problem: a fruit seller had some apples . he sells 40 % apples and still has 420 apples . originally , he had :
Options: a ) 588 apples , b ) 742 apples , c ) 750 apples , d ) 600 apples , e ) 700 apples
Rationale: "suppose originally he had x apples . then , ( 100 - 40 ) % of x = 420 . 60 / 100 x x = 420 x = ( 420 x 100 ) / 60 = 700 . answer e"
Answer: e
Problem: it costs $ 2 for the first 1 / 6 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 15 per hour . if a certain customer uses the laundry machine for 2 hours and 25 minutes , how much will it cost him ?
Options: a ) $ 42.25 . , b ) $ 40.25 . , c ) $ 38.25 . , d ) $ 36.25 . , e ) $ 34.25
Rationale: "2 hrs 25 min = 145 min first 10 min - - - - - - > $ 2 time left is 135 min . . . now , 60 min costs $ 15 1 min costs $ 15 / 60 145 min costs $ 15 / 60 * 145 = > $ 36.25 so , total cost will be $ 36.25 + $ 2 = > $ 38.25 hence answer will be c"
Answer: c
Problem: when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 86.12 , what is the value of y ?
Options: a ) 96 , b ) 87 , c ) 75 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 9 / y . the remainder in decimal form is given as . 12 therefore , 9 / y = . 12 solve for y and get 75 . c"
Answer: c
Problem: a truck driver starts with the speed of 70 kmph with the truck driver decreasing speed every two hours by 10 kmph . the truck driver ' s speed does not drop below 50 kmph . in how many hours will it take the truck driver to travel 500 kms ?
Options: a ) 480 minutes , b ) 492 minutes , c ) 504 minutes , d ) 528 minutes , e ) 540 minutes
Rationale: distance covered in first two hours = 70 ã — 2 = 140 km distance covered in next two hours = 60 ã — 2 = 120 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in next two hours = 50 ã — 2 = 100 km distance covered in first eight hours 140 + 120 + 100 + 100 = 460 km remaining distance = 500 â € “ 460 = 40 km . now , this distance will be covered at the speed of 50 km / hr . â ˆ ´ time taken = 40 â  „ 50 = 4 â  „ 5 hour . total time = 8 + 4 â  „ 5 = 8 4 â  „ 5 hour answer d
Answer: d
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 57.76 , the number of the member is the group is :
Options: a ) 57 , b ) 76 , c ) 77 , d ) 87 , e ) 97
Rationale: "money collected = ( 57.76 x 100 ) paise = 5776 paise numbers of members = 5776 squareroot = 76 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 16 - meter platform and caught it after it had traveled 44 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 3 , e ) 9
Rationale: "going down = 16 m going up = 8 - - > total = 24 going down = 8 - - > total = 32 going up = 4 - - > total = 36 going down = 4 - - > total = 40 going up = 2 - - > total = 42 going down = 2 - - > total = 44 ( caught ) no of bounce = 3 . . answer : d"
Answer: d
Problem: how many cubes of edge 2 dm can be cut out of a meter cube ?
Options: a ) 296
b ) 289
c ) 270
d ) 125
e ) 278
Rationale: 1 * 1 * 1 = 2 / 10 * 2 / 10 * 2 / 10 * x x = 125 answer : d
Answer: d
Problem: length of a rectangular plot is 20 mtr more than its breadth . if the cost of fencing the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 59 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 18 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 18 ) + x ] = 200 2 x + 18 = 100 2 x = 82 x = 41 . hence , length = x + 18 = 59 m a"
Answer: a
Problem: a cistern is filled by pipe a in 16 hours and the full cistern can be leaked out by an exhaust pipe b in 20 hours . if both the pipes are opened , in what time the cistern is full ?
Options: a ) 50 hrs , b ) 60 hrs , c ) 70 hrs , d ) 80 hrs , e ) 90 hrs
Rationale: "time taken to full the cistern = ( 1 / 16 - 1 / 20 ) hrs = 1 / 80 = 80 hrs answer : d"
Answer: d
Problem: village x has a population of 76000 , which is decreasing at the rate of 1200 per year . village y has a population of 42000 , which is increasing at the rate of 800 per year . in how many years will the population of the two villages be equal ?
Options: a ) 15 , b ) 17 , c ) 11 , d ) 18 , e ) 13
Rationale: "let the population of two villages be equal after p years then , 76000 - 1200 p = 42000 + 800 p 2000 p = 34000 p = 17 answer is b ."
Answer: b
Problem: average of 10 matches is 34 , how many runs one should should score to increase his average by 5 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 89 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 39 so , required score = ( 11 * 39 ) - ( 10 * 34 ) = 429 - 340 = 89 answer : option d"
Answer: d
Problem: two pipes can fill a cistern in 14 and 16 hours respectively . the pipes are opened simultaneously and it is found that due to leakage in the bottom , 32 minutes extra are taken for the cistern to be filled up . if the cistern is full , in what time would the leak empty it ?
