regisss/math_qa huggingface dataset:
Problem: on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 15 more transactions than cal . how much transactions did jade handled ?
Options: a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
Rationale: solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 15 more transactions than cal . jade = 66 + 15 = 81 jade handled = 81 transactions . answer : b
Answer: b
Problem: peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 850 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 664 , c ) 698 , d ) 744 , e ) 710
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 850 - 815 = 35 interest earned for 3 years = 35 * 3 = 105 amount invested = 815 - 105 = 710 answer : e"
Answer: e
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.2 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 2 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 120 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 120 - x ) = 8000 × 1000 = > ( 120 - x ) = 8000 × 1000 / 320 = 100 = > x = 20 cm = 2 dm . answer : b"
Answer: b
Problem: the sector of a circle has perimeter 83 cm and central angle 225 o . find its radius ?
Options: a ) 21 cm , b ) 15 cm , c ) 14 cm , d ) 24 cm , e ) 28 cm
Rationale: let radius = x cm perimeter of the sector = length of the arc + 2 ( radius ) 83 = ( 225 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 83 = 55 x / 14 + 2 x 83 = 83 x / 14 1162 = 83 x x = 14 answer : c
Answer: c
Problem: a transport company ’ s 120 buses running 20 hrs a day consume 360 of fuel in a day . in the next 3 days , the company will invest in 30 more green buses that use 30 % less fuel . how many lts of fuel will be consumed in a 5 day week after the new buses are added to the fleet ?
Options: a ) 3060 , b ) 1 , 512 , c ) 1800 , d ) 1260 , e ) 3,312
Rationale: old buses use 360 * 5 days = 1,800 lts new buses use ( 0.70 * 360 ) / 120 * 5 days * 30 buses = 1,512 lts total fuel is 3,312 lts answer is e
Answer: e
Problem: at a restaurant , glasses are stored in two different - sized boxes . one box contains 12 glasses , and the other contains 16 glasses . if the average number of glasses per box is 15 , and there are 16 more of the larger boxes , what is the total number of glasses at the restaurant ? ( assume that all boxes are filled to capacity . )
Options: a ) 96 , b ) 240 , c ) 56 , d ) 384 , e ) 480
Rationale: "1 small box and 17 large boxes = 1 ( 12 ) + 17 ( 16 ) = 12 + 272 = 284 glasses at the minimum since the question asks for the total number of glasses , we can now eliminate answers a , b and c . . . . the difference in the number of boxes must be 16 though , so we could have . . . . 2 small boxes and 18 large boxes 3 small boxes and 19 large boxes etc . with every additional small box + large box that we add , we add 12 + 16 = 28 more glasses . thus , we can just ` ` add 28 s ' ' until we hit the correct answer . . . . 284 + 28 = 312 312 + 28 = 340 340 + 28 = 368 368 + 28 = 396 at this point , we ' ve ' gone past ' answer d , so the correct answer must be answer e . . . . . but here ' s the proof . . . . 396 + 28 = 424 424 + 28 = 452 452 + 28 = 480 final answer : e"
Answer: e
Problem: in a certain alphabet , 9 letters contain a dot and a straight line . 24 letters contain a straight line but do not contain a dot . if that alphabet has 40 letters , all of which contain either a dot or a straight line or both , how many letters contain a dot but do not contain a straight line ?
Options: a ) 7 , b ) 8 , c ) 14 , d ) 20 , e ) 28
Rationale: "we are told that all of the letters contain either a dot or a straight line or both , which implies that there are no letters without a dot and a line ( no line / no dot box = 0 ) . first we find the total # of letters with lines : 9 + 24 = 33 ; next , we find the total # of letters without line : 40 - 33 = 7 ; finally , we find the # of letters that contain a dot but do not contain a straight line : 7 - 0 = 7 . a"
Answer: a
Problem: if a train , travelling at a speed of 90 kmph , crosses a pole in 4 sec , then the length of train is ?
Options: a ) 281 , b ) 125 , c ) 288 , d ) 100 , e ) 121
Rationale: "d = 90 * 5 / 18 * 4 = 100 m answer : d"
Answer: d
Problem: john ' s bank ' s saving amount is decreased 20 % due to loan payment and current balance is rs . 24000 . find the actual balance before deduction ?
Options: a ) 8000 , b ) 8500 , c ) 9000 , d ) 9500 , e ) 30000
Rationale: "20 % decreased 80 % balance = 24000 100 % = 24000 / 80 * 100 = 30000 answer : e"
Answer: e
Problem: 987.650 - ? + 56.98 = 126.654
Options: a ) a ) 899.015 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 629.906 , e ) 917.976
Rationale: "explanation : 917.976 answer : option e"
Answer: e
Problem: two employees x and y are paid a total of rs . 700 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.18 , b ) s . 240.18 , c ) s . 290.18 , d ) s . 300.18 , e ) s . 318.18
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 700 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 700 ⇒ y [ 12 / 10 + 1 ] = 700 ⇒ 22 y / 10 = 700 ⇒ 22 y = 7000 ⇒ y = 7000 / 22 = rs . 318.18 e )"
Answer: e
Problem: james took a 3 - hour bike ride . in the second hour he travlled 12 miles , which was 20 percent farther than he traveled the first hour . if he traveled 25 percent farther in the third hour than he did in the second hour , how many miles did jose travel during the entire ride ?
