Cheukting/mathqa huggingface dataset:
Question (other): a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 3 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 12 : 15 , b ) 1 : 4 , c ) 1 : 5 , d ) 2 : 5 , e ) 1 : 3
Rationale: "say theratio of cats to dogs is a / b . then the numberof cats would be ax and the number of dogs bx , for some positive integer x . we are told that ax - bx = 3 - - > x ( a - b ) = 3 . since 3 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 13 . the above implies that either x = 1 and ( a - b ) = 3 or x = 3 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13 . for the original question only option which fits is e , 4 : 5 . cats = 3 * 4 = 12 and dogs = 3 * 5 = 15 . answer : a ."
Answer: a
Question (physics): in one hour , a boat goes 13 km / hr along the stream and 9 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 11 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 13 + 9 ) kmph = 11 kmph . answer : option a"
Answer: a
Question (gain): 6 mat - weavers can weave 6 mats in 6 days . at the same rate , how many mats would be woven by 8 mat - weavers in 8 days ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "let the required number of mats be x more mat - weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) hence we can write as ( mat - weavers ) 6 : 8 } : : 6 : x ( days ) 6 : 8 ⇒ 6 × 6 × x = 8 × 8 × 6 ⇒ x = 10 answer : b"
Answer: b
Question (gain): if the cost price is 80 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 25 % , e ) 19 %
Rationale: "let s . p . = $ 100 c . p . = $ 80 profit = $ 20 profit % = 20 / 80 * 100 = 25 / 6 = 25 % answer is d"
Answer: d
Question (general): dacid obtained 81 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 38 , c ) 76 , d ) 37 , e ) 75
Rationale: "average = ( 81 + 65 + 82 + 67 + 85 ) / 5 = 76 . answer : c"
Answer: c
Question (general): he average of 30 numbers is zero . of them , at the most , how many may be greater than zero ?
Options: a ) 29 , b ) 1 , c ) 10 , d ) 30 , e ) 8
Rationale: average of 30 numbers = 0 . sum of 30 numbers ( 0 x 30 ) = 0 . it is quite possible that 29 of these numbers may be positive and if their sum is a the 30 th number is ( - a ) . answer : option a
Answer: a
Question (general): in a certain deck of cards , each card has a positive integer written on it , in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer . if the each possible product is between 11 and 200 , then the least and greatest integer on the card would be
Options: a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 13 , d ) 4 and 14 , e ) 5 and 14
Rationale: "given : 11 < x ( x + 1 ) < 200 . now , it ' s better to test the answer choices here rather than to solve : if x = 3 then x ( x + 1 ) = 12 > 11 - - > so , the least value is 4 . test for the largest value : if x = 15 then x ( x + 1 ) = 15 * 16 = 240 > 200 - - > discard b . answer : a ."
Answer: a
Question (general): a number when divided by 342 gives a remainder 47 . when the same number if it divided by 19 , what would be the remainder ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 9 , e ) 11
Rationale: "on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number – 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 .  the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . answer d"
Answer: d
Question (general): √ ( 36 ) ^ 2
Options: a ) 6 , b ) 14 , c ) 36 , d ) 21 , e ) none of these
Rationale: explanation √ ( 36 ) ^ 2 = ? or , ? = 36 answer c
Answer: c
Question (gain): a and b start a business , with a investing the total capital of rs . 100000 , on the condition that b pays a interest @ 10 % per annum on his half of the capital . a is a working partner and receives rs . 10000 per month from the total profit and any profit remaining is equally shared by both of them . at the end of the year , it was found that the income of a is twice that of b . find the total profit for the year ?
