Cheukting/mathqa huggingface dataset:
Question (physics): there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 17 days more ?
Options: a ) 89 men , b ) 120 men , c ) 90 men , d ) 60 men , e ) 134 men
Rationale: "760 - - - - 22 760 - - - - 20 x - - - - - 17 x * 17 = 760 * 20 x = 894 760 - - - - - - - 134 answer : e"
Answer: e
Question (general): find large number from below question the difference of two numbers is 1015 . on dividing the larger number by the smaller , we get 9 as quotient and the 15 as remainder
Options: a ) 1209 , b ) 1324 , c ) 1245 , d ) 1140 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1015 ) . x + 1015 = 9 x + 15 8 x = 1000 x = 125 large number = 125 + 1015 = 1140 answer : d"
Answer: d
Question (general): a store owner estimates that the average price of type a products will increase by 35 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,755 , b ) $ 15,205 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.35 * 4500 = 6075 cost of type b products next year = 1.1 * 8300 = 9130 total 6075 + 9130 = 15205 option b"
Answer: b
Question (general): in a classroom , the average age of boys ( b ) is g and the average age of girls ( g ) is b . the average age of all is b + g . at the time of calculation , the class teacher , who is 42 years old was also present in the class . can you find the value of b + g ?
Options: a ) 8 , b ) 3 , c ) 7 , d ) 9 , e ) 10
Rationale: a b + g = 8 for b in range ( 199 ) : for g in range ( 199 ) : sum 1 = 2 * b * g + 42 sum 2 = ( b + g ) * ( b + g + 1 ) if ( sum 1 = = sum 2 ) : print ( b , g , sum 1 ) ( b , g ) = ( 35 ) = > b + g = 8
Answer: a
Question (gain): mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?
Options: a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000
Rationale: x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c
Answer: c
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 176 in 4 years ?
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 9 % , e ) 5.5 %
Rationale: "176 = ( 180 * 4 * r ) / 100 r = 5.5 % answer : e"
Answer: e
Question (gain): a 6 litre sol is 35 % alcohol . how many litres of pure alcohol must be added to produce a sol that is 50 % alcohol ?
Options: a ) a . 0.6 , b ) b . 1 , c ) c . 2.1 , d ) d . 1.8 , e ) e . 5.4
Rationale: "35 % of 6 = 2.1 50 % of 6 = 3 shortage is 0.9 so we need to have 0.9 / 50 % to get 50 % alcohol content . = 1.8 d"
Answer: d
Question (general): sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 170 . if the ratio of his marks in english and maths is 1 : 4 , find his marks in science ?
Options: a ) 17 , b ) 77 , c ) 66 , d ) 55 , e ) 31
Rationale: s : e = 1 : 3 e : m = 1 : 4 - - - - - - - - - - - - s : e : m = 1 : 4 : 12 1 / 17 * 170 = 17 answer : a
Answer: a
Question (physics): if 6 parallel lines in a plane is intersected by a family of another 8 parallel lines , how many parallelograms are there in the network thus formed ?
Options: a ) 80 , b ) 63 , c ) 420 , d ) 160 , e ) 1260
Rationale: "parallelogram can formed by 2 horizontal and 2 vertical lines for horizontal 6 c 2 for vertical 8 c 2 total parallelogram is 6 c 2 * 8 c 2 = 15 * 28 = 420 answer : c"
Answer: c
Question (general): what is the remainder if 7 ^ 8 is divided by 100 ?
Options: a ) 7 , b ) 1 , c ) 9 , d ) 10 , e ) 11
Rationale: "7 ^ 8 can be written as ( 7 ^ 4 ) ^ 2 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 2 by 100 , the reminder is 1 ^ 2 = 1 answer : b"
Answer: b
Question (general): 65 % of x = 20 % of 617.50 . find the value of x ?
Options: a ) 100 , b ) 190 , c ) 150 , d ) 180 , e ) 199
Rationale: "65 % of x = 20 % of 615.50 then , 65 / 100 * x = 20 / 100 * 6175 / 10 x = 190 answer is b"
Answer: b
Question (general): find the smallest number of five digits exactly divisible by 24 , 48,64 and 88 .
