Cheukting/mathqa huggingface dataset:
Question (physics): a train crosses a platform of 350 m in 15 sec , same train crosses another platform of length 500 m in 20 sec . then find the length of the train ?
Options: a ) 100 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 152 m
Rationale: "length of the train be ‘ x ’ x + 350 / 15 = x + 500 / 20 4 x + 1400 = 3 x + 1500 x = 100 m answer : a"
Answer: a
Question (general): 0.001 ã — 0.001 = ?
Options: a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 1.0 e - 06 , e ) none of these
Rationale: "0.001 ã — 0.001 = ? or , ? = 0.000001 answer d"
Answer: d
Question (general): if doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product , the number is
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: solution let the number be x . = then , 2 x + 20 = 8 x – 4 = 6 x = 24 ‹ = › x = 4 . answer c
Answer: c
Question (general): x + ( 1 / x ) = 3.5 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 3.25 , c ) 10.25 , d ) 5.25 , e ) 6.25
Rationale: squaring on both sides ( x + 1 / x ) ^ 2 = 3.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 12.25 - 2 x ^ 2 + 1 / x ^ 2 = 10.25 answer : c
Answer: c
Question (general): what is the difference between the largest number and the least number written with the digits 9 , 2 , 1 , 5 ?
Options: a ) 6084 , b ) 3788 , c ) 2077 , d ) 8262 , e ) 1812
Rationale: "explanation : 1259 9521 - - - - - - - - - - - - 8262 answer : d"
Answer: d
Question (other): the ratio of flour to water to sugar in a recipe is 7 : 2 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the ratio of flour to water is 14 : 2 . the ratio of flour to sugar is 3.5 : 1 = 14 : 4 . the new ratio of flour to water to sugar is 14 : 2 : 4 if we need 2 cups of water , then we need 4 cups of sugar . the answer is c ."
Answer: c
Question (physics): a train , 130 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
Options: a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
Rationale: explanation : assume the length of the bridge = x meter total distance covered = 130 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 130 + x ) / 30 m / s = > 45 × ( 10 / 36 ) = ( 130 + x ) / 30 = > 45 × 10 × 30 / 36 = 130 + x = > 45 × 10 × 10 / 12 = 130 + x = > 15 × 10 × 10 / 4 = 130 + x = > 15 × 25 = 130 + x = 375 = > x = 375 - 130 = 245 answer : option b
Answer: b
Question (general): the unit digit in the product 1258 * 6754 * 4512 * 9783 is ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "unit digit in the given product = unit digit in 8 * 4 * 2 * 3 = 2 answer is c"
Answer: c
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 671.5 , b ) 600 , c ) 672.5 , d ) 673 , e ) 773.5
Rationale: "many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 900 kilometers per hour is 1 / 900 hours = 3,600 / 900 seconds = 4 seconds ; time to cover this distance at regular speed is 900 + 2 = 902 seconds = 902 / 3,600 hours = 1 / 600 hours ; so , we get that to cover 1 kilometer 1 / 600 hours is needed - - > regular speed 600 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b ."
Answer: b
Question (general): a school has 4 section of chemistry in class x having 70 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
Options: a ) 50.9 , b ) 52.9 , c ) 51.9 , d ) 53.25 , e ) none of the above
Rationale: "required average marks = 70 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 70 + 35 + 45 + 42 = 3500 + 2100 + 2475 + 1890 / 192 = 9965 â  „ 192 = 51.90 answer c"
Answer: c
Question (general): how much is 40 % of 60 is greater than 4 / 5 of 25 ?