Options: a ) a ) 2520000 , b ) b ) 2620000 , c ) c ) 2820000 , d ) d ) 2920000 , e ) e ) 2420000
Rationale: "interest received by a from b = 10 % of half of rs . 100000 = 10 % * 50000 = 5000 . amount received by a per annum for being a working partner = 10000 * 12 = rs . 120000 . let ' p ' be the part of the remaining profit that a receives as his share . total income of a = ( 5000 + 120000 + p ) total income of b = only his share from the remaining profit = ' p ' , as a and b share the remaining profit equally . income of a = twice the income of b ( 5000 + 120000 + p ) = 2 ( p ) p = 125000 total profit = 2 p + 120000 = 2 * 125000 + 120000 = 2620000 answer : b"
Answer: b
Question (gain): double of quarter of 1 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 1 % = 2 * ( 1 / 4 * 1 / 100 ) = 1 / 400 = 2 * 0.0025 = 0.005 . answer : d"
Answer: d
Question (physics): 15 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 30 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 15 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 15 * 21 * 8 = 14 * x * 6 x = 30 answer : c"
Answer: c
Question (geometry): the number 49 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 11 , b ) 16 , c ) 15 , d ) 14 , e ) 13
Rationale: "i think brute force with some common sense should be used to solve this problem . write down all perfect squares less than 49 : 1 , 4 , 9 , 16 , 25 , 36 , 49 . . now , 49 should be the sum of 3 of those 7 numbers . also to simplify a little bit trial and error , we can notice that as 49 is an odd numbers then either all three numbers must be odd ( odd + odd + odd = odd ) or two must be even and one odd ( even + even + odd = odd ) . we can find that 49 equals to 4 + 9 + 36 = 2 ^ 2 + 3 ^ 2 + 6 ^ 2 = 49 - - > 2 + 3 + 6 = 11 . answer : a ."
Answer: a
Question (general): he total marks obtained by a student in physics , chemistry and mathematics is 140 more than the marks obtained by him in physics . what is the average mark obtained by him in chemistry and mathematics ?
Options: a ) 55 , b ) 70 , c ) 75 , d ) 85 , e ) 95
Rationale: "let the marks obtained by the student in physics , chemistry and mathematics be p , c and m respectively . p + c + m = 140 + p c + m = 140 average mark obtained by the student in chemistry and mathematics = ( c + m ) / 2 = 140 / 2 = 70 . answer : b"
Answer: b
Question (physics): 4 men can check exam papers in 8 days working 5 hours regularly . what is the total hours when 2 men will check the double of the papers in 20 days ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 1 , e ) 5
Rationale: let a man can do 1 unit of work in 1 hour . total units of work = 4 x 8 x 5 = 160 units . now work = 2 x 160 = 320 units . now 2 men work for 20 days . let in x hours they have to work per day . now total work = 2 × x × 20 = 40 x 40 x = 320 so x = 320 / 40 = 8 hours . answer : a
Answer: a
Question (general): given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 1 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > only in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . i . e 0 , 1,5 or 6 intersection of values is 6 , thus the units digit of p + 1 is 6 + 1 = 9 . answer : a ."
Answer: a
Question (gain): the population of a town is 10000 . it increases annually at the rate of 30 % p . a . what will be its population after 2 years ?
Options: a ) 14000 , b ) 14400 , c ) 14500 , d ) 14600 , e ) 16900
Rationale: "formula : 10000 × 130 / 100 × 130 / 100 = 16900 answer : e"
Answer: e
Question (geometry): find the area of a parallelogram with base 18 cm and height 16 cm ?
Options: a ) 423 cm 2 , b ) 122 cm 2 , c ) 420 cm 2 , d ) 251 cm 2 , e ) 288 cm 2
Rationale: "area of a parallelogram = base * height = 18 * 16 = 288 cm 2 answer : e"
Answer: e
Question (general): evaluate : 50 - 12 ÷ 2 × 2 =
Options: a ) a ) 36 , b ) b ) 38 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
Rationale: "according to order of operations , 12 ÷ 2 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 2 × 2 = 6 × 2 = 12 hence 50 - 12 ÷ 6 × 2 = 50 - 12 = 38 correct answer is b ) 38"
Answer: b
Question (general): when positive integer n is divided by 3 , the remainder is 2 . when n is divided by 5 , the remainder is 5 . how many values less than 100 can n take ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "a quick approac to this q is . . the equation we can form is . . 3 x + 2 = 7 y + 5 . . 3 x - 3 = 7 y . . . 3 ( x - 1 ) = 7 y . . . so ( x - 1 ) has to be a multiple of 7 as y then will take values of multiple of 3 . . here we can see x can be 1 , 8,15 , 22,29 so 5 values till 100 is reached as ( 29 - 1 ) * 3 = 84 and next multiple of 7 will be 84 + 21 > 100 . . ans 0 . . a"
Answer: a
Question (physics): 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 24 girls will take to construct ?