Options: a ) 11952 , b ) 11852 , c ) 11752 , d ) 11652 , e ) 11552
Rationale: "smallest number of five digits is 10000 . required number must be divisible by l . c . m . of 24,48 , 64,88 i . e 2012 , on dividing 10000 by 2012 , we get 60 as remainder . therefore , required number = 10000 + ( 2012 â € “ 60 ) = 11952 . answer is a ."
Answer: a
Question (general): how many numbers from 12 to 82 are exactly divisible by 6 ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "option ' d ' 12 / 6 = 2 and 82 / 6 = 13 = = > 13 - 2 = 11 numbers"
Answer: d
Question (physics): 10 men and 15 women finish a work in 6 days . one man alone finishes that work in 100 days . in how many days will a woman finish the work ?
Options: a ) 125 days , b ) 150 days , c ) 90 days , d ) 225 days , e ) none of these
Rationale: 15 women ' s work of a day = 1 ⁄ 6 - 1 ⁄ 10 ⇒ 1 ⁄ 15 part ∴ for 1 whole part a woman will take = 15 × 15 = 225 days . answer d
Answer: d
Question (general): a certain quantity is measured on two different scales , the r - scale and the s - scale , that are related linearly . measurements on the r - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the r - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: question says they are both related linearly so they the relationships can be represented by standard linear definition y = mx + b . let s scale = y . and r scale = x . 30 = 6 m + b eqn 1 60 = 24 m + b eqn 2 eqn 2 - eqn 1 = > 30 = 18 m = > m = 5 / 3 solving for b using either equation gives us b = 20 linear relationship is represented by y = ( 5 / 3 ) x + 20 solve for 100 : 100 = 5 / 3 x + 20 80 = 5 / 3 x x = 48 ans = c
Answer: c
Question (gain): a fruit seller had some apples . he sells 30 % and still has 420 apples . originally , he had ?
Options: a ) 30 apples , b ) 600 apples , c ) 420 apples , d ) 70 apples , e ) none
Rationale: "answer â ˆ µ 70 % of n = 420 â ˆ ´ n = ( 420 x 100 ) / 70 = 600 correct option : b"
Answer: b
Question (general): a family x went for a vacation . unfortunately it rained for 13 days when they were there . but whenever it rained in the mornings , they had clear afternoons and vice versa . in all they enjoyed 11 mornings and 12 afternoons . how many days did they stay there totally ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 13 , e ) 14
Rationale: explanation : clearly 11 mornings and 12 afternoons = 23 half days = > since 13 days raining means 13 half days . = > so 23 - 13 = 10 halfdays ( not effecetd by rain ) = > so 10 halfdays = 5 fulldays hence , total no . of days = 13 + 5 = 18 days answer : b
Answer: b
Question (gain): what is 92 % of 4 / 5 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.736 , d ) 0.6859 , e ) 0.69
Rationale: "92 % * ( 4 / 5 ) = 0.92 * 0.8 = 0.736 answer : c"
Answer: c
Question (general): a textile manufacturing firm employees 125 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 125 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 2800 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 124 / 125 ) â ˆ ’ 150000 ã — ( 124 / 125 ) â ˆ ’ 75000 . = > rs 2 , 72,200 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 72,200 = > rs . 2,800 . answer : d"
Answer: d
Question (gain): a milk man has 20 liters of milk . if he mixes 25 liters of water , which is freely available , in 20 liters of pure milk . if the cost of pure milk is rs . 18 per liter , then the profit of the milkman , when he sells all the mixture at cost price is :
Options: a ) 20 % , b ) 45 % , c ) 33.33 % , d ) 18 % , e ) none of these
Rationale: "explanation : when the water is freely available and all the water is sold at the price of the milk , then the water gives the profit on the cost of 20 liters of milk . therefore , profit percentage = 45 % . answer : b"
Answer: b
Question (physics): a thief is spotted by a policeman from a distance of 100 meters . when the policeman starts the chase , the thief also starts running . if the speed of the thief be 8 km / hr and that of the policeman 10 km / hr , how far the thief will have run before he is overtaken ?
