regisss/math_qa huggingface dataset:
Problem: x varies inversely as square of y . given that y = 3 for x = 1 . the value of x for y = 2 will be equal to :
Options: a ) 3 , b ) 6 , c ) 1 / 9 , d ) 1 / 3 , e ) 9 / 4
Rationale: "explanation : solution : given x = k / y ^ 2 , where k is constant . now , y = 3 and x = 1 gives k = 9 . . ' . x = 9 / y ^ 2 = > x = 9 / 2 ^ 2 = 9 / 4 answer : e"
Answer: e
Problem: it takes 1.5 hours for tim to mow the lawn . linda can mow the same lawn in 2 hours . how long will it take john and linda , work together , to mow the lawn ?
Options: a ) 51.1 minutes , b ) 51.3 minutes , c ) 51.5 minutes , d ) 51.7 minutes , e ) 51.9 minutes
Rationale: we first calculate the rate of work of john and linda john : 1 / 1.5 and linda 1 / 2 let t be the time for john and linda to mow the lawn . the work done by john alone is given by t * ( 1 / 1.5 ) the work done by linda alone is given by t * ( 1 / 2 ) when the two work together , their work will be added . hence t * ( 1 / 1.5 ) + t * ( 1 / 2 ) = 1 multiply all terms by 6 6 ( t * ( 1 / 1.5 ) + t * ( 1 / 2 ) ) = 6 and simplify 4 t + 3 t = 6 solve for t t = 6 / 7 hours = 51.5 minutes . answer c
Answer: c
Problem: you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 19 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 31 , d ) 42 , e ) 43
Rationale: "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 ã — 2 = 50 pens . sharon takes 19 pens from you : 50 - 19 = 31 pens . so you have 31 at the end . correct answer : c"
Answer: c
Problem: the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 50,000 , how much profit did the business make ?
Options: a ) $ 80,000 , b ) $ 100,000 , c ) $ 120,000 , d ) $ 150,000 , e ) $ 200,000
Rationale: let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 50000 p = $ 80,000 the answer is a .
Answer: a
Problem: in a group of 28 junior high school students , 7 take french , 10 take spanish , and 2 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 8
Rationale: "c 9 add 7 + 10 + 2 to get 19 then subtract 21 from the total students ⇒ 28 – 19 = 9 . answer is c"
Answer: c
Problem: a wheel rotates 10 times every minute and moves 20 cm during each rotation . how many ems does the wheel move in 1 hour ?
Options: a ) 20000 , b ) 14000 , c ) 23000 , d ) 120000 , e ) none of these
Rationale: explanation : number of wheel moves in 1 hour = 10 * 60 = 600 distance moved = 600 * 200 = 12000 answer : d
Answer: d
Problem: the average ( arithmetic mean ) of the integers from 200 to 400 , inclusive , is how much greater than the average of the integers from 100 to 200 , inclusive ?
Options: a ) 150 , b ) 175 , c ) 200 , d ) 225 , e ) 300
Rationale: "for an ap the mean or average of series is average of first and last term . so , average of numbers between 200 to 400 , inclusive = ( 200 + 400 ) / 2 = 300 average of numbers between 100 to 200 , inclusive = ( 100 + 200 ) / 2 = 150 difference = 300 - 150 = 150 answer is a"
Answer: a
Problem: the total circumference of two circles is 64 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 6.7 , d ) 10.2 , e ) 18.0
Rationale: let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 64 where 2 r = r thus : 2 π r + 4 π r = 64 6 π r = 64 r = approx 3.4 π r + 2 r π = 64 3 π r = 64 r = approx 6.8 r + r = approx 10.2 answer d
Answer: d
Problem: a car takes 6 hours to cover a distance of 469 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 48 kmph , b ) 50 kmph , c ) 52 kmph , d ) 56 kmph , e ) 60 kmph
Rationale: "time = 6 distence = 469 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 469 / 9 = 52 kmph c"
Answer: c
Problem: excluding stoppages , the speed of a bus is 62 kmph and including stoppages , it is 56 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 70 min , b ) 16 min , c ) 7 min , d ) 6 min , e ) 40 min
Rationale: "d 10 min due to stoppages , it covers 6 km less . time taken to cover 6 km = ( 6 / 62 x 60 ) min = 6 min"
Answer: d
Problem: the greatest number that divides 3560 and 3450 leaving remainder 4 and 6 respectively is :
Options: a ) 23 , b ) 25 , c ) 26 , d ) 28 , e ) 30
Rationale: "explanation : 3560 - 4 = 3556 , 3450 - 6 = 3444 highest number that can divide 3556 and 3444 is hcf of numbers hcf of 3556 and 3444 = 28 answer : d"
Answer: d
Problem: if the cost price is 75 % of selling price then what is the profit percentage .
Options: a ) 30.33 , b ) 31.33 , c ) 32.33 , d ) 33.33 , e ) 34.33
Rationale: "selling price = rs 100 : then cost price = rs 75 : profit = rs 25 . profit = { ( 25 / 75 ) * 100 } % = 33.33 % answer is d ."
Answer: d
Problem: find the simple interest on $ 500 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 150 , e ) $ 100
Rationale: "si = ptr / 100 = 500 * 3 * 10 / 100 = $ 150 answer is d"
Answer: d
Problem: what is the sum of all possible solutions to | x - 4 | ^ 2 + | x - 4 | = 12 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "denote | x - 4 | as y : y ^ 2 + y = 12 - - > y = - 4 or y = 3 . discard the first solution since y = | x - 4 | , so it ' s an absolute value and thus can not be negative . y = | x - 4 | = 3 - - > x = 7 or x = 0 . the sum = 7 . answer : e ."