Options: a ) 4 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 24 girls = 8 ã — 6 / 4 + 12 = 12 + 24 = 36 girls 4 days to complete the work answer : option a"
Answer: a
Question (other): the incomes of two persons a and b are in the ratio 3 : 4 . if each saves rs . 100 per month , the ratio of their expenditures is 1 : 2 . find their incomes ?
Options: a ) 150,287 , b ) 150,219 , c ) 150,200 , d ) 150,298 , e ) 150,217
Rationale: the incomes of a and b be 3 p and 4 p . expenditures = income - savings ( 3 p - 100 ) and ( 4 p - 100 ) the ratio of their expenditure = 1 : 2 ( 3 p - 100 ) : ( 4 p - 100 ) = 1 : 2 2 p = 100 = > p = 50 their incomes = 150 , 200 answer : c
Answer: c
Question (general): a certain country is divided into 6 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 / 9 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 / 9 the total number of traditionalists is 6 p / 9 = 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 (gain): a tradesman sold an article at a loss of 10 % . if the selling price had been increased by $ 50 , there would have been a gain of 10 % . what was the cost price of the article ?
Options: a ) $ 150 , b ) $ 200 , c ) $ 250 , d ) $ 120 , e ) $ 100
Rationale: "let c . p . be $ x then 110 % of x - 90 % of x = 50 20 % of x = 50 x / 5 = 50 x = 250 answer is c"
Answer: c
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.20 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 799.2 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.2 = 799.2 answer : c"
Answer: c
Question (gain): in business , a and c invested amounts in the ratio 2 : 1 , whereas the ratio between amounts invested by a and b was 2 : 3 , if rs 15,0000 was their profit , how much amount did b receive .
Options: a ) 12653 , b ) 14587 , c ) 36975 , d ) 75000 , e ) 12874
Rationale: explanation : a : b = 2 : 3 = 2 : 3 = > a : c = 2 : 1 = 2 : 1 = > a : b : c = 2 : 3 : 1 b share = ( 3 / 6 ) * 150000 = 75000 option d
Answer: d
Question (general): if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2015 ) = ?
Options: a ) 2016 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2015 ) = 2016 ans : a"
Answer: a
Question (gain): a pair of articles was bought for $ 810 at a discount of 10 % . what must be the marked price of each of the article ?
Options: a ) $ 300 , b ) $ 500 , c ) $ 350 , d ) $ 450 , e ) $ 600
Rationale: "s . p . of each of the article = 810 / 2 = $ 405 let m . p = $ x 90 % of x = 405 x = 405 * 100 / 90 = $ 450 answer is d"
Answer: d
Question (physics): a person crosses a 600 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 3.6 , b ) 7.2 , c ) 8.4 , d ) 10 , e ) 8
Rationale: "speed = 600 / ( 5 x 60 ) m / sec . = 2 m / sec . converting m / sec to km / hr = ( 2 x ( 18 / 5 ) ) km / hr = 7.2 km / hr . answer : b"
Answer: b
Question (general): if a and b are two events such that p ( a ) = 3 / 4 , p ( b ) = 1 / 2 and p ( a n b ) = 3 / 8 , find p ( not a and not b ) .
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 11 , d ) 1 / 13 , e ) 2 / 5
Rationale: p ( not a and not b ) = 1 - ( p ( a ) + p ( b ) - p ( ab ) ) which you might find somewhere in your text . substituting in our probabilities we get : p ( not a and not b ) = 1 - ( 3 / 4 + 1 / 2 - 3 / 8 ) p ( not a and not b ) = 1 - ( 7 / 8 ) p ( not a and not b ) = 1 / 8 . b
Answer: b
Question (physics): when sourav increases his speed from 20 km / hr to 25 km / hr , he takes one hour less than the usual time to cover a certain distance . what is the distance usually covered by him ?
