regisss/math_qa huggingface dataset:
Problem: find two integers , neither of which ends in a zero , and whose product is exactly 1 , 000,000
Options: a ) 64 and 15,625 , b ) 60 and 15,625 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625
Rationale: "1 , 000,000 = 10 ^ 6 = 10 x 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 6 ) x ( 5 ^ 6 ) = 64 x 15625 so the numbers are 64 and 15,625 answer : a"
Answer: a
Problem: the average of 17 numbers is 59 . average of the first 9 of them is 56 and that of the last 9 is 63 . find the 9 th number ?
Options: a ) 64 , b ) 68 , c ) 65 , d ) 66 , e ) 67
Rationale: sum of all the 17 numbers = 17 * 59 = 1,003 sum of the first 9 of them = 9 * 56 = 504 sum of the last 9 of them = 9 * 63 = 567 so , the 8 th number = 504 + 567 - 1,003 = 68 . answer : b
Answer: b
Problem: a boat can travel with a speed of 24 km / hr in still water . if the speed of the stream is 4 km / hr , find the time taken by the boat to go 56 km downstream
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: "explanation : speed of the boat in still water = 24 km / hr speed of the stream = 4 km / hr speed downstream = ( 22 + 5 ) = 28 km / hr distance travelled downstream = 56 km time taken = distance / speed = 56 / 28 = 2 hours answer : option a"
Answer: a
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 10,000 loan he has taken . the bank charges him a quarterly compound rate of 7 % . what is the approximate interest he pays annually ?
Options: a ) 1000 , b ) 1500 , c ) 3000 , d ) 2500 , e ) 2400
Rationale: "an easy way too attempt this is by approximation : for the first quarter , he pays 7 % of 10,000 which is $ 700 . so for the four quarters in the year , he will approximately play 700 * 4 = 2800 over the entire year . because of compound interest it will be more than 2800 . approx . option c is correct . answer : c"
Answer: c
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) rs . 450 , b ) rs . 600 , c ) rs . 800 , d ) rs . 375 , e ) rs . 400
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 24 . a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . c ' s share ( for 3 days ) = rs . ( 3 x 1 / 24 x 3200 ) = rs . 400 . correct option ` ` e ' ' ."
Answer: e
Problem: 1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 9 / 13 , e ) 0
Rationale: "1 / 2 - [ ( 2 / 5 * 5 / 32 ) + 1 ] + 9 / 16 = 1 / 2 - [ ( 1 / 16 ) + 1 ] + 9 / 16 = 1 / 2 - [ 17 / 16 ] + 9 / 16 = 8 / 16 - 17 / 16 + 9 / 16 = 0 the answer is e ."
Answer: e
Problem: mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 20 candidates . she plans to have one working interview with 3 of the 20 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
Options: a ) 520 , b ) 120 , c ) 300 , d ) 30 , e ) 333
Rationale: 520 . answer a
Answer: a
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm . what is the perimeter of the square ?
Options: a ) 802 , b ) 800 , c ) 829 , d ) 389 , e ) 245
Rationale: "area of the square = s * s = 5 ( 125 * 64 ) = > s = 25 * 8 = 200 cm perimeter of the square = 4 * 200 = 800 cm . answer : b"
Answer: b
Problem: when positive integer x is divided by 10 , the quotient is y and the remainder is 3 . when 2 x is divided by 7 , the quotient is 3 y and the remainder is 1 . what is the value of 11 y – x ?
Options: a ) 2 , b ) - 2 , c ) 3 , d ) - 3 , e ) 4
Rationale: "( 1 ) x = 10 y + 3 ( 2 ) 2 x = 21 y + 1 ( 2 ) - ( 1 ) : x = 11 y - 2 11 y - x = 2 the answer is a ."
Answer: a
Problem: at an upscale fast - food restaurant , shin can buy 3 burgers , 7 shakes , and one cola for $ 120 . at the same place it would cost $ 160.50 for 4 burgers , 10 shakes , and one cola . how much would it cost for a meal of one burger , one shake , and one cola ?