Options: a ) 110 hours , b ) 112 hours , c ) 115 hours , d ) 100 hours , e ) none of these
Rationale: cistern filled by both pipes in one hour = 1 ⁄ 14 + 1 ⁄ 16 = 15 ⁄ 112 th ∴ both pipes filled the cistern in 112 ⁄ 15 hrs . now , due to leakage both pipes filled the cistern in 112 ⁄ 15 + 32 ⁄ 60 = 8 hrs . ∴ due to leakage , filled part in one hour 1 ⁄ 8 ∴ part of cistern emptied , due to leakage in one hour = 15 ⁄ 112 - 1 ⁄ 8 = 1 ⁄ 112 th ∴ in 112 hr , the leakage would empty the cistern . answer b
Answer: b
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1110 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 11
Rationale: explanation : 1500 - - - - 390 100 - - - - ? = > 26 % answer : c
Answer: c
Problem: a restaurant spends one quarter of its monthly budget for rent and quarter of the rest for food and beverages . what percentage of the budget does the restaurant spend for food and beverages ?
Options: a ) 23.5 % , b ) 32.5 % , c ) 35 % , d ) 18.75 % , e ) 20 %
Rationale: spend on rent = 1 / 4 spend on food and beverage = 1 / 4 of remaining = 1 / 4 * 3 / 4 = 3 / 16 so 3 / 16 = 18.75 % d is the answer
Answer: d
Problem: a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 10 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 10 % , b ) 12 % , c ) 14 % , d ) 16 % , e ) 18 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.1 x ) = 0.88 x . the difference is 12 % . the answer is b ."
Answer: b
Problem: of 3 numbers , the third is twice the second and the second is 4 times the first . if their average is 78 , the smallest of the 3 numbers is :
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: explanation : let first number be x . so , 2 nd no . = 4 x & 3 rd no . = 8 x . so , x + 4 x + 8 x = 78 × 3 = 234 . 13 x = 234 x = 234 / 13 hence , smallest number x = 18 . answer : a
Answer: a
Problem: the area of a square is 625 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 20 cm less than the side of the square .
Options: a ) 5 : 12 , b ) 5 : 13 , c ) 2 : 9 , d ) 1 : 15 , e ) 1 : 5
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 625 a = 25 l = 3 a and b = a - 20 b : l = a - 20 : 3 a = 5 : 75 = 1 : 15 answer : d"
Answer: d
Problem: two pipes a and b can separately fill a tank in 20 and 15 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 540 liters , c ) 820 liters , d ) 900 liters , e ) 580 liters
Rationale: "1 / 20 + 1 / 15 - 1 / x = 1 / 15 x = 12 20 * 45 = 900 answer : d"
Answer: d
Problem: the area of a triangle is with base 3 m and height 10 m ?
Options: a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 15 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 3 * 5 = 15 m 2 answer : c"
Answer: c
Problem: a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 50 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 2 hours ?
Options: a ) 32 % , b ) 36 % , c ) 40 % , d ) 44 % , e ) 48 %
Rationale: "the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.5 ( 6 ) = 3 gallons at the start , the amount of water is 0.5 ( 6 ) = 3 gallons after 2 hours , the amount of water is 3 - 0.5 ( 2 ) = 2 gallons the concentration of water is 2 / ( 3 + 2 ) = 2 / 5 = 40 % the answer is c ."
Answer: c
Problem: in what time will a train 55 m long cross an electric pole , it its speed be 36 km / hr ?
Options: a ) 5.5 , b ) 4.5 , c ) 3.5 , d ) 2.5 , e ) 1.5
Rationale: "speed = 36 * 5 / 18 = 10 m / sec time taken = 55 / 10 = 5.5 sec . answer : a"
Answer: a
Problem: a leak in the bottom of a tank can empty the tank in 6 hrs . an pipe fills water at the rate of 4 ltrs / minute . when the tank is full in inlet is opened and due to the leak the tank is empties in 8 hrs . the capacity of the tank is ?
Options: a ) 2345 , b ) 2350 , c ) 2457 , d ) 4657 , e ) 5760
Rationale: "1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 4 = 5760 e"
Answer: e
Problem: if m and n are positive integers and m ^ 2 + n ^ 2 = 20 , what is the value of m ^ 3 + n ^ 3 ?
Options: a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,600
Rationale: "you need to integers which squared are equal 20 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 stop . the integers ca n ' t be greater than 4 or we will score above 20 . the second integer need to be picked up the same way . 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 the only pair that matches is 4 ^ 2 + 2 ^ 2 = 20 . so 4 ^ 3 + 2 ^ 3 = 72 . answer a . )"
Answer: a
Problem: a train is moving at 6 / 7 of its usual speed . the train is 10 minutes too late . what is the usual time ( in hours ) for the train to complete the journey ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 2.5
Rationale: "new time = d / ( 6 v / 7 ) = 7 / 6 * usual time 10 minutes represents 1 / 6 of the usual time . the usual time is 1 hour . the answer is b ."
