regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 20 x + 25 . if the sum of the perimeters of both squares is 44 , what is the value of x ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "the areas are ( x + 4 ) ^ 2 and ( 2 x - 5 ) ^ 2 . the lengths of the sides are x + 4 and 2 x - 5 . if we add the two perimeters : 4 ( x + 4 ) + 4 ( 2 x - 5 ) = 44 12 x = 48 x = 4 the answer is b ."
Answer: b
Problem: what is the probability of getting exactly three heads on five flips of a fair coin ?
Options: a ) 1 / 32 , b ) 3 / 32 , c ) 1 / 4 , d ) 5 / 16 , e ) 1 / 2
Rationale: "5 flips of a fair coin to get = hhhtt = no . of ways this can be achieved = 5 ! / 3 ! x 2 ! = 10 probability to get any of the above 10 arrangements ( hhhtt ) = ( 1 / 2 ) ^ 5 = 1 / 32 total probability = 1 / 32 x 10 = 5 / 16 answer : d"
Answer: d
Problem: simple interest on a certain sum of money for 4 years at 10 % per annum is half the compound interest on rs . 3000 for 3 years at 12 % per annum . the sum placed on simple interest is
Options: a ) rs . 3000 , b ) rs . 607.39 , c ) rs . 1214.78 , d ) rs . 1518.48 , e ) none
Rationale: "solution c . i . = rs [ 3000 x ( 1 + 12 / 100 ) 3 - 3000 ] rs . ( 3000 x 112 / 100 x 112 / 100 x 112 / 100 - 3000 ) = rs . 1214.78 . sum = rs . [ 607.39 x 100 / 4 x 10 ] = rs . 1518.48 . answer d"
Answer: d
Problem: in a certain lottery , the probability that a number between 14 and 20 , inclusive , is drawn is 1 / 6 . if the probability that a number 14 or larger is drawn is 2 / 3 , what is the probability that a number less than or equal to 20 is drawn ?
Options: a ) 1 / 18 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 5 / 6
Rationale: "you can simply use sets concept in this question . the formula total = n ( a ) + n ( b ) - n ( a and b ) is applicable here too . set 1 : number 14 or larger set 2 : number 20 or smaller 1 = p ( set 1 ) + p ( set 2 ) - p ( set 1 and set 2 ) ( combined probability is 1 because every number will be either 14 or moreor 20 or lessor both ) 2 / 3 + p ( set 2 ) - 1 / 6 = 1 p ( set 2 ) = 1 / 2 answer ( c )"
Answer: c
Problem: x is the product of each integer from 1 to 50 , inclusive and y = 100 ^ k , where k is an integer . what is the greatest value of k for which y is a factor of x ?
Options: a ) 0 , b ) 5 , c ) 6 , d ) 10 , e ) 12
Rationale: x = 1 * 2 * 3 * 4 * 5 * . . . . . . * 49 * 50 = 50 ! y = 100 ^ k 100 = 10 ^ 2 = 2 ^ 2 * 5 ^ 2 on prime factorization of x , power of 5 will always be greater than power of 2 concept : in every factorial value ( x ! ) , on prime factorization , the power of bigger prime number > the power of smaller prime number also , power of any prime number in any factorial can be calculated by following understanding power of prime x in n ! = [ n / x ] + [ n / x ^ 2 ] + [ n / x ^ 3 ] + [ n / x ^ 4 ] + . . . and so on where , [ x ] = greatest integer less than or equal to x and the explanation of terms is as follows [ n / x ] = no . of integers that are multiple of x from 1 to n [ n / x ^ 2 ] = no . of integers that are multiple of x ^ 2 from 1 to n whose first power has been counted in previous step and second is being counted at this step [ n / x ^ 3 ] = no . of integers that are multiple of x ^ 3 from 1 to n whose first two powers have been counted in previous two step and third power is counted at this step and so on . . . . . where [ n / x ] is greatest integer value of ( n / x ) less than or equal to ( n / x ) i . e . [ 100 / 3 ] = [ 33.33 ] = 33 i . e . [ 100 / 9 ] = [ 11.11 ] = 11 etc . power of 5 in x = [ 50 / 5 ] + [ 50 / 5 ^ 2 ] + [ 50 / 5 ^ 3 ] . . . = 10 + 2 + 0 = 12 power of 2 in x = [ 50 / 2 ] + [ 50 / 2 ^ 2 ] + [ 50 / 2 ^ 3 ] . . . = 25 + 12 + 6 + 3 + 1 = 47 i . e . x = 50 ! = 2 ^ 47 * 5 ^ 12 * . . . = 10 ^ 12 * . . . = 100 ^ 6 * . . . i . e . x is divisible by a 6 th power of 100 at the most i . e . y = 100 ^ k = 100 ^ 6 i . e . k = 6 answer : option c
Answer: c
Problem: in a can , there is a mixture of milk and water in the ratio 3 : 7 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 4 : 7 . find the capacity of the can ?