Options: a ) $ 21 , b ) $ 27 , c ) $ 31 , d ) $ 39 , e ) it can not be determined
Rationale: "let ' s suppose that the price of a burger is bb , of a shake - ss and that of a cola is cc . we can then construct these equations : 3 b + 7 s + c = 120 4 b + 10 s + c = 160.5 subtracting the first equation from the second gives us b + 3 s = 40.5 now if we subtract the new equation two times from first or 3 times from second we will get b + s + c = 39 . in any case , there is no necessity to know each item ' s price , just the sum . answer : d"
Answer: d
Problem: if 300 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 75 , b ) 74 , c ) 79 , d ) 77 , e ) 72
Rationale: "the question actually asks the highest power of 10 which divides 300 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 300 factorial will have 74 as - 300 / 5 = 60 60 / 5 = 12 12 / 5 = 2 so answer will be ( d ) 74"
Answer: d
Problem: 15.06 * 0.0001 = ?
Options: a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 0.1506 , e ) none of these
Rationale: "explanation : clearly after decimal 6 digits should be there . option b"
Answer: b
Problem: addison high school ’ s senior class has 200 boys and 160 girls . if 60 % of the boys and 75 % of the girls attended college , what percentage of the total class that did not attend college ?
Options: a ) 33.33 , b ) 60 , c ) 80 , d ) 66.67 , e ) 64
Rationale: "number of boys attending the college : 0.60 * 200 = 120 number of girls attending the college : 0.75 * 160 = 120 total attending = 120 + 120 = 240 total people = 200 + 160 = 360 % of people attending = 240 / 360 = 66.67 % . d is the correct answer"
Answer: d
Problem: find the fraction which has the same ratio to 1 / 13 that 5 / 34 has to 7 / 48 .
Options: a ) 110 / 1547 , b ) 120 / 1547 , c ) 140 / 1547 , d ) 160 / 1547 , e ) 220 / 1547
Rationale: p : 1 / 13 = 5 / 34 : 7 / 48 as the product of the means is equal to the product of the extremes . p * 7 / 48 = 1 / 13 * 5 / 34 p * 7 / 48 = 5 / 442 p = 240 / 3094 = > p = 120 / 1547 answer : b
Answer: b
Problem: two numbers are such that the square of one is 224 less than 8 times the square of the other . if the numbers be in the ratio of 3 : 4 , the numbers are
Options: a ) 6 , 8 , b ) 9 , 12 , c ) 12 , 16 , d ) 16 , 20 , e ) none
Rationale: solution let the numbers be 3 x and 4 x . then , ( 4 x ) 2 = 8 x ( 3 x ) 2 - 224 ‹ = › 16 x 2 = 72 x 2 - 224 ‹ = › 56 x 2 = 224 . ‹ = › x 2 = 4 . ‹ = › x = 2 . so , the numbers are 6 and 8 . answer a
Answer: a
Problem: a and b invests rs . 3500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 21 : 5 , b ) 21 : 16 , c ) 21 : 2 , d ) 9 : 9 , e ) 21 : 11
Rationale: "( 3.5 * 6 + 7 * 6 ) : ( 4 * 12 ) 63 : 48 = > 21 : 16 answer : b"
Answer: b
Problem: a searchlight on top of the watchtower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 5 / 6 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 5
Rationale: "the searchlight completes one revolution every 30 seconds . the probability that the man ' s area will be lit up is 10 / 30 = 1 / 3 . the probability that he will stay in the dark is 1 - 1 / 3 = 2 / 3 the answer is c ."
Answer: c
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 4 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 7 / 15 , b ) 9 / 20 , c ) 11 / 25 , d ) 13 / 27 , e ) 15 / 31
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 3 / 4 ) = 4 / 9 hours peter worked for 13 / 9 hours so he painted 13 / 9 * 1 / 3 = 13 / 27 of the room . the answer is d ."
Answer: d
Problem: the distance from city a to city b is 30 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 88 , c ) 120 , d ) 152 , e ) 154
Rationale: "the time it takes bob to drive to city b is 30 / 40 = 0.75 hours . alice needs to take less than 0.25 hours for the trip . alice needs to exceed a constant speed of 30 / 0.25 = 120 miles per hour . the answer is c ."
Answer: c
Problem: if x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year , the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $ 83 . if $ 2,000 is the total amount invested , how much is invested at 8 percent ?
Options: a ) $ 550 , b ) $ 650 , c ) $ 750 , d ) $ 850 , e ) $ 950
Rationale: "0.1 x = 0.08 ( 2000 - x ) + 83 0.18 x = 243 x = 1350 then the amount invested at 8 % is $ 2000 - $ 1350 = $ 650 the answer is b ."
