Cheukting/mathqa huggingface dataset:
Question (gain): a reduction of 48 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.6 , b ) 8.6 , c ) 7.6 , d ) 3.6 , e ) 1.6
Rationale: "explanation : 40 * ( 48 / 100 ) = 19.2 - - - 64 ? - - - 12 = > rs . 3.6 answer : d"
Answer: d
Question (general): what is the remainder when 1271 * 1275 * 1279 * 1285 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 11 , d ) 3 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 - 1 ) ( 1272 + 3 ) ( 1284 - 5 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 1 ) ( 3 ) ( - 5 ) ( 1 ) = 15 . thus the question becomes : what is the remainder upon division of 15 by 12 ? the answer to this question is 3 answer : d ."
Answer: d
Question (gain): the s . i . on a certain sum of money for 3 years at 8 % per annum is half the c . i . on rs . 4000 for 2 years at 10 % per annum . the sum placed on s . i . is ?
Options: a ) 3000 , b ) 2802 , c ) 1750 , d ) 2990 , e ) 2982
Rationale: "c . i . = [ 4000 * ( 1 + 10 / 100 ) 2 - 4000 ] = ( 4000 * 11 / 10 * 11 / 10 - 4000 ) = rs . 840 . sum = ( 420 * 100 ) / ( 3 * 8 ) = rs . 1750 answer : c"
Answer: c
Question (general): in plutarch enterprises , 70 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 60,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 220,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 7 marketers , 2 engineers , and 1 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 60,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 420,000 - $ 160,000 = $ 220,000 . the correct answer is e ."
Answer: e
Question (gain): a person buys an article at rs . 460 . at what price should he sell the article so as to make a profit of 18 % ?
Options: a ) 542 , b ) 882 , c ) 772 , d ) 662 , e ) 521
Rationale: "cost price = rs . 460 profit = 18 % of 460 = rs . 82 selling price = cost price + profit = 460 + 82 = 542 answer : a"
Answer: a
Question (general): if an integer n is to be chosen at random from the integers 1 to 86 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 55 / 86 , e ) 3 / 4
Rationale: "n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 86 , there are 43 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 = ( 43 + 12 ) / 96 = 55 / 86 ans isd"
Answer: d
Question (general): a school has received 60 % of the amount it needs for a new building by receiving a donation of $ 600 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 200 , b ) $ 177.78 , c ) $ 100 , d ) $ 277.78 , e ) $ 377.78
Rationale: let the amount school needs = x let total people school plans to solicit = t school has received 60 % of x = > ( 3 / 5 ) x people already solicited = 40 % of t = > ( 2 / 5 ) t now , as per the information given in the question : ( 3 / 5 ) x = $ 400 . ( 2 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 remaning amount is 40 % i . e ( 2 / 5 ) x - - - - - - because school has already received 60 % and the remaining people are 60 % i . e ( 3 / 5 ) . t - - - - - because 40 % of the people are already solicited so , average contribution required from the remaining targeted people is ( 2 / 5 ) x = ( amount required ) . ( 3 / 5 ) . t - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 divide eqn 1 by eqn 2 amount required = $ 277.78 d
Answer: d
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 1,000 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 9 = 512 < 1,000 , then the greatest possible length of integer z is 9 . the answer is c ."
Answer: c
Question (other): in a group of 6 boys and 4 girls are to be selected . in how many different ways can they be selected such that at least one boy should be there ?
Options: a ) 209 , b ) 200 , c ) 210 , d ) 225 , e ) 221
Rationale: no of boys = 6 no of girls = 4 therefore , no of ways at least 1 boy can be selected = 6 c 4 * 4 c 0 + 6 c 3 * 4 c 1 + 6 c 2 * 4 c 2 + 6 c 1 * 4 c 3 = 15 + 80 + 90 + 24 = 209 ans - a
Answer: a
Question (general): the youngest of 4 children has siblings who are 1 , 4 , and 7 years older than she is . if the average ( arithmetic mean ) age of the 4 siblings is 17 , what is the age of the youngest sibling ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "x + ( x + 1 ) + ( x + 4 ) + ( x + 8 ) = 68 4 x + 12 = 68 4 x = 56 x = 14 the answer is e ."
Answer: e
Question (general): a , b , c weighted separately 1 st like a , b , c , then a & b , then b & c , then c & a at last a & b & c , the last weight was 167 , then what will be the average weight of the 7 reading ?
Options: a ) 95 , b ) 95.42 , c ) 95.45 , d ) 94 , e ) 93
Rationale: the sum of 7 weights = weights of [ a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] = weights of [ 4 * ( a + b + c ) = 4 * 167 = 668 therefore the average weight of 7 readings is 668 / 7 = 95.428 answer : b
Answer: b
Question (physics): a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a plce and come back , how far is the place ?
