Cheukting/mathqa huggingface dataset:
Question (gain): bruce purchased 8 kg of grapes at the rate of 70 per kg and 11 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1040 , b ) b ) 1165 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 11 kg of mangoes = 55 × 11 = 605 . total cost he has to pay = 560 + 605 = 1165 b"
Answer: b
Question (general): a 56 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: "amount of salt = 5.6 assume x gallons of water are added . 5.6 / 56 + x = 8 / 100 560 = 8 x + 448 8 x = 112 x = 14 correct option : d"
Answer: d
Question (general): a , b and c invest in the ratio of 3 : 4 : 5 . the percentage of return on their investments are in the ratio of 6 : 5 : 4 . find the total earnings , if b earns rs . 120 more than a :
Options: a ) 2348 , b ) 3480 , c ) 2767 , d ) 1998 , e ) 2771
Rationale: "explanation : a b c investment 3 x 4 x 5 x rate of return 6 y % 5 y % 4 y % return \ inline \ frac { 18 xy } { 100 } \ inline \ frac { 20 xy } { 100 } \ inline \ frac { 20 xy } { 100 } total = ( 18 + 20 + 20 ) = \ inline \ frac { 58 xy } { 100 } b ' s earnings - a ' s earnings = \ inline \ frac { 2 xy } { 100 } = 120 total earning = \ inline \ frac { 58 xy } { 100 } = 3480 answer : b ) rs . 3480"
Answer: b
Question (other): if log 2 = 0.3010 and log 3 = 0.4771 , the value of log 5 ( 512 )
Options: a ) 3.876 , b ) 2.967 , c ) 2.87 , d ) 3.912 , e ) 1.9
Rationale: "log 5 ( 512 ) = log ( 512 ) / log 5 = log 2 ^ 9 / log ( 10 / 2 ) = 9 log 2 / ( log 10 - log 2 ) = ( 9 x 0.3010 ) / ( 1 - 0.3010 ) = 2.709 / 0.699 = 2709 / 699 = 3.876 answer is a ."
Answer: a
Question (general): what is the smallest positive integer x such that 507 + x is the cube of a positive integer ?
Options: a ) 15 , b ) 5 , c ) 50 , d ) 2 , e ) 4
Rationale: "given 507 + x is a perfect cube so we will take 512 = 8 * 8 * 8 507 + x = 512 x = 512 - 507 = 5 correct option is b"
Answer: b
Question (physics): a train which has 440 m long , is running 45 kmph . in what time will it cross a person moving at 9 kmph in same direction ?
Options: a ) 56 sec , b ) 44 sec , c ) 36 sec , d ) 29 sec . , e ) 19 sec .
Rationale: "time taken to cross a moving person = length of train / relative speed time taken = 440 / ( ( 45 - 9 ) ( 5 / 18 ) = 440 / 36 * ( 5 / 18 ) = 440 / 10 = 44 sec answer : b"
Answer: b
Question (physics): two numbers have a h . c . f of 16 and a product of two numbers is 2560 . find the l . c . m of the two numbers ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 2560 / 16 = 160 . answer : c"
Answer: c
Question (general): what is the tens digit of 36 ^ 4 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "36 ^ 10 = 6 ^ 20 ( 6 ^ 2 ) = 6 * 6 = 36 ( 6 ^ 3 ) = 36 * 6 = . 16 ( 6 ^ 4 ) = . 16 * 6 = . . 96 ( 6 ^ 5 ) = . . 96 * 6 = . . 76 ( 6 ^ 6 ) = . . 76 * 6 = . . . 56 ( 6 ^ 7 ) = . . . . 56 * 6 = . . . . 36 if you see there is a pattern here in tens digits 3 , 1,9 , 7,5 , 3,1 and so on . . . continue the pattern up to 6 ^ 6 ( dont actually calculate full values ) and answer is c : 5"
Answer: c
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 38 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 38 % of 1100 ) + ( 32 % of 900 ) = 418 + 288 = 706 failed = 2000 - 706 = 1294 failed % = [ ( 1294 / 2000 ) x 100 ] % = 64.7 % . answer : b"
Answer: b
Question (gain): an article is bought for rs . 600 and sold for rs . 450 , find the loss percent ?
Options: a ) 16 % , b ) 18 % , c ) 19 % , d ) 20 % , e ) 25 %
Rationale: "600 - - - - 150 100 - - - - ? = > 16 2 / 3 % answer : e"
Answer: e
Question (general): 0.003 * 0.5 = ?
Options: a ) 0.00015 , b ) 0.0015 , c ) 0.015 , d ) 0.15 , e ) none of these
Rationale: "explanation : 3 * 5 = 15 . sum of decimal places = 4 . 0.003 * 0.5 = 0.0015 = 0.0015 answer b"
Answer: b
Question (physics): a man rows his boat 60 km downstream and 30 km upstream taking 3 hrs each time . find the speed of the stream ?