Options: a ) 54.0 , b ) 54.9 , c ) 55.5 , d ) 37.0 , e ) 63.0
Rationale: "let the distance travelled in the first hour be x . thus , 1.2 x = 12 , x = 10 . now , the distance travelled in the 3 rd hour = 12 + 1 / 4 â ˆ — 12 = 15 therefore 12 + 15 + 10 = 37 answer : d"
Answer: d
Problem: in a group of 100 cars , 47 cars do not have air conditioning . if at least 53 cars have racing stripes , what is the greatest number of cars that could have air conditioning but not racing stripes ?
Options: a ) 45 , b ) 47 , c ) 49 , d ) 51 , e ) 53
Rationale: "lets assume ac = 53 ( includesonly ac carsandcars with ac and racing stripes ) lets assume rs ( racing stripes ) > = 53 ( includescars with ac and racing stripesandonly racing stripes ) . now since we want to maximize ( only ac ) we have to see to it thatcars with ac and racing stripesis minimal ( assume 0 ) but since rs > = 53 . . we have to assign atleast 6 tocars with ac and racing stripes . hence ac = 53 - 6 = 47 . the answer is b"
Answer: b
Problem: how many bricks each measuring 22 cm x 10.25 cm x 8 cm , will be needed to build a wall 9 m x 7 m x 10.5 m
Options: a ) 5600 , b ) 3066 , c ) 3055 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 900 x 700 x 10.5 ) / ( 22 x 10.25 x 8 ) = 3066 answer : b"
Answer: b
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "let ' s take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 32 ( 44 - 12 ) must be those with four screens or more c is the answer"
Answer: c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 600 resolutions ?
Options: a ) 844.8 m , b ) 704 m , c ) 774 m , d ) 714 m , e ) 744 m
Rationale: in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84480 cm = 844.8 m answer : a
Answer: a
Problem: mr . depak has $ 449774 in his bank account . what is the least amount of money ( in whole number of dollars ) that he must add to his account if he wants to split this money evenly among her 6 best friends ? options :
Options: a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6
Rationale: to find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends , he needs to make the total divisible by 6 simply add the individual digits of the total = 4 + 4 + 9 + 7 + 7 + 4 = 35 if you add 1 , the number is divisible by 6 ( 35 + 1 ) correct option : a
Answer: a
Problem: the ages of two person differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 25 , 5 , c ) 29 , 9 , d ) 50 , 30 , e ) 20 , 8
Rationale: "let their ages be x and ( x + 12 ) years . then , 5 ( x - 5 ) = ( x + 12 - 5 ) = > 4 x = 32 = > x = 8 their present ages are 20 years and 8 year . answer : e"
Answer: e
Problem: a cab driver 5 days income was $ 300 , $ 150 , $ 750 , $ 200 , $ 600 . then his average income is ?
Options: a ) $ 350 , b ) $ 375 , c ) $ 400 , d ) $ 425 , e ) $ 450
Rationale: "avg = sum of observations / number of observations avg income = ( 300 + 150 + 750 + 200 + 600 ) / 5 = 400 answer is c"
Answer: c
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 4 men and 2 women will do that task .
Options: a ) 5 / 7 , b ) 3 / 10 , c ) 5 / 18 , d ) 5 / 16 , e ) 5 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 4 m + 2 w = 10 w answer is 10 / 14 = 5 / 7 answer : a"
Answer: a
Problem: a trained covered x km at 90 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 22 , b ) 99 , c ) 27 , d ) 66 , e ) 887
Rationale: total time taken = x / 90 + 2 x / 20 hours = x / 9 hours average speed = 3 x / ( x / 9 ) = 27 kmph answer : c
Answer: c
Problem: sachin is younger than rahul by 4 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 24.5 , c ) 24.3 , d ) 24.9 , e ) 14
Rationale: "if rahul age is x , then sachin age is x - 4 , so ( x - 4 ) / x = 7 / 9 = > 9 x - 36 = 7 x = > 2 x = 36 = > x = 18 so sachin age is 18 - 4 = 14 answer : e"
Answer: e
Problem: a triangle and a parallelogram are constructed on the same base such that their areas are equal . if the altitude of the parallelogram is 100 m , then the altitude of the triangle is .
Options: a ) 10 √ 2 m
b ) 100 m
c ) 100 √ 2 m
d ) 200 m
e ) none
Rationale: solution let the altitude of the triangle be h ï and base of each be b . then , ( ½ × b × h 1 ) where h 2 = 100 m . = h 1 = 2 h 2 = ( 2 x 100 ) m = 200 m . answer d
Answer: d
Problem: a man buys an item at rs . 1200 and sells it at the loss of 20 percent . then what is the selling price of that item
Options: a ) rs . 660 , b ) rs . 760 , c ) rs . 860 , d ) rs . 960 , e ) none of these
Rationale: "explanation : here always remember , when ever x % loss , it means s . p . = ( 100 - x ) % of c . p when ever x % profit , it means s . p . = ( 100 + x ) % of c . p so here will be ( 100 - x ) % of c . p . = 80 % of 1200 = 80 / 100 * 1200 = 960 option d"
Answer: d
Problem: a sum of money is distributed among w , x , y , z in the proportion of 4 : 2 : 5 : 3 . if y gets $ 500 more than z , what is the x ' s share ?