Options: a ) 2 , b ) 5 , c ) 12 , d ) 8 , e ) 4
Rationale: "( 40 / 100 ) * 60 â € “ ( 4 / 5 ) * 25 24 - 20 = 4 answer : e"
Answer: e
Question (gain): today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 6512.50 , b ) $ 7512.50 , c ) $ 5512.50 , d ) $ 4512.50 , e ) $ 5250.00
Rationale: "interest for 1 st year = 5000 * 5 / 100 = 250 interest for 2 nd year = 5250 * 5 / 100 = 262.50 total = 5000 + 250 + 262.50 = 5512.50 answer : c"
Answer: c
Question (geometry): if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c"
Answer: c
Question (general): a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 18 % next year . this year , the total amount paid for type a products was $ 4600 and the total price paid for type b products was $ 8400 . 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 ) $ 15,202 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.15 * 4600 = 5290 cost of type b products next year = 1.18 * 8400 = 9912 total 5290 + 9912 = 15202 answer : a"
Answer: a
Question (general): when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 10 and the remainder is 3 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 43 , e ) 87
Rationale: "n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 10 1 / ( p + 2 ) = 10 p + 20 + 3 solving these two equations we get p = 2 n = 43 answer is d"
Answer: d
Question (general): ashok borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years and at the rate of 14 % p . a . for the period beyond 5 years . if he pays a total interest of 11400 / - at the end of 9 years , how much money did he borrow ?
Options: a ) 16060 , b ) 14000 , c ) 18000 , d ) 12000 , e ) none of these
Rationale: we have , si = p × r × t / 100 ∴ 11400 = p × 6 × 2 / 100 + p × 9 × 3 / 100 + p × 14 × 4 / 100 or , 12 p + 27 p + 56 p = 11400 × 100 or , 95 p = 11400 × 100 ∴ p = 12000 answer d
Answer: d
Question (general): ` ` i am 8 times as old as you were when i was as old as you are ` ` , said a man to his son . find out their present ages if the sum of the their ages is 75 years .
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: present age of boy x and previous age of boy y so present age of dad : 8 y and previous age is x so the gap between duration must be same so 8 y - x = x - y - - > x = 9 y / 2 and x + 8 y = 75 ( given ) - - > 9 y / 2 + y = 75 so y = 6 and and x = 27 therefore fathers age is 8 y = 8 * 6 = 48 and child ' s age = x = 27 answer : e
Answer: e
Question (general): ada and paul received their scores on 3 tests . on the first test , ada ' s score was 10 points higher than paul ' s score . on the second test , ada ' s score was 4 points higher than paul ' s score . if paul ' s average ( arithmetic mean ) score on the 3 tests was 4 points higher than ada ' s average score on the 3 tests , then paul ' s score on the third test was how many points higher than ada ' s score ?
Options: a ) 9 , b ) 14 , c ) 17 , d ) 23 , e ) 26
Rationale: my take is option d ( 23 ) i followed a simple approach ( explained below ) : test 1 : ada ' s score = paul ' s score + 10 test 2 : ada ' s score = paul ' s score + 4 avg . of paul ' s score = 4 points higher than avg . of ada ' s score this implies that : sum of paul ' s score [ 3 tests ] = 12 points higher than sum of ada ' s score [ 3 tests ] ( 12 points higher since 3 points were given in terms of average of 3 scores ) so , paul needs to score 23 points higher than ada in test 3 , since paul needs to compensate for the lower score in test 1 and test 2 ( 26 = 10 + 4 + 12 ) e
Answer: e
Question (gain): the simple interest on a certain sum of money for 3 years at 8 % per annum is half the compound interest on $ 4000 for 2 years at 10 % per annum . the sum placed on simple interest is ?
Options: a ) $ 1250 , b ) $ 1300 , c ) $ 1750 , d ) $ 2015 , e ) $ 1452
Rationale: c . i . = 4000 * ( 1 + 10 / 100 ) ^ 2 - 4000 = 4000 * 11 / 10 * 11 / 10 - 4000 = $ 840 sum = 420 * 100 / 3 * 8 = $ 1750 answer is c
Answer: c
Question (other): teas 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 156 per kg , the price of the third variety per kg will be ?