Answer: b
Problem: line q has the equation 5 y – 3 x = 90 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 58 , b ) 61 , c ) 64 , d ) 67 , e ) 70
Rationale: 5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d .
Answer: d
Problem: the ratio of expenditure and savings is 3 : 2 . if the income increases by 15 % and the savings increases by 6 % , then by how much percent should his expenditure increases ?
Options: a ) 22 , b ) 21 , c ) 88 , d ) 76 , e ) 29
Rationale: answer : b ) 21
Answer: b
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 160 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 750 , b ) 400 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 160 ( 40 * 4 = 160 ) 100 % - - - - - > 400 ( 100 * 4 = 400 ) answer : option b"
Answer: b
Problem: the sum of three consecutive even numbers is 48 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 24 , e ) 64
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 48 6 p = 48 = > p = 8 . the middle number is : 8 p = 64 . answer : e"
Answer: e
Problem: there are 8 stores in town that had a total of 24 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 9 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "9 people visited 2 stores each for 18 visits . to maximize the number of stores that one person visited , let ' s assume that 2 people visited 1 store each . the number of remaining visits is 24 - 18 - 2 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Problem: if a train , travelling at a speed of 80 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 110.111 m , b ) 121.111 m , c ) 111.11 m , d ) 141.111 m , e ) 181.111 m
Rationale: "d = 80 * 5 / 18 * 5 = 111.11 m answer : c"
Answer: c
Problem: in how many ways can the integer 120 be expressed as a product of two different positive integers ?
Options: a ) 10 , b ) 8 , c ) 5 , d ) 4 , e ) 2
Rationale: "120 = ( 2 ^ 3 ) * 3 * 5 since 120 is not a perfect square , no of ways = 5 answer c"
Answer: c
Problem: a fruit - salad mixture consists of apples , peaches , and grapes in the ratio 4 : 5 : 2 , respectively , by weight . if 44 pounds of the mixture is prepared , the mixture includes how many more pounds of apples than grapes ?
Options: a ) 15 , b ) 12 , c ) 8 , d ) 6 , e ) 4
Rationale: "we can first set up our ratio using variable multipliers . we are given that a fruit - salad mixture consists of apples , peaches , and grapes , in the ratio of 4 : 5 : 2 , respectively , by weight . thus , we can say : apples : peaches : grapes = 4 x : 5 x : 2 x we are given that 39 pounds of the mixture is prepared so we can set up the following question and determine a value for x : 4 x + 5 x + 2 x = 44 11 x = 44 x = 4 now we can determine the number of pounds of apples and of grapes . pounds of grapes = ( 2 ) ( 4 ) = 8 pounds of apples = ( 4 ) ( 4 ) = 16 thus we know that there are 16 – 8 = 8 more pounds of apples than grapes . answer is c ."
Answer: c
Problem: if an integer n is to be selected at random from 1 to 99 , inclusive , what is probability n ( n + 1 ) will be divisible by 3 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 3 , either n or n + 1 has to be a multiple of 3 . thus n must be of the form 3 k or 3 k - 1 , but not 3 k + 1 . the probability is 2 / 3 . the answer is d ."
Answer: d
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3267 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 10 , c ) 28 , d ) 24 , e ) 35
Rationale: "explanation : 2420 - - - 847 100 - - - ? = > 35 % answer : option e"
Answer: e
Problem: workers in a factory store products inside two different sized boxes . the bigger of the boxes can store 50 products while the smaller box can store 40 products . if a fresh batch of products numbering 212 in total were to be stored , what is the least number of products that will not be boxed ?
Options: a ) 23 , b ) 11 , c ) 2 , d ) 10 , e ) 12
Rationale: total products to be stored 212 the big box can store 50 small box can store 40 storing 212 products in big box 212 / 50 = 4 r 12 least number of toys that will be left unboxed = 12 answer : e
Answer: e
Problem: a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes william can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Problem: in a hostel , the number of students decreased by 5 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 12.3 % , c ) 25 % , d ) 40 % , e ) 9.4 %
Rationale: cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 5 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.95 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.95 * 1.2 ) = > f ( new ) = 0.877 f therefore the new cost of food must be 87.7 % of the old cost , or the cost of food must decrease by 12.28 % ( optionb )
Answer: b
Problem: at 15 : 00 there were 21 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 8 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 27 d
Answer: d
Problem: a boy wants to make cuboids of dimension 5 m , 6 m and 7 m from small cubes of . 03 m 3 . later he realized he can make same cuboids by making it hollow . then it takes some cubes less . what is the number of the cubes to be removed ?
