regisss/math_qa huggingface dataset:
Problem: from a total of 5 boys and 6 girls , how many 4 - person committees can be selected if the committee must have exactly 2 boys and 2 girls ?
Options: a ) 16 , b ) 24 , c ) 60 , d ) 120 , e ) 150
Rationale: answer = e = 150 no of 4 person committees that can be formed = 5 c 2 * 6 c 2 = 150 answer e
Answer: e
Problem: the simple interest on a sum of money will be rs . 1400 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 2800 , b ) 3799 , c ) 1200 , d ) 2693 , e ) 1732
Rationale: "p - - - 10 - - - - 1400 p - - - 5 - - - - - 700 3 p - - - 5 - - - - - 2100 - - - - - - = > 2800 answer : a"
Answer: a
Problem: if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 3 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 710
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 3 d = 3 * 270 = 710 answer : option e"
Answer: e
Problem: two cars start at the same time from opposite ends of a highway that is 175 miles long . one car is riding at 25 mph and the second car is riding at 45 mph . how long after they begin will they meet ?
Options: a ) 2 , b ) 2.5 , c ) 3 , d ) 3.5 , e ) 4
Rationale: "as cars are moving in opposite directions their speeds will be added . so their relative speeds : 45 + 25 = 70 mph total distance to be covered = 175 miles . time taken would be : 175 miles / 70 mph = 2.5 hours b is the answer ."
Answer: b
Problem: how many seven - digit numbers that do not contain the digits 2 or 9 are there ?
Options: a ) 178546 , b ) 44786544 , c ) 435786 , d ) 1599678 , e ) 1835008
Rationale: "we can have 7 digits ( 1 , 3,4 , 5,6 , 7,8 ) for the first place ( million ' s place ) . and similarly 8 digits for hundred thousands , ten thousands , thousands , hundred ' s , tenth ' s and unit digit . ( 0,1 , 3,4 , 5,6 , 7,8 ) so in total 7 * 8 * 8 * 8 * 8 * 8 * 8 = 1835008 hence e"
Answer: e
Problem: the sum of two consecutive number is 67 . which is the larger number ?
Options: a ) 34 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 67 2 x + 1 = 67 2 x = 66 x = 33 therefore larger number is x + 1 = 34 answer : a"
Answer: a
Problem: a and b together can do a piece of work in 1 days . if a alone can do the same work in 20 days , then b alone can do the same work in ?
Options: a ) 0.35 days , b ) 0.45 days , c ) 0.55 days , d ) 0.25 days , e ) 0.95 days
Rationale: "b = 1 / 1 – 1 / 20 = 0.95 days answer : e"
Answer: e
Problem: in a school of 850 boys , 46 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 136 , b ) b ) 627 , c ) c ) 153 , d ) d ) 721 , e ) e ) 159
Rationale: "46 + 28 + 10 = 84 % 100 – 84 = 16 % 850 * 16 / 100 = 136 answer : a"
Answer: a
Problem: 45 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 943
Rationale: "45 x / 100 - x / 3 = 110 7 x / 60 = 110 x = 943 answer : e"
Answer: e
Problem: there are 7 executives , including the ceo and cfo , that are asked to form a small team of 4 members . however , the ceo and cfo may not both be assigned to the team . given this constraint , how many ways are there to form the team ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 32 , e ) 35
Rationale: "the total number of ways to form a team of 4 is 7 c 4 = 35 . we need to subtract the number of teams that have both the ceo and the cfo . the number of teams with both the ceo and cfo is 5 c 2 = 10 . the number of ways to form an acceptable team is 35 - 10 = 25 . the answer is a ."
Answer: a
Problem: a / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 6 . what is the largest possible value of the expression ?
Options: a ) 2 / 18 , b ) 6 / 3 , c ) 30 / 2 , d ) 18 / 2 , e ) 6 / 18
Rationale: a / ( b / c ) = ( a * c ) / b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 6 * 3 ) / 2 = 18 / 2 answer d
Answer: d
Problem: a work as fast as b . if b can complete a work in 8 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 2 2 / 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: "ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 4 b ' s 1 day work = 1 / 8 a + b 1 day work = 1 / 4 + 1 / 8 = 3 / 8 = > 8 / 3 = 2 2 / 3 a and b can finish the work in 2 2 / 3 days answer is b"
Answer: b
Problem: ravi purchased a refrigerator and a mobile phone for rs . 15000 and rs . 8000 respectively . he sold the refrigerator at a loss of 5 percent and the mobile phone at a profit of 10 percent . overall he make a .