Answer: b
Problem: a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
Options: a ) 15500 , b ) 16000 , c ) 15000 , d ) 17000 , e ) 20000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.90 = 19 x / 25 = 36 x / 50 total sp = 12 x / 50 + 36 x / 50 = 48 x / 50 overall loss = x - 48 x / 50 = 2 x / 50 2 x / 50 = 600 = > x = 15000 answer : c"
Answer: c
Problem: a bag contains 6 green balls and 8 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 5 / 14 , b ) 8 / 21 , c ) 12 / 21 , d ) 43 / 91 , e ) 47 / 91
Rationale: the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 6 c 2 = 15 the number of ways to draw two white balls is 8 c 2 = 28 p ( two balls of the same colour ) = 43 / 91 the answer is d .
Answer: d
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 45 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2700 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 45 = 30 x = 2700 km answer is d"
Answer: d
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 10.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 320 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190
b ) 180
c ) 170
d ) 160
e ) 148
Rationale: let no of sits in vip enclosure is x then x * 40 + 10 ( 320 - x ) = 7500 or 25 x = 7500 - 3200 , x = 4300 / 25 = 172 vip = 172 general = 320 - 172 = 148 e
Answer: e
Problem: if a and b are positive integers , and a = 2 b + 6 , the greatest common divisor of a and b can not be
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 12
Rationale: "since a = 2 b + 6 , so we can say b = ( a / 2 - 3 ) . so we need to find not possible gcd values for a , ( a / 2 - 3 ) . a . 1 , we can easily get this value by making a = 8 . b . 2 . we can again get this value as gcd by keeping a = 10 c . 3 we will get this as gcd by keeping a = 12 d . 6 we can get gcd 6 by keeping ( a / 2 - 3 ) = 6 and a as 18 . e . 12 this is not possible as for 12 ( 2 ^ 2 * 3 ) to be gcd = 2 ^ 2 * 3 both a and a / 2 - 3 should be divisible by 4 and 3 . so a has to be a multiple of 4 . this means a / 2 has to be even and even - odd will be odd and odd number wont be divisible by 4 . this 12 cant be the gcd . answer e ."
Answer: e
Problem: naomi drives to the beauty parlor in 60 minutes . on the way back , her average speed is half the average speed as it was to the way to the parlor . how much time will it take naomi to travel two round trips to the beauty parlor ?
Options: a ) 3 hours . , b ) 4 hours . , c ) 4 hours and 20 minutes . , d ) 5 hours and 50 minutes , e ) 6 hours .
Rationale: s 1 = 2 s 2 since , speed is inversely proportional to time we have , s 1 / s 2 = 2 / 1 = t 2 / t 1 therefore , the time taken for one trip = 60 + 120 = 180 minutes total = 180 * 2 = 360 minutes = 6 hours answer : e
Answer: e
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 39 ° is ?
Options: a ) 40 m 2 , b ) 45 m 2 , c ) 49 m 2 , d ) 51 m 2 , e ) 55 m 2
Rationale: "39 / 360 * 22 / 7 * 12 * 12 = 49 m 2 answer : c"
Answer: c
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Problem: the radius of the wheel of a bus is 175 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 100 , b ) 250 , c ) 300 , d ) 330 , e ) none of these
Rationale: "radius of the wheel of bus = 175 cm . then , circumference of wheel = 2 ï € r = 350 ï € = 1100 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 1100 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 1100 = 100 answer a"
Answer: a
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 60 % profit on the first article and 60 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 278 , c ) 282 , d ) 202 , e ) 600
Rationale: "profit on first article = 60 % of 1000 = 600 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : e"
Answer: e
Problem: how many seconds does sandy take to cover a distance of 500 meters , if sandy runs at a speed of 15 km / hr ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "15 km / hr = 15000 m / 3600 s = ( 150 / 36 ) m / s = ( 25 / 6 ) m / s time = 500 / ( 25 / 6 ) = 120 seconds the answer is b ."
Answer: b
Problem: the compound ratio of 5 : 7 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 7 , b ) 6 : 5 , c ) 6 : 7 , d ) 4 : 7 , e ) 6 : 9
Rationale: "5 / 7 * 3 / 2 * 4 / 5 = 6 / 7 6 : 7 answer : c"
Answer: c
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 480 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 = > 450 hence answer will be ( d ) 450"
Answer: d
Problem: the ratio of the incomes of rajan and balan is 7 : 6 and the ratio of their expenditure is 6 : 5 . if at the end of the year , each saves $ 1000 then the income of rajan is ?