Options: a ) 2 km , b ) 2.4 km , c ) 2.5 km , d ) 3.4 km , e ) none
Rationale: "sol . speed downstream = ( 5 + 1 ) kmph = 6 kmph ; speed upstream = ( 5 - 1 ) kmph = 4 kmph . let the required distance be x km . then , x / 6 + x / 4 = 1 ⇔ 2 x + 3 x = 12 ⇔ 5 x = 12 ⇔ x = 2.4 km . answer b"
Answer: b
Question (probability): a box contains 24 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 24 / 77 , e ) none
Rationale: "solution p ( none is defective ) = 20 c 2 / 24 c 2 = 53 / 77 . p ( at least one is defective ) = ( 1 - 53 / 77 ) = 24 / 77 . answer d"
Answer: d
Question (geometry): one side of a rectangular field is 15 m and one of its diagonals is 17 m . find the area of the field in meter square
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: "other side = ( ( 17 ) 2 - ( 15 ) 2 ) ( 1 / 2 ) = ( 289 - 225 ) ( 1 / 2 ) = ( 64 ) ( 1 / 2 ) = 8 m . area = ( 15 x 8 ) m 2 = 120 m 2 . option c"
Answer: c
Question (gain): in a sample of christ college students , 30 percent are third year students and 90 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 3 / 4 , b ) 2 / 3 , c ) 4 / 7 , d ) 1 / 2 , e ) 1 / 7
Rationale: = 10 / 70 . = 1 / 7 my answer is e too
Answer: e
Question (physics): an electric pump can fill a tank in 3 hours . because of a leak in the tank , it took 12 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 4 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
Rationale: "work done by the leak in 1 hour = 1 / 3 - 1 / 12 = 1 / 4 the leak will empty the tank in 4 hours answer is a"
Answer: a
Question (gain): in a school of 800 students , 45 % wear blue shirts , 23 % wear red shirts , 15 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 120 , b ) 128 , c ) 136 , d ) 144 , e ) 152
Rationale: "45 + 23 + 15 = 83 % 100 – 83 = 17 % 800 * 17 / 100 = 136 the answer is c ."
Answer: c
Question (general): what is the hcf of 2 / 3 , 4 / 12 and 6 / 5
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 4 / 15 , d ) 1 / 30 , e ) 9 / 45
Rationale: "explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 12 , 5 ) = 2 / 60 = 1 / 30 answer : option d"
Answer: d
Question (gain): michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 10 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 127 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: "since michelle earns 10 % interest compounded semiannually , then she earns 5 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 5 % * 5 = 25 % . but , since the interest is compounded every 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 25 % , only answer choice a fits . answer : a"
Answer: a
Question (general): john want to buy a $ 100 trouser at the store , but he think it â € ™ s too expensive . finally , it goes on sale for $ 70 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "the is always the difference between our starting and ending points . in this case , it â € ™ s 100 â € “ 70 = 30 . the â € œ original â €  is our starting point ; in this case , it â € ™ s 100 . ( 30 / 100 ) * 100 = ( 0.3 ) * 100 = 30 % . b"
Answer: b
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 10000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is :
Options: a ) 23 , b ) 19 , c ) 22 , d ) 20 , e ) 14
Rationale: "let the total number of workers be x . then , 8000 x = ( 10000 * 7 ) + 6000 ( x - 7 ) = 2000 x = 28000 = x = 14 . answer : e"
Answer: e
Question (geometry): a picture is copied onto a sheet of paper 8.5 inches by 10 inches . a 1.5 inch margin is left all around . what area in square inches does the picture cover ?
Options: a ) 76
b ) 65
c ) 59.5
d ) 49
e ) 38.5
Rationale: area covered by picture = ( 8.5 - 3 ) * ( 10 - 3 ) = 5.5 * 7 = 38.5 answer e
Answer: e
Question (physics): a cistern 9 m long and 6 m wide contains water up to a breadth of 2 m 25 cm . find the total area of the wet surface .
Options: a ) 142 m sqaure , b ) 122 m sqaure , c ) 135 m sqaure , d ) 188 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 6 * 2.25 + 9 * 2.25 ) ] + 9 * 6 = 122 m square option b"
Answer: b
Question (geometry): a tailor trims 4 feet from opposite edges of a square piece of cloth , and 3 feet from the other two edges . if 120 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 18
b ) 20
c ) 24
d ) 26
e ) 40
Rationale: let the original side of the square be x . ( x - 8 ) * ( x - 6 ) = 120 = 10 * 12 x = 18 the answer is a .
