Cheukting/mathqa huggingface dataset:
Question (physics): fred and sam are standing 55 miles apart and they start walking in a straight line toward each other at the same time . if fred walks at a constant speed of 6 miles per hour and sam walks at a constant speed of 5 miles per hour , how many miles has sam walked when they meet ?
Options: a ) 5 , b ) 9 , c ) 25 , d ) 30 , e ) 45
Rationale: "relative distance = 55 miles relative speed = 6 + 5 = 11 miles per hour time taken = 55 / 11 = 5 hours distance travelled by sam = 5 * 5 = 25 miles = c"
Answer: c
Question (gain): an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 65 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 27.08 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 65 percent of the votes cast number of votes for winning candidate = ( 65 / 100 ) * 525 = 341.25 percent of total membership that voted for winning candidate = ( 341.25 / 1260 ) * 100 = 27.08 % answer d"
Answer: d
Question (general): what is the remainder of ( 3682 * 3684 * 3686 ) divided by 19 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "3686 % 19 = 0 so ans = 0 answer : a"
Answer: a
Question (physics): a can do a work in 24 days and b can do it in 12 days . in how many days a and b can do the work ?
Options: a ) 20 days , b ) 10 days , c ) 6 days , d ) 5 days , e ) 8 days
Rationale: "explanation : a ' s 1 day ' s work = 1 / 24 b ' s 1 day ' s work = 1 / 12 they work together = 1 / 24 + 1 / 12 = 3 / 24 = 24 / 3 = 8 days answer : option e"
Answer: e
Question (general): a prize of $ 1200 is to be distributed among 40 winners , each of whom must be awarded at least $ 40 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 100 , b ) $ 120 , c ) $ 280 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 1200 number of people = 40 2 / 5 of 1200 ( = $ 480 ) should be distributed among 3 / 5 of 40 ( = 24 people ) with each getting $ 40 each . remaining money = 1200 - 480 = $ 720 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 40 . thus , minimising the remaining 15 people ( = 40 - 24 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 15 * 40 = 600 . thus the maximum award can be = 720 - 600 = $ 120 , hence b is the correct answer ."
Answer: b
Question (gain): the profits of qrs company rose 20 % from march to april , then dropped 20 % from april to may , then rose 50 % from may to june . what was the percent increase for the whole quarter , from march to june ?
Options: a ) 15 % , b ) 32 % , c ) 44 % , d ) 62 % , e ) 80 %
Rationale: "assume 100 in march , then 120 in april as 20 % increase , then 96 in may as 20 % decrease from april , and then 144 in june which is 150 % of 96 . so overall increase is from 100 to 144 is 44 % answer c"
Answer: c
Question (physics): if the speed of a man is 63 km per hour , then what is the distance traveled by him in 25 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 375 m , d ) 437.5 m , e ) 440 m
Rationale: "the distance traveled in 25 sec = 63 * ( 5 / 18 ) * 25 = 437.5 m answer : d"
Answer: d
Question (general): john purchased some shirts and trousers for $ 700 . he paid $ 400 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 11
Rationale: "given that the total purchase of two items cost 700 . so the average purchase of one item will cost 700 / 2 = 350 . its given as total shirt cost 400 $ less . hence total shirt cost = 350 - 50 and total trouser cost = 350 + 50 5 shirts = 150 $ = = > one shirt = 30 $ one trouser = 30 + 20 = 50 $ total trousers = 550 / 50 = 11 . e"
Answer: e
Question (gain): if a sum of money doubles itself in 10 years at simple interest , the ratepercent per annum is
Options: a ) 10 , b ) 12.5 , c ) 13 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 10 ) = 10 option a"
Answer: a
Question (physics): a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 7 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "on the way down , the rate is 1.5 * 7 = 10.5 miles per day . the distance of the route down the mountain is 2 * 10.5 = 21 miles . the answer is d ."
Answer: d
Question (general): of the goose eggs laid at a certain pond , 1 / 4 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1200 , b ) 1300 , c ) 1400 , d ) 1500 , e ) 1600
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 4 ) x = 120 ( 8 / 100 ) x = 120 x = 1500 the answer is d ."