Options: a ) 125 km , b ) 100 km , c ) 80 km , d ) 120 km , e ) 60 km
Rationale: detailed solution here , the distance travelled by sourav is constant in both the cases . so , 20 x t = 25 x ( t - 1 ) = d = ) 20 t = 25 t - 25 = ) 5 t = 25 = ) t = 5 hrs so , distance travelled = 20 x 5 = 100 km . correct answer b .
Answer: b
Question (general): what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 3 , and 4 if each digit can be used only once in each number ?
Options: a ) 1443 , b ) 1554 , c ) 1665 , d ) 1776 , e ) 1887
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 333 ) + 2 ( 444 ) = 1776 the answer is d ."
Answer: d
Question (gain): 4000 was divided into two parts such a way that when first part was invested at 3 % and the second at 5 % , the whole annual interest from both the investments is rs . 144 , how much was put at 3 % ?
Options: a ) rs . 2500 , b ) rs . 2700 , c ) rs . 2800 , d ) rs . 5000 , e ) rs . 6000
Rationale: explanation : ( x * 3 * 1 ) / 100 + [ ( 4000 - x ) * 5 * 1 ] / 100 = 144 3 x / 100 + 200 â € “ 5 x / 100 = 144 2 x / 100 = 56 ã ¨ x = 2800 answer is c
Answer: c
Question (gain): if 20 % of a number = 200 , then 120 % of that number will be ?
Options: a ) 20 , b ) 120 , c ) 360 , d ) 1200 , e ) 820
Rationale: "let the number x . then , 20 % of x = 200 x = ( 200 * 100 ) / 20 = 1000 120 % of x = ( 120 / 100 * 1000 ) = 1200 . answer : d"
Answer: d
Question (general): solve the equation for x : 14 ( - x + z ) + 18 = - 14 ( x - z ) - 10
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: d 1 - 14 x + 14 z + 18 = - 14 x + 14 z - 10 - 28 x + 28 = 0 - 28 x = - 28 = > x = 1
Answer: d
Question (other): tea worth rs . 126 per kg and rs . 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 153 per kg , the price of the third variety per kg will be :
Options: a ) rs . 169.50 , b ) rs . 170 , c ) rs . 175.50 , d ) rs . 180 , e ) rs . 190
Rationale: explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . 126 + 135 = rs . 130.50 2 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 153 / 22.50 = 1 x - 153 = 22.50 x = 175.50 answer is c
Answer: c
Question (gain): in an election between two candidates , one got 45 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 2000 , the number of valid votes that the other candidate got , was :
Options: a ) 2200 , b ) 3600 , c ) 3270 , d ) 3700 , e ) 4000
Rationale: "number of valid votes = 80 % of 4000 = 3200 . valid votes polled by other candidate = 55 % of 4000 = ( 55 / 100 ) x 8000 = 2200 answer = a"
Answer: a
Question (other): if log 10 2 = 0.30103 , find the value of log 10 50
Options: a ) 1.69897 , b ) 2.69897 , c ) 1.99897 , d ) 0.69897 , e ) 5.69897
Rationale: "log 10 50 = log 10 ( 100 / 2 ) = log 100 - log 2 = 2 log 10 - log 2 = 2 ( 1 ) - 0.30103 = 1.69897 answer : a"
Answer: a
Question (other): divide $ 672 among a , b in the ratio 5 : 3 . how many $ that a get ?
Options: a ) $ 120 , b ) $ 500 , c ) $ 420 , d ) $ 610 , e ) $ 315
Rationale: "sum of ratio terms = 5 + 3 = 8 a = 672 * 5 / 8 = $ 420 answer is c"
Answer: c
Question (general): the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 5 years ago , the sum of their ages was 75 , what will be the age of aman 10 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 35 , e ) 40
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 5 + 8 x - 5 + 7 x - 5 = 75 x = 3 present age of aman = 5 * 3 = 15 aman ' s age 10 years hence = 15 + 10 = 25 answer = b"
Answer: b
Question (general): if 1 / 3 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 5 are from africa , 1 / 6 are from asia and the remaining 42 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 240 , b ) 250 , c ) 280 , d ) 300 , e ) 320
Rationale: "1 / 3 + 1 / 8 + 1 / 5 + 1 / 6 = ( 40 + 15 + 24 + 20 ) / 120 = 99 / 120 let x be the number of passengers on the ship . 42 = ( 21 / 120 ) x = 7 x / 40 x = 240 the answer is a ."