Options: a ) 50 , b ) 288 , c ) 27 , d ) 200 , e ) 881
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . answer : a"
Answer: a
Problem: a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning .
Options: a ) 39 , b ) 88 , c ) 26 , d ) 87 , e ) 11
Rationale: "explanation : consider the avg for first 16 innings is x . then total runs scored till 16 innings is 16 x . total runs after 17 innings = 16 x + 87 . thus , 16 x + 8717 = x + 316 x + 8717 = x + 3 ⇒ x = 36 so his average after 17 innings = 39 . answer : a"
Answer: a
Problem: the area of a square is equal to five times the area of a rectangle of dimensions 32 cm * 10 cm . what is the perimeter of the square ?
Options: a ) 289 cm
b ) 160 cm
c ) 829 cm
d ) 288 cm
e ) 289 cm
Rationale: area of the square = s * s = 5 ( 32 * 10 ) = 1600 = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b
Answer: b
Problem: working alone , mary can pave a driveway in 4 hours and hillary can pave the same driveway in 3 hours . when they work together , mary thrives on teamwork so her rate increases by 33.33 % , but hillary becomes distracted and her rate decreases by 50 % . if they both work together , how many hours will it take to pave the driveway ?
Options: a ) 2 hours , b ) 4 hours , c ) 5 hours , d ) 6 hours , e ) 7 hours
Rationale: initial working rates : mary = 1 / 4 per hour hillary = 1 / 3 per hour rate when working together : mary = 1 / 4 + ( 1 / 3 * 1 / 4 ) = 1 / 3 per hour hillary = 1 / 3 - ( 1 / 2 * 1 / 3 ) = 1 / 6 per hour together they work 1 / 3 + 1 / 6 = 1 / 2 per hour so they will need 2 hours to complete the driveway . the correct answer is a .
Answer: a
Problem: if y is a positive number and 1 / 2 the square root of x is the cube root of y , then y =
Options: a ) 64 , b ) 32 , c ) 16 , d ) 4 , e ) 1
Rationale: 1 / 2 the square root of x is cube root of y . if y = 64 . . then 1 / 2 the square root of y = 4 and cube of y is 64 . option a .
Answer: a
Problem: the perimeter of a semi circle is 180 cm then the radius is ?
Options: a ) 22 , b ) 28 , c ) 35 , d ) 37 , e ) 13
Rationale: "36 / 7 r = 180 = > r = 35 answer : c"
Answer: c
Problem: the sum of the ages of 4 children born at the intervals of 1 years each is 12 years . what is the age of the youngest child ?
Options: a ) 2.5 , b ) 1.5 , c ) 1 , d ) 3.5 , e ) 4.5
Rationale: "let x = the youngest child . each of the other four children will then be x + 1 , x + 2 , x + 3 we know that the sum of their ages is 12 so , x + ( x + 1 ) + ( x + 2 ) + ( x + 3 ) = 12 therefore the youngest child is 1.5 years old answer : b"
Answer: b
Problem: what is the decimal equivalent of ( 1 / 2 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 2 ) ² = ( 1 / 2 ) ( 1 / 2 ) = 1 / 4 approach # 1 : use long division to divide 4 into 1 to get 1 / 4 = 0.25 d"
Answer: d
Problem: when x is even , [ x ] = x / 2 + 1 , when x is odd [ x ] = 2 x + 1 then [ 6 ] * [ 3 ] = ?
Options: a ) [ 22 ] , b ) [ 44 ] , c ) [ 45 ] , d ) [ 28 ] , e ) [ 10 ]
Rationale: [ 6 ] * [ 3 ] = ( 6 / 2 + 1 ) ( 3 * 2 + 1 ) = [ 28 ] . ans - d
Answer: d
Problem: the sum of all the integers a such that - 26 < a < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 10 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 a = - 49 . d is the answer .
Answer: d
Problem: in what time will a railway train 52 m long moving at the rate of 24 kmph pass a telegraph post on its way ?
Options: a ) 3 sec , b ) 4 sec , c ) 8 sec , d ) 6 sec , e ) 7 sec
Rationale: t = 52 / 24 * 18 / 5 = 8 sec answer : c
Answer: c
Problem: find the smallest number which should be multiplied with 36963 to make it a perfect square .
Options: a ) 4 , b ) 7 , c ) 4 , d ) 3 , e ) 6
Rationale: "36963 = 111 * 111 * 3 required smallest number = 3 3 is the smallest number which should be multiplied with 36963 to make it a perfect square . answer : d"
Answer: d
Problem: one computer can upload 100 megabytes worth of data in 2 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 10 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6.6 , b ) 7 , c ) 9 , d ) 11 , e ) 13
Rationale: "since the first computer can upload 100 megabytes worth of data in 2 seconds then in 2 * 10 = 20 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 20 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 6.6 seconds . answer : a ."