Options: a ) 16.6 , b ) 44 , c ) 27 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 3 / 10 ( t - 8 ) after adding milk , quantity of milk in the mixture = 4 / 11 t . 4 t / 11 - 8 = 3 / 10 ( t - 8 ) 37 t = 880 - 264 = > t = 16.6 . answer : a"
Answer: a
Problem: dawson and henry are in a relay race . dawson runs the first leg of the course in 38 seconds . henry runs the second leg of the course in 7 seconds . what was the average time they took to run a leg of the course ?
Options: a ) 20.5 , b ) 21.5 , c ) 22.5 , d ) 23.5 , e ) 24.5
Rationale: ( 38 seconds + 7 seconds ) / 2 = 22.5 seconds correct option is : c
Answer: c
Problem: if 1500 is increased by 20 % , and then reduced by y % , yielding 1080 , what is y ?
Options: a ) 20 % , b ) 40 % , c ) 60 % , d ) 80 % , e ) 100 %
Rationale: soln : - 1,500 * 1.2 = 1,800 . 1,800 ( 1 - y / 100 ) = 1,080 - - > ( 1 - y / 100 ) = 0.6 - - > y = 40 % . answer : b
Answer: b
Problem: if a is thrice as fast as b and together can do a work in 24 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 42 , c ) 28 , d ) 32 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 24 = 3 + 1 / 3 x = 4 / 3 x = 1 / 24 x = 24 * 4 / 3 = 32 answer : d"
Answer: d
Problem: the figure above shows the dimensions of a semicircular cross section of a one - way tunnel . the single traffic lane is 12 feet wide and is equidistant from the sides of the tunnel . if vehicles must clear the top of the tunnel by at least ½ foot when they are inside the traffic lane , what should be the limit u on the height of vehicles that are allowed to use the tunnel ?
Options: a ) 5 ½ ft , b ) 7 ½ ft , c ) 8 ½ ft , d ) 9 ½ ft , e ) 10 ft
Rationale: "let ' s label the midpoint of the circle o . since the base of the semi - circle is 20 , we know that the diameter is 20 and , accordingly , the radius is 10 . we also know that the traffic lane is 12 feet long and there ' s an equal amount of space on either side , so the traffic lane extends 6 feet on either side of o . let ' s call the leftmost point on the base of the traffic lane a . so , the distance oa is 6 . now draw a line straight up from a to the top of the tunnel . let ' s label the point at which the line intersects the circle b . the answer to the question will , therefore , be the height ab - . 5 feet ( we need to leave . 5 feet of clearance ) . here ' s the key to solving the question : if we draw a line from o to b , that line is a radius of the circle and , therefore , has length 10 . we now have right triangle oab ( the right angle is at point a ) , with leg oa = 6 and hypotenuse ob = 10 . we can now solve for leg ab = 8 ( either by applying the pythagorean theorum or by applying the 3 / 4 / 5 special right triangle ratio ) . finally : ab = 8 , so the correct answer u is 8 - . 5 = 7.5 . . . choose ( b ) ! from a strategic guessing point of view , as soon as we realize that the height of the tunnel is 10 in the middle , we should quickly eliminate ( d ) and ( e ) as too big ; worse case you have a 1 / 3 shot at picking up the points . b"
Answer: b
Problem: find the product of the local value and absolute value of 4 in 20468 ?