Answer: e
Problem: a cistern is normally filled in 4 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 12 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 4 - 1 / x = 1 / 6 , solving 1 / x = 1 / 12 so in 12 hours full cistern will be empty . answer : e"
Answer: e
Problem: in a house a hall is 20 m long , 15 m wide and 5 m high . its interior has to be covered with mat . what will be the total expenditure if it costs rs . 30 per square m ?
Options: a ) s . 28500 , b ) s . 50000 , c ) s . 57000 , d ) s . 60000 , e ) s . 62000
Rationale: "length ( l ) = 20 m , breadth ( b ) = 15 m and height ( h ) = 5 m total area of the hall to be covered with mat = 2 ( lb + bh + hl ) = 2 ( 20 * 15 + 15 * 5 + 5 * 20 ) = 2 ( 300 + 75 + 100 ) = 2 * 475 = 950 sq . m total expenditure = 30 * 950 = rs . 28,500 a"
Answer: a
Problem: an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 16 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 16 , e ) 40
Rationale: "let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 16 ( x - y ) - - > x + y = 16 . answer : d ."
Answer: d
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 960 grams . find the profit percent .
Options: a ) 4.166 , b ) 3.1 , c ) 2.1 , d ) 1.256 , e ) 3.759
Rationale: "explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 960 100 + g / 100 + 0 = 1000 / 960 100 + g = 100 / 96 * 100 g = 4.166 answer : a"
Answer: a
Problem: the sum of the numbers is 220 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 60 , e ) 27
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 220 11 x / 3 = 220 x = 60 answer : d"
Answer: d
Problem: the profit earned by selling an article for 832 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 1060 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 832 – x = 448 + x or , x = 384 ⁄ 2 = 192 \ cost price of the article = 832 – x = 448 + x = 640 \ sp of the article = 640 × 150 ⁄ 100 = 960 answer a"
Answer: a
Problem: for what value of â € œ k â €  will the equation ( 2 kx 2 + 6 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 4 / 9 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 6 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 4 / 9 answer : b"
Answer: b
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1305 , find the loss % ?
Options: a ) 13 % , b ) 16 % , c ) 17 % , d ) 78 % , e ) 28 %
Rationale: "1500 - - - - 195 100 - - - - ? = > 13 % answer : a"
Answer: a
Problem: $ 366 is divided amongst a , b and c so that a may get 1 / 2 as much as b and c together , b may get 2 / 3 as much as a and c together , then the share of a is
Options: a ) $ 122 , b ) $ 150 , c ) $ 176 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 1 : 2 a ' s share = 366 * 1 / 3 = $ 122 answer is a"
Answer: a
Problem: a constructor estimates that 5 people can repair mr rohan ' s house in 6 days . if he uses 6 people instead of 5 , how long will they take to complete the job ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 3 , e ) 5
Rationale: explanation : use formula for a work members ã — days = constant 5 ã — 6 = 6 ã — a a = 5 so answer is 3 days answer : e
Answer: e
Problem: if 12 boys meet at a reunion and each boy shakes hands exactly once with each of the others , then what is the total number of handshakes
Options: a ) 41 , b ) 42 , c ) 43 , d ) 66 , e ) 45
Rationale: "n ( n - 1 ) / 2 = 12 * 11 / 2 = 66 answer : d"
Answer: d
Problem: if the cost price is 25 % of selling price . then what is the profit percent .
Options: a ) 150 % , b ) 200 % , c ) 300 % , d ) 350 % , e ) none of these
Rationale: "explanation : let the s . p = 100 then c . p . = 25 profit = 75 profit % = ( 75 / 25 ) * 100 = 300 % . answer : c"
Answer: c
Problem: in a certain animal shelter , the ratio of the number of dogs to the number of cats is 15 to 7 . if 16 additional cats were to be taken in by the shelter , the ratio of the number of dogs to the number of cats would be 15 to 11 . how many dogs are in the shelter ?
Options: a ) 15 , b ) 25 , c ) 30 , d ) 45 , e ) 60
Rationale: "this ratio question can be solved in a couple of different ways . here ' s an algebraic approach . . . we ' re told that the ratio of the number of dogs to the number of cats is 15 : 7 . we ' re then told that 16 more cats are added to this group and the ratio becomes 15 : 11 . we ' re asked for the number of dogs . algebraically , since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7 , we can write this initial relationship as . . . 15 x / 7 x when we add the 12 cats and factor in the ' ending ratio ' , we have an equation . . . . 15 x / ( 7 x + 16 ) = 15 / 11 here we have 1 variable and 1 equation , so we can solve for x . . . . ( 15 x ) ( 11 ) = ( 7 x + 16 ) ( 15 ) ( x ) ( 11 ) = ( 7 x + 16 ) ( 1 ) 11 x = 7 x + 16 4 x = 16 x = 4 with this x , we can figure out the initial number of dogs and cats . . . initial dogs = 15 x = 15 ( 4 ) = 60 final answer : e"
Answer: e
Problem: in a rectangular coordinate system , what is the area of a quadrilateral whose vertices have the coordinates ( 4 , - 3 ) , ( 4 , 7 ) , ( 12 , 2 ) , ( 12 , - 7 ) ?