Answer: a
Problem: 6 / 9 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 64 % , b ) 41 % , c ) 45 % , d ) 72 % , e ) 78 %
Rationale: total population = 90 ( assume ) . 6 / 9 * 90 = 60 people from montague . 3 / 9 * 90 = 30 people from capulet . 0.2 * 60 = 12 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 12 + 21 ) = ~ 64 . answer : a
Answer: a
Problem: if a 2 - b 2 = 10 and a * b = 5 , find a 4 + b 4 .
Options: a ) 50 , b ) 100 , c ) 150 , d ) 92 , e ) 25
Rationale: a 2 - b 2 = 10 : given a 4 + b 4 - 2 a 2 b 2 = 102 : square both sides and expand . a * b = 5 : given a 2 b 2 = 52 : square both sides . a 4 + b 4 - 2 ( 25 ) = 100 : substitute a 4 + b 4 = 150 correct answer c
Answer: c
Problem: in an office , totally there are 2800 employees and 25 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 390 , b ) 490 , c ) 400 , d ) 460 , e ) none of these
Rationale: number of male employees = 2800 * 25 / 100 = 700 required number of male employees who are less than 50 years old = 700 * ( 100 - 30 ) % = 700 * 70 / 100 = 490 . answer : b
Answer: b
Problem: when 3 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
Options: a ) 32 , b ) 81 , c ) 60 , d ) 27 , e ) 90
Rationale: explanation : let the number be 3 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 3 = a / 30 = > a = 90 answer : e
Answer: e
Problem: how many integers between 314,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,439
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 314,700 and 458,600 is 458,600 - 314,700 = 143,900 - one number per each hundred gives 143,900 / 100 = 1,439 numbers . answer : e ."
Answer: e
Problem: a certain psychologist charges $ 20 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 300 , what is the total charge to a patient who receives only 3 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 188
Rationale: "let the charge for first hour = x + 20 then charge for each additional hour = x x + 20 + 4 x = 300 = > 5 x = 280 = > x = 56 total charge for patient for 3 hours of therapy = x + 20 + 2 x = 3 x + 20 = 188 $ answer e"
Answer: e
Problem: 4 athletes , wendy , michelle , brenda , and jamal , scored in a soccer ( football ) game . if michelle scored 1 more goal than brenda did , jamal scored 3 less than wendy did , and wendy scored 3 more than michelle did , how many fewer goals did brenda score than jamal ?
Options: a ) - 8 , b ) - 6 , c ) - 2 , d ) - 1 , e ) - 3
Rationale: in this word problem , the first key is to turn the story into equations : michelle scored 1 more than brenda did : m = 1 + b jamal scored 3 less than wendy did : j = w - 3 wendy scored 3 more than michelle did : w = 3 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more goals did brenda score than jamal did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 1 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 3 + m so that both b and j are in terms of m : j = ( 3 + m ) - 3 . so if b = m - 1 and j = m , then : b - j = ( m - 1 ) - ( m ) b - j = m - 1 - m ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is d .
Answer: d
Problem: a bus trip of 550 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: the time is the distance / speed . the time difference is 1 hour . 550 / v - 550 / ( v + 5 ) = 1 550 ( v + 5 ) - 550 v = ( v ) ( v + 5 ) 2750 = ( v ) ( v + 5 ) 50 * 55 = ( v ) ( v + 5 ) v = 50 mph the answer is c .
Answer: c
Problem: the sum of the squares of 3 consecutive natural number is 2030 . what is the middle number ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26
Answer: b
Problem: ( √ 112 + √ 567 ) / √ 175 = ?
Options: a ) 2 √ 2 , b ) 13 / 5 , c ) 3 √ 2 , d ) 3 √ 3 , e ) √ 2
Rationale: ( √ 112 + √ 567 ) / √ 175 = ( 4 √ 7 + 9 √ 7 ) / 5 √ 7 = 13 / 5 hence , the correct answer is b .
Answer: b
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 percent is cut away . in the second week 20 percent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "a 105 kg 250 × 0.7 × 0.8 × 0.75 = 105 kg ."
Answer: a
Problem: dan can do a job alone in 12 hours . annie , working alone , can do the same job in just 9 hours . if dan works alone for 8 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: dan can complete 1 / 12 of the job per hour . in 8 hours , dan completes 8 ( 1 / 12 ) = 2 / 3 of the job . annie can complete 1 / 9 of the job per hour . to complete the job , annie will take 1 / 3 / 1 / 9 = 3 hours . the answer is b .