Options: a ) $ 4000 , b ) $ 500 , c ) $ 2500 , d ) $ 2800 , e ) $ 1400
Rationale: "let the shares of w , x , y , z are 4 a , 2 a , 5 a , 3 a 5 a - 3 a = 500 2 a = 500 , a = 250 x ' s share = 2 a = $ 500 answer is b"
Answer: b
Problem: a man rows his boat 110 km downstream and 90 km upstream , taking 3 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 5 , c ) 7.5 , d ) 3.5 , e ) 2.5
Rationale: "speed downstream = d / t = 110 / ( 3 ) = 37 kmph speed upstream = d / t = 90 / ( 3 ) = 30 kmph the speed of the stream = ( 37 - 30 ) / 2 = 3.5 kmph answer : d"
Answer: d
Problem: five women can do a work in ten days . 7 men can complete the same work in 5 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 10 : 7 , b ) 11 : 10 , c ) 2 : 3 , d ) 3 : 2 , e ) none of these
Rationale: explanation : ( 50 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 50 ( 7 ã — 5 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 35 so , required ratio = 1 / 50 : 1 / 35 = 10 : 7 answer : a
Answer: a
Problem: a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 340 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 40 , b ) 110 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 340 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 340 = 3320 - 2720 = 600 i . e . a = 150 and b = 340 - 150 = 190 more seats in balcony than orchestra = b - a = 190 - 150 = 40 answer : option a"
Answer: a
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 8 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 4032 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: we have the rectangle with dimensions 9 * 8 ( 9 horizontal dots and 8 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 8 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 7 c 1 , ( 8 - 1 = 7 as 1 vertical dot is already occupied by a ) . 9 c 1 * 8 c * 8 c 1 * 7 c 1 = 4032 . answer : b .
Answer: b
Problem: there are 8 stores in town that had a total of 22 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: 8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 22 - 16 - 3 = 3 , which is the maximum that one person could have visited . the answer is b .
Answer: b
Problem: a set s = { x , - 8 , - 5 , - 1 , 1 , 6 , 9 , y } with elements arranged in increasing order . if the median and the mean of the set are the same , what is the value of | x | - | y | ?
Options: a ) - 1 , b ) can not be determined , c ) 1 , d ) 0 , e ) 2
Rationale: "median of the set = ( - 1 + 1 ) / 2 = 0 as per statement , mean of the set = 0 mean of the set | y | - | x | + 16 - 14 = 0 ( where x is negative n y is positive ) | y | - | x | = - 2 so the absolute difference between two numbers is 2 answer e"
Answer: e
Problem: it takes avery 3 hours to build a brick wall while tom can do it in 3 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 60 , c ) 30 , d ) 40 , e ) 50
Rationale: "avery takes 3 hours tom takes 3 hours efficiency of avery is 1 / 3 units / hr efficiency of tom is 1 / 3 units / hr combined efficiency of tom and avery is 1 / 3 + 1 / 3 = 2 / 3 units / hr since they worked for 1 hour they completed 2 / 3 units of work and 1 / 3 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 3 / 1 / 3 hours = > 1 * 60 = 60 minutes . . . answer will be ( b )"
Answer: b
Problem: a student got 70 % in one subject , 80 % in other . to get overall 75 % how much he should get in third subject .
Options: a ) 65 % , b ) 75 % , c ) 85 % , d ) 95 % , e ) 88 %
Rationale: already average of two subjects is ( 70 + 80 ) / 2 = 75 % to maintain the percentage at 75 % , he shouls get 75 % marks in third subject answer : b
Answer: b
Problem: 4 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 144 , c ) 18 , d ) 21 , e ) 24
Rationale: the list should be wmwmw . hence , from women 3 ! and men 4 ! , we get ( 3 ! ) ( 4 ! ) = 144 . therefore , the correct answer is b .
Answer: b
Problem: in a class , 10 students like to play basketball and 8 like to play cricket . 4 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 15 , c ) 16 , d ) 18 , e ) 14
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 10 + 8 - 4 = 14 e )"
Answer: e
Problem: a box contains 9 apples , 8 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 5 times in a row ) = 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 * 4 / 5 = 4 / 9 < 0.5 the answer is c ."
Answer: c
Problem: what is the units digit of ( 5 ! * 4 ! - 3 ! * 5 ! ) / 120
Options: a ) 7 , b ) 8 , c ) 9 , d ) 4 , e ) 1
Rationale: "( 5 ! * 4 ! - 3 ! * 5 ! ) / 9 = 5 ! ( 4 ! - 3 ! ) / 120 = 120 ( 24 - 6 ) / 120 = 18 units digit of the above product will be equal to 8 answer b"
Answer: b
Problem: the area of circle o is added to its diameter . if the circumference of circle o is then subtracted from this total , the result is 4 . what is the area of circle o ?
