Cheukting/mathqa huggingface dataset:
Question (general): a professional janitor can clean a certain high school in ( 4 + 4 ) hours , working at a constant rate . a student sentenced to detention can clean that same high school in 20 hours , also working at a constant rate . if the student is paid $ 7 total per hour and the janitor is paid $ 21 per hour , how much more would it cost the school to pay the janitor to do the job himself than it would to pay the student and the janitor to do the job together ?
Options: a ) - $ 56 , b ) - $ 6 , c ) $ 0 , d ) $ 6 , e ) $ 8
Rationale: a professional janitor can clean a certain high school in ( 4 + 4 ) or 8 hours so ( applying rule # 1 ) , the janitor can clean 1 / 8 of the school in one hour a student sentenced to detention can clean that same high school in 20 hours so ( applying rule # 1 ) , the student can clean 1 / 20 of the school in one hour so , combined , the student and janitor can clean ( 1 / 8 + 1 / 20 ) of the school in one hour 1 / 8 + 1 / 20 = 5 / 40 + 2 / 40 = 7 / 40 so , in one hour they can clean 7 / 40 of the school . applying rule # 2 , it will takethem 40 / 7 hoursto clean the entire school . the janitor earns $ 21 / hour and the student earns $ 7 / hour , so their combined rate is $ 28 / hour . theircombined wages = ( pay rate ) ( time ) = ( $ 28 / hour ) ( 40 / 7 hours ) = $ 160 working alone , the janitor takes 8 hours and earns $ 21 / hour so , working alone , the janitor ' s earnings = ( pay rate ) ( time ) = ( $ 21 / hour ) ( 8 hours ) = $ 168 $ 168 - $ 160 = $ 8 , so the answer is e
Answer: e
Question (physics): 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 2 men and 3 women will do that task .
Options: a ) 1 / 2 , b ) 1 / 10 , c ) 1 / 18 , d ) 1 / 16 , e ) 1 / 11
Rationale: "3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 2 m + 3 w = 7 w answer is 7 / 14 = 1 / 2 answer : a"
Answer: a
Question (gain): a light has a rating of 60 watts , it is replaced with a new light that has 12 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 67 , c ) 80 , d ) 60 , e ) 100
Rationale: "final number = initial number + 12 % ( original number ) = 60 + 12 % ( 60 ) = 60 + 7 = 67 answer b"
Answer: b
Question (gain): a sum of money becomes 7 / 6 of itself in 6 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 50 / 9 , b ) 50 / 13 , c ) 50 / 17 , d ) 25 / 9 , e ) 5 5 / 1
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 6 years . rate = ( 100 * x ) / ( x * 6 * 6 ) = 25 / 9 % . answer : d"
Answer: d
Question (gain): find the missing figures : 0.3 % of ? = 0.15
Options: a ) 50 , b ) 45 , c ) 150 , d ) 450 , e ) 500
Rationale: let 0.3 % of x = 0.15 . then , 0.30 * x / 100 = 0.15 x = [ ( 0.15 * 100 ) / 0.3 ] = 50 . answer is a .
Answer: a
Question (gain): the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 265 , then the mean profit for the last 15 days would be
Options: a ) rs . 435 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these
Rationale: average would be : 350 = ( 265 + x ) / 2 on solving , x = 435 . answer : a
Answer: a
Question (other): the ratio of the number of females to males at a party was 1 : 2 but when 5 females and 5 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 26 , b ) 28 , c ) 30 , d ) 32 , e ) 34
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 5 ) = 2 x - 5 x = 10 there were 3 x = 30 people at the party originally . the answer is c ."
Answer: c
Question (general): the least number which when increased by 8 each divisible by each one of 24 , 32 , 36 and 54 is :
Options: a ) 427 , b ) 859 , c ) 869 , d ) 856 , e ) none of these
Rationale: "solution required number = ( l . c . m . of 24 , 32 , 36 , 54 ) - 8 = 864 - 8 = 856 . answer d"
Answer: d
Question (physics): find the length of the wire required to go 10 times round a square field containing 53824 m 2 .