Options: a ) 1000
b ) 2000
c ) 3000
d ) 4000
e ) 5000
Rationale: volume of the small cube = 0.03 m ^ 3 so side of this cube = cubic root of 0.03 m ^ 3 = . 312 m so after removing the outermost layer the dimensions for the inner cuboid will be ( 5 - 2 * 0.312 ) , ( 6 - 2 * 0.312 ) , ( 7 - 2 * 0.312 ) so total volume will be ( 4.376 ) * ( 5.376 ) * ( 6.376 ) = 150 m ^ 3 so no of cubes will be 150 / 0.03 = 5000 so we can remove 5000 inner cubes answer : e
Answer: e
Problem: if a speaks the truth 70 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.42 , e ) 0.411
Rationale: "explanation : probability that a speaks truth is 70 / 100 = 0.7 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.7 × 0.6 = 0.42 answer : d"
Answer: d
Problem: find the curved surface area , if the radius of a cone is 21 m and slant height is 15 m ?
Options: a ) 660
b ) 770
c ) 880
d ) 900
e ) 990
Rationale: cone curved surface area = ï € rl 22 / 7 ã — 21 ã — 15 = 66 ã — 15 = 990 m ( power 2 ) answer is e .
Answer: e
Problem: of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 130 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 280 , b ) 400 , c ) 540 , d ) 650 , e ) 840
Rationale: "of the goose eggs laid at a certain pond , 2 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month : 2 / 3 * 3 / 4 = 1 / 2 survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year : ( 1 - 3 / 5 ) * 1 / 2 = 1 / 5 survived the first year . 130 geese survived the first year : 1 / 5 * ( total ) = 130 - - > ( total ) = 650 . answer : d ."
Answer: d
Problem: a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 22 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 190 , c ) 276 , d ) 270 , e ) 281
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 22 sec . let the length of the train be x meters . then , ( x + 250 ) / 22 = 20 x = 190 m . answer : b"
Answer: b
Problem: john was thrice as old as tom 6 years ago . john will be 9 / 7 times as old as tom in 6 years . how old is tom today ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "j - 6 = 3 ( t - 6 ) , so j = 3 t - 12 j + 6 = 9 / 7 * ( t + 6 ) 7 j + 42 = 9 t + 54 7 ( 3 t - 12 ) + 42 = 9 t + 54 12 t = 96 t = 8 the answer is b ."
Answer: b
Problem: how many integers from 0 to 48 , 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 , . . . . . 46 , 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 , 46 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 45 or , n - 1 = 15 or , n = 16 b"
Answer: b
Problem: what is the prime factors ’ number of 36 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 2 * 3 ^ 2 prime factors ’ number will be 2 + 2 = 4 . hence , answer is c ."
Answer: c
Problem: how much time will a train of length 250 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 55 , b ) 99 , c ) 88 , d ) 76 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 250 + 300 = 550 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 550 / 10 = 55 sec . answer : a"
Answer: a
Problem: for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 20 , then v =
Options: a ) 36 , b ) 39 , c ) 42 , d ) 45 , e ) 48
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 20 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 45 the answer is d ."