Options: a ) 2 / π
b ) 2
c ) 8
d ) 4
e ) 4 π
Rationale: area + diameter - circumference = 4 pi * r ^ 2 + 2 r = 4 + 2 pi * r isolate r and get r ( pi * r + 2 ) = 4 + 2 pi * r r = ( 4 + 2 pi * r ) / ( pi * r + 2 ) = > 2 ( 2 + pi * r ) / ( pi * r + 2 ) r = 2 area = pi * r ^ 2 = > pi * 4 e
Answer: e
Problem: ( 3080 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 330 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9240 ) / 28 = 330 option c"
Answer: c
Problem: the length of the bridge , which a train 130 metres long and travelling at 45 km / hr can cross in 30 seconds , is
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 250 m , e ) none
Rationale: "sol . speed = [ 45 x 5 / 18 ] m / sec = ( 25 / 2 ) m / sec ; time = 30 sec . let the length of bridge be x metres . then , 130 + x / 30 = 25 / 2 ⇔ 2 ( 130 + x ) = 750 ⇔ x = 245 m . answer c"
Answer: c
Problem: the sum of the even numbers between 1 and n is 89 * 90 , where n is an odd number , then n = ?
Options: a ) 167 , b ) 173 , c ) 179 , d ) 185 , e ) 193
Rationale: "let n - 1 = 2 a . 2 + 4 + . . . + 2 a = 2 * ( 1 + 2 + . . . + a ) = 2 * ( a ) ( a + 1 ) / 2 = ( a ) ( a + 1 ) = 89 * 90 then a = 89 and n = 179 . the answer is c ."
Answer: c
Problem: a train 360 m long is running at a speed of 45 km / hr . in what time will be pass a bridge 140 m long ?
Options: a ) 40 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) none
Rationale: "sol . speed = [ 45 x 5 / 18 ] m / sec = 25 / 2 m / sec . total distance covered = ( 360 + 140 ) m = 500 m . ∴ required time = ( 500 x 2 / 25 ) sec = 40 sec . answer a"
Answer: a
Problem: a person distributed 10 % of his income to his 2 children each . he deposited 20 % of his income to his wife ' s account . he donated 10 % of remaining amount to an orphan house . finally he has $ 500 . find his total income ?
Options: a ) $ 900 , b ) $ 1000 , c ) $ 1200 , d ) $ 1150 , e ) $ 1500
Rationale: "2 children got = 2 * 10 % = 20 % wife got = 20 % orphan house = 10 % total = 20 + 20 + 10 = 50 % remaining = 100 - 50 = 50 % 50 % = 500 100 % = 500 * 100 / 50 = $ 1000 answer is b"
Answer: b
Problem: if q is a positive integer and q ^ 2 is divisible by 12 , then the largest positive integer that must divide q ^ 3 is
Options: a ) 2 ^ 3 , b ) 2 ^ 6 , c ) 3 ^ 3 , d ) 6 ^ 3 , e ) 12 ^ 2
Rationale: since q is an integer so q can not have a 2 and sqrt 3 ( because squaring this will give us a 2 ^ 2 and 3 ( making the product as 12 , and making q ^ 2 as a multiple of 12 ) ) q ^ 2 is divisible by 12 ( 12 = 2 * 2 * 3 ) , so , q should have at least one 2 and one 3 so that q ^ 2 has a 2 ^ 2 and two 3 so , q will have a 2 and a 3 . or q will be a multiple of 6 so , largest possible integer than should divide q ^ 3 is 6 ^ 3 so , answer will be d
Answer: d
Problem: the average weight of 8 persons increases by 5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 105 kg
Rationale: "total weight increased = ( 8 x 5 ) kg = 40 kg . weight of new person = ( 65 + 40 ) kg = 105 kg . answer : e"
Answer: e
Problem: two cubes of their volumes in the ratio 64 : 343 . the ratio of their surface area is :
Options: a ) 1.5 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 1 : 5 , e ) 4 : 7
Rationale: "the ratio of their surface area is 64 : 343 4 : 7 answer is e ."
Answer: e
Problem: if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 27 , e ) 24
Rationale: "2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 28 = > 4 x 2 ^ 2 n = 4 ^ 28 = 2 ^ 56 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 56 = > 2 ^ ( 2 n + 2 ) = 2 ^ 56 = > 2 n + 2 = 56 = > n = 27 so . answer will be d ."
Answer: d
Problem: a welder received an order to make a 1 million liter cube - shaped tank . if he has only 4 x 2 meter sheets of metal that can be cut , how many metal sheets will be required for this order y ? ( 1 cubic meter = 1000 liters )
Options: a ) 92 , b ) 90 , c ) 82 , d ) 78 , e ) 75
Rationale: i get 75 . a cube with 1 million liters cube would be a cube with the dimensions of 100 * 100 * 100 . 4 * 2 covers 8 sq liters so 100 / 8 = 12.5 . y = 12.5 * 6 = 75 . e
Answer: e
Problem: if a / b = 4 / 3 , then ( 3 a + 2 b ) / ( 3 a - 2 b ) = ?
Options: a ) 6 , b ) 3 , c ) 5 , d ) - 1 , e ) none
Rationale: answer dividing numerator as well as denominator by b , we get given exp . = ( 3 a + 2 b ) / ( 3 a - 2 b ) = ( 3 a / b + 2 ) / ( 3 a / b - 2 ) = [ ( 3 x 4 ) / 3 + 2 ] / [ ( 3 x 4 ) / 3 - 2 ] = ( 4 + 2 ) / ( 4 - 2 ) = 3 option : b
Answer: b
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 60 . what is sum of the numbers ?
