Cheukting/mathqa huggingface dataset:
Question (general): if a person has two rectangular fields . the larger field has thrice the length and 4 times the width of the smaller field . if the smaller field has a length 50 % more than the width . if a person takes 20 minutes to complete one round of a smaller field then what is the time required to complete one round of a larger field ?
Options: a ) 69 minutes , b ) 68 minutes , c ) 58 minutes , d ) 48 minutes , e ) 67 minutes
Rationale: let the width of the smaller rectangle is 4 units then , the length of the smaller rectangle is 6 units ( that is 50 % more than the width ) now the perimeter of the rectangle is 2 ( 6 + 4 ) = 20 units so , 20 units is covered in 20 units , implies covers one unit in one minute so now coming to the larger rectangle the width = 16 units , length = 18 units , perimeter = 2 ( 16 + 18 ) 68 units thus , to cover the larger field , 68 minutes required to cover the rectangle . answer : b
Answer: b
Question (physics): the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 7 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 40 , e ) 160
Rationale: "actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 7 miles / gallon . additional 5 miles / gallon is required to match the actual mileage . imo option c ."
Answer: c
Question (gain): some of 40 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 20 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 1
Rationale: "let total paint = 1 let amount replaced = x 40 ( 1 - x ) + 20 x = 20 x = 1 / 1 answer : e"
Answer: e
Question (gain): there are two concentric circles with radii 10 and 6 . if the radius of the outer circle is increased by 20 % and the radius of the inner circle decreased by 50 % , by what percent does the area between the circles increase ?
Options: a ) 11 , b ) 111 , c ) 211 , d ) 311 , e ) 411
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 100 pi . the area of the small circle is 36 pi . the area a 1 between the circles is 64 pi . when the big circle ' s radius increases , the new area is 144 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 135 pi . the ratio of a 2 / a 1 is 135 / 64 = 2.11 which is an increase of 111 % . the answer is b ."
Answer: b
Question (gain): a man ' s speed with the current is 15 km / hr and the speed of the current is 3.2 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 20 , c ) 50 , d ) 8.6 , e ) 40
Rationale: "man ' s speed with the current = 15 km / hr = > speed of the man + speed of the current = 15 km / hr speed of the current is 3.2 km / hr hence , speed of the man = 15 - 3.2 = 11.8 km / hr man ' s speed against the current = speed of the man - speed of the current = 11.8 - 3.2 = 8.6 km / hr answer is d ."
Answer: d
Question (gain): the majority owner of a business received 25 % of the profit , with each of 4 partners receiving 25 % of the remaining profit . if the majority owner and two of the owners combined to receive $ 46,875 , how much profit did the business make ?
Options: a ) $ 55,000 , b ) $ 75,000 , c ) $ 95,000 , d ) $ 115,000 , e ) $ 125,000
Rationale: "let p be the total profit . p / 4 + 1 / 2 * ( 3 p / 4 ) = p / 4 + 3 p / 8 = 5 p / 8 = 46875 p = $ 75,000 the answer is b ."
Answer: b
Question (physics): x can do a piece of work in 40 days . he works at it for 8 days and then y finished it in 24 days . how long will y take to complete the work ?
Options: a ) 30 , b ) 12 , c ) 15 , d ) 18 , e ) 20
Rationale: "work done by x in 8 days = 8 * 1 / 40 = 1 / 5 remaining work = 1 - 1 / 5 = 4 / 5 4 / 5 work is done by y in 24 days whole work will be done by y in 24 * 5 / 4 = 30 days answer is a"
Answer: a
Question (general): linda bought 3 notebooks at $ 1.20 each ; a box of pencils at $ 1.50 and a box of pens at $ 1.70 . how much did linda spend ?
Options: a ) $ 6.80 , b ) $ 8.40 , c ) $ 7.70 , d ) $ 4.70 , e ) $ 3.90
Rationale: linda spent 1.20 ? 3 = $ 3.60 on notebooks the total amount of money that linda spent is equal to 3.60 + 1.50 + 1.70 = $ 6.80 correct answer a
Answer: a
Question (geometry): a park square in shape has a 3 metre wide road inside it running along its sides . the area occupied by the road is 1764 square metres . what is the perimeter along the outer edge of the road ?