Options: a ) $ 7600 , b ) $ 7000 , c ) $ 8000 , d ) $ 9000 , e ) $ 5000
Rationale: let the income of rajan and balan be $ 7 x and $ 6 x let their expenditures be $ 6 y and $ 5 y 7 x - 6 y = 1000 - - - - - - - 1 ) 6 x - 5 y = 1000 - - - - - - - 2 ) from 1 ) and 2 ) x = 1000 rajan ' s income = 7 x = 7 * 1000 = $ 7000 answer is b
Answer: b
Problem: two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 12 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 66 , c ) 80 , d ) 36 , e ) 96
Rationale: d 36 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 12 mph = 36 miles
Answer: d
Problem: a 300 meter long train crosses a platform in 51 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 550 , b ) 289 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 51 = 50 / 3 3 ( x + 300 ) = 2550 è x = 550 m . answer : a"
Answer: a
Problem: find the perimeter and area of the rectangle of length 15 cm and breadth 11 cm .
Options: a ) 71 cm 2 , b ) 121 cm 2 , c ) 165 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 15 cm , breadth = 11 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 11 ) cm = 2 × 26 cm = 52 cm we know that the area of rectangle = length × breadth = ( 15 × 11 ) cm 22 = 165 cm 2 answer : c"
Answer: c
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be :
Options: a ) 43 , b ) 26 , c ) 33 , d ) 21 , e ) 28
Rationale: "b 26 let the number of hens be x and the number of cows be y . then , x + y = 48 . . . . ( i ) and 2 x + 4 y = 140 x + 2 y = 70 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 26 , y = 22 . the required answer = 26 ."
Answer: b
Problem: when 1 / 10 percent of 2,000 is subtracted from 1 / 10 of 2,000 , the difference is
Options: a ) 1980 , b ) 1998 , c ) 198 , d ) 200 , e ) 20
Rationale: "( 1 / 10 ) * 2000 - ( 1 / 10 ) % * 2000 = 200 - ( 1 / 1000 ) * 2000 = 200 - 2 = 198 the answer is c ."
Answer: c
Problem: find the compound interest on rs . 16,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2875 , b ) 2654 , c ) 2645 , d ) 2456 , e ) 2522
Rationale: principal = rs . 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = rs . [ 16000 x ( 1 + ( 5 / 100 ) ) 3 ] = rs . 18522 . ci . = rs . ( 18522 - 16000 ) = rs . 2522 answer : e
Answer: e
Problem: a number is doubled and 9 is added . if the resultant is trebled , it becomes 51 . what is that number ?
Options: a ) 3.5 , b ) 6 , c ) 8 , d ) 7 , e ) 4
Rationale: "let the number be x . then , 3 ( 2 x + 9 ) = 51 2 x = 8 = > x = 4 answer : e"
Answer: e
Problem: a certain quantity of 40 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "original quantity = a substituted quantity = b then : ( a * 0.4 + 0.25 * b т а у 0.4 * b ) / a = 0.35 0.4 + ( b / a ) * ( - 0.15 ) = 0.35 b / a = - 0.05 / - 0.15 = 1 / 3 answer : b"
Answer: b
Problem: on the first day of her vacation , louisa traveled 250 miles . on the second day , traveling at the same average speed , she traveled 350 miles . if the 250 - mile trip took 3 hours less than the 350 - mile trip , what was the average speed , in miles per hour ?
Options: a ) 31 , b ) 33.33 , c ) 35 , d ) 37 , e ) 39.33
Rationale: "( time ) * ( rate ) = ( distance ) - - > ( rate ) = ( distance ) / ( time ) - - > given : ( rate ) = 250 / t = 350 / ( t + 3 ) - - > 5 / t = 7 / ( t + 3 ) - - > 5 t + 15 = 7 t - - - - > 2 t = 15 . t = 7.5 - - - - > ( rate ) = 250 / 7.5 = 33.33 answer : b"
Answer: b
Problem: a 90 - liter solution of cool - drink is made from 5 % jasmine water . if 6.5 liters of jasmine and 13.5 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 8 % , b ) 8.5 % , c ) 9 % , d ) 9.5 % , e ) 10 %
Rationale: "the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.05 ( 90 ) + 6.5 ) / 110 = 11 / 110 = 10 % the answer is e ."
Answer: e
Problem: if an object travels at six feet per second , how many feet does it travel in one hour ?
Options: a ) 21600 , b ) 3778 , c ) 12788 , d ) 18000 , e ) 2881
Rationale: "explanation : if an object travels at 6 feet per second it covers 6 x 60 feet in one minute , and 6 x 60 x 60 feet in one hour . answer = 21600 answer : a ) 21600"
Answer: a
Problem: 30 square stone slabs of equal size were needed to cover a floor area of 67.5 sq . m . find the length of each stone slab ?