Options: a ) 35 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 60 = > 12 x = 60 = > x = 60 / 12 = 5 sum of the numbers = 3 x + 4 x = 7 x = 7 x 5 = 35 answer : option a"
Answer: a
Problem: a train traveled the first d miles of its journey it an average speed of 40 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 96 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 100 , d ) 120 , e ) 135
Rationale: "average speed = total distance traveled / total time taken 3 d / d / 40 + d / y + d / 160 = 96 solving for d and y , 15 y = 11 y + 480 4 y = 400 y = 100 answer c"
Answer: c
Problem: a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 15000 left with him . find salary . .
Options: a ) $ 150000 , b ) $ 18000 , c ) $ 180000 , d ) $ 1800 , e ) none
Rationale: [ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 15000 , = [ 1 - 9 / 10 ] * total salary = $ 15000 , total salary = $ 15000 * 10 = $ 150000 , correct answer ( a )
Answer: a
Problem: 17200 x 223 + 17200 x 77 = ?
Options: a ) 2736900 , b ) 2738800 , c ) 2658560 , d ) 5160000 , e ) none of them
Rationale: "= 17200 x ( 223 + 77 ) ( by distributive law ) = 17200 x 300 = 5160000 answer is d"
Answer: d
Problem: how many cuboids of length 5 m , width 3 m and height 2 m can be farmed from a cuboid of 12 m length , 14 m width and 10 m height .
Options: a ) 82 , b ) 56 , c ) 80 , d ) 56 , e ) 100
Rationale: "( 12 ã — 14 ã — 10 ) / ( 5 ã — 3 ã — 2 ) = 56 answer is b ."
Answer: b
Problem: what is the lowest positive integer that is divisible by each of the integers 1 through 12 inclusive ?
Options: a ) 420 , b ) 840 , c ) 1260 , d ) 2520 , e ) 27,720
Rationale: "we have to find the lcm of 1 , 2 , 3 , 2 ^ 2 , 5 , 2 * 3 , 7 , 2 ^ 3 , 3 ^ 2 , 2 * 5 , 11 , and 2 ^ 2 * 3 . the lcm is 1 * 2 ^ 3 * 3 ^ 2 * 5 * 7 * 11 = 27,720 the answer is e ."
Answer: e
Problem: the length of the bridge , which a train 160 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 377 , b ) 367 , c ) 237 , d ) 215 , e ) 267
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 160 + x ) / 30 = 25 / 2 x = 215 m . answer : d"
Answer: d
Problem: car dealership x , the total profit from sales increased by 30 percent over the previous years , while the number of cars sold decreased by 30 percent over the previous years . approximately what was the average percent increase in profit per car over the previous year .
Options: a ) 18 % , b ) 30 % , c ) 52 % , d ) 63 % , e ) 85.71 %
Rationale: let profit be x and cars sold be y originally profit / car = x / y now it is 1.3 x / 0.7 y = 13 / 7 ( x / y ) increase in profit per car = ( ( 6 / 7 ) ( x / y ) ) / ( x / y ) * 100 = 85.71 % answer = e
Answer: e
Problem: arun and tarun can do a work in 10 days . after 4 days tarun went to his village . how many days are required to complete the remaining work by arun alone . arun can do the work alone in 30 days .
Options: a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 19 days . , e ) 20 days .
Rationale: "they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 30 * 6 / 10 = 18 days . answer : c"
Answer: c
Problem: 10 men and 15 women together can complete a work in 8 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 127 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 600 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 8 15 women ' s 1 day work = ( 1 / 8 - 10 / 100 ) = 1 / 40 1 woman ' s 1 day work = 1 / 600 1 woman alone can complete the work in 600 days . answer : e"
Answer: e
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 28 !
Options: a ) 13 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 , 24,27 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 24 = 3 x 8 - > 1 27 = 3 x 3 x 3 - > 3 - - - - count 3 ' s = 13 so answer is 13 answer : a"
Answer: a
Problem: a train which has 390 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 26 sec , b ) 39 sec , c ) 36 sec , d ) 29 sec , e ) 30 sec
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 390 / ( ( 45 - 9 ) ( 5 / 18 ) = 390 / 36 * ( 5 / 18 ) = 390 / 10 = 39 sec answer : b"
Answer: b
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) rs . 51.25 , b ) rs . 51.27 , c ) rs . 51.79 , d ) rs . 51.8 , e ) rs . 51.93
Rationale: "sum = ( 50 * 100 ) / ( 2 * 5 ) = rs . 500 amount = [ 500 * ( 1 + 5 / 100 ) 2 ] = rs . 551.25 c . i . = ( 551.25 - 500 ) = rs . 51.25 . answer : a"
Answer: a
Problem: the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 6.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 5.50 , e ) $ 6.50
Rationale: "i tried using time / rate approach : - initial price difference = 6.80 - 3.20 = 3.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 3.6 = t ( 5.4 x ) - > t = ( 3.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 3.6 / 5.4 = 6.5 answer e ."
Answer: e
Problem: a person borrows 9000 for 9 years at 3 % p . a . simple interest . he immediately lends it to another person at 7 % p . a . for 9 years . find his gain in the transaction per year .