Options: a ) 1000 , b ) 1200 , c ) 1340 , d ) 1450 , e ) 1600
Rationale: "local value of 4 = 4 x 100 = 400 place value of 4 = 4 there fore = 4 x 400 = 1600 e"
Answer: e
Problem: a train 500 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 28 , c ) 49 , d ) 64 , e ) 21
Rationale: "s = ( 500 + 300 ) / 45 = 800 / 45 * 18 / 5 = 64 answer : d"
Answer: d
Problem: a and b invests rs . 3000 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 ) 9 : 6 , b ) 9 : 8 , c ) 9 : 0 , d ) 9 : 2 , e ) 9 : 1
Rationale: "( 3 * 6 + 6 * 6 ) : ( 4 * 12 ) 54 : 48 = > 9 : 8 answer : b"
Answer: b
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 30 , and the difference between the total number of strawberries and the total number of blueberries would increase by 100 . each blue box contains how many blueberries ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "let x be the number of blueberries in each blue box . then there are x + 30 strawberries in each red box . x + ( x + 30 ) = 100 x = 35 the answer is a ."
Answer: a
Problem: there are an average of 117 jellybeans in each of 34 bags of various sizes . after adding another bag , the average number of jellybeans per bag increases by 7 . how many jellybeans are in the new bag ?
Options: a ) 124 , b ) 97 , c ) 117 , d ) 229 , e ) 362
Rationale: total jellybeans in 34 bags = 34 * 117 = 3978 total jellybeans in 35 bags = 35 * 124 = 4340 number of jellybeans in new bag = 3978 - 4340 = 362 jellybeans answer is e
Answer: e
Problem: a student has to obtain 33 % of the total marks to pass . he got 175 marks and failed by 89 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 800 , d ) 610 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 175 + 89 33 x / 100 = 264 x = 800 answer is c"
Answer: c
Problem: a solution of 90 litres contains milk and water in the ratio 7 : x . if 10 litres of water is added to the solution , the ratio becomes 3 : 2 , find the value of x ?
Options: a ) 2 , b ) 1.5 , c ) 3.5 , d ) 2.5 , e ) 3
Rationale: exp . total new quantity = original sol + water = 90 + 10 = 100 new ratio = 3 : 2 , new quantity of milk = 3 / 5 * 100 = 60 lit , new quantity of water = 2 / 5 * 100 = 40 lit water present initially = ( 40 - 10 ) = 30 lit ratio = 60 / 30 = 7 / x there for x = 3.5 answer : c
Answer: c
Problem: a rectangle has a perimeter of 176 inches . the length of the rectangle is 8 inches more than its width . what is the area of the rectangle ?
Options: a ) 1,408 square inches
b ) 1,920 square inches
c ) 1,936 square inches
d ) 2,304 square inches
e ) none of these
Rationale: explanation : we have : ( l - b ) = 8 and 2 ( l + b ) = 176 or ( l + b ) = 88 . solving the two equations , we get : l = 48 and b = 40 . area = ( l x b ) = ( 48 x 40 ) in 2 = 1920 in 2 . correct answer : b
Answer: b
Problem: in an election between the two candidates , the candidates who gets 70 % of votes polled is winned by 240 vote ’ s majority . what is the total number of votes polled ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 850 , e ) none of these
Rationale: "explanation : note : majority ( 40 % ) = difference in votes polled to win ( 70 % ) & defeated candidates ( 30 % ) 40 % = 70 % - 30 % 40 % - - - - - > 280 ( 40 * 6 = 240 ) 100 % - - - - - > 600 ( 100 * 6 = 600 ) answer : option a"
Answer: a
Problem: in covering a distance of 42 km , abhay takes 2 hours more than sameer . if abhay doubles his speed , then he would take 1 hour less than sameer . abhay ' s speed is :
Options: a ) 5 kmph , b ) 6 kmph , c ) 6.25 kmph , d ) 7 kmph , e ) 7.8 kmph
Rationale: "let abhay ' s speed be x km / hr . then , 42 / x - 42 / 2 x = 3 6 x = 42 x = 7 km / hr . answer : option d"
Answer: d
