regisss/math_qa huggingface dataset:
Problem: a worker can load one truck in 6 hours . a second worker can load the same truck in 4 hours . if both workers load one truck simultaneously while maintaining their constant rates , how long , in hours , will it take them to fill one truck ?
Options: a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3
Rationale: the workers fill the truck at a rate of 1 / 6 + 1 / 4 = 10 / 24 = 5 / 12 of the truck per hour . then the time to fill one truck is 12 / 5 which is 2.4 hours . the answer is b .
Answer: b
Problem: 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 3 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 3 40 + 10 + 3 - 7 = 46 like apple answer : b
Answer: b
Problem: in a group of cows and hens , the number of legs are 16 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 16 2 x = 16 x = 8 . answer : d"
Answer: d
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 10 a . m . and travels towards b at 100 km / hr . another starts from b at 11 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 10 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 10 + 5 = 3 p . m . answer is c"
Answer: c
Problem: 3 candidates in an election and received 1256 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 56.7 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1256 + 7636 + 11628 ) = 20520 so , required percentage = 11628 / 20520 * 100 = 56.7 % a"
Answer: a
Problem: the sum of two numbers is 16 and the sum of their squares is 113 . find the numbers .
Options: a ) 1 and 2 , b ) 4 and 5 , c ) 7 and 8 , d ) 2 and 3 , e ) 6 and 7
Rationale: let the numbers be x and ( 15 - x ) . then , x 2 + ( 15 - x ) 2 = 113 = > x 2 + 225 + x 2 - 30 x = 113 = > 2 x 2 - 30 x + 112 = 0 = > x 2 - 15 x + 56 = 0 = > ( x - 7 ) ( x - 8 ) = 0 = > x = 7 or x = 8 . so , the numbers are 7 and 8 . answer is c
Answer: c
Problem: the ratio of the radius of two circles is 1 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 5 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 1 : 3 π r 12 : π r 22 r 12 : r 22 = 1 : 9 answer : c"
Answer: c
Problem: if the population of a certain country increases at the rate of one person every 45 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 80 , b ) 120 , c ) 150 , d ) 180 , e ) 160
Rationale: "answer = 1.33 * 60 = 80 answer is a"
Answer: a
Problem: a cube has one of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 6 , b ) 1 : 11 , c ) 2 : 5 , d ) 1 : 8 , e ) 3 : 11
Rationale: "let x be the area of each face of the cube . the area painted red is x / 2 the area painted white is x / 2 + 5 x = 11 x / 2 the ratio of red to white is ( x / 2 ) : ( 11 x / 2 ) which is 1 : 11 . the answer is b ."
Answer: b
Problem: what is the units digit of ( 3 ^ 13 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 13 = 3 ^ 4 * 3 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 13 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Problem: bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 63 more . what was his original selling price ?
Options: a ) $ 850 , b ) $ 990 , c ) $ 1050 , d ) $ 1180 , e ) $ 1340
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 63 0.07 = 63 p = 900 the original selling price was 900 * 1.1 = 990 . the correct answer is b ."
Answer: b
Problem: one - third of 1206 is what percent of 162 ?
Options: a ) 324.11 , b ) 300.12 , c ) 248.14 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 162 . ∵ 1206 / 3 = ( n x 162 ) / 100 ∴ n = ( 402 x 100 ) / 162 = 248.14 correct option : c"
Answer: c
Problem: 1399 x 1399
Options: a ) 1957201 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1399 x 1399 = ( 1399 ) 2 = ( 1400 - 1 ) 2 = ( 1400 ) 2 + ( 1 ) 2 - ( 1 x 1400 x 1 ) = 1957201 . answer : option a"
Answer: a
Problem: on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 50 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 20 %
Rationale: 0.1 m = 0.50 e = > e / m = 1 / 5 * 100 = 20 % so answer is e . m - # of motorists e - # of motorists exceeding speed
Answer: e
Problem: in a group of 7 boys and 8 girls , 5 members are to be selected . in how many different ways can they be selected such that at least 3 boys should be there ?
Options: a ) 1200 , b ) 1500 , c ) 1281 , d ) 1339 , e ) 1296
Rationale: no of boys = 7 no of girls = 8 therefore , no of ways at least 3 boy can be selected = 7 c 5 * 8 c 0 + 7 c 4 * 8 c 1 + 7 c 3 * 8 c 2 = 1281 ans - c
Answer: c
Problem: the average marks of a class of 40 students is 44 and that of another class of 45 students is 70 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 69.5 , e ) 52.9
Rationale: "sum of the marks for the class of 40 students = 40 * 44 = 1760 sum of the marks for the class of 45 students = 45 * 70 = 3150 sum of the marks for the class of 85 students = 2760 + 3150 = 5910 average marks of all the students = 5910 / 85 = 69.5 . answer : d"
Answer: d
Problem: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x + 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = - 5 , x = - 10 andx = 5 / 2 = 2.5 . so , three solutions present in our set of 12 distinct numbers , therefore p = 3 / 12 = 1 / 4 . answer : c .