Options: a ) 15840
b ) 9280
c ) 2667
d ) 8766
e ) 66711
Rationale: a 2 = 53824 = > a = 232 4 a = 928 928 * 10 = 9280 answer : b
Answer: b
Question (gain): a man invested rs . 14,400 in rs . 100 shares of a company at 20 % premium . if the company declares 4 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 600 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: "solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 4 / 100 x 12000 ) = rs . 480 . answer e"
Answer: e
Question (geometry): what should be added to 4329 so that it may become a perfect square ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: "66 x 66 = 4356 4356 - 4329 = 27 if added to 27 get perfect square answer = d"
Answer: d
Question (general): the number of the members of a club is more than 20 and less than 50 . when 4 people sit at a table , other people exactly divided to 6 - people groups ( 6 people sit at a table ) or 7 - people groups ( 7 people sit at a table ) . if the members are divided to 8 - people groups , how many people will be left ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the number of members is 7 k + 4 = 6 j + 4 the only number in this range which satisfies this is 46 . 46 / 8 = 5 ( 8 ) + 6 the answer is d ."
Answer: d
Question (gain): the income of a company increases 20 % per annum . if its income is 2664000 in the year 1999 what was its income in the year 1997 ?
Options: a ) 2220000 , b ) 2850000 , c ) 2121000 , d ) 1855000 , e ) none of these
Rationale: let income in 1997 = x according to the question , income in 1998 = x + x ⁄ 5 = 6 x ⁄ 5 income in 1999 = 6 x ⁄ 5 + 6 x ⁄ 25 = 36 x ⁄ 25 but given , income in 1999 = 2664000 ∴ 36 x ⁄ 25 = 2664000 ⇒ x = 1850000 answer e
Answer: e
Question (general): when 242 is divided by a certain divisor the remainder obtained is 11 . when 698 is divided by the same divisor the remainder obtained is 18 . however , when the sum of the two numbers 242 and 698 is divided by the divisor , the remainder obtained is 9 . what is the value of the divisor ?
Options: a ) 11 , b ) 17 , c ) 13 , d ) 20 , e ) none of these
Rationale: "let that divisor be x since remainder is 11 or 18 it means divisor is greater than 18 . now 242 - 11 = 231 = kx ( k is an integer and 234 is divisble by x ) similarly 698 - 18 = 680 = lx ( l is an integer and 689 is divisible by x ) adding both 698 and 242 = ( 231 + 680 ) + 11 + 18 = x ( k + l ) + 29 when we divide this number by x then remainder will be equal to remainder of ( 29 divided by x ) = 9 hence x = 29 - 9 = 20 hence d"
Answer: d
Question (gain): anil brought a scooter for a certain sum of money . he spent 10 % of the cost on repairs and sold the scooter for a profit of rs . 1100 . how much did he spend on repairs if he made a profit of 20 % ?
Options: a ) 220 , b ) 420 , c ) 250 , d ) 700 , e ) 500
Rationale: e c . p . be rs . x . then , 20 % of x = 1100 20 / 100 * x = 1100 = > x = 5500 c . p . = rs . 5500 , expenditure on repairs = 10 % actual price = rs . ( 100 * 5500 ) / 110 = rs . 5000 expenditures on repairs = ( 5500 - 5000 ) = rs . 500 .
Answer: e
Question (physics): if 7 persons can do 7 times of a particular work in 7 days , then , 9 persons can do 9 times of that work in ?
Options: a ) 3 days , b ) 8 days , c ) 9 days , d ) 11 days , e ) 7 days
Rationale: that is , 1 person can do one time of the work in 7 days . therefore , 9 persons can do 9 times work in the same 7 days itself . option ' e '
Answer: e
Question (general): the cost per pound of green tea and coffee were the same in june . in july , the price of coffee shot up by 100 % and that of green tea dropped by 90 % . if in july , a mixture containing equal quantities of green tea and coffee costs $ 3.15 for 3 lbs , how much did a pound of green tea cost in july ?
Options: a ) $ 4 , b ) $ 0.1 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: "lets assume price of coffee in june = 100 x price of green tea in june = 100 x price of coffee in july = 200 x ( because of 100 % increase in price ) price of green tea in july = 10 x ( because of 90 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of green tea in july will be = 300 x + 15 x = 315 x as per question 315 x = 3.15 $ x = 0.01 s so the price of green tea in july = 10 x = 10 x 0.01 = 0.1 $ / pound answer b"
Answer: b
Question (general): if xy > 0 , 1 / x + 1 / y = 4 , and 1 / xy = 6 , then ( x + y ) / 2 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 4 canbe solved as { ( x + y ) / xy } = 6 . substituting for 1 / xy = 6 , we get x + y = 4 / 6 = = > ( x + y ) / 2 = 4 / ( 6 * 2 ) = 1 / 3 . d"
Answer: d
Question (gain): what is 0.01 percent of 12,356 ?
