Cheukting/mathqa huggingface dataset:
Question (general): total dinning bill of 6 people was $ 139.00 and 10 % tip divided the bill evenly ? what is the bill amount each person shared .
Options: a ) 21.84 , b ) 22.84 , c ) 23.84 , d ) 24.84 , e ) 25.48
Rationale: dinner bill of 6 person = 139 + 10 % tip so , 10 % of 139 = ( 139 * 10 ) / 100 = 13.9 so , the actual total amount = 139 + 13.9 = $ 152.9 so per head bill = 152.9 / 6 = $ 25.48 answer : e
Answer: e
Question (general): in a t . v . factory , an average of 63 tvs are produced per day for the fist 25 days of the months . a few workers fellill for the next 5 daysreducing the daily avg for the month to 58 sets / day . the average production per day for day last 5 days is ?
Options: a ) 35 , b ) 33 , c ) 48 , d ) 50 , e ) 52
Rationale: production during these 5 days = total production in a month - production in first 25 days . = 30 x 58 - 25 x 63 = 165 â ˆ ´ average for last 5 days = 165 / 5 = 33 b
Answer: b
Question (general): a part - time employee ’ s hourly wage was increased by 25 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 20 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 25 % wage increase , the employee makes $ 1.25 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.25 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.25 to get : new # of hours = 100 / 1.25 ≈ 80 hours so , the number of hours decreases from 100 hours to ( approximately ) 80 hours . this represents a 20 % decrease ( approximately ) . answer : c"
Answer: c
Question (physics): a man rows his boat 120 km downstream and 92 km upstream , taking 4 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 4 kmph , c ) 2 kmph , d ) 8 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 120 / ( 4 ) = 30 kmph speed upstream = d / t = 92 / ( 4 ) = 23 kmph the speed of the stream = ( 30 - 23 ) / 2 = 4 kmph answer : b"
Answer: b
Question (physics): a student completes a 3 part exam as follows . the student completes sections a in 4 minutes and takes an equal time to complete the two remaining sections . what is the ratio of time spent on section c to section a if the total duration is 1 hour ?
Options: a ) 10 : 3 , b ) 9 : 2 , c ) 7 : 1 , d ) 8 : 3 , e ) 11 : 2
Rationale: "the time spent on section b and section c is 28 minutes each . the ratio of c to a is 28 : 4 = 7 : 1 the answer is c ."
Answer: c
Question (physics): a is twice as good a workman as b and they took 10 days together to do the work b alone can do it in .
Options: a ) 25 days , b ) 88 days , c ) 30 days , d ) 11 days , e ) 13 days
Rationale: wc = 2 : 1 2 x + x = 1 / 10 x = 1 / 30 = > 30 days answer : c
Answer: c
Question (general): which number can we add to 425897 to get a number exactly divisible by 456 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "425897 / 456 = 933 with a remainder of 449 . we need to add 456 - 449 = 7 the answer is c ."
Answer: c
Question (physics): the speed at which a man can row a boat in still water is 9 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 34 seconds , c ) 14 seconds , d ) 18 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 9 + 3 = 12 kmph = 12 * 5 / 18 = 10 / 3 m / s hence time taken to cover 60 m = 60 * 3 / 10 = 18 seconds . answer : d"
Answer: d
Question (geometry): the roof of an apartment building is rectangular and its length is 3 times longer than its width . if the area of the roof is 588 feet squared , what is the difference between the length and the width of the roof ?
Options: a ) 28 . , b ) 40 . , c ) 42 . , d ) 44 . , e ) 46 .
Rationale: "answer is a : 28 let w be the width , so length is 3 w . therefore : w * 3 w = 588 , solving for , w = 14 , so 3 w - w = 2 w = 2 * 14 = 28"
Answer: a
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 8 seconds to pass a telegraph post , then the length of the train is
Options: a ) 100 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 8 ) m = 160 m answer : option d"
Answer: d
Question (general): how many numbers from 15 to 65 are exactly divisible by 5 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: "option ' d ' 15 / 5 = 3 and 65 / 5 = 13 = = > 13 - 3 = 10 numbers"
Answer: d
Question (geometry): if the area of a circle decreases by 66 % , then the radius of a circle decreases by
Options: a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 66 ) % = ( 100 − 10 √ 64 ) % = 100 - 58 = 42 % answer e"
Answer: e
Question (probability): two cards are drawn together from a pack of 52 cards the probability that one is the spade and one is a heart is ?
Options: a ) 85 / 852 , b ) 45 / 69 , c ) 18 / 456 , d ) 13 / 102 , e ) 23 / 125
Rationale: "let s be the sample space then n ( s ) = 52 c 2 = ( 52 * 51 ) / ( 2 * 1 ) = 1326 let e be the event of getting 1 spade kings and 1 heart let n ( e ) = number of ways of chossing 1 spade out of 13 and 1 heart out of 13 = ( 13 c 1 * 13 c 1 ) = 13 * 13 = 169 p ( e ) = n ( e ) / n ( s ) = 169 / 1326 = 13 / 102 answer ( d )"
Answer: d
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (other): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (other): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (other): 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
Question (geometry): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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