Answer: c
Problem: a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 38 % , e ) 40 %
Rationale: "let original length = x and original breadth = y . decrease in area = xy - 80 x x 90 y 100 100 = xy - 18 xy 25 = 7 xy . 25 decrease % = 7 xy x 1 x 100 % = 28 % . 25 xy a )"
Answer: a
Problem: 5 / 8 of 3 / 10 of a number is greater than 4 / 9 of 1 / 4 of the same number by 55 . what is half of that number ?
Options: a ) 310 , b ) 312 , c ) 320 , d ) 314 , e ) 360
Rationale: "let no . be x 5 / 8 * 3 / 10 * x - 4 / 9 * 1 / 4 * x = 55 by further solving 15 x / 80 - 4 x / 36 = 55 11 x / 144 = 55 x = 720 we have to find x / 2 = 720 / 2 = 360 answer : e"
Answer: e
Problem: the average of 10 numbers is calculated as 18 . 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 ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 18 + 36 – 26 = 190 = > 190 / 10 = 19 c )"
Answer: c
Problem: the speed of a boat in still water in 42 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 34.5 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 5 ) = 47 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 47 = 34.5 km answer : c"
Answer: c
Problem: what is the remainder when 1024 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1024 / 33 , 1047 / 33 and so on . . 1024 / 33 gives remainder = 1 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 1 * 24 * 27 * 30 break them into pairs 1 * 24 / 33 gives remainder 24 and 27 * 30 / 33 gives remainder 18 so 24 * 18 / 33 gives remainder 3 . a"
Answer: a
Problem: the average of first 20 natural numbers is ?
Options: a ) 10.5 , b ) 11.4 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 20 natural no . = 420 / 2 = 210 average = 210 / 20 = 10.5 answer : a"
Answer: a
Problem: by investing in 1623 % stock at 64 , one earns rs . 1500 . the investment made is
Options: a ) rs . 9600 , b ) rs . 7500 , c ) rs . 5640 , d ) rs . 5760 , e ) rs . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d"
Answer: d
Problem: the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1240 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8215 , e ) 9255
Rationale: "sum of square of n numbers is found using the formula [ n ( n + 1 ) ( 2 n + 1 ) ] / 6 we have sum of 1 st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1 st 30 + ve integers - sum of squares of 1 st 15 + ve integers . we will get d - 8215 ; answer : d"
Answer: d
Problem: in a department store prize box , 40 % of the notes give the winner a dreamy vacation ; the other notes are blank . what is the approximate probability that 3 out of 5 people that draw the notes one after the other , and immediately return their note into the box get a dreamy vacation ?
Options: a ) 0.12 , b ) 0.23 , c ) 0.35 , d ) 0.45 , e ) 0.65
Rationale: the probability of winning is 40 % = 40 / 100 = 2 / 5 . the probability of not winning is 60 % = 3 / 5 . p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 ( we multiply by 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! , because wwwnn scenario can occur in several ways : wwwnn , wwnwn , wnwwn , nwwwn , . . . the # of such cases basically equals to the # of permutations of 5 letters wwwnn , which is 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! ) . answer : b .
Answer: b
Problem: if the volume of the cube is 729 cm 3 , then the surface area of the cube will be
Options: a ) 486 sq . cm
b ) 456 sq . cm
c ) 446 sq . cm
d ) 476 sq . cm
e ) none of these
Rationale: explanation : a 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 cm 2 answer : a
Answer: a
Problem: what is the rate percent when the simple interest on rs . 1600 amount to rs . 200 in 4 years ?
Options: a ) 4 % , b ) 3.125 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "interest for 1 year = 200 / 4 = 50 interest on rs 1600 p / a = 50 interest rate = 50 / 1600 * 100 = 3.125 % answer : b"
Answer: b
Problem: if the simple interest on a certain sum of money for 2 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 14 % , b ) 7 % , c ) 10 % , d ) 15 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 2 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 2 ) = 20 / 2 = 10 % answer : option c"
Answer: c
Problem: a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ?
Options: a ) 3 / 14 , b ) 5 / 28 , c ) 3 / 28 , d ) 1 / 7 , e ) 9 / 28
Rationale: total number of arrangement is = 8 ! = 40320 favorable event i . e ) a , b and c can be arranged in 3 ! and the remaining can be arranged in 6 ! since ab can be in any of the four positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : c
Answer: c
Problem: there are 2 sections a and b in a class , consisting of 50 and 50 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 70 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 50 students = 50 * 60 + 50 * 80 = 3000 + 4000 average weight of the class is = 7000 / 100 = 70 kg answer is d"
Answer: d
Problem: in a school with 632 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 250 , d ) 158 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 632 - x ) . then , ( 11 3 / 4 × 632 ) ⇔ 11 x + 12 ( 632 - x ) ⇔ x = 7584 - 7426 ⇔ 158 . answer d"
Answer: d
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.15 km and 0.6 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 42 , b ) 9 , c ) 7 , d ) 67 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.15 + 0.6 = 1.75 km = 1750 m . required time = 1750 * 3 / 125 = 42 sec . answer : a"
Answer: a
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 152 . if the ratio of his marks in english and maths is 1 : 5 , find his marks in science ?