Options: a ) 576 metres
b ) 589 metres
c ) 600 metres
d ) 700 metres
e ) none
Rationale: solution let the length of the outer edges be x metres . then , length of the inner edge = ( x - 6 ) m . ∴ x 2 - ( x - 6 ) 2 = 1764 ‹ = › x 2 - ( x 2 - 12 x + 36 ) = 1764 ‹ = › 12 x = 1800 ‹ = › x = 150 . ∴ required perimeter = ( 4 x ) m ‹ = › ( 4 x 150 ) m = 600 m . answer c
Answer: c
Question (gain): two numbers are respectively 20 % and 50 % more than a third number . the percentage that is first of the second is ?
Options: a ) 45 % , b ) 80 % , c ) 78 % , d ) 94 % , e ) 68 %
Rationale: "i ii iii 120 150 100 150 - - - - - - - - - - 120 100 - - - - - - - - - - - ? = > 80 % answer : b"
Answer: b
Question (general): an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 22932 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 11 % , e ) 30 %
Rationale: "explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 22932 / - - 17640 / - = rs . 5292 / - rate of interest = ( 5292 / 22932 ) × ( 100 / 1 ) = > 30 % answer : option e"
Answer: e
Question (general): for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 60 ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 60 4 n < 53 n < 13 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 13 ) combining the two - 1.5 < n < 13.25 n = 1 to 13 ( 48 integers ) and n = - 1 and 0 so 15 integers . b"
Answer: b
Question (general): the average of first 25 natural numbers is ?
Options: a ) 14 , b ) 13 , c ) 15 , d ) 18 , e ) 12
Rationale: "sum of 25 natural no . = 650 / 2 = 325 average = 325 / 25 = 13 answer : b"
Answer: b
Question (general): r = { 2 , 3 , 4 , 5 } b = { 4 , 5 , 6 , 7 , 8 } two integers will be randomly selected from the sets above , one integer from set r and one integer from set b . what is the probability that the sum of the two integers will equal 9 ?
Options: a ) 0.15 , b ) 0.20 , c ) 0.25 , d ) 0.30 , e ) 0.33
Rationale: the total number of pairs r , b possible is 4 * 5 = 20 . out of these 20 pairs only 4 sum up to 9 : ( 2 , 7 ) ; ( 3 , 6 ) , ( 4 , 5 ) and ( 5 , 4 ) . the probability thus is 4 / 20 = 0.2 . answer : b .
Answer: b
Question (general): a $ 79.95 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 = 79.95 $ discounted selling price of chair = 59.95 $ discount = 79.95 - 59.95 = 20 $ % decrease in price of chair = ( 20 / 79.95 ) * 100 % = 25 % approx answer c"
Answer: c
Question (general): 5 drainage pipes , each draining water from a pool at the same constant rate , together can drain a certain pool in 16 days . how many additional pipes , each draining water at the same constant rate , will be needed to drain the pool in 4 days ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 12 , e ) 15
Rationale: this is an inverse proportional problem . . . . . . 5 pipes in 16 days ; so for 4 days , it will be = 16 x 5 / 4 = 20 so , 20 - 5 = 15 answer e
Answer: e
Question (general): a heap of grapes is divided into groups of 3 , 5 and 7 and each time one coconut is left over . the least number of grapes in the heap is ? a . 31 b . 41 c . 51 d . 61
Options: a ) a ) 31 , b ) b ) 41 , c ) c ) 106 , d ) d ) 61 , e ) e ) 71
Rationale: lcm = 105 = > 105 + 1 = 106 answer : c
Answer: c
Question (geometry): the diagonals of a rhombus are 12 cm and 10 cm . find its area ?
Options: a ) 158 , b ) 129 , c ) 150 , d ) 123 , e ) 60
Rationale: "1 / 2 * 12 * 10 = 60 answer : e"
Answer: e
Question (probability): three 6 faced dice are thrown together . the probability that no two dice show the same number on them is
Options: a ) 5 / 0 , b ) 5 / 9 , c ) 5 / 1 , d ) 5 / 3 , e ) 5 / 6
Rationale: "explanation : no two dice show same number would mean all the three faces should show different numbers . the first can fall in any one of the six ways . the second die can show a different number in five ways . the third should show a number that is different from the first and second . this can happen in four ways . thus 6 * 5 * 4 = 120 favourable cases . the total cases are 6 * 6 * 6 = 216 . the probability = 120 / 216 = 5 / 9 . answer : b"
Answer: b
Question (general): find the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively .
Options: a ) 121 , b ) 124 , c ) 127 , d ) 122 , e ) 129
Rationale: "required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 _______ 1651 ) 2032 ( 1 1651 1651 _______ 381 ) 1651 ( 4 1524 _________ 127 ) 381 ( 3 381 0 required number = 127 . answer is c ."