Options: a ) 64
b ) 68
c ) 72
d ) 76
e ) 80
Rationale: by graphing the points , we can see that this figure is a trapezoid . a trapezoid is any quadrilateral that has one set of parallel sides , and the formula for the area of a trapezoid is : area = ( 1 / 2 ) × ( base 1 + base 2 ) × ( height ) , where the bases are the parallel sides . we can now determine the area of the quadrilateral : area = 1 / 2 × ( 10 + 9 ) × 8 = 76 . the answer is d .
Answer: d
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 5 more revolutions than gear p ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 5 = 30 / 6 more revolutions is 60 / 6 = 10 seconds . the answer is c ."
Answer: c
Problem: the length and breadth of a rectangle is increased by 30 % and 45 % respectively . what is the increase in the area ?
Options: a ) 88.25 , b ) 87.5 , c ) 86.0 , d ) 88.0 , e ) 88.5
Rationale: "100 * 100 = 10000 130 * 145 = 18850 - - - - - - - - - - - 8850 10000 - - - - 8850 100 - - - - - 88.50 answer e"
Answer: e
Problem: 8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 21.2 % , b ) 21.6 % , c ) 22.0 % , d ) 22.4 % , e ) 22.8 %
Rationale: the total amount of alcohol is 0.25 ( 8 ) + 0.12 ( 2 ) = 2.24 liters . the percentage is 2.24 / 10 = 22.4 / 100 which is 22.4 % the answer is d .
Answer: d
Problem: a certain university will select 1 of 6 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 270 , c ) 140 , d ) 165 , e ) 315
Rationale: "1 of 6 will be chosen for the math 2 of 10 will be chosen for the computer none of the 3 chosen people can be in more than one departments . we can choose any of the 6 candidates for the math dep . , which gives as 6 selections . we can choose 2 of the 10 candidates for the computer dep . , which gives us 2 selections and 8 rejections . so , the way to find how many different selections of 2 candidates we can have for the computer dep . , we do : 10 ! / 2 ! * 8 ! = ( 9 * 10 ) / 2 = 90 / 2 = 45 . we are multiplying our individual selections : 6 * 45 = 270 in the bolded part , we do n ' t have to multiply all of the numbers , as those in 8 ! are included in 10 ! , so we simplify instead . ans b"
Answer: b
Problem: in a school 20 % of the boys are same in number as 1 / 4 th of the girls . what is the ratio of boys to the girls in the school ?
Options: a ) 5 : 4 , b ) 2 : 3 , c ) 1 : 4 , d ) 3 : 7 , e ) 2 : 5
Rationale: "20 % of b = 1 / 4 g 20 b / 100 = g / 4 b = 5 g / 4 b / g = 5 / 4 b : g = 5 : 4 answer is a"
Answer: a
Problem: find the least number must be subtracted from 5264 so that remaining number is divisible by 17 .
Options: a ) 11 , b ) 14 , c ) 18 , d ) 20 , e ) 29
Rationale: when dividing 5264 by 17 , we get the remainder 11 , so 11 should be subtracted . the answer is a .
Answer: a
Problem: a salesman ' s income consists of a commission and a base salary of $ 400 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 315 , e ) $ 730
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1430 - $ 800 = $ 630 for 2 weeks avg weekly commission = $ 315 answer d"
Answer: d
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 4 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 260 miles , d ) 425 miles , e ) 525 miles
Rationale: during each hour , the car travels 65 miles . for 4 hours it will travel 65 + 65 + 65 + 65 = 4 × 65 = 260 miles correct answer is c ) 260 miles
Answer: c
Problem: a can give b 150 meters start and c 300 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 111.64 , d ) 111.11 , e ) 176.47
Rationale: "a runs 1000 m while b runs 850 m and c runs 700 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 700 ) / 850 = 823.53 m . b can give c = 1000 - 823.53 = 176.47 m . answer : e"
Answer: e
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 100 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 100 - 55 = 45 n = 9 the answer is d ."
Answer: d
Problem: 5 is added to a certain number , the sum is multiplied by 5 , the product is divided by 5 and 5 is subtracted from the quotient . the remainder left is half of 60 . what is the number ?
Options: a ) 21 , b ) 20 , c ) 2 , d ) 30 , e ) 45
Rationale: "let number is x . when 5 added to it , = ( x + 5 ) 5 multiplied to sum , = 5 * ( x + 5 ) now , = [ { 5 * ( x + 5 ) } / 5 ] and , = [ { 5 * ( x + 5 ) } / 5 ] - 5 according to question , [ { 5 * ( x + 5 ) } / 5 ] - 5 = half of 60 [ ( 5 x + 25 ) / 5 ) = 30 + 5 5 x + 25 = 35 * 5 x + 5 = 7 * 1 x + 5 = 7 x = 7 - 5 x = 2 so , required number is : 2 . answer : c"
Answer: c
Problem: how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) one , b ) 4 , c ) 5 , d ) 8 , e ) 9
Rationale: "slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"
Answer: c
Problem: a train 250 m long running at 72 kmph crosses a platform in 15 sec . what is the length of the platform ?