Options: a ) 8 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: "s : e = 1 : 3 e : m = 1 : 5 - - - - - - - - - - - - s : e : m = 1 : 3 : 15 1 / 19 * 152 = 8 answer : a"
Answer: a
Problem: the salary of a person was reduced by 28 % . by what percent should his reduced salary be raised so as to bring it at par with his original salary ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 38.9 %
Rationale: "let the original salary be $ 100 new salary = $ 72 increase on 72 = 28 increase on 100 = [ ( 28 / 72 ) 100 ] % = 38.9 % answer is e"
Answer: e
Problem: the average height of 35 boys in a class was calculated as 183 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 181.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 183 cm . wrong total height of 35 boys = 183 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 183 cm - ( 166 cm - 106 cm ) / 35 = 183 cm - 60 / 35 cm = 183 cm - 1.71 cm = 181.29 cm . answer : b"
Answer: b
Problem: a is half good a work man as b and together they finish a job in 14 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 36 , e ) 48
Rationale: "c 21 wc = 1 : 2 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 = > 21 days"
Answer: c
Problem: each of the products produced yesterday was checked by worker x or worker y . 0.5 % of the products checked by worker x are defective and 0.8 % of the products checked by worker y are defective . if the total defective rate of all the products checked by worker x and worker y is 0.55 % , what fraction of the products was checked by worker y ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8
Rationale: "x : 0.5 % is 0.05 % - points from 0.55 % . y : 0.8 % is 0.25 % - points from 0.55 % . therefore the ratio of products checked by y : x is 1 : 5 . thus , worker y checked 1 / 6 of the products . the answer is d ."
Answer: d
Problem: a baseball card decreased in value 40 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 46 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.6 = 60 after second year price = 60 * 0.9 = 54 final decrease = [ ( 100 - 54 ) / 100 ] * 100 = 46 % correct answer - d"
Answer: d
Problem: from a group of 3 boys and 3 girls , 4 children are to be randomly selected . what is the probability that equal numbers of boys and girls will be selected ?
Options: a ) 1 / 10 , b ) 4 / 9 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: prob reqd = 1 - probab of not having eq numbers prob of not having eq no ' s is = prob of having 3 boys and 1 girl or prob of having 3 girls and 1 boy = ( 1 * 3 / 15 ) + ( 3 / 15 * 1 ) = 2 / 5 reqd prob = 1 - 2 / 5 = 3 / 5 answer : d
Answer: d
Problem: 9 years ago i was 5 times as old as my eldest son . today i am 3 times his age . how old am i now ?
Options: a ) 45 , b ) 54 , c ) 34 , d ) 58 , e ) 56
Rationale: x - 9 = 5 ( y - 9 ) & x = 3 y x - 9 = 5 x / 3 - 45 x = 54 answer : b
Answer: b
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
Options: a ) 2 : 0 , b ) 2 : 3 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
Rationale: "by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 90 = 2 : 3 answer : b"
Answer: b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is 4 times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 12 : 8 , b ) 8 : 16 , c ) 9 : 16 , d ) 8 : 12 , e ) 16 : 9
Rationale: water : soap = 3 : 2 soap : salt = 12 : 8 = > for 12 soap , salt = 8 = > for 2 soap , salt = ( 8 / 12 ) * 2 = 16 / 12 = 4 / 3 so , water : soap : salt = 3 : 2 : 4 / 3 = 9 : 6 : 4 after open container , water : soap : salt = 2.25 : 6 : 4 so , water : salt = 2.25 : 4 = 9 : 16 answer : c
Answer: c
Problem: initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many q women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number q = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Problem: a caterer ordered 125 ice - cream bars and 125 sundaes . if the total price was $ 225.00 and the price of each ice - cream bar was $ 0.60 , what was the price of each sundae ?
Options: a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
Rationale: "let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 225 = > 125 * s = 150 = > s = 1.2 answer d"
Answer: d
Problem: a and b invests rs . 3000 and rs . 5500 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 ) 8 : 8 , b ) 9 : 8 , c ) 9 : 7 , d ) 9 : 5 , e ) 9 : 11
Rationale: "( 3 * 6 + 6 * 6 ) : ( 5.5 * 12 ) 54 : 66 = > 9 : 11 answer : e"
Answer: e
Problem: if a lends rs . 3150 to b at 8 % per annum and b lends the same sum to c at 12.5 % per annum then the gain of b in a period of 2 years is ?