Options: a ) 350 m , b ) 200 m , c ) 400 m , d ) 500 m , e ) none of them
Rationale: "relative speed of the policeman = ( 10 - 8 ) km / hr = 2 km / hr . time taken by police man to cover ( 100 m / 1000 ) x 1 / 2 hr = 1 / 20 hr . in 1 / 20 hrs , the thief covers a distance of 8 x 1 / 20 km = 2 / 5 km = 400 m answer is c ."
Answer: c
Question (gain): a major airplane manufacturer announced the sale of 150 small airliners at $ 125 million each , 75 medium sized airliners at $ 175 million each , and 60 large airliners at $ 220 million each . what percentage of the company ' s income came from large and medium airliners ?
Options: a ) 29 % , b ) 41 % , c ) 58 % , d ) 69 % , e ) 70 %
Rationale: answer is ( money from mid and large plane ) / ( total money from all the planes ) x 100 = ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 ( 175 ∗ 75 + 220 ∗ 60 ) / ( 125 ∗ 150 + 175 ∗ 75 + 220 ∗ 60 ) ∗ 100 = 58.4 % you could just multiply add divide to get answer . however sometimes its much better to make it easy we should see if we have any common terms 125 * 150 = ( 5 * 5 * 5 ) * ( 2 * 3 * 5 * 5 ) 175 * 75 = ( 5 * 5 * 7 ) * ( 3 * 5 * 5 ) 220 * 60 = ( 2 * 2 * 11 * 5 ) * ( 2 * 2 * 3 * 5 ) 3 * 5 * 5 is common cancel it ans becomes ( 175 + 176 ) / ( 176 + 175 + 250 ) * 100 = ~ = ~ 350 / 600 * 100 = ~ = ~ 7 / 12 * 100 = 60 % > > > 58 % is closest . answer : c
Answer: c
Question (other): if 75 percent of a class answered the first question on a certain test correctly , 30 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 25 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "i did n ' t understand how to connect 20 percent with the whole equation . why 20 is out of the percentile diagram ( circles ) but inside of 100 ? 20 % appeared in the exam ; however did not answer question aquestion b correctly so they are out of the two circles , however as they have appeared in the exam , they have to be taken into consideration for calculation purpose i am doing it this way : suppose the total class size is 100 , then 20 percent of the class answered incorrectly and rest 80 percent answered correctly in question 1 or 2 or both . now , 100 - [ ( 75 - x ) + x + ( 30 - x ) ] = 20 . . . . . . . . . . values are in percent x = 20 - 100 + 105 x = 25 ans : a"
Answer: a
Question (general): what is the decimal equivalent of ( 1 / 4 ) ^ 4 ?
Options: a ) 0.0039 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 4 ) ^ 4 = 1 / 256 = 0.0039 answer : a"
Answer: a
Question (general): ( ( a + b ) / c ) / 2 in the expression above , a , b , and c are different numbers and each is one of the numbers 2 , 3 , or 5 . what is the least possible value of the expression ?
Options: a ) 2 / 10 , b ) 5 / 10 , c ) 10 / 5 , d ) 7 / 6 , e ) 6 / 7
Rationale: ( ( a + b ) / c ) / 2 = ( a + b ) / 2 c the expression will have the least value when numerator ( a + b ) is the smallest . = ( 2 + 3 ) / 2 * 5 = 5 / 10 answer b
Answer: b
Question (gain): 85 % of the population of a city is 85000 . the total population of the city is ?
Options: a ) 95000 , b ) 97500 , c ) 100000 , d ) 105000 , e ) 102500
Rationale: "x * ( 85 / 100 ) = 85000 x = 1000 * 100 x = 100000 answer : c"
Answer: c
Question (general): if the median of a list of numbers is m , the first quartile of the list is the median of the numbers in the list that are less than m . what is the first quartile of the list of numbers 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 25
Rationale: it is given that a quartile is the middle number of all numbers less than median . . so lets arrange the number in ascending order - 42 , 24 , 30 , 22 , 26 , 27 , 33 and 35 22 , 24 , 26 , 27 , 30 , 33 , 35 , 42 , . . . numbers less than median are 22 , 24 , 26 , 27 . . the median of these numbers = center of 24 and 26 = 25 e
Answer: e
Question (geometry): what is the perimeter of a square with area 9 p ^ 2 / 64 ?