Answer: b
Problem: two cars start from the opposite places of a main road , 105 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : c ) 20 km
Answer: c
Problem: 4 dice are thrown simultaneously on the board . find the probability show the same face ?
Options: a ) 2 / 113 , b ) 1 / 215 , c ) 1 / 216 , d ) 3 / 113 , e ) 4 / 113
Rationale: "the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"
Answer: c
Problem: every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 126 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 126 - - > x = 7 . g - b = 8 x - 3 x = 5 x = 35 . the answer is d .
Answer: d
Problem: ben left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?
Options: a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600
Rationale: in order not to lose money because of the change ben ' s total commission must beat least $ 75,000 - $ 45,000 = $ 30,000 , so total sales must beat least $ 30,000 / 0.15 = $ 200,000 . which means that he must makeat least $ 200,000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d .
Answer: d
Problem: if there are 86 workers in a factory , and on a certain day , 72 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 82.7 % , b ) 81.7 % , c ) 83.7 % , d ) 89.7 % , e ) 88.7 %
Rationale: "72 / 86 * 100 = 83.72 83.7 % correct answer c"
Answer: c
Problem: x does a work in 20 days . y does the same work in 40 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 30 , e ) 13.33
Rationale: x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 40 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 40 ) = 1 / 13.33 both together will finish the work in 13.33 days . correct option is e
Answer: e
Problem: in a school the ratio of boys and girls are in the ration 5 : 6 . 25 % of boys will get scholar ship and 20 % of girls will get scholar ship what % of students wont get scholarship ?
Options: a ) 60 % , b ) 78 % , c ) 88 % , d ) 98 % , e ) 99 %
Rationale: boys : girls = > 5 x : 6 x total no . of students including boys nd girls = 5 x + 6 x = 11 x 25 % of boys = > 5 x * 25 / 100 = 5 x / 4 20 % of girls = > 6 x * 20 / 100 = 6 x / 5 no . of students who are getting scholarship = > 5 x / 4 + 6 x / 5 = 49 x / 20 no . of students who are not getting scholarship = 11 x - 49 x / 20 = 171 x / 20 % of students not getting scolorship = > 171 x / 20 / 11 x * 100 = > 100 * 171 x / 220 x = 77.7 % answer : b
Answer: b
Problem: a start walking from a place at a uniform speed of 7 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 7.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 7 + 5 / 9 = 7.55 answer b
Answer: b
Problem: find large number from below question the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1623
Rationale: "let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 large number = 268 + 1355 = 1623 e"
Answer: e
Problem: six persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of the 7 th person .
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Rationale: "let ‘ x ’ be the average of 6 persons since there are 6 after 2 years the age will be increased by 2 for each . so 6 * 2 = 12 after two years age will be = x + 12 average age is 43 that is ( x + 12 ) / 6 = 43 = > x = 246 let ‘ y ’ be the 7 th person age ( x + y ) / 7 = 45 ( 246 + y ) / 7 = 45 y = ( 45 * 7 ) - 246 y = 69 answer a"
Answer: a
Problem: solve below question 2 x + 1 = - 13
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 13 x = - 7 e"
Answer: e
Problem: car a is 16 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 3.5
Rationale: relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it ' ll need 24 / 8 = 3 hours . answer : d
Answer: d
Problem: if x + y = 290 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 245 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 290 x - y = 200 2 x = 90 x = 45 y = 245 answer is b"
Answer: b
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 5 ] * [ 8 ] equivalent to ?
Options: a ) [ 40 ] , b ) [ 60 ] , c ) [ 80 ] , d ) [ 120 ] , e ) [ 150 ]
Rationale: "[ 5 ] * [ 8 ] = 15 * 4 = 60 = ( 1 / 2 ) ( 120 ) = [ 120 ] the answer is d ."