Options: a ) 280 , b ) 295 , c ) 283.5 , d ) 245 , e ) 200
Rationale: "( 3150 * 4.5 * 2 ) / 100 = > 283.5 answer : c"
Answer: c
Problem: apple costs l rupees per kilogram for first 30 kgs and q rupees per kilogram for each additional kilogram . if the price of 33 kilograms is 663 and for 36 kgs of apples is 726 then the cost of first 10 kgs of apples is
Options: a ) 100 , b ) 150 , c ) 200 , d ) 350 , e ) 450
Rationale: ans : by framing equations we get 30 l + 3 q = 663 30 l + 6 q = 726 eliminate q by multiplying the first equation by 2 and subtracting second equation from the first then we get l = 20 cost of 10 kgs of apples = 10 x 20 = 200 answer : c
Answer: c
Problem: 10 + 19
Options: a ) 29 , b ) 13 , c ) 28 , d ) 6 , e ) 2
Rationale: a
Answer: a
Problem: a and b started a business investing rs . 80,000 and rs 20,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 4 : 1 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4
Rationale: "a : b = 80000 : 20000 = 8 : 2 = 4 : 1 answer : a"
Answer: a
Problem: a rower can row 7 km / h in still water . when the river is running at 2 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.92 , b ) 3.04 , c ) 3.12 , d ) 3.21 , e ) 3.35
Rationale: let x be the distance to big rock . time = x / 5 + x / 9 = 1 x = 45 / 14 = 3.21 km the answer is d .
Answer: d
Problem: the average of first 35 prime numbers is ?
Options: a ) 14.54 , b ) 15.6 , c ) 15.8 , d ) 14.7 , e ) 14.8
Rationale: "explanation : average = ( 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 ) / 11 = 160 / 11 = 14.54 ( approx ) answer is a"
Answer: a
Problem: a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a women alone in 18 days , how long will a boy take to complete the work ?
Options: a ) 6 days , b ) 8 days , c ) 9 days , d ) 7 days , e ) 5 days
Rationale: "explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 womans 1 day ’ s work = 1 / 18 ( 1 man + 1 woman ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 18 = 2 / 9 therefore , 1 boys 1 day ’ s work = 1 / 3 – 2 / 9 = 3 - 2 / 9 = 1 / 9 therefore , the boy alone can finish the work in 9 days . answer : option c"
Answer: c
Problem: the least number which should be added to 1789 so that the sum is exactly divisible by 5 , 6 , 4 and 3 is ?
Options: a ) 1 , b ) 11 , c ) 21 , d ) 31 , e ) 41
Rationale: l . c . m . of 5 , 6 , 4 and 3 = 60 . on dividing 1789 by 60 , the remainder is 49 . number to be added = ( 60 - 49 ) = 11 b )
Answer: b
Problem: i chose a number and divide it by 8 . then i subtracted 160 from the result and got 12 . what was the number i chose ?
Options: a ) 1376 , b ) 1800 , c ) 1400 , d ) 2500 , e ) 100
Rationale: "let x be the number i chose , then x / 8 − 160 = 12 x / 8 = 172 x = 1376 answer is a ."
Answer: a
Problem: solve for x and check : - 12 x = 72
Options: a ) - 4 , b ) - 2 , c ) - 6 , d ) - 12 , e ) none of these
Rationale: "solution : dividing each side by - 12 , we obtain ( - 12 x / - 12 ) = ( 72 / - 12 ) therefore : x = - 6 check : - 12 x = 72 ( - 12 * - 6 ) = 72 72 = 72 answer : c"
Answer: c
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 40 , how many horses are there ?
Options: a ) 8 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: legs 8 * 4 = 32 now half on their horses so remaining on the walk so 4 men 4 men has 8 legs so , 8 + 32 = 40 legs walking answer : a
Answer: a
Problem: workers at a campaign office have 3000 fliers to send out . if they send out 1 / 5 of them in the morning and 1 / 4 of the remaining ones out during the afternoon , how many are left for the next day ?
Options: a ) 1800 , b ) 800 , c ) 1100 , d ) 1200 , e ) 1900
Rationale: "( 1 / 5 ) * 3000 = 600 remaining = 3000 - 600 = 2400 ( 1 / 4 ) of remaining = ( 1 / 4 ) * 2400 = 600 remaining now = 2400 - 600 = 1800 answer : option a"
Answer: a
Problem: find the average of first 20 multiples of 7 ?
Options: a ) 73.5 , b ) 70.5 , c ) 63.5 , d ) 54.5 , e ) 40.5
Rationale: "required average = 7 ( 1 + 2 + 3 + … … . + 20 ) / 20  ( 7 * 20 * 21 ) / ( 20 * 2 )  ( 147 / 2 ) = 73.5 . answer a 73.5"
Answer: a
Problem: the diagonal of a rhombus are 70 m and 160 m . its area is :
Options: a ) 1940 , b ) 4800 , c ) 5600 , d ) 5200 , e ) 5000
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 70 ã — 160 ) cm ( power ) 2 = 70 ã — 80 = 5600 cm ( power ) 2 answer is c ."
Answer: c
Problem: 50 % of a number is more than 40 % of 120 by 180 . find the number ?