Answer: a
Question (gain): in a company , 54 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 55 % , b ) 60 % , c ) 65 % , d ) 70 % , e ) 75 %
Rationale: the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 46 % of all employees are women , so non - union women are 46 % - 18 % = 28 % 40 % of all employees are non - union . the percent of non - union employees who are women is 28 % / 40 % = 70 % the answer is d .
Answer: d
Question (physics): 10 women can complete a work in 7 days & 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 5 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) 11 days
Rationale: 1 woman ' s 1 day ' s work = 1 / 70 1 child ' s 1 day ' s work = 1 / 140 5 women and 10 children 1 day work = ( 5 / 70 + 10 / 140 ) = 1 / 7 so 5 women and 10 children will finish the work in 7 days . b )
Answer: b
Question (general): 5 n + 7 > 12 and 7 n - 5 < 44 ; n must be between which numbers ?
Options: a ) 1 and 8 , b ) 2 and 6 , c ) 0 and 9 , d ) 1 and 7 , e ) 2 and 9
Rationale: "5 n > 5 - - > n > 1 7 n < 49 - - > n < 7 1 < n < 7 answer : d"
Answer: d
Question (general): the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 30 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 360 , c ) $ 400 , d ) $ 500 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 120 substituting the value of p from the first equation onto the second we get p = 120 . plugging in the value of p in the first equation , we get c = 360 . which leads us to answer choice b"
Answer: b
Question (gain): a survey was sent to 75 customers , 7 of whom responded . then the survey was redesigned and sent to another 60 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 5 % , c ) 14 % , d ) 60 % , e ) 73 %
Rationale: "rate of first survey = 7 / 75 rate of second survey = 9 / 60 % response rate increase ( 9 / 60 - 7 / 75 ) / ( 7 / 75 ) = 60 % answer is d = 60 %"
Answer: d
Question (general): mary ' s income is 60 % more than tim ' s income and tim ' s income is 20 % less than juan ' s income . what % of juan ' s income is mary ' s income .
Options: a ) 128 % , b ) b . 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: even i got 96 % j = 100 t = 100 * 0.8 = 80 m = 80 * 1.6 = 128 if mary ' s income is x percent of j m = j * x / 100 x = m * 100 / j = 128 * 100 / 100 = 128 ans : a
Answer: a
Question (physics): a train 125 m long passes a man , running at 9 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 50 , c ) 88 , d ) 65 , e ) 54
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 9 ) km / hr . x - 9 = 45 = = > x = 54 km / hr . answer : e"
Answer: e
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 80 mph . what is his average speed of travel for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 80 * 3 = 240 miles . therefore , total distance covered = 80 + 240 = 320 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 320 / 5 = 64 miles per hour . choice d"
Answer: d
Question (physics): a brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 25 m * 2 m * 0.75 m ?
Options: a ) 24000 , b ) 23000 , c ) 22000 , d ) 25000 , e ) 26000
Rationale: "25 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 25 = 1 / 100 * x = > x = 25000 answer : d"
Answer: d
Question (other): the ratio of the incomes of a and b is 5 : 4 and the ratio of their expenditure is 3 : 2 . if at the end of the year , each saves $ 1600 then the income of a is ?
Options: a ) $ 1500 , b ) $ 4000 , c ) $ 2000 , d ) $ 2500 , e ) $ 3200
Rationale: let the income of a and b be $ 5 x and $ 4 x let their expenditures be $ 3 y and $ 2 y 5 x - 3 y = 1600 - - - - - - - 1 ) 4 x - 2 y = 1600 - - - - - - - 2 ) from 1 ) and 2 ) x = 800 a ' s income = 5 x = 5 * 800 = $ 4000 answer is b
Answer: b
Question (physics): a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 7 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 1200000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 8 * 7 * 6 = 1000000 answer : b
Answer: b
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 19 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 565 , b ) 444 , c ) 676 , d ) 420 , e ) 663
Rationale: "1 h - - - - - 3 ? - - - - - - 60 12 h rs = 16 + 19 = 35 t = 12 d = 35 * 12 = 420 answer : d"
Answer: d
Question (physics): the speed of the boat in still water in 12 kmph . it can travel downstream through 60 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 15 hours , e ) 6 hours
Rationale: "still water = 12 km / hr downstream = 60 / 3 = 20 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 20 / 2 = 4 km / hr so time taken in upstream = 60 / 4 = 15 hrs answer : d"
Answer: d
Question (general): if there are 200 questions in a 3 hr examination . among these questions are 25 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 40 min , b ) 62 min , c ) 70 min , d ) 74 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 175 x + 25 * 2 x = 180 x = 180 / 225 x = 0.8 time taken for type a problem = 25 * 2 * 0.8 = 40 min answer : a"
Answer: a
Question (geometry): the size of a television screen is given as the length of the screen ' s diagonal . if the screens were flat , then the area of a square 20 - inch screen would be how many square inches greater than the area of a square 18 - inch screen ?