Options: a ) 3 p / 2
b ) 3 p ^ 2 / 4
c ) 3 p
d ) 3 p ^ 2
e ) 4 p / 3
Rationale: area of square , ( side ) ^ 2 = ( 3 p / 8 ) ^ 2 therefore side of the square = 3 p / 8 perimeter of square = 4 * side = 4 * ( 3 p / 8 ) = 3 p / 2 answer is a .
Answer: a
Question (general): 14 . the sum and the product of two numbers are 25 and 144 respectively , the difference of the number is ?
Options: a ) 7 , b ) 9 , c ) 8 , d ) 5 , e ) 4
Rationale: x + y = 25 xy = 144 ( x - y ) 2 = ( x + y ) 2 â € “ 4 xy ( x - y ) 2 = 625 â € “ 576 = > ( x â € “ y ) = 7 answer : a
Answer: a
Question (general): ( x ) + 1789 + 9011 - 7819 = 90510 . calculate the value of x
Options: a ) 87501 , b ) 87599 , c ) 87529 , d ) 87520 , e ) 87521
Rationale: "x + 1789 + 9011 - 7819 = 90510 = x + 1789 + 9011 = 90510 + 7819 = x + 10800 = 98329 = x = 98329 - 10800 = 87529 answer is c"
Answer: c
Question (general): an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2500 , what will be the difference between q and r ' s share ?
Options: a ) 2225 , b ) 2325 , c ) 2425 , d ) 2625 , e ) 2525
Rationale: "4 - - - 2100 5 - - - ? = > 2625 answer : d"
Answer: d
Question (physics): a certain industrial loom weaves 0.132 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.132 : 15 : : 1 : x = > 0.132 * x = 15 = > x = 15 / 0.132 = > x = 114 answer : a"
Answer: a
Question (general): if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 + x - 20 = 0 , then x =
Options: a ) 1 , b ) - 4 , c ) 4 , d ) - 5 , e ) 5
Rationale: x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 + x - 20 = ( x - 4 ) ( x + 5 ) = 0 then x = 4 or x = - 5 . thus x = - 5 . the answer is d .
Answer: d
Question (general): the rate at which a sum becomes 4 times of itself in 15 years at s . i . , will be :
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) none
Rationale: sol . let sum = x . then , s . i . = 3 x ∴ rate = [ 100 * s . i . / p * t ] = [ 100 * 3 x / x * 15 ] % = 20 % . answer c
Answer: c
Question (geometry): 20 business executives and 7 chairmen meet at a conference . if each business executive shakes the hand of every other business executive and every chairman once , and each chairman shakes the hand of each of the business executives but not the other chairmen , how many handshakes would take place ?
Options: a ) 144 , b ) 131 , c ) 330 , d ) 390 , e ) 445
Rationale: "there are 20 business exec and in each handshake 2 business execs are involved . hence 20 c 2 = 190 also , each of 20 exec will shake hand with every 7 other chairmen for total of 140 handshake . total = 190 + 140 = 330 ans : c"
Answer: c
Question (gain): a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 9 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 11 / 20 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: x * 6 / 100 * 1 + ( 20000 - x ) * 9 / 100 * 1 = 1440 6 x - 8 x = 144000 - 180000 = > - 2 x = - 18000 = > x = 9000 so 11000 / 20000 = 11 / 20 answer - a
Answer: a
Question (gain): in a school of 850 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 163 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 850 * 18 / 100 = 153 answer : c"
Answer: c
Question (general): 109 × 109 + 91 × 91 = ?
Options: a ) 20162 , b ) 18322 , c ) 13032 , d ) 18662 , e ) none of these
Rationale: "explanation : ( a + b ) 2 + ( a − b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1092 + 912 = ( 100 + 9 ) 2 + ( 100 − 9 ) 2 = 2 ( 1002 + 92 ) = 2 ( 10000 + 81 ) = 20162 . answer : option a"
Answer: a
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price q per glass on the second day ?