Options: a ) 456 , b ) 480 , c ) 420 , d ) 445 , e ) 320
Rationale: "( 50 / 100 ) * x – ( 40 / 100 ) * 120 = 180 1 / 2 x = 228 x = 456 answer : a"
Answer: a
Problem: sheela deposits rs . 5000 in bank savings account . if this is 20 % of her monthly income . what is her monthly income in ?
Options: a ) 22000 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: "explanation : 20 % of income = rs . 5000 100 % of income = 5000 x 100 / 20 = rs . 25000 answer : c"
Answer: c
Problem: there are 4 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 8 , c ) 40 , d ) 60 , e ) 120
Rationale: "each person is one participant of 4 games . so there are in all 4 * 4 = 16 instances of one participant games . but each game has 2 participants so total number of games = 16 / 2 = 8 b"
Answer: b
Problem: a 24 ' ' x 24 ' ' square metal plate needs to be fixed by a carpenter on to a wooden board . the carpenter uses nails all along the edges of the square such that there are 25 nails on each side of the square . each nail is at the same distance from the neighboring nails . how many nails does the carpenter use ?
Options: a ) 94
b ) 95
c ) 96
d ) 97
e ) 98
Rationale: every corner will have one , 4 corners will have 4 + and for 4 sides 23 no of nails = 4 + ( 4 * 23 ) = 96 answer : c
Answer: c
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the eldest child ?
Options: a ) 16 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 â ‡ ” 5 x = 20 â ‡ ” x = 4 . â ˆ ´ age of the eldest child = x + 12 = 4 + 12 = 16 years . answer a"
Answer: a
Problem: let the number which when multiplied by 15 is increased by 280 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: "solution let the number be x . then , 15 x - x = 280 ‹ = › 14 x = 280 x ‹ = › 20 . answer b"
Answer: b
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 105 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 105 5 x - 20 = 105 5 x = 125 x = 25 the answer is b ."
Answer: b
Problem: at 15 : 00 there were 22 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 ) 32
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 = 32 e"
Answer: e
Problem: 475.124 x 15.98 ÷ 8.001 + 33.33 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 781.189 , d ) 656.112 , e ) 456.512
Rationale: "explanation : ? = 475.124 x ( 15.98 ÷ 8.001 ) + 33.33 ≈ ( 475.124 x 16 / 8 ) + 33.33 ≈ 950.248 + 33.33 ≈ 983.578 answer : option a"
Answer: a
Problem: 20 men can cut 30 trees in 4 hours . if 4 men leave the job , how many trees will be cut in 6 hours ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 22 , e ) 32
Rationale: "20 men - working 4 hrs - cut 30 trees 1 men - working 1 hr - cuts = 30 / 20 * 4 thus 16 men - working 6 hrs - cut = 30 * 16 * 6 / 20 * 4 = 36 trees answer is b"
Answer: b
Problem: 4 dices are thrown at the same time . what is the probability of getting only 2 dices showing the same face ?
Options: a ) 4 / 9 , b ) 5 / 9 , c ) 11 / 18 , d ) 7 / 9 , e ) none of the above
Rationale: probability of getting two same faces : 1 and 1 / 6 for other two faces , probabilities : 5 / 6 and 4 / 6 respectively . the dice combinations can be arranged in 4 ! / 2 ! ways total probability = 1 * 1 / 6 * 5 / 6 * 4 / 6 * 4 ! / 2 ! = 5 / 9 answer : b
Answer: b
Problem: mr . loyd wants to fence his square shaped land of 60 sqft each side . if a pole is laid every 12 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 60 * 4 = 240 poles every 12 feet hence no of poles = 240 / 12 = 20 answer : a"
Answer: a
Problem: the average of first six prime numbers greater than 20 is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 34
Rationale: "23 + 29 + 31 + 37 + 41 + 43 = 204 / 6 = 34 answer : e"
Answer: e
Problem: a boat having a length 7 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 100 kg , b ) 120 kg , c ) 89 kg , d ) 80 kg , e ) 210 kg
Rationale: "volume of water displaced = ( 7 x 3 x 0.01 ) m 3 = 0.21 m 3 . mass of man = volume of water displaced x density of water = ( 0.21 x 1000 ) kg = 210 kg . answer : e"
Answer: e
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 50 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 5 , e ) 6
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 50 run rate needed = 250 / 50 = 5 answer : option d"
Answer: d
Problem: the toll t , in dollars , for a truck using a certain bridge is given by the formula t = 0.50 + 0.50 ( x − 2 ) , where x is the number of axles on the truck . what is the toll for an 18 - wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles ?
Options: a ) $ 2.00 , b ) $ 3.00 , c ) $ 3.50 , d ) $ 4.00 , e ) $ 5.00
Rationale: "number of wheels in truck = 18 number of wheels on its front axle = 2 number of wheels remaining = 16 number of axles remaining axles = 16 / 4 = 4 total number of axles = 5 t = 0.50 + 0.50 ( x − 2 ) = 0.50 + . 5 * 3 = 0.5 + 1.5 = 2 $ answer a"
Answer: a
Problem: if a : b : : 3 : 7 , then what is ( 5 a + 2 b ) : ( a - 2 b ) ?