Problem: a store sells chairs and tables . if the price of 2 chairs and 1 table is 60 % of the price of 1 chair and 2 tables , and the price of 1 table and 1 chair is $ 96 , what is the price , in dollars , of 1 table ? ( assume that every chair has the same price and every table has the same price . )
Options: a ) 81 , b ) 84 , c ) 85 , d ) 88 , e ) 90
Rationale: let c = chair ; t = table 2 c + 1 t = 0.6 ( 1 c + 2 t ) or c ( 2 - 0.6 ) = 1.2 t - 1 t or 1.4 c = 0.2 t therefore c = 0.2 / 1.4 t = 1 / 7 t ic + 1 t = 96 or 1 / 7 t + 1 t = 96 therefore t = 96 * 7 / 8 = 84 b
Answer: b
Problem: the length of the bridge , which a train 140 meters long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 328 , b ) 279 , c ) 235 , d ) 288 , e ) 211
Rationale: speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 140 + x ) / 30 = 25 / 2 = = > 2 ( 140 + x ) = 750 = = > x = 235 m . answer : c
Answer: c
Problem: maths , physics and chemistry books are stored on a library shelf that can accommodate 25 books . currently , 20 % of the shelf spots remain empty . there are twice as many maths books as physics books and the number of physics books is 4 greater than that of chemistry books . among all the books , 12 books are soft cover and the remaining are hard - cover . if there are a total of 7 hard - cover books among the maths and physics books . what is the probability t , that a book selected at random is either a hard cover book or a chemistry book ?
Options: a ) 1 / 10 , b ) 3 / 20 , c ) 1 / 5 , d ) 1 / 4 , e ) 9 / 20
Rationale: "first phase of this problem requires you to determine how many mathematics and chemistry books are even on the shelf . to do so , you have the equations : m + p + c = 20 ( since 4 / 5 of the 25 spots are full of books ) m = 2 p p = 4 + c from that , you can use substitution to get everything down to one variable . c = p - 4 m = 2 p p = p then ( p - 4 ) + 2 p + p = 20 , so 4 p = 24 and p = 6 . that means that there are 12 math , 6 physics , and 2 chemistry books on the shelf . with those numbers , you also know that there are 8 total hardcovers , 1 of which is chemistry . so if your goal is to get either a hardcover or a chemistry , there are 9 ways towin - either one of the 7 hardcovers that are n ' t chemistry or the two chemistry books . so out of the 20 total , t = 9 provide the desired outcome , making the answer e ."
Answer: e
Problem: evaluate : 86 x 863 - 86 x 237
Options: a ) 45823 , b ) 53836 , c ) 44824 , d ) 66524 , e ) none of them
Rationale: "86 x 863 + 986 x 237 = 986 x ( 863 - 237 ) = 86 x 626 = 53836 . answer is b"
Answer: b
Problem: a man complete a journey in 40 hours . he travels first half of the journey at the rate of 20 km / hr and second half at the rate of 30 km / hr . find the total journey in km .
Options: a ) 960 km , b ) 224 km , c ) 230 km , d ) 232 km , e ) 234 km
Rationale: "0.5 x / 20 + 0.5 x / 30 = 40 - - > x / 20 + x / 30 = 80 - - > 5 x = 60 x 80 - - > x = ( 60 x 80 ) / 5 = 960 km . answer : a"
Answer: a
Problem: a large box contains 19 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 475 , b ) 350 , c ) 450 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 19 * 25 = 475 correct answer a"
Answer: a
Problem: a store has 10 bottles of juice , including 6 bottles of apple juice . in the evening , 6 bottles of juice are sold one by one . what is the probability of selling 4 bottles of apple juice among the 6 bottles ? assume that every bottle has an equal chance of being bought .
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 2 / 3 , d ) 1 / 2 , e ) 3 / 7
Rationale: "the total number of ways to sell 6 bottles from 10 is 10 c 6 = 210 . the number of ways to sell 4 bottles of apple juice is 6 c 4 * 4 c 2 = 15 * 6 = 90 p ( selling 4 bottles of apple juice ) = 90 / 210 = 9 / 21 = 3 / 7 the answer is e ."