Options: a ) 150 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 67.5 / 30 m 2 = 2.25 m 2 length of each slab √ 2.25 = 1.5 m = 150 cm"
Answer: a
Problem: machine r takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine r to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of r is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and r reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of r . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Problem: i bought two books ; for rs . 480 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) rs . 28 , b ) rs . 280 , c ) rs . 140 , d ) rs . 70 , e ) rs . 80
Rationale: x * ( 85 / 100 ) = ( 480 - x ) 119 / 100 x = 280 answer : b
Answer: b
Problem: a gardener changed the size of his rectangle shaped garden by increasing it ' s length by 40 % & decreasing is ' s width by 20 % . find area of new garden .
Options: a ) 1.04
b ) 1.12
c ) 1.24
d ) 1.4
e ) 1.5
Rationale: a 1 = l * b a 2 = ( l * 140 / 100 ) * ( b * 80 / 100 ) = 1.12 * lb so , area of garden is by 1.12 times of old area . answer : b
Answer: b
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 dennison 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 dennison 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: what is the sum of the integers from - 190 to 191 inclusive ?
Options: a ) 0 , b ) 191 , c ) 375 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 190 + 191 / 2 = 0.5 number of items ( n ) = b - a + 1 = 191 - ( - 190 ) + 1 = 195 + 191 = 382 . sum = average * n = 0.5 * 382 = 191 . answer is b"
Answer: b
Problem: 9000 + 16 2 / 3 % of ? = 10500
Options: a ) 2387 , b ) 2888 , c ) 9000 , d ) 2837 , e ) 2271
Rationale: "explanation : 9000 + 16 2 / 3 % of ? = 10500 = > 9000 + 50 / 3 % of ? = 10500 50 / ( 3 * 100 ) of ? = 1500 = > ? = 1500 * 6 ? = 9000 answer : c"
Answer: c
Problem: the ratio of the cost price and selling price is 2 : 3 . the profit percent is ?
Options: a ) 20 % , b ) 25 % , c ) 50 % , d ) 75 % , e ) 100 %
Rationale: let the c . p . = $ 2 x then s . p . = $ 3 x then , gain = 3 x - 2 x = $ x gain % = x / 2 x * 100 = 50 % answer is c
Answer: c
Problem: 10 is 6 % of a , and 6 is 10 % of b . c equals b / a . what is the value of c ?
Options: a ) 3 / 10 , b ) 6 / 17 , c ) 9 / 25 , d ) 10 / 33 , e ) 12 / 35
Rationale: "6 a / 100 = 10 a = 500 / 3 b / 10 = 6 b = 60 c = b / a = 60 * 3 / 500 = 9 / 25 the answer is c ."
Answer: c
Problem: the slant height of a cone is 12 cm and radius of the base is 4 cm , find the curved surface of the cone ?
Options: a ) 26 , b ) 28 , c ) 48 , d ) 26 , e ) 28
Rationale: "π * 12 * 4 = 48 answer : c"
Answer: c
Problem: points a , b , c , and d , in that order , lie on a line . if ab = 2 cm , ac = 5 cm , and bd = 6 cm , what is cd , in centimeters ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: putting a value to each point , lets use the following : a - 0 b - 2 ( ab = 2 ) c - 5 ( ac = 5 ) d - 8 ( bd = 6 ) cd is 8 - 5 = 3 . ans c
Answer: c
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 8 and the other one , that is cheaper , costs $ 3 . the factory holds a $ 100 worth stock of 25 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 23 , e ) 24
Rationale: "so the number of $ 3 modules must be 20 so that the leftover 5 modules are of $ 8 which will give a total value $ 100 . 20 * 3 + 5 * 8 = 60 + 40 = 100 . answer : b"
Answer: b
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 . 500 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 1000 , d ) d ) 2393 , e ) e ) 2009
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 = 500 = > x = 500 . b ' s share = rs . 2 x = 2 * 500 = rs . 1000 . answer : c"
Answer: c
Problem: due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 19.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 20 = 10 * 3 = 30 time difference = 19.1 ans : d"
Answer: d
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 11 , 0 ) , ( 0 , - 3.5 ) , ( - 11 , 0 ) ?
Options: a ) 56 , b ) 77 , c ) 112 , d ) 116 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 11 + 11 = 22 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 22 * 7 = 77 b is the answer"
Answer: b
Problem: a 21 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 210 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 21 , money invested = rs . ( 100 / 10 x 21 ) = rs . 210 . â ˆ ´ market value of rs . 100 stock = rs . 210 answer b"
Answer: b
Problem: which no . need to add to 859622 to get a no . exactly divisible by 456 ?
Options: a ) 546577 , b ) 674645 , c ) 566578 , d ) 465766 , e ) 859622
Rationale: dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e
Answer: e
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 4 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 864 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 4 ( 9 horizontal dots and 4 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 4 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 3 c 1 , ( 4 - 1 = 3 as 1 vertical dot is already occupied by a ) . 9 c 1 * 4 c 1 * 8 c 1 * 3 c 1 = 864 . answer : c ."