Options: a ) 57 : 11 , b ) - 57 : 11 , c ) 11 : 10 , d ) - 29 : 11 , e ) - 1 : 10
Rationale: "a / b = 3 / 7 dividing numerator & denominator of ' ( 5 a + 6 b ) / ( a - 2 b ) ' by b , [ 5 ( a / b ) + 2 ] / [ ( a / b ) - 2 ] = [ 5 * ( 3 / 7 ) + 2 ] / [ ( 3 / 7 ) - 2 ] = - 29 / 11 answer : d"
Answer: d
Problem: in a group of 100 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
Options: a ) 0.1 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
Rationale: number of people whose age is less than 20 is given by 100 - 90 = 10 probability p that a person selected at random from the group is less than 20 is given by 10 / 100 = 0.1 correct answer a
Answer: a
Problem: an article is bought for rs . 1200 and sold for rs . 800 , find the loss percent ?
Options: a ) 16 % , b ) 35 % , c ) 33 % , d ) 18 % , e ) 12 %
Rationale: "1200 - - - - 400 100 - - - - ? = > 33 % answer : c"
Answer: c
Problem: how much is 80 % of 45 is greater than 4 / 5 of 25 ?
Options: a ) 15 , b ) 57 , c ) 16 , d ) 16 , e ) 73
Rationale: "( 80 / 100 ) * 45 â € “ ( 4 / 5 ) * 25 36 - 20 = 16 answer : c"
Answer: c
Problem: a small water pump would take 3 hours to fill an empty tank . a larger pump would take 3 / 4 hour to fill the same tank . how many hours would it take both pumps , working at their respective constant rates , to fill the empty tank if they began pumping at the same time ?
Options: a ) 3 / 4 , b ) 3 / 5 , c ) 5 / 7 , d ) 1 / 2 , e ) 4 / 5
Rationale: "rate of the small pump is 1 / 3 tank / hour rate of the larger pump is 1 / ( 3 / 4 ) or 4 / 3 tank / hour ; combined rate of the two pumps is 1 / 3 + 4 / 3 = 5 / 3 tank / hour , together they will fill the empty tank in 1 / ( 5 / 3 ) ) = 3 / 5 hours ( time = job / rate ) . answer : b"
Answer: b
Problem: if p ( a ) = 5 / 7 and p ( b ) = 2 / 5 , find p ( a n b ) if a and b are independent events .
Options: a ) 7 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 7 , e ) 3 / 17
Rationale: "p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 5 / 7 . 2 / 5 p ( a n b ) = 2 / 7 . d"
Answer: d
Problem: divide rs . 5500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 1 / 5 as a and c together . a ' s share is ?
Options: a ) 1227 , b ) 1268 , c ) 1375 , d ) 1200 , e ) 1210
Rationale: "a + b + c = 5500 a = 1 / 3 ( b + c ) ; b = 1 / 5 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 5500 = > 1375 answer : c"
Answer: c
Problem: in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 100 cu . m , b ) 1000 cu . m , c ) 10000 cu . m , d ) 2000 cu . m , e ) 4000 cu . m
Rationale: "20 * 10 * 5 = 1000 answer : b"
Answer: b
Problem: in traveling from a dormitory to a certain city , a student went 1 / 3 of the way by foot , 3 / 5 of the way by bus , and the remaining 2 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 3 x + 3 / 5 x + 2 x - 1 / 3 x - 3 / 5 x = 2 x = 30 km option : a"
Answer: a
Problem: a factory produces 6500 toys per week . if the workers at this factory work 5 days a week and if these workers make the same number of toys everyday , how many toys are produced each day ?
Options: a ) 1375 toys , b ) 2375 toys , c ) 1300 toys , d ) 1375 toys , e ) 2375 toys
Rationale: "to find the number of toys produced every day , we divide the total number of toys produced in one week ( of 5 days ) by 5 . 6500 / 5 = 1300 toys correct answer c"
Answer: c
Problem: a farmer spent $ 37 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 20 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 40.70
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 37 = $ 14.8 on chicken feed , thus he spent the remaining 37 - 14.8 = $ 22.2 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.8 = $ 14.8 - - > x = $ 18.5 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 18.5 + 22.2 = $ 40.7 . answer : e"
Answer: e
Problem: the charge for a single room at hotel p is 20 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 15 % , b ) 20 % , c ) 12.5 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 80 x g = 100 y p = 90 y thus 80 x = 90 y or x = 1.125 y ans r = 112.5 y so increase = 12.5 % answer : c"
Answer: c
Problem: the ratio of the volumes of two cubes is 729 : 125 . what is the ratio of their total surface areas ?