Answer: d
Problem: if log 10 2 = 0.3010 , the value of log 10 80 is :
Options: a ) 1.5252 , b ) 1.903 , c ) 3.9252 , d ) 3.903 , e ) 2.5252
Rationale: "= log 10 8 + log 10 10 = log 10 ( 23 ) + 1 = 3 log 10 2 + 1 = ( 3 x 0.3010 ) + 1 = 1.9030 . answer b"
Answer: b
Problem: the bankers discount of a certain sum of money is rs . 18 and the true discount on the same sum for the same time is rs . 15 . the sum due is :
Options: a ) 89 , b ) 90 , c ) 91 , d ) 92 , e ) 93
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 18 * 15 ) / 18 - 15 ; 90 answer : b"
Answer: b
Problem: the mean of 50 observations is 200 . but later he found that there is decrements of 34 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 166 , c ) 190 , d ) 198 , e ) 199
Rationale: "166 answer is b"
Answer: b
Problem: the sum of first 45 natural numbers is
Options: a ) 1035 , b ) 1280 , c ) 2070 , d ) 2140 , e ) none
Rationale: solution we know that ( 1 + 2 + 3 + . . . . . + 45 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 45 ) = ( 45 × 46 / 2 ) = 1035 . answer a
Answer: a
Problem: what is the dividend . divisor 13 , the quotient is 17 and the remainder is 1
Options: a ) 222 , b ) 224 , c ) 226 , d ) 228 , e ) 230
Rationale: "a = d * q + r a = 13 * 17 + 1 a = 221 + 1 a = 222"
Answer: a
Problem: a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is :
Options: a ) 125 km , b ) 130 km , c ) 135 km , d ) 140 km , e ) none
Rationale: "sol . let the total journey be x km . then 3 x / 5 + 7 x / 20 + 6.5 = x ⇔ 12 x + 7 x + 20 * 6.5 = 20 x ⇔ x = 130 km . answer b"
Answer: b
Problem: there are 300 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 200 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 300 = 2 / 5 t , or 2 / 5 ( t - m ) = 300 , from here we get that t - m = 750 , that would be total number of female employees and the answer ( c )
Answer: c
Problem: of the seven - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 36 , c ) 72 , d ) 152409600 , e ) 216
Rationale: "of the seven - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; choosing the digit for t - 5 ways ; choosing the digit for u - 4 ways ; # of permutations of 3 digits in ppqrstu - 7 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 * 4 * 7 ! / 2 ! = 152409600 . answer : d ."
Answer: d
Problem: the true discount on a bill of rs . 2260 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 428 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2260 td = rs . 360 pw = f - td = 2260 - 360 = rs . 1900 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1900 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2260 for unexpired time = 360 / 1900 × 2260 = 0.19 × 2260 = rs . 428 answer : option a"
Answer: a
Problem: in the first 20 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 30 overs to reach the target of 302 runs ?
Options: a ) 5 , b ) 6.25 , c ) 6.75 , d ) 6.87 , e ) 7.25
Rationale: required run rate = 302 - ( 4.8 x 20 ) / 30 = 206 / 30 = 6.87 option d
Answer: d
Problem: a trader sells 85 meters of cloth for rs . 8500 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 85 , c ) rs . 90 , d ) rs . 95 , e ) none of these
Rationale: "sp of 1 m of cloth = 8500 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 15 = rs . 85 . answer : b"
Answer: b
Problem: anne bought doughnuts for a class breakfast party . she bought 9 chocolate doughnuts , 7 coconut doughnuts , and 9 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 9 + 7 + 9 = 25 . answer is a ."
Answer: a
Problem: the length of a rectangle i s two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units
b ) 149
c ) 148
d ) 17
e ) 143
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : option a
Answer: a
Problem: a cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.9 , c ) 8.6 , d ) 8.3 , e ) 9.0
Rationale: distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 10 miles per hour time = t 2 = distance / speed = x / 10 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 8 = x ( 1 / 10 + 1 / 8 ) = = 9 x / 40 speed = 2 x / ( 9 x / 40 ) = 80 / 9 = 8.9 answer : b
Answer: b
Problem: sandy is younger than molly by 6 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 45
Rationale: "s = m - 6 s / m = 7 / 9 9 s = 7 m 9 ( m - 6 ) = 7 m m = 27 the answer is c ."
Answer: c
Problem: the average weight of 25 persons sitting in a boat had some value . a new person added to them whose weight was 46 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 25 persons ?
Options: a ) 55 kg , b ) 48 kg , c ) 52 kg , d ) none , e ) 55 kg
Rationale: "answer : option d 25 x + 46 = 26 ( x â € “ 5 ) x = 176"
Answer: d
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 38 years . what is molly ' s age right now ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: now , sandy is 38 - 6 = 32 molly ' s age is ( 3 / 4 ) * 32 = 24 the answer is d .
Answer: d
Problem: a hexagon is formed abcdef which perimeter 36 cm . a polygon is formed by joining the points ae & bd . find the area of the polygon abde ?