Options: a ) 50 m , b ) 200 m , c ) 250 m , d ) 270 m , e ) 300 m
Rationale: "d = 72 * 5 / 18 = 15 = 300 â € “ 250 = 50 m answer : a"
Answer: a
Problem: a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be green ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: "given : 2 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 2 red and 3 green marbles after one red has been picked , we need to pick 1 green from a total of 2 green and 2 red marbles . p ( both green ) = ( 3 / 5 ) * ( 2 / 4 ) = 3 / 10 option c"
Answer: c
Problem: a baseball card decreased in value 20 % in its first year and 30 % 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 ) 36 % , e ) 44 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.8 = 80 after second year price = 80 * 0.7 = 56 final decrease = [ ( 100 - 56 ) / 100 ] * 100 = 44 % correct answer - e"
Answer: e
Problem: a batsman makes a score of 300 runs in the 17 th inning and thus increases his averages by 10 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 140 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 300 then average run after 17 th inning = ( 16 x + 300 ) / 17 ( 16 x + 300 ) / 17 = x + 10 = > 16 x + 300 = 17 x + 170 x = 130 average after 17 th inning = 130 + 10 = 140 answer : b"
Answer: b
Problem: solve : 0.6 * 0.6 + 0.6 * 0.6
Options: a ) 0.46 , b ) 0.56 , c ) 0.64 , d ) 0.65 , e ) none of them
Rationale: "= 0.6 * 0.6 + ( 0.6 * 6 ) = 0.36 + 0.1 = 0.46 answer is a ."
Answer: a
Problem: in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 78 , c ) 86 , d ) 126 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 12 = 30 5 * quotient = 30 quotient = 6 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 6 ) + 6 = 126 . d )"
Answer: d
Problem: a can do a piece of work 30 days . b can do work in 55 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19.4 days , d ) 17.2 days , e ) 18 days
Rationale: "lcm = 330 , ratio = 30 : 45 = 6 : 11 no of days = 330 / ( 6 + 11 ) = 330 / 17 = 19.4 days answer : c"
Answer: c
Problem: the diameter of a garden roller is 1.2 m and it is 2 m long . how much area will it cover in 5 revolutions ? ( use ï € = 22 â  „ 7 )
Options: a ) 40 m 2
b ) 44 m 2
c ) 48 m 2
d ) 37.7 m 2
e ) none of these
Rationale: required area covered in 5 revolutions = 5 ã — 2 ï € rh = 5 ã — 2 ã — 22 â  „ 7 ã — 0.6 ã — 2 = 37.7 m 2 answer d
Answer: d
Problem: rs . 2080 is divided so that 3 times the first share , thrice the 2 nd share and four times the third share amount to the same . what is the value of the second share ?
Options: a ) s 802 , b ) s 208 , c ) s 960 , d ) s 690 , e ) s 906
Rationale: "a + b + c = 2080 3 a = 2 b = 4 c = x a : b : c = 1 / 3 : 1 / 2 : 1 / 4 = 4 : 6 : 3 6 / 13 * 2080 = rs 960 answer : c"
Answer: c
Problem: two trains running in opposite directions cross a man standing on the platform in 67 seconds and 17 seconds respectively and they cross each other in 73 seconds . the ratio of their speeds is :
Options: a ) 3 / 2 , b ) 3 / 9 , c ) 3 / 6 , d ) 3 / 1 , e ) 3 / 5
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 23 = = > 27 x + 17 y = 23 x + 23 y = = > 4 x = 6 y = = > x / y = 3 / 2 . answer : a"
Answer: a
Problem: you make a cube that is made of 10 x 10 x 10 smaller cubes which sums up to a total of 1000 smaller cubes . now , if someone takes one layer of cubes , how many will remain ?
Options: a ) 357 , b ) 834 , c ) 500 , d ) 512 , e ) 216
Rationale: d 512 the cube that remains will be 8 x 8 x 8 . this will make a total of 512 . this is because , when a layer is taken , it will be taken from all sides of the cube which will reduce the dimension be two and not one .
Answer: d
Problem: if a - b = 4 and a 2 + b 2 = 30 , find the value of ab .
Options: a ) a ) 7 , b ) b ) 12 , c ) c ) 15 , d ) d ) 18 , e ) e ) 20
Rationale: "explanation : 2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 30 - 16 = 14 ab = 7 answer : a"
Answer: a
Problem: in a regular week , there are 5 working days and for each day , the working hours are 8 . a man gets rs . 2.40 per hour for regular work and rs . 3.20 per hours for overtime . if he earns rs . 432 in 4 weeks , then how many hours does he work for ? a . 160 b . 175 c . 180 d . 195 explanation :
Options: a ) 160 , b ) 175 , c ) 180 , d ) 185 , e ) 195
Rationale: suppose the man works overtime for x hours . now , working hours in 4 weeks = ( 5 x 8 x 4 ) = 160 . 160 x 2.40 + x x 3.20 = 432 3.20 x = 432 - 384 = 48 x = 15 . hence , total hours of work = ( 160 + 15 ) = 175 . answer : option b
Answer: b
Problem: of the 200 stamps in a collection , 90 are foreign and 60 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 50 , b ) 70 , c ) 100 , d ) 130 , e ) 150
Rationale: "20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 40 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 40 ) = 70 the answer is b ."