Options: a ) 81 : 21 , b ) 81 : 22 , c ) 81 : 24 , d ) 81 : 25 , e ) 81 : 29
Rationale: "ratio of the sides = 3 √ 729 : 3 √ 125 = 9 : 5 ratio of surface areas = 9 ^ 2 : 5 ^ 2 = 81 : 25 answer : option d"
Answer: d
Problem: how many multiples of 10 are there between 10 and 290 ?
Options: a ) 8 , b ) 18 , c ) 27 , d ) 51 , e ) 60
Rationale: "it should be mentioned whether 10 and 290 are inclusive . if 10 and 290 are inclusive , then the answer is ( 290 - 10 ) / 10 + 1 = 29 . if 10 and 290 are not inclusive , then the answer is ( 280 - 20 ) / 10 + 1 = 27 . since oa is c , then we have not inclusive case ."
Answer: c
Problem: what is the remainder when 1041 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1041 / 33 , 1047 / 33 and so on . . 1044 / 33 gives remainder = 18 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 18 * 24 * 27 * 30 break them into pairs 18 * 24 / 33 gives remainder 3 and 27 * 30 / 33 gives remainder 18 so 3 * 18 / 33 gives remainder 21 . d"
Answer: d
Problem: if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 170 , what is the value of a − c ?
Options: a ) − 120 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 220 b + c = 340 a - c = - 120 . imo option a ."
Answer: a
Problem: line m lies in the xy - plane . the y - intercept of line m is - 2 , and line m passes through the midpoint of the line segment whose endpoints are ( 2 , 8 ) and ( 144 ) . what is the slope of line m ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: the midpoint of ( 2,8 ) and ( 14,4 ) is ( 8,6 ) . the slope of a line through ( 0 , - 2 ) and ( 8,6 ) is ( 6 - ( - 2 ) ) / ( 8 - 0 ) = 8 / 8 = 1 the answer is d .
Answer: d
Problem: the average weight of a , b and c is 60 kg . if the average weight of a and b be 70 kg and that of b and c be 50 kg , then the weight of b is :
Options: a ) 50 kg , b ) 60 kg , c ) 55 kg , d ) 57 kg , e ) 62 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 60 x 3 ) = 180 â € ¦ . ( i ) a + b = ( 70 x 2 ) = 140 â € ¦ . ( ii ) b + c = ( 50 x 2 ) = 100 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 240 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 60 . b â € ™ s weight = 60 kg . answer b"
Answer: b
Problem: length of a rectangular plot is 22 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 51 m , b ) 61 m , c ) 71 m , d ) 81 m , e ) 91 m
Rationale: "let breadth = x metres . then , length = ( x + 22 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 22 ) + x ] = 200 2 x + 22 = 100 2 x = 78 x = 39 . hence , length = x + 22 = 61 m b"
Answer: b
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 600 , what is the reduced price for kg ?
Options: a ) 20 , b ) 40 , c ) 36 , d ) 30 , e ) 35
Rationale: "600 * ( 20 / 100 ) = 120 - - - - 4 ? - - - - 1 = > rs . 30 answer : d"
Answer: d
Problem: after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 2500 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 2500 = 18000 exp in % = 100 - 10 = 90 % , 18000 = 90 % saving = 10 % = 18000 x 10 / 90 = rs . 2000 answer : c"
Answer: c
Problem: jim drove 384 miles of a 1200 miles journey . how many more miles does he need to drive to finish his journey ?
Options: a ) 113 miles , b ) 432 miles , c ) 456 miles , d ) 816 miles , e ) 767 miles
Rationale: "the number of miles to drive to finish his journey is given by 1200 - 384 = 816 miles correct answer d"
Answer: d
Problem: find the product of the local value and absolute value of 4 in 564823
Options: a ) 1600 , b ) 8000 , c ) 16000 , d ) 12000 , e ) 18000
Rationale: explanation : place value = local value face value = absolute value the place value of 4 in 564823 is 4 x 1000 = 4000 the face value of 4 in 564823 is nothing but 4 . = > 4000 x 4 = 16000 answer : option c
Answer: c
Problem: the banker â € ™ s gain on a sum due 3 years hence at 10 % per annum is rs . 60 . the banker â € ™ s discount is
Options: a ) rs . 960 , b ) rs . 840 , c ) rs . 1020 , d ) rs . 760 , e ) rs . 260
Rationale: "solution t . d = ( b . g x 100 / r x t ) = rs . ( 60 x 100 / 10 x 3 ) = rs . 200 . b . d = rs ( 200 + 60 ) = rs . 260 . answer e"
Answer: e
Problem: robert ' s salary was decreased by 70 % and subsequently increased by 70 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 49 %
Rationale: "let original salary be $ 100 salary after decreasing 70 % = 100 - 100 x 70 / 100 = $ 30 salary after increasing 70 % on $ 30 = 30 + 30 x 70 / 100 = $ 51 percentage of loss = 100 - 51 = 49 % answer : e"
Answer: e
Problem: a train covers a distance of 54 km in 15 min . if it takes 8 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 470 , b ) 480 , c ) 490 , d ) 500 , e ) 510
Rationale: "speed = ( 54 / 15 * 60 ) km / hr = ( 216 * 5 / 18 ) m / sec = 60 m / sec . length of the train = 60 * 8 = 480 m . answer : option b"
Answer: b
Problem: the difference between the value of a number increased by 12.5 % and the value of the original number decreased by 25 % is 30 . what is the original number e ?