Answer: d
Question (general): 2.08 can be expressed in terms of percentage as
Options: a ) 2.08 % , b ) 20.8 % , c ) 208 % , d ) 0.208 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 2.08 * 100 = 208 answer : option c"
Answer: c
Question (gain): the population of a town is 8000 . it decreases annually at the rate of 30 % p . a . what will be its population after 2 years ?
Options: a ) 3920 , b ) 5120 , c ) 5200 , d ) 5400 , e ) 5500
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 70 / 100 ã — 70 / 100 = 3920 answer : a"
Answer: a
Question (geometry): a hall is 15 meters long and 10 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 900 the answer is d ."
Answer: d
Question (general): a basketball team composed of 12 players scored 100 points in a particular contest . if none of the individual players scored fewer than 7 points , what is the greatest number of points e that an individual player might have scored ?
Options: a ) 7 , b ) 13 , c ) 16 , d ) 21 , e ) 23
Rationale: "general rule for such kind of problems : to maximize one quantity , minimize the others ; to minimize one quantity , maximize the others . thus to maximize the number of points of one particular player minimize the number of points of all other 11 players . minimum number of points for a player is 7 , so the minimum number of points of 11 players is 7 * 11 = 77 . therefore , the maximum number of points e for 12 th player is 100 - 77 = 23 . answer : e ."
Answer: e
Question (general): a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1990 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2009 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: she must gain at least 70 points , now she has 31 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1990 + 19 = 2009 . answer : b .
Answer: b
Question (general): the average age of 17 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?
Options: a ) 39 , b ) 41 , c ) 45 , d ) 42 , e ) 50
Rationale: "age of the 15 th student = 17 * 15 - ( 14 * 5 + 16 * 9 ) = 255 - 214 = 41 years answer is b"
Answer: b
Question (physics): ajay can ride 50 km in 1 hour . in how many hours he can ride 1500 km ?
Options: a ) 30 hrs , b ) 15 hrs , c ) 20 hrs , d ) 25 hrs , e ) 18 hrs
Rationale: "1 hour he ride 50 km he ride 1500 km in = 1500 / 50 * 1 = 30 hours answer is a"
Answer: a
Question (geometry): a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 54 inches and the width of the wall is 68 inches , what is the length of the wall , in inches ?
Options: a ) 25.7
b ) 72.7
c ) 70.7
d ) 85.7
e ) 56.7
Rationale: since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 54 ^ 2 = 2916 . area of rectangle is double of that 2 * 2916 = 5832 . now a = lw and we need find w so a / l = w ; 5832 / 68 = 85.7 answer ! answer is d
Answer: d
Question (gain): fresh grapes contain 80 % water by weight and raisins obtained by drying fresh grapes contain 25 % water by weight . how many kgs of fresh grapes are needed to get 40 kgs of raisins ?
Options: a ) 150 kgs , b ) 64 kgs , c ) 72 kgs , d ) 65 kgs , e ) 70 kgs
Rationale: "the weight of non - water in 40 kg of dried grapes ( which is 100 - 25 = 75 % of whole weight ) will be the same as the weight of non - water in x kg of fresh grapes ( which is 100 - 80 = 20 % of whole weight ) , so 40 * 0.75 = x * 0.2 - - > x = 150 . answer : a ."
Answer: a
Question (physics): a is twice as good a work man as b and together they finish the work in 4 days . in how many days a alone can finish the work ?
Options: a ) 3 , b ) 2 , c ) 7 , d ) 9 , e ) 6
Rationale: "wc = 2 : 1 2 x + x = 1 / 4 = > x = 1 / 12 2 x = 1 / 6 a can do the work in 6 days . answer : e"
Answer: e
Question (general): if p is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "no need to actually find the product of 1 to 30 . just look at the numbers that have factors of 3 . 3 = 3 6 = 3 * 2 9 = 3 * 3 12 = 3 * 2 * 2 15 = 3 * 5 18 = 3 * 3 * 2 21 = 3 * 7 24 = 3 * 2 * 2 * 2 27 = 3 * 3 * 3 30 = 3 * 2 * 5 there are 14 3 ' s , so the largest factor of p for 3 k is 3 * 14 answer : c"
Answer: c
Question (probability): the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ?