Answer: b
Problem: a cylindrical cube of radius 12 cm contains water upto a depth of 20 cm . a spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm . the radius of the ball is :
Options: a ) 7 cm
b ) 8.5 cm
c ) 9 cm
d ) 9.5 cm
e ) none
Rationale: sol . let the radius of the ball be r cm . volume of ball = volume of water displaced by it . ∴ 4 / 3 ∏ r ³ = ∏ * 12 * 12 * 6.75 ⇒ r ³ = 9 * 9 * 9 ⇒ r = 9 cm . answer c
Answer: c
Problem: a batsman in his 12 th innings makes a score of 92 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
Options: a ) 42 , b ) 43 , c ) 70 , d ) 45 , e ) 46
Rationale: "let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 92 ∴ x = 70 answer c"
Answer: c
Problem: a snail , climbing a 36 feet high wall , climbs up 8 feet on the first day but slides down 4 feet on the second . it climbs 8 feet on the third day and slides down again 4 feet on the fourth day . if this pattern continues , how many days will it take the snail to reach the top of the wall ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 20 , e ) 21
Rationale: "total transaction in two days = 8 - 4 = 4 feet in 15 days it will climb 36 feet thus reaching the top therefore , total no of days required = 15 c"
Answer: c
Problem: what is the least number by which 16800 must be divided to get a number perfect square
Options: a ) 21 , b ) 42 , c ) 24 , d ) 40 , e ) 45
Rationale: 16,800 / 42 = 400 400 = ( 20 ) ^ 2 ans - 42 answer : b
Answer: b
Problem: addison high school ’ s senior class has 300 boys and 240 girls . if 30 % of the boys did not attend the college then 70 % of the total class attended college , what percentage of the girls class did not attend college ?
Options: a ) 70 , b ) 45 , c ) 50 , d ) 46 , e ) 30
Rationale: "% of boy attending the college = 100 - 30 = 70 % number of boys attending the college : 0.70 * 300 = 210 total people = 300 + 240 = 540 total number of students attending the college : 0.70 * 540 = 378 number of girls attending the college = 378 - 210 = 168 number of girls not attending the college = 240 - 168 = 72 % of girls not attending = 72 / 240 = 30 % . e is the correct answer"
Answer: e
Problem: if the average ( arithmetic mean ) of a and b is 140 , and the average of b and c is 100 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 135 , e ) 80
Rationale: "a + b = 280 b + c = 200 a - c = 80 . imo option e ."
Answer: e
Problem: on dividing 95 by a number , the quotient is 6 and the remainder is 5 . find the divisor .
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "d = ( d - r ) / q = ( 95 - 5 ) / 6 = 90 / 6 = 15 b"
Answer: b
Problem: if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 54 / r years . if joe ' s parents invested $ 5,000 in a long - term bond that pays 6 percent interest , compounded annually , what will be the approximate total amount of the investment 18 years later , when joe is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 54 / r years , then for r = 6 it ' ll double in 54 / 6 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus after 18 years investment will become $ 5,000 * 2 = $ 10,000 . answer : d ."
Answer: d
Problem: find out the square of a number which when doubled exceeds its one nineth by 17 ?
Options: a ) 16 , b ) 25 , c ) 81 , d ) 26 , e ) 17
Rationale: "let the number be p , then the square will be p ^ 2 according to question : 2 p = ( p / 9 ) + 17 = > 18 p = p + 153 = > p = 9 p ^ 2 = 9 ^ 2 = 81 answer : c"
Answer: c
Problem: the inner circumference of a circular race track , 25 m wide , is 880 m . find radius of the outer circle ?
Options: a ) 165 m , b ) 120 m , c ) 100 m , d ) 190 m , e ) 220 m
Rationale: "let inner radius be r metres . then , 2 π r = 880 ⇔ r = ( 880 x ( 7 / 44 ) ) = 140 m . radius of outer circle = ( 140 + 25 ) m = 165 m . hence a"
Answer: a
Problem: find the compound interest on $ 800 for 1 year at 10 % p . a . if ci is component yearly ?
Options: a ) $ 40 , b ) $ 400 , c ) $ 840 , d ) $ 800 , e ) $ 80
Rationale: "a = p ( 1 + r / 100 ) ^ t = 800 ( 1 + 10 / 100 ) ^ 1 = 800 * 21 / 20 = $ 840 ci = a - p = 840 - 800 = $ 40 answer is a"
Answer: a
Problem: how many boxes do you need if you have to pack 1080 apples into cases that each hold one dozen apples ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: e 90 1080 apples = 90 dozens the required number of boxes = 90 . answer : e
Answer: e
Problem: a sum of money lent out at s . i . amounts to rs . 820 after 2 years and to rs . 1020 after a further period of 4 years . the sum is ?
Options: a ) s . 440 , b ) s . 500 , c ) s . 720 , d ) s . 740 , e ) s . 840
Rationale: s . i for 5 years = ( 1020 - 820 ) = rs . 200 . s . i . for 2 years = 200 / 4 * 2 = rs . 100 . principal = ( 820 - 100 ) = rs . 720 . answer : c
Answer: c
Problem: the weights of one liter vegetable ghee packet of two brands ‘ a ’ and ‘ b ’ are 900 gm and 750 gm respectively . if they are mixed in the ratio of 3 : 2 by volumes to form a mixture of 4 liters , what is the weight ( in kg ) of the mixture ?