Options: a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
Answer: d
Question (general): if x = 3 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.02 , c ) 0.25 , d ) 4 , e ) 8
Rationale: "quickly we can spot that answer is neither integer nor negative . eliminate a , de answer : b"
Answer: b
Question (general): last year , for every 100 million vehicles that travelled on a certain highway , 98 vehicles were involved in accidents . if 3 billion vehicles travelled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 100000000 )
Options: a ) 288 , b ) 320 , c ) 2,940 , d ) 3,200 , e ) 28,800
Rationale: to solve we will set up a proportion . we know that “ 100 million vehicles is to 98 accidents as 3 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 3,000 million rather than 3 billion . creating a proportion we have : 100 / 98 = 3,000 / x cross multiplying gives us : 100 x = 3,000 * 98 x = 30 * 98 = 2,940 correct answer is c .
Answer: c
Question (physics): in what time will a train 125 m long cross an electric pole , it its speed be 130 km / hr ?
Options: a ) 3.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 130 * 5 / 18 = 36 m / sec time taken = 125 / 36 = 3.5 sec . answer : a"
Answer: a
Question (other): if 85 percent of the test takers taking an old paper and pencil gmat exam answered the first question on a given math section correctly , and 80 percent of the test takers answered the second question correctly , and 5 percent of the test takers answered neither question correctly , what percent answered both correctly ?
Options: a ) 60 % , b ) 65 % , c ) 70 % , d ) 75 % , e ) 80 %
Rationale: "{ total } = { first correctly } + { second correctly } - { both correctly } + { neither correctly } 100 = 85 + 80 - { both correctly } + 5 { both correctly } = 70 . answer : c ."
Answer: c
Question (general): 23 , 29 , 31 , 37 , 41 , 43 , 47 , 53 , 59 , 61 , 67 , ( . . . )
Options: a ) 53 , b ) 47 , c ) 48 , d ) 59 , e ) 71
Rationale: "explanation : all are prime numbers in their order , starting from 23 hence , next number is 71 answer : e"
Answer: e
Question (physics): due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 30 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 8 , c ) c ) 10 , d ) d ) 9.1 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 30 = 10 * 2 = 20 time difference = 9.1 ans : d"
Answer: d
Question (general): 96 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 77 , c ) 42 , d ) 88 , e ) 12
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 96 = 42 . answer : c"
Answer: c
Question (physics): the length of a side of a hexagon is 8 inches . what is the perimeter ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 38
Rationale: "hexagon . it means 6 equal sides . p = 6 ( 8 ) = 48 inches answer c"
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 11 . if n / j = 724.04 , what is value of j ?
Options: a ) 140 , b ) 150 , c ) 260 , d ) 275 , e ) 280
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 724.04 here 724 is the quotient . given that remainder = 11 so , 724.04 = 724 + 11 / j so , j = 275"
Answer: d
Question (physics): a can complete the job in 2 hours and b can complete the same job in 4 hours . a works for 1 hour and then b joins and both complete the job . what fraction of the job did b complete
Options: a ) 1 / 6 , b ) 3 / 10 , c ) 1 / 2 , d ) 5 / 6 , e ) 8 / 9
Rationale: a = 1 / 6
Answer: a
Question (gain): if a ' s income is 25 % less than b ' s . by what % b ' s income is greater than a ?
Options: a ) 11 , b ) 12 , c ) 33 , d ) 15 , e ) 36
Rationale: if b ' s income is rs 100 , a ' s income = rs 75 % b ' s income is greater than a = 100 * 25 / 75 = 33.33 % answer : c
Answer: c
Question (other): x starts a business with rs . 56000 . y joins in the business after 4 months with rs . 44000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 21 : 11 , b ) 11 : 21 , c ) 22 : 23 , d ) 25 : 23 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 56000 * 12 : 44000 * 8 = 56 * 12 : 44 * 8 = 7 * 3 : 11 = 21 : 11 . answer : option a"
Answer: a