Answer: e
Problem: in a class of 50 students , 18 take chorus , 26 take band , and 2 take both chorus and band . how many students in the class are not enrolled in either chorus or band ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: 16 + 2 + 24 + x = 50 42 + x = 50 x = 8 students a )
Answer: a
Problem: a shopkeeper sold an article offering a discount of 5 % and earned a profit of 34.9 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 28.5 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) 42
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 34.9 ) / ( 100 â ˆ ’ 5 ) = 142 hence , required % profit = 142 â € “ 100 = 42 % answer e"
Answer: e
Problem: how long will a boy take to run round a square field of side 30 meters , if he runs at the rate of 12 km / hr ?
Options: a ) 52 sec , b ) 45 sec , c ) 60 sec , d ) 25 sec , e ) 36 sec
Rationale: "speed = 12 km / hr = 12 * 5 / 18 = 10 / 3 m / sec distance = 30 * 4 = 120 m time taken = 120 * 3 / 10 = 36 sec answer is e"
Answer: e
Problem: the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 280 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: "let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 280 hence , x = 200 . so , number of timeshare condos available at playa del mar = 200 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 2 / 5 x = 3 / 5 ( 200 ) = 120 the correct answer is c"
Answer: c
Problem: the price of a coat in a certain store is $ 500 . if the price of the coat is to be reduced by $ 350 , by what percent is the price to be reduced ?
Options: a ) 70 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "price of a coat in a certain store = $ 500 the price of the coat is to be reduced by $ 350 % change = ( final value - initial value ) * 100 / initial value % reduction = ( reduction in price ) * 100 / initial value i . e . % reduction = ( 350 ) * 100 / 500 = 70 % answer : option a"
Answer: a
Problem: ratio of two numbers x and y is 7 : 9 . if x is increased by 20 % and y is increased by 33 then the new ratio becomes 1 : 5 . what is the ratio 2 y : ( x + 4 )
Options: a ) 18 : 11 , b ) 8 : 1 , c ) 11 : 18 , d ) 1 : 8 , e ) 1 : 1
Rationale: let : x = 7 n y = 9 n 8.4 n / ( 9 n + 33 ) = 1 / 5 42 n = 9 n + 33 n = 1 so , x = 7 ; y = 9 2 y / ( x + 4 ) = 18 / 11 answer = a
Answer: a
Problem: of 70 players on a football team , 52 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 64 , e ) 92
Rationale: "total = 70 thrower = 52 rest = 70 - 52 = 18 left handed = 18 / 3 = 6 right handed = 12 if all thrower are right handed then total right handed is 52 + 12 = 64 so d . 64 is the right answer"
Answer: d
Problem: a man can row upstream at 15 kmph and downstream at 35 kmph , and then find the speed of the man in still water ?
Options: a ) 65 , b ) 86 , c ) 30 , d ) 78 , e ) 25
Rationale: "us = 15 ds = 35 m = ( 35 + 15 ) / 2 = 25 answer : e"
Answer: e
Problem: 39 ! is divided by 41 . then what is the remainder ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 9
Rationale: "substituting p = 41 in the wilson ' s theorem , we get 40 ! + 141 = 0 40 × 39 ! + 141 = 0 − 1 × 39 ! 41 = − 1 cancelling - 1 on both sides , 39 ! 41 = 1 a"
Answer: a
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if x invested rs . 40,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 40000 / y = 2 / 3 ‹ = › y = ( 40000 × 3 / 2 ) . ‹ = › y = 60000 . answer c"
Answer: c
Problem: if the product of two numbers is 82500 and their h . c . f . is 55 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 1500 , d ) 1574 , e ) none of these
Rationale: "explanation : hcf * lcm = 82500 , because we know product of two numbers = product of hcf and lcm lcm = 82500 / 55 = 1500 option c"
Answer: c
Problem: what is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between the two sides is 150 o ?