Answer: d
Problem: ( 4300231 ) - ? = 2535618
Options: a ) 1865113 , b ) 1775123 , c ) 1764613 , d ) 1675123 , e ) none of them
Rationale: "let 4300231 - x = 2535618 then x = 4300231 - 2535618 = 1764613 answer is c"
Answer: c
Problem: the difference of 2 digit no . & the no . obtained by interchanging the digits is 36 . what is the difference the sum and the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 13
Rationale: let the number be xy . given xy – yx = 36 . this means the number is greater is than the number got on reversing the digits . this shows that the ten ’ s digit x > unit digit y . also given ratio between digits is 1 : 2 = > x = 2 y ( 10 x + y ) – ( 10 y + x ) = 36 = > x – y = 4 = > 2 y – y = 4 . hence , ( x + y ) – ( x – y ) = 3 y – y = 2 y = 8 b
Answer: b
Problem: the average of 5 numbers is calculated as 15 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 12.5 , b ) 26.2 , c ) 6.5 , d ) 7.5 , e ) 12
Rationale: "5 * 15 + 36 – 26 = 75 / 10 = 7.5 answer : d"
Answer: d
Problem: the length of a rectangle is reduced by 10 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 10 % , b ) 11.1 % , c ) 25 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 10 * 100 ) / ( 100 - 10 ) = 11.1 % b"
Answer: b
Problem: rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
Options: a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 1500 , e ) s 1550
Rationale: "explanation : average rate = ( 144 / 3500 ) * 100 = 4.11 ratio = 8.85 : 11.14 so , first part = ( 8.85 / 20 ) * 3500 = rs 1550 . answer : e"
Answer: e
Problem: a train 110 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 4 sec , d ) 2 sec , e ) 9 sec
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 110 * 3 / 55 = 6 sec . answer : b"
Answer: b
Problem: what is the sum of all 4 digit integers formed using the digits 2 , 3 , 4 and 5 ( repetition is allowed )
Options: a ) 444440 , b ) 610000 , c ) 666640 , d ) 995456 , e ) 880000
Rationale: n = 4 * 4 * 4 * 4 = 256 < x > = ( 5555 + 2222 ) / 2 = 3888.5 sum = number of integers x average value n * < x > = 256 * 3888.5 = 711040 answer = d
Answer: d
Problem: length of a rectangular plot is 10 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 ) 55 m , b ) 60 m , c ) 80 m , d ) 82 m , e ) 84 m
Rationale: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m a"
Answer: a
Problem: what is the diagonal of a square field whose perimeter is 24 m ?
Options: a ) 8 m
b ) 2 m
c ) 7 m
d ) 10 m
e ) 6 √ 2 m
Rationale: sol : let the side of the square be x meters . therefore , 4 x = 24 x = 6 diagonal of the square is = √ 2 * ( 6 ) ^ 2 = 6 √ 2 answer : e
Answer: e
Problem: due to construction , the speed limit along an 5 - mile section of highway is reduced from 55 miles per hour to 35 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 ) 3.12 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 55 = 5 * 12 / 11 = 5.45 new time in minutes to cross 5 miles stretch = 5 * 60 / 35 = 5 * 12 / 7 = 8.57 time difference = 3.12 ans : a"
Answer: a
Problem: the average age of an adult class is 40 years . 2 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was the original strength of class ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 2 , e ) 22
Rationale: "let original strength = y then , 40 y + 2 x 32 = ( y + 2 ) x 36 â ‡ ’ 40 y + 64 = 36 y + 72 â ‡ ’ 4 y = 8 â ˆ ´ y = 2 d"
Answer: d
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 16 hours and 9 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 5 , b ) 4 : 3 , c ) 4 : 4 , d ) 4 : 9 , e ) 3 : 4
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 9 : √ 16 = 3 : 4 answer : e"
Answer: e
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr , 5 km / hr . and takes a total time of 47 minutes . find the total distance ?
Options: a ) 3 , b ) 2 , c ) 5 , d ) 4 , e ) 6
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 4 ) + ( x / 5 ) = 47 / 60 x = 1 total distance = 3 * 1 = 3 km correct option is a"
Answer: a
Problem: the product of a and b is equal to 11 more than twice the sum of a and b . if b = 5 , what is the value of b - a ?
Options: a ) - 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 11 + 2 ( a + b ) 5 a = 11 + 2 a + 10 3 a = 21 a = 7 b - a = 5 - 7 = - 2 a is the answer"
Answer: a
Problem: in town x , 64 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "let population be 100 total employed people = 64 % of the population = 64 employed males = 48 % of the population = 48 employed females = 16 % of the population = 16 employed females % in terms of employed people = ( 16 / 64 ) * 100 = 25 % answer is b ."
Answer: b
Problem: if s is a positive integer , and if the units ' digit of s ^ 2 is 4 and the units ' digit of ( s + 1 ) ^ 2 is 1 , what is the units ' digit of ( s + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: a for me . _ 1 ² = _ 1 _ 2 ² = _ 4 _ 3 ² = _ 9 _ 4 ² = _ 6 _ 5 ² = _ 5 _ 6 ² = _ 6 _ 7 ² = _ 9 _ 8 ² = _ 4 _ 9 ² = _ 1 _ 0 ² = _ 0 on the list , the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _ 8 . so , s = _ 8 , that has square 4 . the next square is 1 andnext nextsquare is 0 .