Options: a ) 0.12356 , b ) 1.2356 , c ) 12.356 , d ) 0.012356 , e ) 0.0012356
Rationale: "soln : - 0.01 % of 12,356 = 0 . 011000.01100 x 12,356 = 1100 ∗ 1001100 ∗ 100 x 12,356 = 12,356100 ∗ 10012,356100 ∗ 100 = 1.2356 answer : b"
Answer: b
Question (gain): indu gave bindu rs . 2500 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 2 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2500 = d ( 100 / 2 ) 2 d = 1 answer : a"
Answer: a
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent e of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is e = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Question (general): for what values of k will the pair of equations 3 ( 3 x + 4 y ) = 36 and kx + 12 y = 30 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: "we have 2 equations 1 . 3 ( 3 x + 4 y ) = 36 - - > 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b"
Answer: b
Question (physics): working at constant rate , pump x pumped out half of the water in a flooded basement in 5 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 26 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 26 hours d"
Answer: d
Question (other): there 3 kinds of books in the library physics , chemistry and biology . ratio of physics to chemistry is 3 to 2 ; ratio of chemistry to biology is 4 to 3 , and the total of the books is more than 3000 . which one of following can be the total r of the book ?
Options: a ) 3003 , b ) 3027 , c ) 3024 , d ) 3021 , e ) 3018
Rationale: "first , you have to find the common ratio for all 3 books . you have : p : c : b 3 : 2 - - > multiply by 2 ( gives you row 3 ) 4 : 6 6 : 4 : 3 hence : p : c : b : t ( total ) r 6 : 4 : 3 : 13 - - - - > this means , the total number must be a multiple of 13 . answer a is correct since 299 is divisible by 13 , hence is 2990 and so is 3003 ( 2990 + 13 ) ."
Answer: a
Question (general): on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 5 cups of tea . last week mo drank a total of 36 cups of tea and hot chocolate together . if during that week mo drank 14 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 2 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 36 t - c = 14 - > t = 25 . c = 11 . mo drinks 5 cups of tea a day then number of days that are not rainy = 25 / 5 = 5 so number of rainy days = 7 - 5 = 2 d is the answer ."
Answer: d
Question (general): there are 2 sections a and b in a class , consisting of 16 and 14 students respectively . if the average weight of section a is 20 kg and that of section b is 25 kg , find the average of the whole class ?
Options: a ) 33.5 kg , b ) 37.25 kg , c ) 42.45 kg , d ) 55.12 kg , e ) 29.78 kg
Rationale: "total weight of 36 + 44 students = 16 * 20 + 14 * 25 = 670 average weight of the class is = 670 / 20 = 33.5 kg answer is a"
Answer: a
Question (physics): a car traveled 75 % of the way from town a to town b at an average speed of 60 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 40 miles per hour . what is s ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 37.5
Rationale: total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 60 = 1.25 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 40 = 1.25 + t » 100 / 40 = 1.25 + t » 2.5 = 1.25 + t » t = 1.25 back to 2 nd part of the trip formula : 25 / s = 1.25 » s = 20 ans b
Answer: b
Question (gain): the price of a jacket is reduced by 35 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 70.9 , b ) 75 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 35 % , therefore bringing down the price to $ 65 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 58.5 4 ) now 58.5 has to be added byx % in order to equal the original price . 58.5 + ( x % ) 58.5 = 100 . solving this eq for x , we get x = 70.9 ans is a ."
Answer: a
Question (other): the number of stamps that p and q had were in the ratio of 7 : 3 respectively . after p gave q 13 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 5 : 4 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 10 , b ) 25 , c ) 40 , d ) 65 , e ) 90
Rationale: "p started with 7 k stamps and q started with 3 k stamps . ( 7 k - 13 ) / ( 3 k + 13 ) = 5 / 4 28 k - 15 k = 117 k = 9 p has 7 ( 9 ) - 13 = 50 stamps and q has 3 ( 9 ) + 13 = 40 stamps . the answer is a ."