Answer: c
Problem: at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 135 male associates , how many female managers are there ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "well , first let ’ s take care of the “ totals ” . the numbers in the “ totals ” row must add up . if 90 are females , the other 250 – 90 = 160 must be males . similarly , the numbers in the “ totals ” column must add up . if 40 are managers , then the other 250 – 40 = 210 must be associates . now , in the “ associate ” row , 135 + e = 210 , which means e = 75 — the other 75 associates must be female . now , to find b , which is what the question is asking , we need only look at the sum in the “ female ” column : b + 75 = 90 , which means b = 15 . there are fifteen female managers in this company . thus , the answer = ( a ) ."
Answer: a
Problem: a sum of money amounts to rs . 9800 after 5 years and rs . 12005 after 8 years at the same rate of simple interest . the rate of interest per annum is
Options: a ) 15 % , b ) 12 % , c ) 8 % , d ) 7 % , e ) 5 %
Rationale: "explanation : simple interest for 3 years = ( rs . 12005 - rs . 9800 ) = rs . 2205 simple interest for 5 years = 22053 × 5 = rs . 3675 principal ( p ) = ( rs . 9800 - rs . 3675 ) = rs . 6125 r = 100 × si / pt = 100 × 3675 / 6125 × 5 = 12 % answer : option b"
Answer: b
Problem: if 3 / p = 5 & 3 / q = 15 then p - q = ?
Options: a ) 5 / 24 , b ) 6 / 24 , c ) 2 / 15 , d ) 8 / 24 , e ) 9 / 24
Rationale: "p = 3 / 5 , q = 3 / 15 = > q = 1 / 5 therefore p - q = ( 3 / 5 ) - ( 1 / 5 ) = 2 / 15 answer : c"
Answer: c
Problem: a invested some money in 8 % stock at 96 . if b wants to invest in an equally good 10 % stock , he must purchase a stock worth of :
Options: a ) rs . 120 , b ) rs . 60 , c ) rs . 128 , d ) rs . 130 , e ) rs . 140
Rationale: "solution for an income of rs . 8 , investment = rs . 96 . for an income of rs . 10 , investment = rs . ( 96 / 8 x 10 ) = rs . 120 answer a"
Answer: a
Problem: how many digits 2 ^ 400 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 121
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 100 = ( 1.024 ) ^ 10 * 10 ^ 120 therefore 121 digits would be my best guess e"
Answer: e
Problem: a committee is reviewing a total of 40 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 ) 20 / 11 , b ) 16 / 11 , c ) 17 / 11 , d ) 10 / 11 , e ) 19 / 11
Rationale: "say x = y = 10 . in this case we would have : 40 x = 200 black - and - white films ; 4 y = 40 color films . y / x % = 10 / 10 % = 1 % of the black - and - white films , so 4 black - and - white films and all 40 color films , thus total of 44 films were selected . color films thus compose 40 / 44 = 10 / 11 of the selected films . answer : d"
Answer: d
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 8 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 6 / 25 , b ) 5 / 16 , c ) 4 / 9 , d ) 3 / 7 , e ) 2 / 5
Rationale: let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 8 ( 1 - x ) p 12 xp = 8 p - 8 xp 20 xp = 8 p x = 2 / 5 the answer is e .
Answer: e
Problem: if x is equal to the sum of the integers from 50 to 70 , inclusive , and y is the number of even integers from 50 to 70 , inclusive , what is the value of x + y ?
Options: a ) 1211 , b ) 1231 , c ) 1251 , d ) 1271 , e ) 1291
Rationale: "x = 50 + 51 + . . . + 70 = 21 ( 60 ) = 1260 y = 11 x + y = 1271 the answer is d ."
Answer: d
Problem: 12 times a positive integer is more than its square by 36 , then the positive integer is
Options: a ) 6 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 12 x = x 2 + 36 = > x 2 - 12 x + 36 = 0 = > ( x - 6 ) ( x - 6 ) = 0 = > x = 6 answer : a"
Answer: a
Problem: renu can do a piece of work in 8 days , but with the help of her friend suma , she can do it in 4 days . in what time suma can do it alone ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 15 , e ) 17
Rationale: "renu â € ™ s one day â € ™ s work = 1 / 8 suma â € ™ s one day â € ™ s work = 1 / 4 - 1 / 8 = 1 / 8 suma can do it alone in 8 days . answer : a"
Answer: a
Problem: 90 percent of the members of a study group are women , and 60 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.34 , b ) 0.44 , c ) 0.54 , d ) 0.64 , e ) 0.74
Rationale: "say there are 100 people in that group , then there would be 0.9 * 0.60 * 100 = 54 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 54 / 100 . answer : c"
Answer: c
Problem: a train covers a distance of 12 km in 10 min . if it takes 12 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 298 m , b ) 188 m , c ) 240 m , d ) 178 m , e ) 189 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 12 = 240 m . answer : c"
Answer: c
Problem: a new home buyer pays 4 % annual interest on her first mortgage and 9 % annual interest on her second mortgage . if she borrowed a total of $ 310000 , 80 % of which was in the first mortgage , what is her approximate monthly interest payment ?