Options: a ) 380 , b ) 360 , c ) 340 , d ) 300 , e ) 180
Rationale: "gain in 9 years = [ ( 9000 ã — 9 ã — 7 / 100 ) â ˆ ’ ( 9000 ã — 9 ã — 3 / 100 ) ] = ( 5670 â € “ 2430 ) = 3240 â ˆ ´ gain in 1 year = ( 3240 / 9 ) = 360 answer b"
Answer: b
Problem: 2001 + 1015
Options: a ) 8390 , b ) 3016 , c ) 2808 , d ) 3890 , e ) 2080
Rationale: b
Answer: b
Problem: a shopkeeper has 280 kg of apples . he sells 40 % of these at 30 % profit and remaining 60 % at 30 % profit . find his % profit on total .
Options: a ) 24 % , b ) 25 % , c ) 26 % , d ) 28 % , e ) 30 %
Rationale: "if the total quantity was 100 then 40 x 30 % + 60 x 30 % = 30 this profit will remain same for any total quantity unless the % of products remains the same . hence ' e ' is the answer"
Answer: e
Problem: the speed of a boat in still water in 42 km / hr and the rate of current is 4 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 33.7 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 4 ) = 46 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 46 = 33.7 km answer : c"
Answer: c
Problem: the average expenditure of a labourer for 5 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 69.5 , b ) 71.2 , c ) 60.4 , d ) 62.1 , e ) 72.1
Rationale: "income of 6 months = ( 5 × 85 ) – debt = 425 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 695 average monthly income = 695 ÷ 10 = 69.5 answer a"
Answer: a
Problem: a rectangular field has a length 10 meters more than it is width . if the area of the field is 119 , what is the length ( in meters ) of the rectangular field ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "area = l * w = ( l ) * ( l - 10 ) = 171 trial and error : 20 * 10 = 200 ( too high ) 19 * 9 = 171 ( too high ) 18 * 8 = 144 ( too high ) 17 * 7 = 119 the length is 17 meters . the answer is c ."
Answer: c
Problem: in country z , 12 % of the people do not have a university diploma but have the job of their choice , and 25 % of the people who do not have the job of their choice have a university diploma . if 40 % of the people have the job of their choice , what percent of the people have a university diploma ?
Options: a ) 35 % , b ) 43 % , c ) 55 % , d ) 65 % , e ) 75 %
Rationale: "setting up a matrix is how i solve this one . diploma no diploma totals job of choice w / diploma job of choice w / o diploma = 12 % job of choice total = 40 % not job of choice with diploma = . 25 x not job of choice w / o diploma = . 75 x total not job of choice = x total with diploma total without diploma total citizen = 100 if 40 % of people have their job of choice , then 60 % of people do not have their job of choice . 25 % of 60 % = 15 % . we can also see that 28 % of the people have their job of choice and a diploma ( 40 % - 12 % = 28 % ) . 28 % + 15 % = 43 % . therefore 43 % of the people in country z have a diploma . ans b"
Answer: b
Problem: in a village of 2,500 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
Options: a ) 221 / 250 , b ) 199 / 250 , c ) 33 / 50 , d ) 8 / 25 , e ) 51 / 250
Rationale: "to solve this we would need to know the number of people who are less than 70 years old , the number of males , and the number of males who are less than 70 years old . overlapping sets : quantity of a or b = a + b - ( a ∩ b ) = quantity of a + quantity of b - ( intersection of a and b ) number of males = 2500 - 850 = 1650 number of people below 70 years old = 2500 - 800 = 1700 number of males below 70 years old = 1700 - ( 850 * 0.4 ) = 1360 total number of people who are male or below 70 = 1650 + 1700 - 1360 = 1990 probability of male or below 70 = 1990 / 2500 = 199 / 250 answer : b"
Answer: b
Problem: two pipes a and b can separately fill a tank in 12 and 15 minutes respectively . a third pipe c can drain off 56 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 549 , b ) 540 , c ) 542 , d ) 672 , e ) 279
Rationale: "1 / 12 + 1 / 15 - 1 / x = 1 / 15 x = 12 12 * 56 = 672 answer : d"
Answer: d
Problem: country c imposes a two - tiered tax on imported cars : the first tier imposes a tax of 12 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 8 % . if ron imported a $ 14,000 imported car and ended up paying $ 1640 in taxes , what is the first tier ' s price level ?
Options: a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 7050 , e ) $ 13000
Rationale: "let t be the tier price , p be total price = 14000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1640 - - - - > t = 13000 . e is the correct answer ."
Answer: e
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 5 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 35 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 5 = > 2 b - b - 5 = 30 b = 35 so the present age of b is 35 years answer : d"
Answer: d
Problem: a multiple choice test consists of 4 questions , and each question has 5 answer choices . in how many ways can the test be completed if every question is unanswered ?
Options: a ) 24 , b ) 120 , c ) 625 , d ) 720 , e ) 1024
Rationale: "5 choices for each of the 4 questions , thus total of 5 * 5 * 5 * 5 = 5 ^ 4 = 625 ways . answer : c ."
Answer: c
Problem: 1257 1275 1527 . . . . . . . . . . . . . . . . + 7521 the addition problem above shows 4 of the 24 different integers that can be formed by using each of the digits 1 , 25 and 7 exactly once in each integer . what is the sum t of the 24 integers ?