Answer: a
Question (general): if x and y are positive integers and 25 x = 10 y what is the least possible value of xy ?
Options: a ) 14 , b ) 25 , c ) 63 , d ) 84 , e ) 252
Rationale: "25 x = 10 y = > x / y = 2 / 5 = > 5 x = 2 y 5 ( 3 ) = 2 ( 3 ) = > x * y = 9 but it is not given 5 ( 5 ) = 2 ( 5 ) = > x * y = 25 b"
Answer: b
Question (general): a retailer bought a shirt at wholesale and marked it up 80 % to its initial price of $ 27 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let x be the wholesale price . then 1.8 x = 27 and x = 27 / 1.8 = 15 . to achieve a 100 % markup , the price needs to be $ 30 . the retailer needs to increase the price by $ 3 more . the answer is c ."
Answer: c
Question (geometry): the ratio of the volumes of two cubes is 2744 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 196 : 121 , b ) 81 : 127 , c ) 181 : 196 , d ) 81 : 161 , e ) 81 : 182
Rationale: "explanation : ratio of the sides = ³ √ 2744 : ³ √ 1331 = 14 : 11 ratio of surface areas = 14 ^ 2 : 11 ^ 2 = 196 : 121 answer : option a"
Answer: a
Question (gain): evaluate 28 % of 350 + 45 % of 280
Options: a ) 224 , b ) 242 , c ) 252 , d ) 262 , e ) 282
Rationale: "explanation : = ( 28 / 100 ) * 350 + ( 45 / 100 ) * 280 = 98 + 126 = 224 answer : option a"
Answer: a
Question (probability): three unbiased coins are tossed . what is the probability of getting 1 heads , 1 tail ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 2 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { tht , hth } p ( e ) = n ( e ) / n ( s ) = 2 / 8 answer is e"
Answer: e
Question (other): divide rs . 32000 in the ratio 3 : 7 ?
Options: a ) 12000 , 20000 , b ) 9600 , 22400 , c ) 12000 , 20007 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: 3 / 10 * 32000 = 9600 7 / 8 * 32000 = 22400 answer : b
Answer: b
Question (physics): a train is running with a speed of 60 kmph and its length is 110 metres . calculate the time by which it will pass a man running opposite with speed of 6 kmph
Options: a ) 2 second , b ) 4 second , c ) 6 second , d ) 8 second , e ) 10 second
Rationale: explanation : from the given question , we will first calculate the speed of train relative to man , = > ( 60 + 6 ) = 66 km / hr ( we added 6 because man is running opposite ) convert it in metre / second = 66 ã — 5 / 18 = 55 / 3 m / sec time it will take to pass man = 110 ã — 3 / 55 = 6 seconds answer is c
Answer: c
Question (general): the total of the ages of amar , akbar and anthony is 66 years . what was the total of their ages 4 years ago ?
Options: a ) 71 , b ) 44 , c ) 54 , d ) 16 , e ) 18
Rationale: explanation : required sum = ( 66 - 3 x 4 ) years = ( 66 - 12 ) years = 54 years . answer : c
Answer: c
Question (physics): kim finds a 3 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 8 / 15 , d ) 1 / 2 , e ) 7 / 5
Rationale: 3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is b
Answer: b
Question (general): a certain country is divided into 8 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 8 p / 12 = 2 p / 3 . the total population is p + 2 p / 3 = 5 p / 3 p / ( 5 p / 3 ) = 3 / 5 the answer is e ."
Answer: e
Question (general): n and m are each 3 - digit integers . each of the numbers 1 , 2 , 3 , 45 and 6 is a digit of either n or m . what is the smallest possible positive difference between n and m ?
Options: a ) 59 , b ) 49 , c ) 58 , d ) 113 , e ) 131
Rationale: you have 6 digits : 12 , 3 , 4 , 5 , 6 each digit needs to be used to make two 3 digit numbers . this means that we will use each of the digits only once and in only one of the numbers . the numbers need to be as close to each other as possible . the numbers can not be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other . the first digit ( hundreds digit ) of both numbers should be consecutive integers now let ' s think about the next digit ( the tens digit ) . to minimize the difference between the numbers , the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . so let ' s not use 1 and 6 in the hundreds places and reserve them for the tens places now what are the options ? try and make a pair with ( 2 * * and 3 * * ) . make the 2 * * number as large as possible and make the 3 * * number as small as possible . 265 and 314 ( difference is 49 ) or try and make a pair with ( 4 * * and 5 * * ) . make the 4 * * number as large as possible and make the 5 * * number as small as possible . we get 463 and 512 ( difference is 49 ) b
Answer: b
Question (physics): with both inlets open , a water tank will be filled with water in 36 minutes . the first inlet alone would fill the tank in 2 hours . if in every minutes the second inlet admits 50 cubic meters of water than the first , what is the capacity of the tank ?