Options: a ) 34 √ 3 cm 2
b ) 35 √ 3 cm 2
c ) 36 √ 3 cm 2
d ) 37 √ 3 cm 2
e ) 38 √ 3 cm 2
Rationale: a regular hexagon consist of 6 equilateral triangle . each of side 6 cm . so the area of 1 equilateral triangle is = ¼ ( √ 3 a 2 ) = 9 √ 3 cm 2 the figure formed by joining polygon abde consist of 2 equilateral triangle and 4 half equilateral triangle which employs area of 4 equilateral triangle . so , the area of polygon abde = 4 * ( area of equilateral traingle ) = 4 * 9 √ 3 = 36 √ 3 cm 2 answer : c
Answer: c
Problem: 10 , 1000 , 100000 , 10000000 . . . .
Options: a ) 100 , 000,000 , b ) 1,000 , 000,000 , c ) 1 , 000,000 , 000,000 , d ) 100 , e ) 1 , 000,000
Rationale: "each number in this sequence is multiplied by 100 . with multiples of ten , it is easiest to remember that you can just transfer all the zeroes on the end of the end of any number . example : 10 x 100 = 1,000 . add two digits to the end of 10 , 000,000 and you get 1,000 , 000,000 . answer is b"
Answer: b
Problem: an investor deposited $ 10,000 to open a new savings account that earned 12 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 10,300 , b ) $ 10,303 , c ) $ 10,600 , d ) $ 10,609 , e ) $ 10,900
Rationale: "the amount in the account after 6 months is 1.03 * 1.03 ( $ 10,000 ) = $ 10,609 . the answer is d ."
Answer: d
Problem: in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 18 % , e ) 22 %
Rationale: "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 2 / 5 = 1 / 15 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 15 = 13 / 60 which is about 22 % the answer is e ."
Answer: e
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 500 and $ 300 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "the smallest amount that the company can spend is the lcm of 500 and 300 , which is 1500 for each , which is total 3000 . the number of 1 st type of computers which costing $ 500 = 1500 / 500 = 3 . the number of 2 nd type of computers which costing $ 300 = 1500 / 300 = 3 . total = 3 + 3 = 6 answer is d ."
Answer: d
Problem: 212 : 436 : : 560 : ?
Options: a ) 786 , b ) 682 , c ) 784 , d ) 688 , e ) 622
Rationale: "2 + 2 = 4 1 + 2 = 3 2 + 4 = 6 like that , 5 + 2 = 7 6 + 2 = 8 0 + 4 = 4 answer c"
Answer: c
Problem: circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 45 more revolutions than gear p ?
Options: a ) 45 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 45 = 30 * 1.5 more revolutions is 60 * 1.5 = 90 seconds . the answer is c ."
Answer: c
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 6 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: 6 ” 3 = 9 - 6 = 3 answer : b
Answer: b
Problem: the sides of a square region , measured to the nearest centimeter , are 4 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 15.25 sq cm , b ) 18.25 sq cm , c ) 12.25 sq cm , d ) 21.25 sq cm , e ) 25.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 3.5 is equidistant from both 3 and 4 ) the answer still should be : 3.5 ^ 2 = 12.25 . answer : c"
Answer: c
Problem: what sum of money will produce rs . 80 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 571.4 , c ) 367 , d ) 368 , e ) 339
Rationale: "80 = ( p * 4 * 7 / 2 ) / 100 p = 571.4 answer : b"
Answer: b
Problem: two - third of a positive number and 144 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 1
Rationale: "let the number be x . then , 2 / 3 x = 144 / 216 * 1 / x x 2 = 144 / 216 * 3 / 2 = 144 / 144 x = 1 answer : e"
Answer: e
Problem: from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is ?
Options: a ) 45 % , b ) 49.6 % , c ) 51.2 % , d ) 55 % , e ) 60.3 %
Rationale: let the total quantity of original milk = 1000 gm milk after 1 st operation = 80 % of 1000 = 800 gm milk after second operation = 80 % of 800 = 640 gm milk after third operation = 80 % of 640 = 512 gm strength of final mixture = 51.2 % answer is c
Answer: c
Problem: after 6 games , team b had an average of 70 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 85 , b ) 74 , c ) 67 , d ) 33 , e ) 28
Rationale: "( 6 * 70 ) + 47 + x > 500 420 + 47 + x > 500 467 + x > 500 = > x > 33 option d"
Answer: d
Problem: if a ' s height is 40 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 40 / ( 100 - 40 ) ] x 100 % = 66.66 % answer : a ) 66.66 %"
Answer: a
Problem: how long will a boy take to run round a square field of side 35 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 22 , b ) 38 , c ) 37 , d ) 56 , e ) 28
Rationale: answer : d ) 56 sec
Answer: d
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 40 to incur a loss 20 % ?
Options: a ) 20 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 40 * ( 100 % + 20 % ) = $ 48 number of articles to be sold for $ 48 to incur a 20 % loss : $ 48 / $ 2.40 = 20 thus , solution a is correct ."