Options: a ) 60 , b ) 80 , c ) 40 , d ) 120 , e ) 160
Rationale: "( 1 + 1 / 8 ) x - ( 1 - 1 / 4 ) x = 30 ( 9 / 8 ) x - ( 3 / 4 ) x = 30 x = 80 = e answer : b"
Answer: b
Problem: what is the remainder when you divide 2 ^ 200 - 3 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is a . this is very similar to the 32 ^ 32 ^ 32 - 3 divided by 7 question .
Answer: a
Problem: the ratio of three numbers is 2 : 3 : 4 and their sum is 180 . the second number of the three numbers is ?
Options: a ) 24 , b ) 60 , c ) 27 , d ) 29 , e ) 30
Rationale: "2 : 3 : 4 total parts = 9 9 parts - - > 180 1 part - - - - > 20 the second number of the three numbers is = 3 * 20 = 60 answer : b"
Answer: b
Problem: if ( log 5 5 ) ( log 4 9 ) ( log 3 2 ) is equal to
Options: a ) 1 , b ) 3 / 2 , c ) 2 , d ) 5 , e ) 7
Rationale: solution given expression = log 9 / log 4 × log 2 / log 3 ‹ = › log 3 ² / log 2 ² × log 2 / log 3 = 2 log 3 / 2 log 2 × log 2 / log 3 = 1 . answer a
Answer: a
Problem: the total marks obtained by a student in mathematics and physics is 32 and his score in chemistry is 20 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 40 , b ) 26 , c ) 27 , d ) 28 , e ) 22
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 32 and c - p = 20 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 32 + 20 ) / 2 = 26 . answer : b"
Answer: b
Problem: in the rectangular coordinate system , if the line x = 4 y + 5 passes through points ( m , n ) and ( m + 2 , n + p ) , what is the value of p ?
Options: a ) 3 , b ) 2 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 4
Rationale: "x = 4 y + 5 , and thus y = x / 4 - 5 / 4 the slope is 1 / 4 . the slope of a line through points ( m , n ) and ( m + 2 , n + p ) is ( n + p - n ) / ( m + 2 - m ) = p / 2 p / 2 = 1 / 4 and thus p = 1 / 2 the answer is c ."
Answer: c
Problem: the average weight of 4 students decreases by 8 kg when one of them weighing 96 kg is replaced by a new student . the weight of the student is
Options: a ) 62 kg , b ) 60 kg , c ) 64 kg , d ) 72 kg , e ) none of these
Rationale: explanation : let the weight of student be x kg . given , difference in average weight = 8 kg = > ( 96 - x ) / 4 = 8 = > x = 64 answer : c
Answer: c
Problem: if 4 men working 10 hours a day earn rs . 800 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1080 , d ) rs 1680 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 800 : x hence 4 * 10 * x = 9 * 6 * 800 or x = 9 * 6 * 800 / 4 * 10 = 1080 answer : c"
Answer: c
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 4.5 ) , ( 8 , 0 ) , ( 0 , - 4.5 ) , ( - 8 , 0 ) ?
Options: a ) 56 , b ) 72 , c ) 112 , d ) 116 , e ) 120
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 4.5 + 4.5 = 9 area = 1 / 2 * 16 * 9 = 72 b is the answer"
Answer: b
Problem: a theater box office sold an average ( arithmetic mean ) of 63 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 78 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 6 : 11 , e ) 4 : 7
Rationale: deviation from the mean for the daytime staff = 78 - 63 = 15 . deviation from the mean for the evening staff = 63 - 60 = 3 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 3 : 15 = 1 : 5 . the answer is c .
Answer: c
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 9 : 00 am and pipe b at 10 : 00 am , at what time will the pool be full ?
Options: a ) 19 : 00 , b ) 17 : 00 , c ) 16 : 00 , d ) 18 : 00 , e ) 20 : 00
Rationale: pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 9 : 00 a . m and pipe b at 10 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 10 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 9 : 00 a . m , pool is full at 19 : 00 hrs answer : a
Answer: a
Problem: a train running at the speed of 100 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 298 m , b ) 250 m , c ) 208 m , d ) 988 m , e ) 299 m
Rationale: "speed = 100 * 5 / 18 = 250 / 9 m / sec length of the train = speed * time = 250 / 9 * 9 = 250 m 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 45 meters . how many times did the ball bounce ?
Options: a ) 5 , b ) 4 , c ) 7 , d ) 8 , 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 going up = 1 - - > total = 45 ( caught ) no of bounce = 4 answer : b"
Answer: b