Options: a ) 3.84
b ) 1.75
c ) 3.36
d ) 2.72
e ) none of these
Rationale: here ' s how i did it . my notes from reading the problem were : 1 l a = 900 gm 1 l b = 850 gm we are mixing five parts ( 3 parts a plus 2 parts b , 5 parts total ) to get 4 l , so 5 x = 4 - - - > x = 4 / 5 . eachpartis 4 / 5 of a liter . so if we have 3 parts a , we have 900 * 3 * ( 4 / 5 ) = 2160 if we have 2 parts b , we have 750 * 2 * ( 4 / 5 ) = 1200 2160 + 1200 = 3360 solving for units gives us 3.36 so the answer is c
Answer: c
Problem: a train 800 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 , b ) 660 , c ) 500 , d ) 267 , e ) 298
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 800 + x ) / 60 = 65 / 3 x = 500 m . answer : c"
Answer: c
Problem: the sector of a circle has radius of 42 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 183 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 42 ) + 2 ( 42 ) = 99 + 84 = 183 cm answer : e"
Answer: e
Problem: car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 42 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 105 , b ) 140 , c ) 175 , d ) 210 , e ) 245
Rationale: "in 72 minutes , car x travels 42 miles . car y gains 7 miles each hour , so it takes 6 hours to catch car x . in 6 hours , car x travels 210 miles . the answer is d ."
Answer: d
Problem: there are 4 more women than there are men on a local co - ed softball team . if there are a total of 18 players on the team , what is the ratio of men to women ?
Options: a ) 10 / 16 , b ) 6 / 16 , c ) 7 / 11 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 18 m + 4 + m = 18 2 m = 14 m = 7 w = 11 ratio : 7 : 11 ans : c"
Answer: c
Problem: a student gets 50 % in one subject , 60 % in the other . to get an overall of 60 % how much should get in third subject .
Options: a ) 75 % , b ) 70 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "let the 3 rd subject % = x 50 + 60 + x = 3 * 60 110 + x = 180 x = 180 - 110 = 70 answer : b"
Answer: b
Problem: one pump drains one - half of a pond in 6 hours , and then a second pump starts draining the pond . the two pumps working together finish emptying the pond in one - half hour . how long would it take the second pump to drain the pond if it had to do the job alone ?
Options: a ) 1 hour , b ) 1.1 hour , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "first pump drains 1 / 2 of the tank in 6 hours so 12 hours it will take to drain the full tank . let , 2 nd pump drains the full tank in a hours so both together can drain ( 1 / 12 + 1 / a ) part in 1 hour son in 1 / 2 hour they drain 1 / 2 * ( 1 / 12 + 1 / a ) part of the tank given that in 1 / 2 hour they drain 1 / 2 of the tank hence we can say 1 / 2 * ( 1 / 12 + 1 / a ) = 1 / 2 solving u get a = 12 / 11 = 1.1 hence answer is b"
Answer: b
Problem: an amount of rs . 1638 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of b ?
Options: a ) 360 , b ) 358 , c ) 356 , d ) 514 , e ) 504
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of b = 4 / 13 * 1638 = rs . 504 answer : e"
Answer: e
Problem: how much is 80 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 77 , c ) 15 , d ) 12 , e ) 88
Rationale: ( 80 / 100 ) * 40 – ( 4 / 5 ) * 25 32 - 20 = 12 answer : d
Answer: d
Problem: light glows for every 17 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 291 , b ) 292 , c ) 293 , d ) 384 , e ) 285
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 17 = 292 . so total 293 times light ll glow answer : c"
Answer: c
Problem: two trains of length 100 meters and 200 meters are 660 meters apart . they are moving towards each other on parallel tracks , at speeds of 90 km / h and 108 km / h . after how many seconds will the trains meet ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the speeds are 90000 / 3600 = 25 m / s and 108000 / 3600 = 30 m / s the relative speed is 55 m / s . time = 660 / 55 = 12 seconds the answer is a ."
Answer: a
Problem: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 50 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 35 % .
Rationale: "25 % of 2 litres = 0.5 litres 50 % of 6 litres = 3.0 litres therefore , total quantity of alcohol is 3.5 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 35 % answer : e"
Answer: e
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 18300 . a ' s share is ?
Options: a ) 8876 , b ) 2765 , c ) 6000 , d ) 1298 , e ) 6100
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 18300 = 6100 answer : e"
Answer: e
Problem: how many different positive integers exist between 10 ^ 7 and 10 ^ 8 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18
Rationale: so , the numbers should be from 10 , 000,000 to 100 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 10 , 000,001 10 , 000,010 10 , 000,100 10 , 001,000 10 , 010,000 10 , 100,000 11 , 000,000 7 numbers . 2 . one 2 and the rest are 0 ' s : 20 , 000,000 1 number . total = 8 numbers . answer : d
Answer: d
Problem: the workforce of company x is 60 % female . the company hired 26 additional male workers , and as a result , the percent of female workers dropped to 55 % . how many employees did the company have after hiring the additional male workers ?
Options: a ) 160 , b ) 220 , c ) 312 , d ) 360 , e ) 420
Rationale: "let ' s xx be total quantity of employees 0.6 x = females before adding men 0.55 ( x + 26 ) = females after adding men as quantity of women does n ' t change we can make an equation : 0.6 x = 0.55 ( x + 26 ) 0.05 x = 14.3 x = 286 - this is quantity of employees before adding 26 men so after adding it will be 312 answer is c"
Answer: c
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 33.3 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) 74
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 33.3 kg zinc , mixture , melted = [ 20 / 9 x 33.3 ] kg = 74 kg . answer e"
Answer: e
Problem: a good train 800 metres long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 minute , then the length of the tunnel ( in meters ) is :
Options: a ) 600 , b ) 300 , c ) 400 , d ) 500 , e ) 200
Rationale: speed = 78 * 5 / 18 m / sec = = > 65 / 3 length of the tunnel be x then 800 + x / 60 = 65 / 3 3 ( 800 + x ) = 3900 x = 500 answer d
Answer: d
Problem: arun purchased 30 kg of wheat at the rate of rs . 11.50 per kg and 20 kg of wheat at the rate of 14.25 per kg . he mixed the two and sold the mixture . approximately what price per kg should be sell the mixture to make 25 % profit ?