Answer: a
Problem: in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "make a venn diagram , and enter your data . let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10 + 25 = 35 answer b"
Answer: b
Problem: the arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.0 - 2 * 1.5 = 11 . answer : b ."
Answer: b
Problem: if a * b denotes the greatest common divisor of a and b , then ( ( 16 * 20 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: the greatest common divisor of 16 and 20 is 4 . hence 16 * 20 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 16 * 20 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e .
Answer: e
Problem: the average weight of a group of boys is 30 kg . after a boy of weight 39 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 39 kg joins the group , total weight of boys = 30 x + 39 so 30 x + 39 = 31 ( x + 1 ) = > x = 8 . answer : b"
Answer: b
Problem: by selling a book for 260 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 216 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 260 × 100 / 120 = 216 option ' b '"
Answer: b
Problem: a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 12 seconds to pass him . if the goods train is 300 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 30 kmph , e ) 34 kmph
Rationale: "explanation : relative speed = 300 / 12 m / sec = ( ( 300 / 12 ) × ( 18 / 5 ) ) kmph = 90 kmph . speed of goods train = ( 90 - 60 ) kmph = 30 kmph answer : option d"
Answer: d
Problem: solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 65 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "65 % is 15 % - points below 80 % and 10 % - points above 55 % . so the ratio of solution p to solution q is 2 : 3 . mixture p is 2 / 5 = 40 % of the volume of mixture pq . the answer is b ."
Answer: b
Problem: in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 12 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 26 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 12 * 2 = 36 . to maximize the number of books borrowed by 1 student , let ' s assume that 13 students borrowed 3 books and 1 student borrowed the rest . 80 - 36 - 3 * 13 = 5 the maximum number of books borrowed by any student is 5 . the answer is c ."
Answer: c
Problem: shop offered 40 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 933 , e ) 750
Rationale: "sp * ( 60 / 100 ) = 560 sp = 9.33 * 100 = > cp = 933 answer : d"
Answer: d
Problem: the average score of a cricketer for 12 matches is 48 runs . if the average for first 8 matches is 40 , then average for last 4 matches is
Options: a ) 33.25 , b ) 89 , c ) 64 , d ) 68 , e ) 90
Rationale: explanation : = ( 48 × 12 ) − ( 40 × 8 ) / 4 = ( 576 − 320 ) / 4 = 64 answer : option c
Answer: c
Problem: the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?
Options: a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a
Answer: a
Problem: a candidate got 35 % of the votes polled and he lost to his rival by 2340 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 7800 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2340 100 % - - - - - - - - - ? = > 7800 answer : d"
Answer: d
Problem: a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 25,000 earned at the end of 2 years from the startingof the business ?
Options: a ) rs . 5,000 , b ) rs . 5,500 , c ) rs . 5,700 , d ) rs . 6,500 , e ) rs . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 25000 x 3 / 10 = rs . 7,500 . e"
Answer: e
Problem: in a box of 12 pens , a total of 4 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 33 , c ) 14 / 33 , d ) 9 / 16 , e ) 3 / 44
Rationale: "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) [ 11 pen remaining with 8 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) = 14 / 33 answer : option c"
Answer: c
Problem: a bowl was filled with 10 ounces of water , and 0.007 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 ) 4 % , e ) 3.5 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 007 * 50 = . 007 * 100 / 2 = . 7 / 2 = . 35 percent of the original amount of water evaporated during this period = ( . 35 / 10 ) * 100 % = 3.5 % answer e"
Answer: e
Problem: the price of a certain painting increased by 30 % during the first year and decreased by 20 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 104 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.20 = 130 * 0.80 = 104 hence required answer = ( 104 / 100 ) * 100 % = 104 % answer is e ."