Options: a ) 5 kmph , b ) 6 kmph , c ) 8 kmph , d ) 1 kmph , e ) 2 kmph
Rationale: explanation : speed of the boat downstream = speed of the boat upstream \ small \ therefore the speed of the stream = answer : a
Answer: a
Question (general): the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 3 : 2 . if the oil bill for february had been $ 10 more , the corresponding ratio would have been 5 : 3 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140
Rationale: "3 : 2 = 9 : 6 and 5 : 3 = 10 : 6 . an increase in $ 10 increases the ratio by 1 : 6 . therefore , january ' s bill was 6 ( $ 10 ) = $ 60 . the answer is a ."
Answer: a
Question (general): what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 600 inclusive ?
Options: a ) 190 , b ) 195 , c ) 305 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 600 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 60 ( 10 ) = 600 so we know that there are 60 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 600 = 610 20 + 590 = 610 30 + 580 = 610 etc . since there are 60 total terms , this pattern will create 30 ' pairs ' of 610 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 30 ) ( 610 ) / ( 60 ) = 305 final answer : c"
Answer: c
Question (general): a $ 74.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 74.95 $ discounted selling price of chair = 59.95 $ discount = 74.95 - 59.95 = 15 $ % decrease in price of chair = ( 15 / 74.95 ) * 100 % = 20 % approx answer b"
Answer: b
Question (general): if rs . 595 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 420 , b ) s . 360 , c ) s . 389 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 595 * 2 / 17 = rs . 70 b ' s share = 595 * 3 / 17 = rs . 105 c ' s share = 595 * 12 / 17 = rs . 420 . answer : a"
Answer: a
Question (general): a part - time employee ’ s hourly wage was increased by 50 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 15 % , c ) 25 % , d ) 33 % , e ) 50 %
Rationale: let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 50 % wage increase , the employee makes $ 1.50 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.50 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.50 to get : new # of hours = 100 / 1.50 ≈ 67 hours so , the number of hours decreases from 100 hours to ( approximately ) 67 hours . this represents a 33 % decrease ( approximately ) . answer : d
Answer: d
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 3 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 3 ) / ( 10 - 5 ) = 2 / 5 so they should be mixed in the ratio 2 : 5 answer - a"
Answer: a
Question (physics): the q train leaves station a moving at a constant speed , and passes by stations b and c , in this order . it takes the q train 7 hours to reach station b , and 5 additional hours to reach station c . the distance between stations a and b is m kilometers longer than the distance between stations b and c . what is the distance between stations a and c in terms of m ?
Options: a ) 1.8 m , b ) 6 m , c ) 7 m , d ) 9 m , e ) 12 m
Rationale: the reason it is failing for you is that you chose incorrect numbers . if the question says it q took 7 hrs to reach from a to b and 5 hrs to reach from b to c at a constant speed . it shows that distance ab and bc should be in ratio of 7 / 5 . if you take such numbers you can solve problem . ab = 7 , bc = 5 therefore ab - bc = 2 but from question , ab - bc = m = > m = 2 now total distance = ab + bc = 12 substitute 12 to get answer in terms of m total distance = 12 = 6 m ans b
Answer: b
Question (geometry): what is the area of a square field whose sides have a length of 12 meters ?
Options: a ) 225 sq m , b ) 126 sq m , c ) 144 sq m , d ) 267 sq m , e ) 231 sq m
Rationale: "12 * 12 = 144 sq m the answer is c ."
Answer: c
Question (general): if 4 a – 2 b – 2 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d"
Answer: d
Question (general): a room is 6 meters 24 centimeters in length and 4 meters 32 centimeters in width . find the least number of square tiles of equal size required to cover the entire floor of the room .
Options: a ) 107 , b ) 117 , c ) 127 , d ) 137 , e ) 147
Rationale: "let us calculate both the length and width of the room in centimeters . length = 6 meters and 24 centimeters = 624 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 624 and 432 = 48 thus , the number of square tiles required = ( 624 x 432 ) / ( 48 x 48 ) = 13 x 9 = 117 answer : b"
Answer: b
Question (general): how many integers are between 8 and 122 / 7 , inclusive ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 15 , e ) 16
Rationale: 122 / 7 = 17 . xx we are not concerned about the exact value of 122 / 7 as we just need the integers . the different integers between 8 and 122 / 7 would be 8 , 9 , 10 , 11 , 12,13 , 14,15 , 16,17 total number of integers = 10 option b
Answer: b
Question (gain): what percent of 10 is 10 percent of 1 ?
Options: a ) 0.1 % , b ) 1 % , c ) 10 % , d ) 90 % , e ) 100 %
Rationale: "10 percent of 1 is equal to 0.1 so we have to compute what percent of 10 is 0.1 . so this means we have to compute what percent of 100 is 1 . . . . so 1 % answer b ."