Options: a ) $ 1,292 , b ) $ 1,733 , c ) $ 3,466 , d ) $ 12,917 , e ) $ 20,796
Rationale: 0.04 x + 0.09 y = 310000 [ 1 ] 0.04 x = 0.80 * 310000 = 248000 [ 2 ] 248000 + 0.09 y = 310000 - - > 0.09 y = 62000 [ 3 ] 248000 / 12 = 258333.3333 [ 4 ] 62000 / 12 = 5166.67 [ 5 ] adding [ 4,5 ] we get : 25833 [ 6 ] dividing [ 6 ] / 2 to get an average we get 1.292 , ans a
Answer: a
Problem: x and y started a business by investing rs . 5000 / - and rs . 15000 / - respectively . find the x ’ s share out of a total profit of rs . 1600 :
Options: a ) 200 , b ) 250 , c ) 300 , d ) 350 , e ) 400
Rationale: x = rs . 5000 / - y = rs . 15000 / - x share 1 part & y share 3 parts total 4 parts - - - - - > rs . 1600 / - - - - - > 1 part - - - - - - - > rs . 400 / - x share = 1 part - - - - - > rs . 400 / - e
Answer: e
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 48 / r years . if pat ' s parents invested $ 5,000 in a long - term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 48 / r years , then for r = 8 it ' ll double in 48 / 8 = ~ 6 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 3 = $ 15,000 . answer : b ."
Answer: b
Problem: how many multiples of 7 are there between 9 and 89 , 9 and 89 inclusive ?
Options: a ) 11 , b ) 17 , c ) 16 , d ) 13 , e ) 12
Rationale: "7 multiples are . . . 14 , 21,28 , 35,42 , 49,56 , 63,70 , 77,84 , . . . , . . . , the answer is = 11 answer is a"
Answer: a
Problem: 5 men are equal to as many women as are equal to 7 boys . all of them earn rs . 90 only . men ’ s wages are ?
Options: a ) 8 rs . , b ) 7 rs . , c ) 6 rs . , d ) 4 rs . , e ) 5 rs .
Rationale: 5 m = xw = 7 b 5 m + xw + 7 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs . answer : c
Answer: c
Problem: when positive integer n is divided by 4 , the remainder is 2 . when n is divided by 7 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 3 . . c"
Answer: c
Problem: the area of a triangle is with base 8.4 m and height 5.8 m ?
Options: a ) 11.36 m 2 , b ) 10.36 m 2 , c ) 18.36 m 2 , d ) 19.36 m 2 , e ) 24.36 m 2
Rationale: "1 / 2 * 8.4 * 5.8 = 24.36 m 2 answer : e"
Answer: e
Problem: if p ( a ) = 8 / 15 , p ( b ) = 4 / 15 , and p ( a â ˆ ª b ) = 16 / 15 find p ( b | a )
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 2 , d ) 2 , e ) 4 / 7
Rationale: "p ( b | a ) = p ( a â ˆ ª b ) / p ( a ) p ( b | a ) = ( 16 / 15 ) / ( 8 / 15 ) = 2 . d"
Answer: d
Problem: the speed of a car is 90 km in the first hour and 42 km in the second hour . what is the average speed of the car ?
Options: a ) 89 kmph , b ) 92 kmph , c ) 75 kmph , d ) 65 kmph , e ) 66 kmph
Rationale: "s = ( 90 + 42 ) / 2 = 66 kmph e"
Answer: e
Problem: if the sum of the first n positive integers is s , what is the sum of the first n positive integers divisible by 4 , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 4 s
Rationale: "answer is e given sum of 1 2 3 . . . . . n = s sum of 4 , 8 , 12 . . . . 2 n = 4 [ sum ( 1 2 3 . . . . n ) ] = 4 s"
Answer: e
Problem: in how many ways can the integer 48 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "method 1 : listing all multiples since given number is small 48 = 1 * 48 , 2 * 24 , 3 * 16 , 4 * 12 , 6 * 8 = > 5 ways method 2 : express given number as prime factors 48 = 6 * 8 = 2 * 3 * 2 ^ 3 = 2 ^ 4 * 3 total number of factors = ( 4 + 1 ) ( 1 + 1 ) = 5 * 2 = 10 since the given number is not a perfect square , there will be exact 5 pairs possible of the given 10 factors = > 5 ways option c"
Answer: c
Problem: if w is 40 percent less than x , x is 40 percent less than y , and z is 46 percent less than y , then z is greater than w by what percent of w ?