Answer: c
Question (general): ram - leela has $ 100 in her piggy bank . how much will she have in her bank 52 weeks from now if she puts $ 1 in the bank next week , $ 2 two weeks from now , $ 3 3 weeks from now , and continues to increase the amount that she puts in by $ 1 each week ?
Options: a ) 1478 , b ) 1578 , c ) 1678 , d ) 1778 , e ) 1798
Rationale: the dollar deposits are in an a . p . 1,2 , 3,4 . . . 52 with common difference 1 sum of the terms is n ( n + 1 ) / 2 i . e 52 * ( 52 + 1 ) / 2 = 52 * 53 / 2 = 1378 total deposit therefore with chiu - lihas is 100 + 1378 = 1478 $
Answer: a
Question (general): a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 350 pounds of the mixture ?
Options: a ) 250 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: almonds : walnuts = 5 : 2 total mixture has 7 parts in a 350 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 350 = 250 pounds answer ( a )
Answer: a
Question (general): if x = - 5 / 4 and y = - 3 / 2 , what is the value of the expression - 2 x – y ^ 2 ?
Options: a ) 1 / 4 , b ) - 1 , c ) 5 / 4 , d ) 3 / 2 , e ) 3 / 4
Rationale: x = - 5 / 4 and y = - 3 / 2 = = > - 2 ( - 5 / 4 ) - ( 3 / 2 ) ^ 2 = 10 / 4 - 9 / 4 = 1 / 4 ans : a
Answer: a
Question (general): which expression is the greatest
Options: a ) 3252 / 3257 , b ) 3456 / 3461 , c ) 3591 / 3596 , d ) 3641 / 3656 , e ) 3453 / 3458
Rationale: "options can be re - written as ( x - 5 ) x = > 1 - ( 5 / x ) a ) 1 - ( 5 / 3257 ) b ) 1 - ( 5 / 3461 ) c ) 1 - ( 5 / 3596 ) d ) 1 - ( 5 / 3656 ) e ) 1 - ( 5 / 3458 ) to get the largest among these second half should be the least and so denominator to be largest . hence ' d ' ."
Answer: d
Question (general): jerry ’ s average ( arithmetic mean ) score on the first 3 of 4 tests is 78 . if jerry wants to raise his average by 2 points , what score must he earn on the fourth test ?
Options: a ) 87 , b ) 89 , c ) 86 , d ) 93 , e ) 95
Rationale: "total score on 3 tests = 78 * 3 = 234 jerry wants the average to be = 80 hence total score on 4 tests should be = 80 * 4 = 320 score required on the fourth test = 320 - 234 = 86 option c"
Answer: c
Question (physics): guy drives 60 miles to attend a meeting . halfway through , he increases his speed so that his average speed on the second half is 16 miles per hour faster than the average speed on the first half . his average speed for the entire trip is 30 miles per hour . guy drives on average how many miles per hour during the first half of the way ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 24 , e ) 40
Rationale: let x be the average speed for 1 st half of the distance . then the average speed for 2 nd half of the distance will be x + 16 avg speed = total distance / total time 30 = 60 / { ( 30 / x ) + ( 30 / ( x + 16 ) ) } solving we get x ^ 2 - 14 x - 240 = 0 x = - 10 or 24 x cant be negative hence x = 24 answer : d
Answer: d
Question (physics): 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 18 men , 4 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 18 men ’ s 1 day ’ s work = 1 × 18 / 96 = 3 / 16 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 18 men + 4 women + 10 children ) ’ s 1 day ’ s work = 3 / 16 + 1 / 48 + 1 / 24 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Question (geometry): square a is inscribed in circle b . if the perimeter of a is 32 , what is the circumference of b ?
Options: a ) 6 √ 2 π
b ) 4 √ 2 π
c ) 8 √ 2 π
d ) 7 √ 2 π
e ) 5
Rationale: square forms two right angled triangles . any time we have a right angle triangle inside a circle , the hypotenuse is the diameter . hypotenuse here = diagonal of the square = 8 sqrt ( 2 ) = diameter = > radius = 4 sqrt ( 2 ) circumference of the circle = 2 pi r = 8 pi sqrt ( 2 ) answer is c .
Answer: c
Question (general): 15 years hence , rohan will be just 4 times as old as he was 15 years ago . how old is rohan at present ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: let the present age of rohan be x years then , given : x + 15 = 4 ( x - 15 ) x = 25 answer : b
Answer: b
Question (physics): dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 54 of gas ?