Answer: b
Question (general): there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 14 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 37 , c ) 42 , d ) 53 , e ) 64
Rationale: "x + ( x - 14 ) = 60 - - > x = 37 . answer : b ."
Answer: b
Question (physics): a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed . ?
Options: a ) 50 kmph , b ) 58 kmph , c ) 62 kmph , d ) 65 kmph , e ) 75 kmph
Rationale: relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) * ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph . answer : c .
Answer: c
Question (general): the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of the remainingplayers is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 18 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Question (gain): the true discount on a bill of rs . 2160 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2160 td = rs . 360 pw = f - td = 2160 - 360 = rs . 1800 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1800 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 1800 × 2160 = 15 × 2160 = rs . 432 answer : option a"
Answer: a
Question (gain): if the cost price is 82 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 22 % , c ) 13 % , d ) 21 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 82 profit = $ 18 profit % = 18 / 82 * 100 = 25 / 6 = 22 % approximately answer is b"
Answer: b
Question (general): the average of first six prime numbers which are between 50 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 64 , e ) 67
Rationale: "explanation : first six prime numbers which are between 50 and 90 = 53 , 59 , 61 , 67 , 71 , 73 average = ( 53 + 59 + 61 + 67 + 71 + 73 ) / 6 = 64 answer : d"
Answer: d
Question (gain): if 0.5 % of a = 85 paise , then the value of a is ?
Options: a ) rs . 170 , b ) rs . 17 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
Rationale: "answer ∵ 0.5 / 100 of a = 85 / 100 ∴ a = rs . ( 85 / 0.5 ) = rs . 170 correct option : a"
Answer: a
Question (gain): suganya and suriya are partners in a business . suganya invests rs . 15,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 7015.56 , e ) none
Rationale: "solution ratio of their shares = ( 15000 ã — 8 ) : ( 42000 ã — 10 ) = 2 : 7 . suganya ' s share = rs . ( 31570 ã — 2 / 9 ) = rs . 7015.56 answer d"
Answer: d
Question (gain): find the compound interest on $ 1200 for 5 years at 20 % p . a . if ci is component yearly ?
Options: a ) $ 120 , b ) $ 150 , c ) $ 1786 , d ) $ 250 , e ) $ 300
Rationale: "a = p ( 1 + r / 100 ) ^ t = 1200 ( 1 + 20 / 100 ) ^ 5 = $ 2986 ci = $ 1786 answer is c"
Answer: c
Question (other): a person want to give his money of $ 15800 to his 4 children a , b , c , d in the ratio 5 : 9 : 6 : 5 . what is the a + c share ?
Options: a ) $ 4000 , b ) $ 2890 , c ) $ 3005 , d ) $ 6952 , e ) $ 6003
Rationale: "a ' s share = 15800 * 5 / 25 = $ 3160 c ' s share = 15800 * 6 / 25 = $ 3792 a + c = $ 6952 answer is d"
Answer: d
Question (general): a certain class of students is being divided into teams . the class can either be divided into 12 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "let total no of students in the class be n so , we are told that n is divisible by both 12 24 so , lets find the least common multiple of 12 24 , ie 24 so our answer is ( a ) 24"
Answer: a
Question (general): a group of 6 children and 10 adults are going to the zoo . child tickets cost $ 10 , and adult tickets cost $ 16 . how much will the zoo tickets cost in all ?
Options: a ) $ 220 , b ) $ 340 , c ) $ 150 , d ) $ 100 , e ) $ 120
Rationale: step 1 : find the cost of the children ' s tickets . 6 × $ 10 = $ 60 step 2 : find the cost of the adults ' tickets . 10 × $ 16 = $ 160 step 3 : find the total cost . $ 60 + $ 160 = $ 220 the zoo tickets will cost $ 220 . answer is a .
Answer: a
Question (gain): the price of rice falls by 40 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 40 % , new price for 20 kg rice , = ( 100 - 40 % of 100 ) = 60 new price of rice = 60 / 20 = rs . 3 per kg . rice can bought now at = 100 / 3 = 33.33 kg . answer : option e"
Answer: e
Question (general): the sum of the squares of three numbers is 138 , while the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 30 , b ) 15 , c ) 40 , d ) 45 , e ) 20
Rationale: "a 2 + b 2 + c 2 = 138 and ( ab + bc + ca ) = 131 a + b + c ^ 2 = 400 root ( 400 ) = 20 answer e"
Answer: e
Question (general): divide rs . 1200 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) s . 800 , b ) s . 400 , c ) s . 600 , d ) s . 500 , e ) s . 300
Rationale: "a + b + c = 1200 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1200 = > 300 answer : e"
Answer: e
Question (geometry): 108 . triangle a ’ s base is 9 % greater than the base of triangle b , and a ’ s height is 9 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1.3 % more , e ) 9 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 10 / 9 * base of b height of a = 8 / 9 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 10 / 9 * 8 / 9 * area of b = 80 / 81 * area of b area of a is 1.3 % more than the area of b . answer ( d )"
Answer: d
Question (general): tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 62.5 ?