Options: a ) 2 , b ) 4 , c ) 16 , d ) 38 , e ) 40
Rationale: "pythogoras will help here ! let the sides be x and diagonal be d then d ^ 2 = 2 x ^ 2 and area = x ^ 2 now plug in the given diagonal values to find x values and then subtract the areas ans will be 20 ^ 2 / 2 - 18 ^ 2 / 2 = 76 / 2 = 38 ans d ."
Answer: d
Question (other): in a group of 8 engineers , 3 engineers have a phd degree ; the others have only an ms or bs degree . a team of 3 engineers is to be chosen which must have at least 1 engineer with a phd , how many different teams can be chosen ?
Options: a ) 56 , b ) 46 , c ) 64 , d ) 65 , e ) 10
Rationale: the problem asks for a combination , since order does n ' t matter . now , selecting r items from a set of n gives the combination formula : ncr = n ! / r ! ( n - r ) ! n = 8 r = 3 so , total teams is 8 c 3 = 8 ! / ( 3 ! ( 8 - 3 ) ! ) = 56 , and n = 8 - 3 = 5 r = 3 for teams without a phd is 5 c 3 = 5 ! / ( 3 ! ( 5 - 3 ) ! ) = 10 , so , teams with at least 1 phd = 56 - 10 = 46 answer : b
Answer: b
Question (other): in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is three times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 4 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63
Rationale: "f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 4 * 180 / 12 = 60 ounces of water d"
Answer: d
Question (gain): in an election between two candidates , the winner has a margin of 20 % of the votes polled . if 1000 people change their mind and vote for the loser , the loser would have won by a margin of 20 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 10000 , b ) 5000 , c ) 15000 , d ) 20000 , e ) 6000
Rationale: winner - looser 60 % - 40 % if 1000 people change their mind and vote for the loser : winner - looser 40 % - 60 % thus 1,000 people compose 20 % of all voters , which means that the total number of votes is 5,000 . answer : b
Answer: b
Question (other): there are 600 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 243 , b ) 265 , c ) 375 , d ) 390 , e ) 400
Rationale: in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 600 . hence 3 x + 5 x = 600 solve for x 8 x = 600 x = 75 number of boys 3 x = 3 × 75 = 225 number of girls 5 x = 5 × 75 = 375 c
Answer: c
Question (general): 8 is 2 % of a , and 2 is 8 % of b . c equals b / a . what is the value of c ?
Options: a ) 1 / 16 , b ) 1 / 4 , c ) 1 , d ) 4 , e ) 8
Rationale: "2 a / 100 = 8 a = 400 8 b / 100 = 2 b = 25 c = b / a = 25 / 400 = 1 / 16 the answer is a ."
Answer: a
Question (general): a certain psychologist charges $ 30 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 400 , what is the total charge to a patient who receives only 3 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 252
Rationale: "let the charge for first hour = x + 30 then charge for each additional hour = x x + 30 + 4 x = 400 = > 5 x = 370 = > x = 74 total charge for patient for 3 hours of therapy = x + 30 + 2 x = 3 x + 30 = 252 $ answer e"
Answer: e
Question (physics): in a race , the speeds of a and b are in the ratio 3 : 4 . a takes 30 minutes more than b to reach the destination . the time taken by a to reach the destination is ?
Options: a ) 1 hr , b ) 2 hr , c ) 1.5 hr , d ) 2.5 hr , e ) 3 hr
Rationale: explanation : ratio of speeds = 3 : 4 distance remaining constant , the ratio of time taken = 4 : 3 a takes 0.5 hours more than bhence time taken by a = 4 × 0.5 = 2 hour answer : b
Answer: b
Question (gain): by selling an article at rs . 800 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 640 , d ) s . 480 , e ) s . 489
Rationale: sp = 800 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / ( 100 + 25 ) ] = 800 * [ 100 / 125 ] = rs . 640 answer : c
Answer: c
Question (gain): kanul spent $ 500 in buying raw materials , $ 400 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 1010 , b ) $ 1025 , c ) $ 1125 , d ) $ 1100 , e ) $ 1000
Rationale: "let the total amount be x then , ( 100 - 10 ) % of x = 500 + 400 90 % of x = 900 90 x / 100 = 9000 / 9 x = $ 1000 answer is e"
Answer: e