Options: a ) 4 % , b ) 18 % , c ) 36 % , d ) 40 % , e ) 50 %
Rationale: given w = 0.6 x , x = 0.6 y , z = 0.54 y , substituting , w = 2 / 3 z - - - - > z = 1.5 w and thus z is 50 % greater than w . e is the correct answer .
Answer: e
Problem: a boatman goes 2 km against the current of the stream in 2 hour and goes 1 km along the current in 20 minutes . how long will it take to go 5 km in stationary water ?
Options: a ) 2 hr 30 min , b ) 2 hr , c ) 4 hr , d ) 1 hr 15 min , e ) none of these
Rationale: "explanation : speed upstream = 2 / 2 = 1 km / hr speed downstream = 1 / ( ( 20 / 60 ) ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 5 km in still water = 5 / 2 = 2 ( 1 / 2 ) hours = 2 hour 30 minutes . answer : option a"
Answer: a
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 5 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 10210 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 5 = rs 10210 answer : c"
Answer: c
Problem: pencils , pens and exercise books in a shop are in the ratio of 14 : 4 : 3 . if there are 140 pencils , the number of exercise books in the shop is :
Options: a ) 30 , b ) 27 , c ) 35 , d ) 33 , e ) 37
Rationale: explanation : let pencils = 14 x , pens = 4 x & exercise books = 3 x . now , 14 x = 140 hence x = 10 number of exercise books = 3 x = 30 answer : a
Answer: a
Problem: a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 16 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 280 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 16 * 20 = 320 = length of train length of platform = 600 - 320 = 280 answer : c"
Answer: c
Problem: in a quiz the points in each round for the first , second , third and fourth position were 10050 , 2010 . no other points were given . rachel participated in several rounds in the competition and the product of her score was 10000 . in how many rounds did she participate ?
Options: a ) 2 , b ) can not be determined , c ) 4 , d ) 6 , e ) 10
Rationale: correct answer is b because we are given that there wo n ' t be any points awarded for rounds other than 1 st four position . thus , it may happen that she played 150 rounds out of only 8 rounds were there in which she was awarded some points .
Answer: b
Problem: how many positive integers less than 50 have a reminder 2 when divided by 7 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "take the multiples of 7 and add 2 0 x 7 + 2 = 2 . . . . 6 x 7 + 2 = 44 there are 7 numbers answer e"
Answer: e
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 8 m long . if the area of the pond is 1 / 2 of the area of the field . what is the length of the field ?
Options: a ) 13 , b ) 16 , c ) 34 , d ) 43 , e ) 42
Rationale: "explanation : a / 2 = 8 * 8 = > a = 8 * 8 * 2 x * 2 x = 8 * 8 * 2 x = 8 = > 2 x = 16 answer : option b"
Answer: b
Problem: how many three digit numbers n are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well n - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Problem: in one hour , a boat goes 11 km along the stream and 5 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 kmph . answer c"
Answer: c
Problem: arnold and danny are two twin brothers that are celebrating their birthday . the product of their ages today is smaller by 5 from the product of their ages a year from today . what is their age today ?
Options: a ) 2 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 9 .
Rationale: "ad = ( a + 1 ) ( d + 1 ) - 5 0 = a + d - 4 a + d = 4 a = d ( as they are twin brothers ) a = d = 2 a is the answer"
Answer: a
Problem: a and b go around a circular track of length 900 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 186 sec , d ) 180 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 900 / ( 36 * 5 / 18 ) , 900 / ( 54 * 5 / 18 ) } = lcm ( 90 , 60 ) = 180 sec . answer : d"
Answer: d
Problem: working together , jose and jane can complete an assigned task in 12 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 48 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 12 12 ( x + y ) = xy next , we ' re told 1 job takes 48 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 48 x + y = 96 so xy = 1152 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 36 days for jose and 32 days for jane . answer : e
Answer: e
Problem: one fourth of one third of two fifth of a number is 15 . what will be the 40 % of that number is ?
Options: a ) 120 , b ) 130 , c ) 150 , d ) 180 , e ) 250
Rationale: "( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 15 then x = 15 * 30 = 450 40 % of 450 = 180 answer d"
Answer: d
Problem: the ages of ashley and mary are in the ratio 4 : 7 . the sum of their ages is 22 . find the ages of ashley .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: a : m = 4 : 7 let the ages of a & m be x & 22 - x x / 22 - x = 4 / 7 x = 8 a = 8 yrs answer : b
Answer: b
Problem: two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 180 meters , after what time will they meet at the starting point ?
Options: a ) 20 sec , b ) 12 sec , c ) 30 sec , d ) 50 sec , e ) 1 min
Rationale: "they meet every 180 / 7 + 8 = 12 sec answer is b"
Answer: b