Options: a ) 26996 , b ) 44406 , c ) 60444 , d ) 66660 , e ) 99990
Rationale: this is the way i solved it : total no . of different combos = 24 , total digits 4 therefore each digit must repeat 24 / 4 = 6 times in each row . . so the right most row would add up to 1 x 6 + 2 x 6 + 5 x 6 + 7 x 6 = 6 + 12 + 30 + 42 = 90 . . each row would add up to 90 , so 90 in the first means we have 9 that carries over and we get 0 , the second time its 90 + 9 and 9 stays and one 9 goes to the row to the left , so the last two digits of the sum t should be 90 ( e ) . . we could go on and solve the exact number but since only one answer choice has the last digits as 90 we need n ' t go any further . .
Answer: e
Problem: john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 20,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 40,402 , b ) 40404 , c ) 40000 , d ) 50000 , e ) 50005
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 20,000 ( 1 + 0.04 / 4 ) ^ 4 - 20,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 20,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 20,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 20,000 ( 1.0201 + 1 ) = 40,402 . hence answer is a ."
Answer: a
Problem: convert the 1 / 3 m / s into kilometers per hour ?
Options: a ) 2.9 kmph , b ) 9.9 kmph , c ) 1.3 kmph , d ) 1.2 kmph , e ) 5.7 kmph
Rationale: "1 / 3 m / s = 1 / 3 * 18 / 5 = 12 / 10 = 1.2 kmph . answer : d"
Answer: d
Problem: if x , y , and z are positive integers , and 3 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 21 , b ) 28 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 3,5 and 6 = 30 now 3 x = 30 = > x = 10 5 y = 30 = > y = 6 6 z = 30 = > z = 5 10 + 6 + 5 = 21 . option a ."
Answer: a
Problem: evaluate : 19 + sqrt ( - 2 + 12 ã — 6 ã · 9 ) = ?
Options: a ) 51 , b ) 53 , c ) 55 , d ) 57 , e ) 59
Rationale: "according to order of operations , inner brackets first where 12 x 6 ã · 9 is first calculated since it has a multiplication and a division . 12 x 6 ã · 9 = 72 ã · 9 = 8 hence 19 + sqrt ( - 2 + 12 ã — 6 ã · 9 ) = 19 + sqrt ( - 2 + 8 ) = 19 + sqrt ( 6 ) = 19 + 36 = 55 correct answer c ) 55"
Answer: c
Problem: the total number of digits used in numbering the pages of a book having 369 pages is
Options: a ) 732 , b ) 990 , c ) 999 , d ) 1305 , e ) 1405
Rationale: total number of digits = ( no . of digits in 1 - digit page nos . + no . of digits in 2 - digit page nos . + no . of digits in 3 - digit page nos . ) = ( 1 x 9 + 2 x 90 + 3 x 270 ) = ( 9 + 180 + 810 ) = 999 . answer : c
Answer: c
Problem: when 732 is subtracted form the square of a number , the answer that is obtained is 5280 . what is the number ?
Options: a ) 228
b ) 103
c ) 286
d ) 122
e ) 102
Rationale: explanation : let the number be x x 2 - 732 = 5280 x 2 = 5280 + ( 70 + 3 ) 2 = 5280 + 4900 + 420 + 9 = 10609 = 10000 + 2 ( 100 ) ( 3 ) + 32 = ( 100 + 3 ) 2 x = 100 + 3 = 103 . answer : b
Answer: b
Problem: the average height of 35 boys in a class was calculated as 182 cm . it has later found that the height of one of the boys in the class was wrongly written as 166 cm whereas his actual height was 106 cm . find the actual average height of the boys in the class ( round off your answer to two decimal places ?
Options: a ) 187.89 cm , b ) 180.29 cm , c ) 123.98 cm , d ) 149.98 cm , e ) 146.89 cm
Rationale: "calculated average height of 35 boys = 182 cm . wrong total height of 35 boys = 182 * 35 cm . this was as a result of an actual height of 106 cm being wrongly written as 166 cm . correct total height of 35 boys = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - ( 166 cm - 106 cm ) / 35 = 182 cm - 60 / 35 cm = 182 cm - 1.71 cm = 180.29 cm . answer : b"
Answer: b
Problem: the length of a train and that of a platform are equal . if with a speed of 108 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 299 , b ) 266 , c ) 299 , d ) 900 , e ) 261
Rationale: "speed = [ 108 * 5 / 18 ] m / sec = 30 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 30 = > x = 30 * 60 / 2 = 900 answer : d"
Answer: d
Problem: the simple form of the ratio 7 / 6 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 35 : 12
Rationale: "7 / 6 : 2 / 5 = 35 : 12 answer : e"
Answer: e
Problem: ravi and sunil are partners in a business . ravi invests rs . 12,000 for 4 months and sunil invested rs . 10000 for 5 months then after one year ratio of their profits will be
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 24 : 25 , d ) 20 : 22 , e ) 3 : 4
Rationale: = ( 12000 * 4 ) : ( 10000 * 5 ) = 48000 : 50000 = 24 : 25 answer : c
Answer: c
Problem: the value of “ a ” varies in inverse proportion as the square of “ b ” . if the value of “ a ” is equal to 40 when “ b ” is equal to 12 . what would be the value of “ a ” when “ b ” is equal to 24 ?