Answer: e
Problem: the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ra ɵ o less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : let x is subtracted . then , ( 6 − x ) ( 7 − x ) < 162121 ( 6 � x ) < 16 ( 7 � x ) = > 5 x > 14 = x > 2.8 least such number is 3 answer : a
Answer: a
Problem: in what time will a train 134 m long cross an electric pole , it its speed be 169 km / hr ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 169 * 5 / 18 = 46.9 m / sec time taken = 134 / 46.9 = 2.9 sec . answer : c"
Answer: c
Problem: a train 75 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 88 , d ) 22 , e ) 32
Rationale: "speed of the train relative to man = ( 75 / 10 ) m / sec = ( 15 / 2 ) m / sec . [ ( 15 / 2 ) * ( 18 / 5 ) ] km / hr = 27 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 27 = = > x = 32 km / hr . answer : e"
Answer: e
Problem: a train 200 m long crosses a platform 150 m long in 20 sec ; find the speed of the train ?
Options: a ) 73 , b ) 63 , c ) 65 , d ) 70 , e ) 83
Rationale: "d = 200 + 150 = 350 t = 20 s = 350 / 20 * 18 / 5 = 63 kmph . answer : b"
Answer: b
Problem: if ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) = > 5 ^ 13 * 3 ^ 14 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 13 * 3 ^ 14 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 13 answer d
Answer: d
Problem: in one hour , a boat goes 19 km / hr along the stream and 11 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 19 + 11 ) kmph = 15 kmph . answer : option d"
Answer: d
Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , d are sitting together ?
Options: a ) 1 / 5 , b ) 3 / 28 , c ) 1 / 7 , d ) 1 / 14 , e ) 5 / 28
Rationale: "total number of arrangement is = 8 ! = 40320 favorable event i . e a , b and d can be arranged in 3 ! and the remaining can be arranged in 6 ! since abd can be in any of the six positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : b"
Answer: b
Problem: the divisor is 21 , the quotient is 14 and the remainder is 7 . what is the dividend ?
Options: a ) 201 , b ) 394 , c ) 302 , d ) 301 , e ) 294
Rationale: d = d * q + r d = 21 * 14 + 7 d = 294 + 7 d = 301
Answer: d
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 6 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 6 mph ) / 2 = 3.5 mph correct option is : c"
Answer: c
Problem: what annual payment will discharge a debt of rs . 1050 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 543.33 , e ) 564.69
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1050 820 x + 1050 * 441 x = 564.69 so , value of each installment = rs . 564.69 answer : option e"
Answer: e
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 880 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 13.6 % , c ) 65 % , d ) 45 % , e ) 35 %
Rationale: "explanation : 880 - - - 120 100 - - - ? = > 13.6 % answer : b"
Answer: b
Problem: the number of positive integer solutions for the equation x + y + z + t = 21 is
Options: a ) 1140 , b ) 1145 , c ) 1240 , d ) 1340 , e ) 15640
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 21 - 1 c 4 - 1 = 20 c 3 = 1140 answer : a"
Answer: a
Problem: a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 33 % , c ) 20 % , d ) 35 % , e ) 30 %
Rationale: "the total number of mangoes bought by the shopkeeper be 30 . if he buys 6 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 6 profit = sp - cp = 6 - 5 = 1 profit percent = 1 / 5 * 100 = 20 % answer : c"
Answer: c
Problem: machine p and machine q are each used to manufacture 330 sprockets . it takes machine p 10 hours longer to produce 330 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 3 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 330 / x = 330 / 1.1 x + 10 1.1 ( 330 ) = 330 + 11 x 11 x = 33 x = 3 the answer is 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 160 male associates , how many female managers are there ?
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: 250 employees : 90 male , 160 female 40 managers , 210 associates 160 male associates implies 50 female associates which means the remaining 40 females must be managers a . 40
Answer: a
Problem: think of a number , divide it by 5 and add 8 to it . the result is 61 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 265 , e ) 29
Rationale: "explanation : 61 - 6 = 53 53 x 5 = 265 answer : d"
Answer: d
Problem: the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 8 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 8 pounds of clothes doubles the ratio of books to clothes , then 8 pounds represents half the weight of the clothes . 2 k = 8 pounds and then k = 4 pounds . the electronics weigh 3 ( 4 ) = 12 pounds . the answer is d .
Answer: d
Problem: the radius of a semi circle is 2.1 cm then its perimeter is ?
Options: a ) 32.5 , b ) 11.12 , c ) 32.1 , d ) 10.8 , e ) 32.3
Rationale: "36 / 7 r = 2.1 = 10.80 answer : d"
Answer: d
Problem: the dimensions of a rectangular solid are 4 inches , 5 inches , and 10 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 10 : 19 , d ) 25 : 7 , e ) 32 : 25
Rationale: answer : c .