Options: a ) 6 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 6 * 50 300 1800 - 300 1500 24 62.50 b 16 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is a"
Answer: a
Question (gain): what will be the compound interest on rs . 40000 after 3 years at the rate of 12 % per annum
Options: a ) rs 16123.20 , b ) rs 16123.30 , c ) rs 16197.12 , d ) rs 16123.50 , e ) none of these
Rationale: "explanation : ( 40000 × ( 1 + 12 / 100 ) 3 ) = > 40000 × 28 / 25 × 28 / 25 × 28 / 25 = > 56197.12 so compound interest will be 56197.12 - 40000 = rs 16197.12 option c"
Answer: c
Question (physics): how many pieces of 75 cm can be cut from a rope 54 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) 72 , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 54 meters long is = ( 54 meters ) / ( 75 cm ) = ( 54 meters ) / ( 0.75 meters ) = 72 answer : d"
Answer: d
Question (general): working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 16 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 7 / 4 , b ) 10 / 3 , c ) 12 / 5 , d ) 15 / 7 , e ) 18 / 11
Rationale: "the time it takes printer x is 16 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 16 / ( 20 / 3 ) = 3 * 16 / 20 = 12 / 5 the answer is c ."
Answer: c
Question (general): the average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew , who weight 53 kg is replaced by a new man . find the weight of the new man .
Options: a ) 59 kg , b ) 62 kg , c ) 74 kg , d ) 85 kg , e ) 71 kg
Rationale: "total weight increased = 1.8 * 10 = 18 kg weight of the new man = 53 + 18 = 71 kg answer is e"
Answer: e
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 7 , 0 ) , ( 0 , - 3.5 ) , ( - 7 , 0 ) ?
Options: a ) 56 , b ) 88 , c ) 112 , d ) 49 , e ) 120
Rationale: "area of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 7 + 7 = 14 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 14 * 7 = 49 d is the answer"
Answer: d
Question (general): how many multiples of 13 are less than 6000 , and also multiples of 16 ?
Options: a ) 30 , b ) 29 , c ) 34 , d ) 32 , e ) 33
Rationale: "lcm of 13 & 16 = 208 tried dividing 6000 by 208 got quotient 28.84 ' so b is answer"
Answer: b
Question (general): two ants , arthur and amy , have discovered a picnic and are bringing crumbs back to the anthill . amy makes twice as many trips and carries one and a half times as many crumbs per trip as arthur . if arthur carries a total of m crumbs to the anthill , how many crumbs will amy bring to the anthill , in terms of m ?
Options: a ) x / 2 , b ) x , c ) 3 m / 2 , d ) mx , e ) mx
Rationale: "lets do it by picking up numbers . let arthur carry 2 crumbs per trip , this means amy carries 3 crumbs per trip . also let arthur make 2 trips and so amy makes 4 trips . thus total crumbs carried by arthur ( m ) = 2 x 2 = 4 , total crumbs carried by amy = 3 x 4 = 12 . 12 is 3 times 4 , so e"
Answer: e
Question (gain): a man is walking at the rate of 7 km / hr crosses a bridge in 15 minutes . the length of the bridge is
Options: a ) 1000 meters , b ) 1050 meters , c ) 1200 meters , d ) 1750 meters , e ) none of these
Rationale: "explanation : we need to get the answer in meters . so we will first of change distance from km / hour to meter / sec by multiplying it with 5 / 18 and also change 15 minutes to seconds by multiplying it with 60 . speed = 7 â ˆ — 5 / 18 = 35 / 18 m / sec time = 15 â ˆ — 60 seconds = 900 seconds distance = time â ˆ — speed / distance = 35 / 18 â ˆ — 900 = 1750 meter option d"
Answer: d
Question (geometry): if two sides of a triangle are 6 and 13 , respectively , which of the following could not be the area of this triangle ?
Options: a ) 40
b ) 6
c ) 17
d ) 29
e ) 38
Rationale: for this question it would be helpful to know the largest area that this triangle could be , given the two sides of 6 and 12 . we know that the area of a triangle will be maximized when two sides are perpendicular to each other ( consult bunuel ' s drawing above ) . thus we have a max area being equal to one half the base times the height , either ( . 5 ) 13 * 6 - or - ( . 5 ) 6 * 13 will result in a maximum area of 39 for the triangle ; therefore , the triangle could never have an area of 40 . a
Answer: a