Options: a ) 15.75 , b ) 16.33 , c ) 16.35 , d ) 16.3 , e ) 16.32
Rationale: "c . p . of 50 kg wheat = ( 30 * 11.50 + 20 * 14.25 ) = rs . 630 . s . p . of 50 kg wheat = 125 % of rs . 630 = 125 / 100 * 630 = rs . 787.5 s . p . per kg = 787.5 / 50 = 15.75 . answer : a"
Answer: a
Problem: find the c . i . on a sum of rs . 2000 for 6 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 205 , b ) 305 , c ) 3025 , d ) 5540 , e ) 315
Rationale: "c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 205 answer : a"
Answer: a
Problem: ann and bob drive separately to a meeting . ann ' s average driving speed is greater than bob ' s avergae driving speed by one - third of bob ' s average driving speed , and ann drives twice as many miles as bob . what is the ratio q of the number of hours ann spends driving to the meeting to the number of hours bob spends driving to the meeting ?
Options: a ) 8 : 3 , b ) 3 : 2 , c ) 4 : 3 , d ) 2 : 3 , e ) 3 : 8
Rationale: "say the rate of bob is 3 mph and he covers 6 miles then he needs 6 / 3 = 2 hours to do that . now , in this case the rate of ann would be 3 + 3 * 1 / 3 = 4 mph and the distance she covers would be 6 * 2 = 12 miles , so she needs 12 / 4 = 3 hours for that . the ratio q of ann ' s time to bob ' s time is 3 : 2 . answer : b ."
Answer: b
Problem: of 30 applicants for a job , 12 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 9 , d ) 7 , e ) 5
Rationale: "d . 7 30 - 3 = 27 27 - 12 - 18 = - 7 then 7 are in the intersection between 4 years experience and degree . answer d"
Answer: d
Problem: how many multiples of 5 are there between 10 and 100 , exclusive ?
Options: a ) 18 , b ) 17 , c ) 16 , d ) 15 , e ) 14
Rationale: "5 * 2 = 10 5 * 20 = 100 total multiples = ( 20 - 2 ) + 1 = 19 exclude 10 and 100 = 19 - 2 = 17 answer is b"
Answer: b
Problem: suresh can complete a job in 15 hours . ashutosh alone can complete the same job in 25 hours . suresh works for 9 hours and then the remaining job is completed by ashutosh . how many hours will it take ashutosh to complete the remaining job alone ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 10 , e ) none of these
Rationale: "the part of job that suresh completes in 9 hours = 9 â  „ 15 = 3 â  „ 5 remaining job = 1 - 3 â  „ 5 = 2 â  „ 5 remaining job can be done by ashutosh in 2 â  „ 5 ã — 25 = 10 hours answer d"
Answer: d
Problem: find the sum of first 35 natural numbers
Options: a ) 470 , b ) 468 , c ) 630 , d ) 463 , e ) 520
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 35 ( 35 + 1 ) / 2 = 35 ( 36 ) / 2 = 630 answer : option c"
Answer: c
Problem: a line that passes through ( – 1 , – 4 ) and ( 5 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 5 , d ) 2 , e ) 7 / 2
Rationale: slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 5 + 1 ) = > 6 k = k + 4 = > k = 4 / 5 ans c it is !
Answer: c
Problem: total dinning bill for 8 people was $ 211.00 . if they add 15 % tip and divided the bill evenly , approximate . what was each persons find share
Options: a ) $ 30.14 , b ) 45.14 , c ) 34.66 , d ) 32.29 , e ) 30.33
Rationale: "211 * 15 = 3165 / 100 = 31.65 211 + 31.65 = 242.65 242.65 / 8 = 30.33 answer : e"
Answer: e
Problem: how much 50 % of 56 is greater than 30 % of 50 ?
Options: a ) 18 , b ) 99 , c ) 13 , d ) 55 , e ) 71
Rationale: "( 50 / 100 ) * 56 – ( 30 / 100 ) * 50 28 - 15 = 13 answer : c"
Answer: c
Problem: a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 865 in 4 years . the sum is :
Options: a ) s . 665 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 720
Rationale: "s . i . for 1 year = rs . ( 865 - 815 ) = rs . 50 . s . i . for 3 years = rs . ( 50 x 3 ) = rs . 150 . principal = rs . ( 815 - 150 ) = rs . 665 . answer : option a"
Answer: a
Problem: a shopkeeper fixes the marked price of an item 32 % above its cost price . the percentage of discount allowed to gain 7 % is
Options: a ) 18.94 % , b ) 18.93 % , c ) 18.92 % , d ) 18.91 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 132 required gain = 7 % , so selling price = rs 107 discount = 132 - 107 = 25 discount % = ( 25 / 132 ) * 100 = 18.93 % option b"
Answer: b
Problem: the diagonals of the two squares are in the ratio of 2 : 5 find the ratio of their area .