Options: a ) 9,000 , b ) 4,500 , c ) 1,750 , d ) 1,000 , e ) 2,000
Rationale: "the work done by inlet a and b together in 1 min = 1 / 36 the work done by inlet a ( first inlet ) in 1 min = 1 / 120 the work done by inlet b ( second inlet ) in 1 min = ( 1 / 36 ) - ( 1 / 120 ) = 1 / 51 difference of work done by b and a = b - a = 50 cubic meter i . e . ( 1 / 51 ) - ( 1 / 120 ) = 50 cubic meter i . e . 4500 cubic meter answer : option b"
Answer: b
Question (geometry): what is the angle between the hands of a clock when time is 16 : 40 ?
Options: a ) 625 deg , b ) 420 deg , c ) 145 deg , d ) 150 deg , e ) 300 deg
Rationale: "angle between two hands = 40 h - 11 / 2 m = 40 * 16 - 40 * 11 / 2 = 640 - 220 = 420 deg answer : b"
Answer: b
Question (general): solve the equation for x : 8 ( x + y + 2 ) = 8 y - 8
Options: a ) - 3 , b ) - 2 , c ) - 1 , d ) 1 , e ) 2
Rationale: "a - 3 8 ( x + y + 2 ) = 8 y - 8 8 x + 8 y + 16 = 8 y - 8 8 x + 16 = - 8 8 x = - 24 = > x = - 3"
Answer: a
Question (gain): during a special promotion , a certain filling station is offering a 8 percent discount on gas purchased after the first 10 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 105 % , c ) 115 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 4 + 0.9 * 16 = 18.4 gallons , so the overall discount she got was 1.6 / 20 = 8 % . isabella purchased 25 gallons of gas . she paid for 4 + 0.9 * 21 = 22.9 gallons , so the overall discount she got was 2.1 / 25 = 8.4 % . 8.4 / 8 * 100 = 105 % . answer : b ."
Answer: b
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 90 only . men â € ™ s wages are ?
Options: a ) rs . 6 , b ) rs . 6.5 , c ) rs . 8 , d ) rs . 5 , e ) rs . 2
Rationale: "answer : option a 5 m = xw = 8 b 5 m + xw + 8 b - - - - - 90 rs . 5 m + 5 m + 5 m - - - - - 90 rs . 15 m - - - - - - 90 rs . = > 1 m = 6 rs ."
Answer: a
Question (physics): stacy has a 33 page history paper due in 3 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 11 , d ) 8.5 , e ) 6
Rationale: "33 / 3 = 11 answer : c"
Answer: c
Question (general): the smallest value of n , for which 2 n + 1 is not a prime number , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) none , e ) 6
Rationale: "solution ( 2 × 1 + 1 ) = 3 . ( 2 × 2 + 1 ) = 5 . ( 2 × 3 + 1 ) = 7 . ( 2 × 4 + 1 ) = 9 . which is not prime , n = 4 . answer b"
Answer: b
Question (physics): a train running at the speed of 50 km / hr crosses a pole in 18 seconds . find the length of the train .
Options: a ) 150 , b ) 188 , c ) 250 , d ) 288 , e ) 300
Rationale: "speed = 50 * ( 5 / 18 ) m / sec = 125 / 9 m / sec length of train ( distance ) = speed * time ( 125 / 9 ) * 18 = 250 meter answer : c"
Answer: c
Question (general): what sum of money put at c . i amounts in 2 years to rs . 7000 and in 3 years to rs . 9261 ?
Options: a ) 4000 , b ) 8877 , c ) 2877 , d ) 2678 , e ) 1011
Rationale: "7000 - - - - 2261 100 - - - - ? = > 32.3 % x * 1323 / 100 * 1323 / 100 = 7000 x * 1.75 = 7000 x = 7000 / 1.75 = > 3999.25 answer : a"
Answer: a