Options: a ) 236 , b ) 354 , c ) 432 , d ) 512 , e ) 670
Rationale: 54 / 4 = 13.5 gallons 13.5 * 32 = 432 miles the answer is c .
Answer: c
Question (general): if the operation ø is defined for all positive integers x and w by x ø w = ( 2 ^ x ) / ( 2 ^ w ) then ( 3 ø 1 ) ø 1 = ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
Rationale: "3 ø 1 = 2 ^ 3 / 2 ^ 1 = 4 4 ø 1 = 2 ^ 4 / 2 = 8 the answer is c ."
Answer: c
Question (general): what will be the remainder when ( 67 ^ 67 ) + 67 is divided by 68 ?
Options: a ) 52 , b ) 62 , c ) 66 , d ) 68 , e ) 72
Rationale: "x ^ n + 1 will be divisible by x + 1 only when n is odd 67 ^ 67 + 1 will be divisible by 67 + 1 ( 67 ^ 67 + 1 ) + 66 , when divided by 68 will give 66 as remainder answer is c"
Answer: c
Question (physics): walking at the rate of 5 kmph a man cover certain distance in 5 hr . running at a speed of 15 kmph the man will cover the same distance in .
Options: a ) 12 min , b ) 36 min , c ) 40 min , d ) 48 min , e ) 60 min
Rationale: distance = speed * time 5 * 5 = 25 km new speed = 15 kmph therefore time = 25 / 15 = 5 / 3 = 36 min answer : b
Answer: b
Question (general): subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 18 pages .
Options: a ) 8 , b ) 10 , c ) 2 , d ) 14 , e ) 16
Rationale: subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 5 / 2.5 ) = 2 hrs answer : c
Answer: c
Question (gain): a pair of articles was bought for $ 720 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 400 , e ) $ 600
Rationale: "s . p . of each of the article = 720 / 2 = $ 360 let m . p = $ x 90 % of x = 360 x = 360 * 100 / 90 = $ 400 answer is d"
Answer: d
Question (general): average expenditure of a person for the first 3 days of a week is rs . 330 and for the next 4 days is rs . 420 . average expenditure of the man for the whole week is :
Options: a ) 350 , b ) 370 , c ) 390 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 330 total excess than assumed mean = 4 × ( rs . 420 - rs . 350 ) = rs . 280 therefore , increase in average expenditure = rs . 280 / 7 = rs . 40 therefore , average expenditure for 7 days = rs . 330 + rs . 40 = rs . 370 correct option : b"
Answer: b
Question (general): set x consists of 10 integers and has median of 30 and a range of 30 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 43 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 50 this is possible . hence it is the greatest such number . answer ( e )"
Answer: e
Question (other): in a class there are 55 pupil , out of them 10 are in debate only and 18 in singing only . then how many in both ?
Options: a ) 132 , b ) 26 , c ) 17 , d ) 11 , e ) 12
Rationale: explanation : total pupil = 55 debate + singing = 10 + 18 = 28 the intersection for two = 55 â € “ 10 â € “ 28 = 17 play both games . answer : c
Answer: c
Question (general): in a hostel , the number of students decreased by 8 % and the price of food increased by 20 % over the previous year . if each student consumes the same amount of food then by how much should the consumption of food be cut short by every student , so that the total cost of the food remains the same as that of the previous year ?
Options: a ) 19 % , b ) 15 % , c ) 25 % , d ) 40 % , e ) 9.4 %
Rationale: "cost of food ( c ) = food consumed per student ( f ) * number of students ( n ) * price of food ( p ) originally , c = fnp when number of students decrease by 8 % , and the price of food increases by 20 % , c = f ( new ) * ( 0.92 n ) * ( 1.2 p ) = > f ( new ) = f / ( 0.92 * 1.2 ) = > f ( new ) = 0.906 f therefore the new cost of food must be 90.6 % of the old cost , or the cost of food must decrease by 9.4 % answer : e"
Answer: e
Question (general): the total circumference of two circles is 88 . if the first circle has a circumference that is exactly twice the circumference of the second circle , then what is the approximate sum of their two radii ?