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 1 / 24
Rationale: "probability of first member an english teacher = 3 / 9 probability of second member an english teacher = 2 / 8 probability of both being english teacher = 3 / 9 x 2 / 8 = 1 / 12 ( d ) answer : d"
Answer: d
Question (physics): a woman swims downstream 45 km and upstream 15 km taking 3 hours each time , what is the speed of the woman in still water ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 45 - - - 3 ds = 15 ? - - - - 1 15 - - - - 3 us = 5 ? - - - - 1 m = ? m = ( 15 + 5 ) / 2 = 10 answer : a
Answer: a
Question (gain): in order to obtain an income of rs . 1000 from 50 % stock at rs . 500 , one must make an investment of
Options: a ) rs . 17000 , b ) rs . 16050 , c ) rs . 15400 , d ) rs . 10000 , e ) rs . 10500
Rationale: "explanation : market value = rs . 500 . required income = rs . 1000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 50 ( ie , 50 % of the face value 100 ) , investment = rs . 500 to obtain rs . 1000 , investment = 500 / 50 ã — 1000 = 10000 answer : option d"
Answer: d
Question (physics): jack and jill are marathon runners . jack can finish a marathon ( 40 km ) in 4.5 hours and jill can run a marathon in 4.0 hours . what is the ratio of their average running speed ? ( jack : jill )
Options: a ) 14 / 15 , b ) 15 / 14 , c ) 8 / 9 , d ) 5 / 4 , e ) can not be determined
Rationale: "average speed of jack = distance / time = 40 / ( 9 / 2 ) = 80 / 9 average speed of jill = 40 / ( 4.0 ) = 10 ratio of average speed of jack to jill = ( 80 / 9 ) / 10 = 8 / 9 answer c"
Answer: c
Question (geometry): a snooker tournament charges $ 45.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 212 , b ) 240 , c ) 220 , d ) 230 , e ) 225
Rationale: "let no of sits in vip enclosure is x then x * 45 + 15 ( 300 - x ) = 7500 or 30 x = 7500 - 4500 , x = 3000 / 30 = 100 vip = 100 general 220 c"
Answer: c
Question (gain): the length of a rectangular floor is more than its breadth by 100 % . if rs . 600 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
Options: a ) 15.0 m . , b ) 14.4 m . , c ) 12.0 m . , d ) 16.2 m . , e ) 16.5 m .
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 100 % of b = l + 1 b = 2 b area of the floor = 600 / 3 = 200 sq m l b = 200 i . e . , l * l / 2 = 108 l 2 = 216 = > l = 14.4 m . answer : b"
Answer: b
Question (general): 5 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3553 , how much was it in the beginning ?
Options: a ) 2988 , b ) 2776 , c ) 4400 , d ) 4675 , e ) 881
Rationale: "x * ( 95 / 100 ) * ( 80 / 100 ) = 3553 x = 4675 answer : d"
Answer: d
Question (general): what is the sum of the odd integers from 35 to 55 , inclusive ?
Options: a ) 495 , b ) 550 , c ) 555 , d ) 600 , e ) 605
Rationale: "the mean is 45 . sum = mean ( # of elements ) there are 11 odd numbers between 35 - 55 inclusive . 11 * 45 = 495 a"
Answer: a
Question (general): every monday , marina eats one croissant and every tuesday she eats two croissants . on each subsequent day of the week , she eats a number of croissants equal to the sum of the croissants eaten on the two previous days , with the exception that if she eats more than 4 croissants on any particular day , the next day she will eat only one croissant . at the end of the week ( which runs from monday through sunday ) , the cycle resets , and marina goes back to eating one croissant on monday , two on tuesday , and so forth . if a particular month begins on a saturday , how many croissants will marina eat on the 30 th of that month ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: she eat as follow mon - 1 tue - 2 wed - 3 thr - 5 fri - 1 ( since she had more than 4 previous day ) sat - 6 sunday - 1 ( since she had more than 4 previous day ) so 30 th day of month she will have 1 . answer is a
Answer: a
Question (physics): a boy swims downstream 48 km and upstream 12 km taking 6 hours each time ; what is the speed of the current ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "48 - - - 6 ds = 8 ? - - - - 1 12 - - - - 6 us = 2 ? - - - - 1 s = ? s = ( 8 - 2 ) / 2 = 3 answer : c"
Answer: c
Question (geometry): if the sides of a cube are in the ratio 5 : 3 . what is the ratio of their diagonals ?