Options: a ) 24 sq units
b ) 48 sq units
c ) 24 under root 3
d ) 48 under root 3
e ) such a triangle does not exist
Rationale: explanatory answer if two sides of a triangle and the included angle ' y ' is known , then the area of the triangle = 1 / 2 * ( product of sides ) * sin y substituting the values in the formula , we get 1 / 2 * 8 * 12 * sin 150 o = 1 / 2 * 8 * 12 * 1 / 2 . note : sin 150 o = 1 / 2 area = 24 sq units . choice a
Answer: a
Problem: tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 8 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4.5 mph , e ) 0.5 mph
Rationale: "( 1 mph + 8 mph ) / 2 = 4.5 mph correct option is : d"
Answer: d
Problem: the average age of boys in a class is 16 years and that of the girls is 15 years . what is the average age for the whole class ?
Options: a ) 15 , b ) 16 , c ) 15.5 , d ) insufficient data , e ) 17
Rationale: explanation : we do not have the number of boys and girls . hence we can not find out the answer . answer : option d
Answer: d
Problem: there were totally 100 men . 84 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 84 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 16 - 25 - 15 - 30 = 100 - 86 = 14 answer : d"
Answer: d
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 35 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 24 , d ) 20 , e ) 99
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 35 km with stoppages . stoppage time = time take to travel ( 60 - 35 ) km i . e 25 km at 60 km / hr . stoppage time = 25 / 60 hrs = 24 min . answer : c"
Answer: c
Problem: one paper sheet can be used to create 8 paper boats or 6 paper planes . if total exact 80 paper toys are to be made , minimum how many sheets need to be used to make paper boats ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: let us say x sheets are used to create paper boats and y sheets are used to create paper planes . since total 80 paper toys are to be created , 8 x + 6 y = 80 . = > 8 x = 80 - 6 y = > x = 10 - ( 6 / 8 ) y = > x = 10 - ( 3 / 4 ) y to minimize x , we need to maximize y . and y needs to be multiple of 4 . y = 4 , x = 10 - ( 3 / 4 ) 4 = 7 y = 8 , x = 10 - ( 3 / 4 ) 8 = 4 y = 12 , x = 10 - ( 3 / 4 ) 12 = 1 beyond this , x will become negative for greater values of y . so , minimum 1 sheet is required to be used for creating paper boats . answer : e
Answer: e
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 60 , find the other ?
Options: a ) 100 , b ) 240 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 60 = 120 answer is c"
Answer: c
Problem: 1604 x 1604 = ?
Options: a ) a ) 2572816 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1604 x 1604 = ( 1604 ) 2 = ( 1600 + 4 ) 2 = ( 1600 ) 2 + ( 4 ) 2 + ( 2 x 1600 x 4 ) = 2560000 + 16 + 12800 . = 2572816 . a )"
Answer: a
Problem: if abc is a quarter circle and a smaller circle is inscribed in it ; if radius of quarter circle is 1.414 units . find the radius of smaller circle
Options: a ) 0.586
b ) 0.687
c ) 0.784
d ) 0.874
e ) 0.974
Rationale: if r be radius of smaller circle then distance b / n centres = √ 2 * r so , r + r √ 2 = r here , r = 1.414 = √ 2 = > r = ( √ 2 - 1 ) r r = 0 . 586 unit answer : a
Answer: a
Problem: a bag of potatoes weighs 16 kg divided by a quarter of its weight . how much does the bag weigh ?
Options: a ) 4 kg , b ) 8 kg , c ) 7 kg , d ) 3 kg , e ) 9 kg
Rationale: b 8 kg 8 kg : 16 / 2
Answer: b
Problem: the cost price of a radio is rs . 1590 and it was sold for rs . 1450 , find the loss % ?
Options: a ) 8 % , b ) 12 % , c ) 10 % , d ) 14 % , e ) 21
Rationale: "1590 - - - - 140 100 - - - - ? = > 8 % answer : a"
Answer: a
Problem: a retailer bought a machine at a wholesale price of $ 90 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 160
Rationale: "my solution : wholesale price = 90 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 90 + 1 / 5 ( 90 ) x = 120 ; answer : c"
Answer: c
Problem: what is the least number should be added to 1056 , so the sum of the number is completely divisible by 27 ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "( 1056 / 27 ) gives remainder 3 24 + 3 = 27 , so we need to add 24 d"
Answer: d