Answer: a
Problem: if two positive numbers are in the ratio 1 / 7 : 1 / 4 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 75 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 7 : 1 / 4 = 4 : 7 let first number be 4 x and the second number be 7 x . the second number is more than first number by 3 x . required percentage = 3 x / 4 x * 100 = 75 % . answer : c"
Answer: c
Problem: a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.09 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fourth day it is overdue ?
Options: a ) $ 0.66 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.09 2 nd day fine - 0.09 * 2 = 0.18 ( as doubling gives lower value ) 3 rd day fine - 0.18 * 2 = 0.36 ( as doubling gives lower value ) 4 th day fine - 0.36 + 0.3 = 0.66 ( as doubling gives higher value we add 0.3 this time ) answer : a ."
Answer: a
Problem: what is the sum of the numbers between 1 and 14 , inclusive ?
Options: a ) 105 , b ) 110 , c ) 125 , d ) 150 , e ) 160
Rationale: "sol . add up the numbers between 1 and 14 . answer is a , 105"
Answer: a
Problem: how many prime numbers are between 25 / 3 and 84 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "25 / 3 = 8 . xxx 84 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Problem: a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 400 and $ 350 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "the smallest amount that the company can spend is the lcm of 400 and 350 , which is 2800 for each , which is total 5600 . the number of 1 st type of computers which costing $ 400 = 2800 / 400 = 7 . the number of 2 nd type of computers which costing $ 350 = 2800 / 350 = 8 . total = 7 + 8 = 15 answer is c ."
Answer: c
Problem: if 13 = 13 w / ( 1 - w ) , then ( 6 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 6
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 6 w = 3 6 w * 2 = 3 * 2 = 6 answer : e"
Answer: e
Problem: a man can row upstream at 25 kmph and downstream at 55 kmph , and then find the speed of the man in still water ?
Options: a ) 65 , b ) 40 , c ) 30 , d ) 78 , e ) 38
Rationale: "us = 25 ds = 55 m = ( 55 + 25 ) / 2 = 40 answer : b"
Answer: b
Problem: in a room filled with 6 people , all 6 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 3 / 5 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 6 , e ) 7 / 12
Rationale: "the 6 people consist of two sets of 3 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 3 c 2 = 3 . the number of ways to choose 2 from the second group of siblings is 3 c 2 = 3 . the number of ways to choose 2 people who are siblings is 3 + 3 = 6 . the number of ways to choose 2 people who are not siblings is 15 - 6 = 9 . p ( the two people are not siblings ) = 9 / 15 = 3 / 5 the answer is a ."
Answer: a
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 60 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 4080 , d ) s . 3965 , e ) s . 3929
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 60 = rs . 4080 . answer : c"
Answer: c
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 32 hours and 16 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 1 : 2 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 32 = 1 : 2 . answer : d
Answer: d
Problem: an electrical appliances store sold this month 400 % more than the average of all the other months in the year . the sales total for this month was approximately what percent of total sales for this year ?
Options: a ) 14 % , b ) 21 % . , c ) 31 % . , d ) 37 % . , e ) 43 % .
Rationale: the average sales for all the other months ( 11 months ) of the year is x . so , the total sales of those 11 months will be = 11 x now , this month ' s sales , which is 400 % more than the average of other months ' sales , is 5 x , ( x + 400 % of x ) . thus , this month ' s ' sales are ( 5 x / 16 x ) * 100 = 31.25 % of the total yearly sales . [ total sales = 11 x + 5 x = 16 x ] answer is b
Answer: b
Problem: a bag contains 10 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 21 / 44 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15
Rationale: drawing two balls of same color from ten green balls can be done in 10 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 10 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 21 / 44 answer : b
Answer: b
Problem: two bike riders ride in opposite directions around a circular track , starting at the same time from the same point . biker a rides at a speed of 16 kmph and biker b rides at a speed of 14 kmph . if the track has a diameter of 40 km , after how much time ( in hours ) will the two bikers meet ?
Options: a ) 8.18 hrs . , b ) 6.18 hrs . , c ) 4.18 hrs . , d ) 1.18 hrs . , e ) 7.18 hrs .
Rationale: explanation : distance to be covered = = 40 km relative speed of bikers = 16 + 14 = 30 kmph . now , = = 4.18 hrs . answer : c
Answer: c
Problem: a cistern 12 m long and 14 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 224 m 2 , b ) 250 m 2 , c ) 220 m 2 , d ) 230 m 2 , e ) 233 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 14 x 1.25 + 12 x 1.25 ) + 12 x 14 ] m 2 = 233 m 2 . answer : e"
Answer: e
Problem: if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 10 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 20 , e ) 1 / 4
Rationale: say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 10 - - > f = 20 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 20 ) = 3 / 20 . answer : d .