Options: a ) 5 : 9
b ) 9 : 3
c ) 5 : 4
d ) 3 : 5
e ) 5 : 3
Rationale: explanation : diagonal of a cube = a √ 3 where a is side a 1 : a 2 = 5 : 3 d 1 : d 2 = 5 : 3 where √ 3 cancelled both side answer : e
Answer: e
Question (general): the average weight of 26 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 49.05 , b ) 42.25 , c ) 50 , d ) 51.25 , e ) 52.25
Rationale: "explanation : average weight of 26 boys = 50.25 total weight of 26 boys = 50.25 × 26 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 26 ) + ( 45.15 × 8 ) total boys = 26 + 8 = 34 average weight of all the boys = ( 50.25 × 26 ) + ( 45.15 × 8 ) / 34 = 49.05 answer : option a"
Answer: a
Question (general): a one - foot stick is marked in 1 / 4 and 1 / 5 portion . how many total markings will there be , including the end points ?
Options: a ) 18 , b ) 16 , c ) 13 , d ) 9 , e ) 11
Rationale: lcm of 20 = 20 1 / 4 marking are ( table of 5 ) 0 . . . . . . 5 . . . . . . 10 . . . . . 15 . . . . . . 20 ( total = 5 ) 1 / 5 marking are ( table of 4 ) 0 . . . . . . . 4 . . . . . . 8 . . . . . . 12 . . . . . . . . 16 . . . . . . 20 ( total = 6 ) overlapping markings are 0 . . . . . . . . 20 ( total = 2 ) total markings = 5 + 6 - 2 = 9 answer = d
Answer: d
Question (general): find out the c . i on rs . 5000 at 4 % p . a . compound half - yearly for 1 1 / 2 years ?
Options: a ) 272.22 , b ) 128.29 , c ) 306.04 , d ) 198.39 , e ) 212.22
Rationale: "explanation : a = 5000 ( 51 / 50 ) 3 = 5306.04 5000 - - - - - - - - - - - 306.04 answer : c"
Answer: c
Question (general): the average score of a cricketer in 2 matches is 30 and in other 3 matches is 40 . then find the average score in all the 5 matches ?
Options: a ) 25 , b ) 27 , c ) 30 , d ) 35 , e ) 36
Rationale: average in 5 matches = ( 2 * 30 + 3 * 40 ) / 2 + 3 = 60 + 120 / 5 = 180 / 5 = 36 answer is e
Answer: e
Question (physics): two spherical balls lie on the ground touching . if one of the balls has a radius of 9 cm , and the point of contact is 10 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 50 / 4 , b ) 70 / 6 , c ) 80 / 7 , d ) 90 / 8 , e ) 100 / 9
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 1 / 9 = ( r - 10 ) / r r = 9 r - 90 r = 90 / 8 the answer is d ."
Answer: d
Question (other): in what ratio must tea at rs . 62 per kg be mixed with tea at rs . 72 per kg so that the mixture must be worth rs . 64.50 per kg ?