Options: a ) rs . 147.50 , b ) rs . 785.50 , c ) rs . 178.50 , d ) rs . 258.50 , e ) none of these
Rationale: "explanation : since first and second varieties are mixed in equal proportions . so , their average price = rs . ( 126 + 135 ) / 2 . = > rs . 130.50 . 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 . by the rule of alligation , we have : cost of 1 kg cost of 1 kg of 1 st kind of 2 nd kind ( rs . 130.50 ) ( rs . x ) \ / mean price ( rs . 156 ) / \ x â ˆ ’ 156 22.50 = > x â ˆ ’ ( 156 / 22.50 ) = 1 . = > x â ˆ ’ 156 = 22.50 . = > x = 178.50 rs . answer : c"
Answer: c
Question (general): in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "let part time emp = x let full time emp = y then , 48 = x + y . . . . . . . . . ( 1 ) ( 1 / 3 ) x + ( 1 / 4 ) y = no . of ppl taking the subway 4 x + 3 y / 12 = no . of ppl taking the subway using 1 x / 12 + 3 * 48 / 12 = no . of ppl taking the subway so , the minimum value of x has to be 12 . hence to maximize the no . put 36 for x 36 / 12 + 12 / 4 = 15 answer : d"
Answer: d
Question (physics): what is the maximum number of pieces of birthday cake of size 3 ” by 3 ” that can be cut from a cake 21 ” by 21 ” ?
Options: a ) 5 , b ) 7 , c ) 49 , d ) 20 , e ) 25
Rationale: "the prompt is essentially asking for the maximum number of 3 x 3 squares that can be cut from a larger 21 by 21 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 7 ' pieces ' each , we have ( 7 ) ( 7 ) = 49 total smaller squares ( at maximum ) . c"
Answer: c
Question (general): in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 37 . in the company , what is the maximum number of non - managers in a department that has 9 managers ?
Options: a ) 44 , b ) 45 , c ) 46 , d ) 47 , e ) 48
Rationale: "9 / 7 * 37 = 47.6 the answer is d ."
Answer: d
Question (physics): a train covers a distance of 12 km in 10 min . if it takes 7 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 177 m , b ) 189 m , c ) 140 m , d ) 178 m , e ) 188 m
Rationale: "speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 7 = 140 m . answer : c"
Answer: c
Question (other): in a class of 78 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 26 , b ) 27 , c ) 24 , d ) 18 , e ) 11
Rationale: "explanation : you could solve this by drawing a venn diagram . a simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking french to find the number taking only french . likewise find those taking only german . then we have : total = only french + only german + both + neither 78 = ( 41 - 9 ) + ( 22 - 9 ) + 9 + neither . not enrolled students = 24 answer : c"
Answer: c
Question (general): if ( n + 2 ) ! / n ! = 182 , n = ?
Options: a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "( n + 2 ) ! / n ! = 182 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 132 from here , we might just test the answer choices . since ( 14 ) ( 13 ) = 182 , we can see that n = 12 e"
Answer: e
Question (other): in what ratio must tea at rs . 64 per kg be mixed with tea at rs . 74 per kg so that the mixture must be worth rs . 69 per kg ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
Rationale: "required ratio = 500 : 500 = 1 : 1 answer a"
Answer: a
Question (physics): 36 . a 240 m long train crosses a platform of equal length in 27 s . what is the speed of the train in km / h ?
Options: a ) 48 , b ) 60 , c ) 56 , d ) 64 , e ) 68
Rationale: by the formula , speed = distance / time = ( 240 + 240 ) / 27 x ( 18 / 5 ) = 480 / 27 x 18 / 5 = 64 km / h answer : d
Answer: d
Question (geometry): the base of a triangular field is three times its altitude . if the cost of cultivating the field at rs . 24.68 per hectare be rs . 333.18 , find its base and height .
Options: a ) 100 m
b ) 125 m
c ) 150 m
d ) 278 m
e ) 300 m
Rationale: sol . area of the field = total cost / rate = ( 333.18 / 25.6 ) hectares = 13.5 hectares ( 13.5 x 10000 ) m ^ 2 = 135000 m ^ 2 . let altitude = x metres and base = 3 x metres . then , ( 1 / 2 ) * 3 x * x = 135000 < = > x ^ 2 = 90000 < = > x = 300 . base = 900 m and altitude = 300 m . ans : e
Answer: e
Question (gain): a , b and c enter into a partnership by investing $ 11000 , $ 15000 and $ 23000 respectively . at the end of 8 months , b receives $ 1540 as his share . find the share of a .
Options: a ) $ 811 , b ) $ 922 , c ) $ 1033 , d ) $ 1144 , e ) $ 1255
Rationale: "the ratio of capital of a , b and c = 11000 : 15000 : 23000 = 11 : 15 : 23 a ' s share = ( 11 / 15 ) * 1560 = $ 1144 the answer is d ."