Answer: d
Problem: john and david can finish a job together in 2 hours . if john can do the job by himself in 3 hours , what percent of the job does david do ?
Options: a ) 36.33 % , b ) 33.33 % , c ) 39.33 % , d ) 40.33 % , e ) 33 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 18 donuts which is the job ( i picked this as a smart number ) . john on his own works 18 / 3 = 6 donuts per hour . john and david work 18 / 2 = 9 donuts per hour so david works 3 donuts / hour to find out the percentage , david works 3 donuts / hr x 2 hours = 6 donuts per hour . therefore 6 donuts / 18 donuts = 1 / 3 = 33.33 % answer : b"
Answer: b
Problem: find the compound interest on $ 10000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 10000 * ( 1 + 2 / 100 ) ^ 4 = 10000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 10824.32 c . i . = 10824.32 - 10000 = $ 824.32 answer is b"
Answer: b
Problem: if a = 105 and a ^ 3 = 21 × 25 × 45 × z , what is the value of z ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × z = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x z = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z z = 7 ^ 2 = 49 answer d"
Answer: d
Problem: if the cost price of 50 articles is equal to the selling price of 45 articles , then the gain or loss percent is ?
Options: a ) 11.11 , b ) 65 , c ) 78 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 45 articles . let cost price of one article = rs . 1 selling price of 45 articles = rs . 50 but cost price of 45 articles = rs . 45 therefore , the trader made profit . \ percentage of profit = 5 / 45 * 100 = 11.11 % answer : a"
Answer: a
Problem: the area of one square is x ^ 2 + 6 x + 9 and the area of another square is 4 x ^ 2 − 28 x + 49 . if the sum of the perimeters of both squares is 56 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 3 ) ^ 2 and ( 2 x - 7 ) ^ 2 . the lengths of the sides are x + 3 and 2 x - 7 . if we add the two perimeters : 4 ( x + 3 ) + 4 ( 2 x - 7 ) = 56 12 x = 72 x = 6 the answer is d ."
Answer: d
Problem: a train moves with a speed of 162 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) 45
Rationale: "solution speed = 108 kmph = ( 162 x 5 / 18 ) m / sec = 45 m / sec . answer e"
Answer: e
Problem: which number should replace both the asterisks in ( * / 20 ) x ( * / 80 ) = 1 ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 120
Rationale: "let ( y / 20 ) x ( y / 80 ) = 1 y ^ 2 = 20 x 80 = 20 x 20 x 4 y = ( 20 x 2 ) = 40 the answer is b ."
Answer: b
Problem: two trains of equal length , running with the speeds of 60 and 90 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 3.2 , b ) 2.6 , c ) 6.6 , d ) 32.2 , e ) 42.2
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 90 = 150 * 5 / 18 t = 2500 / 9 * 18 / 750 = 6.6 sec . answer : c"
Answer: c
Problem: a couple spent $ 211.20 in total while dining out and paid this amount using a credit card . the $ 211.20 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 120 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 180
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = $ 211.20 x = $ 160 the correct answer is d ."
Answer: d
Problem: at a school , 3 - fifths of the male students and two - thirds of the female students speak a foreign language . if the number of males is equal to the number of females , what fraction of the students speak a foreign language ?
Options: a ) 17 / 30 , b ) 19 / 30 , c ) 11 / 15 , d ) 7 / 15 , e ) 2 / 5
Rationale: let x be the number of students in the school . the number of males who speak a foreign language is ( 3 / 5 ) ( 1 / 2 ) x = ( 3 / 10 ) x the number of females who speak a foreign language is ( 2 / 3 ) ( 1 / 2 ) x = ( 1 / 3 ) x the total number of students who speak a foreign language is ( 3 / 10 ) x + ( 1 / 3 ) x = ( 19 / 30 ) x the answer is b .
Answer: b
Problem: 11 + 12 + 13 + . . . 51 + 52 = ?
Options: a ) 1361 , b ) 1362 , c ) 1323 , d ) 1364 , e ) 1365
Rationale: "sum = 11 + 12 + 13 + . . . 50 + 51 + 52 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 52 positive integers = 52 * 53 / 2 sum of first 10 positive integers = 10 * 11 / 2 sum = 11 + 12 + 13 + 14 + . . . 51 + 52 = 52 * 53 / 2 - 10 * 11 / 2 = 1323 answer : c"
Answer: c