Options: a ) 5 : 89 , b ) 7 : 96 , c ) 4 : 25 , d ) 5 : 84 , e ) 8 : 96
Rationale: "let the diagonals of the square be 2 x and 5 x respectively . ratio of their areas = 1 / 2 ( 2 x ) ^ 2 : 1 / 2 ( 5 x ) = 4 x ^ 2 : 25 x ^ 2 = 4 : 25 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 9 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 6 : 5 , b ) 6 : 3 , c ) 4 : 4 , d ) 4 : 8 , e ) 4 : 1
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 9 = 6 : 3 answer : b"
Answer: b
Problem: carl can wash all the windows of his house in 6 hours . his wife maggie can wash all the windows in 7 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 42 3 / 3 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 42 / 13 = 42 3 / 3 answer is c"
Answer: c
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 2 days , then the fraction of the work that is left is :
Options: a ) 23 / 20 , b ) 5 , c ) 23 / 30 , d ) 23 / 12 , e ) 2
Rationale: "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 2 day ' s work = ( 7 / 60 * 2 ) = 7 / 30 therefore , remaining work = ( 1 - 7 / 30 ) = 23 / 30 . ans : c"
Answer: c
Problem: find the common factors of 15 and 18 .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 70 , e ) 90
Rationale: first of all we need to find the prime factors of 15 and 18 15 = 5 x 3 18 = 3 x 3 x 2 lcm is the product of highest exponent of all the factors . lcm ( 15,18 ) = 5 x 3 ^ 2 x 2 = 90 answer : 90
Answer: e
Problem: half of the workers in palabras bookstore have read the latest book by j . saramago , and 1 / 6 of the workers have read the latest book by h . kureishi . the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book . if there are 42 workers in the palabras bookstore , how many of them have read both books ?
Options: a ) 3 , b ) 12 , c ) 9 , d ) 8 , e ) 7
Rationale: there are total 42 workers . half of the workers in palabras bookstore have read the latest book by j . saramago , so 21 have read saramago . 1 / 6 of the workers have read the latest book by h . kureishi . so ( 1 / 6 ) * 42 = 7 have read kureishi the number of workers that have read neither book is one less than the number of the workers that have read the latest saramago book and have not read the latest kureishi book if b workers have read both books , 20 - b have read saramago but not kureishi . so , ( 21 - b - 1 ) have read neither . total = n ( a ) + n ( b ) - both + neither 42 = 21 + 7 - b + ( 21 - b - 1 ) b = 3 answer ( a )
Answer: a
Problem: find the length of the wire required to go 13 times round a square field containing 24336 m 2 .
Options: a ) 15840 , b ) 3388 , c ) 2667 , d ) 8112 , e ) 66711
Rationale: "a 2 = 24336 = > a = 156 4 a = 624 624 * 13 = 8112 answer : d"
Answer: d
Problem: the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 4 | + 3 is equal to :
Options: a ) – 7 , b ) 7 , c ) 20 , d ) 12 , e ) 14
Rationale: "x ^ 2 - 8 x + 18 = | x - 4 | rhs can be - ve or + ve x ^ 2 - 9 x + 22 = 0 x ^ 2 - 7 x + 14 = 0 x = 11 , 7,2 we test all 3 values in original equation , all ok . thus , sum = 11 + 7 + 2 = 20 ans ( c )"
Answer: c
Problem: rs . 1430 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 540 , e ) s . 660
Rationale: "a + b + c = 1430 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1430 = rs . 660 answer : e"
Answer: e
Problem: last year a worker saved 5 % of her annual salary . this year , she made 20 % more money than last year and she saved 6 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 136 % , b ) 140 % , c ) 144 % , d ) 148 % , e ) 152 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.05 x . this year , she saved 0.06 ( 1.2 x ) = 0.072 x 0.072 x / 0.05 x = 144 % the answer is c ."
Answer: c
Problem: two trains 125 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.16 , b ) 7.16 , c ) 7.12 , d ) 7.15 , e ) 7.2
Rationale: "t = ( 125 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.2 answer : e"
Answer: e
Problem: in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 12 , − 8 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 11 / 22 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Problem: a circular path of 20 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 49 , b ) rs . 40 , c ) rs . 44 , d ) rs . 42 , e ) rs . 66
Rationale: "explanation : π ( 22 ^ 2 - 20 ^ 2 ) = 22 / 7 * ( 484 - 400 ) = 264 264 * 1 / 4 = rs . 66 answer : option e"
Answer: e
Problem: stacy has a 81 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 27 , c ) 10 , d ) 8.5 , e ) 6
Rationale: "81 / 3 = 27 answer : b"
Answer: b
Problem: the side of a square is increased by 20 % then how much % does its area increases ?
Options: a ) 44.00 % , b ) 45.25 % , c ) 48.75 % , d ) 50.00 % , e ) 40.00 %
Rationale: "a = 100 a 2 = 10000 a = 120 a 2 = 14400 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 4400 100 - - - - - - - ? = > 44.00 % answer : a"
Answer: a
Problem: the area of a rectangular plot is 23 times its breadth . if the difference between the length and the breadth is 10 metres , what is its breadth ?
Options: a ) 13 metres , b ) 5 metres , c ) 7.5 metres , d ) data inadequate , e ) none of these
Rationale: "l × b = 23 × b ∴ l = 23 m and l – b = 10 ∴ b = 23 – 10 = 13 m answer a"
Answer: a