Options: a ) 3 : 1 , b ) 2 : 1 , c ) 5 : 2 , d ) 3 : 2 , e ) 3 : 4
Rationale: mean price = ( 72 - 64.5 = 7.5 ) ( 64.5 - 62 = 2.5 ) req ratio = 7.5 : 2.5 = 3 : 1 answer a
Answer: a
Question (geometry): a solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm . the height of the cone is :
Options: a ) 8 cm
b ) 6 cm
c ) 4 cm
d ) 3 cm
e ) none
Rationale: sol . let the height of the cone be h cm . then , 1 / 3 ∏ * 6 * 6 * h = 4 / 3 ∏ * 3 * 3 * 3 ⇒ h = [ 36 * 3 / 36 ] = 3 cm . answer d
Answer: d
Question (gain): the present worth of rs . 2310 due years hence , the rate of interest being 15 % per annum , is :
Options: a ) rs . 1440 , b ) rs . 1750 , c ) rs . 1680 , d ) rs . 1840 , e ) none of these
Rationale: "explanation : p . w . = rs . [ 100 × 2310 / 100 + ( 15 × 52 ) ] = rs . 1680 . answer : c"
Answer: c
Question (general): if x is the median of the set { 8 / 2 , 11 / 3 , 27 / 9 , 21 / 5 , x } , x could be
Options: a ) 4 , b ) 17 / 5 , c ) 16 / 5 , d ) 30 / 7 , e ) 31 / 7
Rationale: the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( a )
Answer: a
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 140 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 24 , c ) 25 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 140 = 240 s = 36 * 5 / 18 = 10 mps t = 240 / 10 = 24 sec answer : option b"
Answer: b
Question (physics): while working alone at their constant rates , computer x can process 240 files in 12 hours , and computer y can process 240 files in 6 hours . if all files processed by these computers are the same size , how many hours would it take the two computers , working at the same time at their respective constant rates , to process a total of 240 files ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
Rationale: "both computers together process files at a rate of 240 / 12 + 240 / 6 = 20 + 40 = 60 files per hour . the time required to process 240 files is 240 / 60 = 4 hours the answer is c ."
Answer: c
Question (physics): a and b together can complete work in 6 days . a alone starts working and leaves it after working for 4 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 12 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : ( a + b ) one day work = 1 / 6 now a does half of the work in 4 days so a can complete the whole work in 8 days a ’ s one day work = 1 / 8 b ’ s one day work = 1 / 6 - 1 / 8 = 2 / 48 = 1 / 24 b alone can complete the work in 24 days so half of the work in 12 days answer : option b"
Answer: b
Question (gain): in town x , 64 percent of the population are employed , and 46 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 28 % , d ) 40 % , e ) 52 %
Rationale: we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 46 are employed males , hence 18 % are employed females . ( employed females ) / ( total employed people ) = 18 / 64 = 28 % answer : c .
Answer: c
Question (physics): the lcm of two numbers is 2310 and hcf is 55 . if one of the numbers is 210 . then what is the other number ?
Options: a ) 715 , b ) 825 , c ) 330 , d ) 605 , e ) 465
Rationale: "first number * second number = lcm * hcf other number = 2310 * 55 / 210 = 11 * 55 = 605 answer : d"
Answer: d
Question (general): what is the sum of all possible solutions to | x - 2 | ^ 2 + | x - 2 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 8 , e ) 14
Rationale: "denote | x - 2 | as y : y ^ 2 + y = 20 - - > y = - 5 or y = 4 . discard the first solution since y = | x - 2 | , so it ' s an absolute value and thus can not be negative . y = | x - 2 | = 4 - - > x = 6 or x = - 2 . the sum = 8 answer : d ."
Answer: d
Question (gain): a and b invests rs . 2500 and rs . 4000 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
Options: a ) 11 : 5 , b ) 15 : 16 , c ) 15 : 2 , d ) 9 : 9 , e ) 11 : 1
Rationale: "( 2.5 * 6 + 5 * 6 ) : ( 4 * 12 ) 45 : 48 = > 15 : 16 answer : b"
Answer: b
Question (general): find the average of first 4 multiples of 11 ?
Options: a ) 10 , b ) 12.6 , c ) 27.5 , d ) 31.3 , e ) 40.8
Rationale: "average = ( 11 + 22 + 33 + 44 ) / 4 = 27.5 answer is c"
Answer: c
Question (physics): a car traveled from san diego to san francisco at an average speed of 54 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: let the time taken be = x one way distance = 54 x total distance traveled = 2 * 54 x = 108 x total time taken = x + 2 x = 3 x average speed = 108 x / 3 x = 36 answer : c
Answer: c
Question (physics): a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 8 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 20 , e ) 24
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 8 t 1 = 8 and so t 2 = 16 . the answer is c ."
Answer: c