Answer: a
Question (physics): a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
Options: a ) 136 , b ) 146 , c ) 166 , d ) 176 , e ) 216
Rationale: area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d
Answer: d
Question (general): average expenditure of a person for the first 3 days of a week is rs . 340 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 ) 380 , d ) 430 , e ) none
Rationale: "explanation : assumed mean = rs . 340 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 . 340 + rs . 40 = rs . 380 correct option : c"
Answer: c
Question (gain): if rs . 400 amount to rs . 540 in 4 years , what will it amount to in 6 years at the same rate % per annum ?
Options: a ) s . 575 , b ) s . 595 , c ) s . 590 , d ) s . 610 , e ) s . 585
Rationale: "80 = ( 400 * 4 * r ) / 100 r = 8.75 % i = ( 400 * 6 * 8.75 ) / 100 = 210 400 + 210 = 610 answer : d"
Answer: d
Question (general): whats the reminder when 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 is divided by 4
Options: a ) 1 , b ) 7 . , c ) 2 . , d ) 3 , e ) 9
Rationale: "a number ending in a 0 is divisible by 2 . a number ending in 2 zeroes is divisible by 4 . given the obscene number , you should immediately be convinced that you will need to focus on a very small part of it . 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,985 = 879,548 , 521,456 , 258,759 , 653,258 , 778,455 , 658,900 + 85 the first number is divisible by 16 . you just have to find the remainder when you divide 5287 by 16 . that will be the remainder when you divide the original number by 4 . 85 / 4 gives remainder 1 . answer ( a )"
Answer: a
Question (physics): 400 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "26 trees have 25 gaps between them , required distance ( 400 / 25 ) = 16 d"
Answer: d
Question (physics): a car averages 30 miles per hour for the first 6 hours of a trip and averages 46 miles per hour for each additional hour of travel time . if the average speed for the entire trip is 34 miles per hour , how many hours long is the trip ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "let t be the total time of the trip . 30 * 6 + 46 ( t - 6 ) = 34 t 12 t = 276 - 180 t = 8 the answer is a ."
Answer: a
Question (gain): 5 / 8 of the population of the country of venezia lives in montague province , while the rest lives in capulet province . in the upcoming election , 80 % of montague residents support romeo , while 70 % of capulet residents support juliet ; each resident of venezia supports exactly one of these two candidates . rounded if necessary to the nearest percent , the probability that a juliet supporter chosen at random resides in capulet is
Options: a ) 28 % , b ) 41 % , c ) 45 % , d ) 72 % , e ) 68 %
Rationale: "total population = 80 ( assume ) . 5 / 8 * 80 = 50 people from montague . 3 / 8 * 80 = 30 people from capulet . 0.2 * 50 = 10 people from montague support juliet . 0.7 * 30 = 21 people from capulet support juliet . the probability that a juliet supporter chosen at random resides in capulet is 21 / ( 10 + 21 ) = ~ 68 . answer : e"
Answer: e
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 5 is
Options: a ) 3 , b ) 7 , c ) 21 , d ) 27 , e ) 189
Rationale: "a prime number greater than 5 can have only the following four units digits : 1 , 3 , 7 , or 9 . if the units digit of p is 1 then the units digit of 2 p + 1 would be 3 , which is a possible units digit for a prime . for example consider p = 11 = prime - - > 2 p + 1 = 23 = prime ; if the units digit of p is 3 then the units digit of 2 p + 1 would be 7 , which is a possible units digit for a prime . for example consider p = 23 = prime - - > 2 p + 1 = 47 = prime ; if the units digit of p is 7 then the units digit of 2 p + 1 would be 5 , which is not a possible units digit for a prime ; if the units digit of p is 9 then the units digit of 2 p + 1 would be 9 , which is a possible units digit for a prime . for example consider p = 29 = prime - - > 2 p + 1 = 59 = prime . the product of all the possible units digits of sophie germain primes greater than 5 is 1 * 3 * 9 = 27 . answer : d ."
Answer: d
Question (general): 32 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.32 * 5 / 8 = 1.6 / 8 = 0.2 correct option : a"
Answer: a