Options: a ) 5.7 , b ) 6.0 , c ) 6.7 , d ) 9.7 , e ) 14.0
Rationale: "let r = radius of smaller circle . let r = radius of larger circle therefore : 2 π r + 2 π r = 88 where 2 r = r thus : 2 π r + 4 π r = 88 6 π r = 88 r = approx 4.7 π r + 2 r π = 88 3 π r = 88 r = approx 9.3 r + r = approx 14.0 answer : e"
Answer: e
Question (general): how many multiples of 2 are there between 101 and 999 ?
Options: a ) 250 , b ) 440 , c ) 510 , d ) 575 , e ) 449
Rationale: "2 multiples are 102 , 104,106 , - - - - - - - - - , 994 , 996,998 it should be mentioned whether 1 and 89 are inclusive . the answer is ( 998 - 102 ) / 2 + 1 = 449 answer is e"
Answer: e
Question (general): find the smallest number which when divided by 13 and 16 leaves respective remainders of 2 and 5 .
Options: a ) 128 , b ) 197 , c ) 127 , d ) 182 , e ) 091
Rationale: "explanation : let ' n ' is the smallest number which divided by 13 and 16 leaves respective remainders of 2 and 5 . required number = ( lcm of 13 and 16 ) - ( common difference of divisors and remainders ) = ( 208 ) - ( 11 ) = 197 . answer : b"
Answer: b
Question (general): how much is 80 % of 40 is greater than 4 / 5 of 20 ?
Options: a ) 12 , b ) 27 , c ) 18 , d ) 16 , e ) 81
Rationale: "( 80 / 100 ) * 40 â € “ ( 4 / 5 ) * 20 32 - 16 = 16 answer : d"
Answer: d
Question (general): if the price of sugar rises from rs . 10 per kg to rs . 13 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 23 % , d ) 30 % , e ) none
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 10 = x × 13 = x = 77 kg . ∴ reduction in consumption = 23 % . answer c"
Answer: c
Question (physics): a train crosses a bridge of length 800 m in 45 seconds and a lamp post on the bridge in 15 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 400 m , d ) 800 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 800 + l ( while crossing the bridge ) time = 45 seconds i . e . speed = distance / time = ( 800 + l ) / 45 case - 2 : distance = l ( while passing the lamp post ) time = 15 seconds i . e . speed = distance / time = ( l ) / 15 but since speed has to be same in both cases so ( 800 + l ) / 45 = ( l ) / 15 i . e . 800 + l = 3 l i . e . 2 l = 800 i . e . l = 400 answer : option c"
Answer: c
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 20 % discount = 648 so , price in day 3 as percentage of the sale price on day 1 will be = 648 / 900 * 100 = > 72 % answer will definitely be ( e )"
Answer: e
Question (physics): the sum of three consecutive numbers is 87 . the greatest among these three number is :
Options: a ) 26 , b ) 28 , c ) 29 , d ) 30 , e ) 31
Rationale: "let the numbers be x , x + 1 and x + 2 then , x + ( x + 1 ) + ( x + 2 ) = 87 3 x = 84 x = 28 greatest number , ( x + 2 ) = 30 . answer : d"
Answer: d
Question (physics): a train travels 290 km in 4.5 hours and 400 km in 5.5 hours . find the average speed of train .
Options: a ) 80 kmph , b ) 69 kmph , c ) 70 kmph , d ) 90 kmph , e ) none of these
Rationale: "as we know that speed = distance / time for average speed = total distance / total time taken thus , total distance = 290 + 400 = 690 km thus , total speed = 10 hrs or , average speed = 690 / 10 or , 69 kmph . answer : b"
Answer: b
Question (general): what is the average of 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1 , 125,2140 , 2345 ?
Options: a ) 419 , b ) 551 , c ) 601 , d ) 620 , e ) 858.54
Rationale: "add 12 , 13 , 14 , 510 , 520 , 530 , 1,115 , 1,120 , and 1,125 , 2140 , 2345 grouping numbers together may quicken the addition sum = 9444 4959 / 11 = 858.54 . e"
Answer: e
Question (general): when a certain tree was first planted , it was 4 feet tall , and the height of the tree increased by a constant amount each year for the next 6 years . at the end of the 6 th year , the tree was 1 / 3 taller than it was at the end of the 4 th year . by how many feet did the height of the tree increase each year ?
Options: a ) 3 / 10 , b ) 2 , c ) 1 / 2 , d ) 2 / 3 , e ) 6 / 5
Rationale: "say , the tree grows by x feet every year . then , 4 + 6 x = ( 1 + 1 / 3 ) ( 4 + 4 x ) or , x = 2 answer b"
Answer: b