Answer: c
Problem: which number should replace both the asterisks in ( * / 21 ) x ( * / 189 ) = 1 ?
Options: a ) 21 , b ) 63 , c ) 3969 , d ) 147 , e ) 167
Rationale: "answer let ( y / 21 ) x ( y / 189 ) = 1 then , y 2 = 21 x 189 = 21 x 21 x 9 ∴ y = ( 21 x 3 ) = 63 . option : b"
Answer: b
Problem: a tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume . if 6,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 15 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 6,000 = 4,000 gallons and sodium chloride is 600 gallons ( 6 % of initial solution of 10,000 gallons ) then sodium chloride is 600 / 4,000 * 100 = 15 % of the remaining solution of 4,000 gallons . answer : e ."
Answer: e
Problem: two pipes a and b can fill a cistern in 12 and 20 minutes respectively , and a third pipe c can empty it in 30 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 13 min , c ) 12 min , d ) 10 min , e ) 17 min
Rationale: "1 / 12 + 1 / 20 - 1 / 30 = 1 / 10 10 / 1 = 10 answer : d"
Answer: d
Problem: two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 231 marks in the second test and failed by 48 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 625 , e ) 248
Rationale: "let the maximum mark in each test be m . the candidate failed by 48 marks in the second test . pass mark in the second test = 231 + 48 = 279 45 / 100 m = 279 pass mark in the first test = 40 / 100 m = 40 / 45 * 279 = 248 . answer : e"
Answer: e
Problem: trains a and b start simultaneously from stations 200 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 20 miles per hour and 20 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 100 , b ) 133 , c ) 150 , d ) 167 , e ) 188
Rationale: "since we know the distance ( 200 ) and the combined rate ( 40 ) , we plug it into the formula : distance = rate * time 200 = 40 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 200 / 40 from dividing 40 on both sides to isolate time in the equation above . time will be 5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 20 * 5 distance = 100 according to answer choice a ."
Answer: a
Problem: x = 13.165 y = 7.686 z = 11.545 the number a is obtained by first rounding the values of x , y , and z to the hundredths place and then adding the resulting values . the number b is obtained by first adding the values of x , y , and z and then rounding the sum to the hundredths place . what is the value of a – b ?
Options: a ) 0.01 , b ) 0.02 , c ) 0.03 , d ) 0.1 , e ) 0.2
Rationale: rounding off the values : x = 13.17 y = 7.69 z = 11.55 a = 13.17 + 7.69 + 11.55 = 32.41 x + y + z = 13.165 + 7.686 + 11.545 = 32.206 b = 32.21 a - b = 0.2 option e
Answer: e
Problem: the area of a square is 144 m ² . find its perimeter .
Options: a ) 18 m
b ) 28 m
c ) 38 m
d ) 42 m
e ) 48 m
Rationale: area of square = side × side given ; area of square = 144 m ² therefore , side ² = 144 m ² therefore , side = √ ( 144 m ² ) = √ ( 2 × 2 × 2 × 2 × 3 × 3 ) m ² = 2 × 2 × 3 m = 12 m now , the perimeter of the square = 4 x side = 4 × 12 m = 48 m answer : e
Answer: e
Problem: how is 1 % expressed as a decimal fraction ?
Options: a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 0.0001 , e ) 1
Rationale: "1 / 100 = 0.01 answer : c"
Answer: c
Problem: salesperson a ' s compensation for any week is $ 350 plus 6 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 ) $ 14,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 350 + 0.06 ( x - 1000 ) = 0.08 x x = 14,500 ans : d"
Answer: d
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
Rationale: "2430 * 1 / 3 = 810 option b"
Answer: b
Problem: a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 8 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.5 , b ) 1.5 , c ) 2.5 , d ) 3.5 , e ) 4.5
Rationale: "time = 4 / 4 + 4 / 8 = 12 / 8 = 1.5 hours the answer is b ."
Answer: b
Problem: dacid obtained 45 , 35 , 52 , 47 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 47 , d ) 89 , e ) 45
Rationale: average = ( 45 + 35 + 52 + 47 + 55 ) / 5 = 234 / 5 = 47 . answer : c
Answer: c