Options: a ) 10
b ) 88
c ) 26
d ) 27
e ) 28
Rationale: explanation : we have , a α 1 / b 2 a * b 2 = k ( constant ) when b = 12 , a = 40 … . . given k = 40 * ( 12 ) 2 = 5760 now , b = 24 . hence , a = 5760 / 576 = 10 answer : a
Answer: a
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
Options: a ) 4000 , b ) 3624 , c ) 5673 , d ) 4530 , e ) 4566
Rationale: "area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 4 = rs . 3624 answer : option b"
Answer: b
Problem: of the 65 cars on a car lot , 45 have power steering , 25 have power windows , and 17 have both power steering and power windows . how many of the cars on the lot have neither power steering nor power windows ?
Options: a ) 2 , b ) 8 , c ) 12 , d ) 15 , e ) 18
Rationale: total - neither = all power steering + all power windows - both or 65 - neither = 45 + 25 - 17 = 53 . = > neither = 12 , hence c . answer : c
Answer: c
Problem: if two painters can complete two rooms in two hours , how many hours 10 painters would it take to do 20 rooms ?
Options: a ) 4 , b ) 3 , c ) 5 , d ) 8 , e ) 7
Rationale: "explanation : two painters can complete two rooms in two hours . so 20 rooms can be painted in 4 hrs by 10 painters answer : a ) 4 painters"
Answer: a
Problem: convert 0.32 in to a vulgar fraction ?
Options: a ) 8 / 25 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.32 = 32 / 100 = 8 / 25 correct option : a"
Answer: a
Problem: the l . c . m . of two numbers is 60 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 40 , d ) 53 , e ) 50
Rationale: "let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 60 or x = 10 . the numbers are 20 and 30 . hence , required sum = ( 20 + 30 ) = 50 . answer : option e"
Answer: e
Problem: the sum of three consecutive even numbers is 63 , find the last one ?
Options: a ) 26 , b ) 24 , c ) 21 , d ) 23 , e ) 19
Rationale: "let the first number be n let the second number be n + 2 let the third number be n + 4 n + n + 2 + n + 4 = 63 combine like terms : 3 n + 6 = 63 3 n = 63 - 6 3 n = 57 n = 19 n + 2 = 21 n + 4 = 23 the last number is 23 answer : d"
Answer: d
Problem: a cycle is bought for rs . 900 and sold for rs . 1170 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 80 % , d ) 30 % , e ) 24 %
Rationale: "900 - - - - 270 100 - - - - ? = > 30 % answer : d"
Answer: d
Problem: rs 378 is divided among the 3 children such that 12 times of anusha is equal to 8 times of babu which is equal to 6 times of esha . how much the rupee anusha get ?
Options: a ) 74 , b ) 84 , c ) 94 , d ) 104 , e ) 114
Rationale: if money with anusha = a , babu = b & esha = e , then a + b + e = 378 - - - ( i ) & 12 a = 8 b = 6 e , so b = 3 a / 2 & e = 2 a substituting these values of b & e in ( i ) , a + ( 3 a / 2 ) + 2 a = 378 , on solving , a = 84 so , b = 126 , e = 168 answer : b
Answer: b
Problem: the price of 10 chairs is equal to that of 4 tables . the price of 15 chairs and 2 tables together is rs . 4000 . the total price of 12 chairs and 3 tables is ?
Options: a ) rs . 3900 , b ) rs . 4900 , c ) rs . 4980 , d ) rs . 5000 , e ) rs . 5900
Rationale: let the cost of a chair and that of a table be rs . x and rs . y respectively . then , 10 x = 4 y or y = 5 x . 2 15 x + 2 y = 4000 15 x + 2 x 5 x = 4000 2 20 x = 4000 x = 200 . so , y = 5 x 200 = 500 . 2 hence , the cost of 12 chairs and 3 tables = 12 x + 3 y = rs . ( 2400 + 1500 ) = rs . 3900 . a )
Answer: a
Problem: a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 12 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 12 + 11 = 23 . the answer is d ."
Answer: d
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 6 students is 14 years and that of the other 8 students is 16 years . the age of the 15 th student is
Options: a ) 9 years , b ) 13 years , c ) 14 years , d ) 21 years , e ) 25 years
Rationale: "solution age of the 15 th student = [ 15 x 15 - ( 14 x 6 + 16 x 8 ) ] = ( 225 - 212 ) = 13 years . answer b"
Answer: b
Problem: a can do a work in 6 days . b can do the same work in 12 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: "a rate = 1 / 6 b rate = 1 / 12 ( a + b ) rate = ( 1 / 6 ) + ( 1 / 12 ) = 1 / 4 a & b finish the work in 4 days correct option is c"
Answer: c
Problem: in an organisation there are 1000 employees out of which 250 earn below 10 k $ and 500 earn between 10 k $ and 50 k $ . what is the total percentage of employees who earn less than 50 k $ ?
Options: a ) 66 % , b ) 75 % , c ) 70 % , d ) 50 % , e ) 82 %
Rationale: total percentage = ( 250 + 500 ) / 1000 = 0.75 b
Answer: b
Problem: how many quarters are equal to 6 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 9 , e ) 24
Rationale: 6 * 4 = 24 quarters answer : e
Answer: e
Problem: the difference between the place value and the face value of 9 in the numeral 856973 is
Options: a ) 973 , b ) 891 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 9 ) - ( face value of 9 ) = ( 900 - 9 ) = 891 answer : option b"
Answer: b