Answer: d
Question (gain): if each year the population of the country grows by 30 % , how many years will elapse before the population of the country doubles ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 3 , e ) 7
Rationale: "till year 2000 , population is 100 . year 2001 : population becomes 130 . . . . . . . . . . . . . 1 year elapsed year 2002 : population becomes 169 . . . . . . . . . . . . . 2 year elapsed year 2004 : population > 200 . . . . . . . . . . . . . . . . . . 3 year elapsed answer : d"
Answer: d
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 , 34 , 26 , 36 , 33 and 35 ?
Options: a ) 33 , b ) 28 , c ) 27 , d ) 24 , e ) 23
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 , 34 , 26 , 36 , 33 and 35 24 , 26 , 30 , 33 , 34 , 35 , 36 , 42 . . . numbers less than median are 24 , 26 , 30 , 33 . . the median of these numbers = center of 26 and 30 = 28 b"
Answer: b
Question (general): how many integers are divisible by 3 between 20 ! and 20 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "b - 7 20 ! is divisible by 3 there are 6 numbers between 10 ! and 10 ! + 20 that are divisible by 3 . hence 7"
Answer: b
Question (physics): the speed of a boat in still water is 20 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 27 minutes is :
Options: a ) 9.25 , b ) 5.25 , c ) 7.25 , d ) 6.25 , e ) 11.25
Rationale: "explanation : speed downstream = ( 20 + 5 ) kmph = 25 kmph distance travelled = ( 25 * ( 27 / 60 ) ) km = 11.25 km . answer : e"
Answer: e
Question (probability): if 4 people are selected from a group of 10 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 63 , c ) 1 / 3 , d ) 43 / 62 , e ) 11 / 12
Rationale: "if we are to select 4 people from 10 couples without any restriction , how many ways can we make the selection ? 20 ! / 4 ! 16 ! = 4845 if we are to select 4 people from 10 couples with restriction that no married couple can both make it to the group , only a representative ? 10 ! / 4 ! 6 ! = 210 but we know that to select a person from each couple , take 2 possibilities 210 * 2 * 2 * 2 * 2 = 3360 probability = desired / all possibilities = 3360 / 4845 = 43 / 62 answer : d"
Answer: d
Question (physics): what is the least number of square tiles required to pave the floor of a room 50 m 00 cm long and 11 m 25 cm broad ?
Options: a ) 724 , b ) 804 , c ) 814 , d ) 9000 , e ) none
Rationale: solution length of largest tile = h . c . f . of 5000 cm & 1125 cm = 25 cm . area of each tile = ( 25 x 25 ) cm 2 ∴ required number of tiles = [ 5000 x 1125 / 25 x 25 ] = 9000 . answer d
Answer: d
Question (general): in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 65 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 380 $ , c ) 420 $ , d ) 450 $ , e ) 528 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 65 ) = 21 + 507 = > 528 hence answer will be ( e ) 528"
Answer: e
Question (general): if the average of 37 , 69 , 47 and x is 46.5 , what is x ?
Options: a ) 37 , b ) 41 , c ) 50 , d ) 59 , e ) 33
Rationale: "x = 33 because : ( 37 + 69 + 47 + x ) / 4 = 46.5 ( 37 + 69 + 47 + x ) / 4 * 4 = 46.5 * 4 ( 37 + 69 + 47 + x ) = 186 ( 37 + 69 + 47 + x ) - 153 = 186 - 153 x = 33 therefore , the answer is e , 33 ."
Answer: e
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 60 . he was allowed to drop his lowest score . after doing so , his average test score improved to 65 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 45 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 60 . so what we can assume is that we have 4 test scores , each 60 . he dropped his lowest score and the avg went to 65 . this means that the lowest score was not 60 and other three scores had given the lowest score 5 each to make it up to 60 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 60 . so the lowest score = 60 - 15 = 45 answer ( b )"
Answer: b
Question (general): if the number 992 , 132,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 0
Rationale: multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 992 , 132,24 x sum of digits at odd places = 9 + 2 + 3 + 2 + x = 16 + x ( i ) sum of digits at even places = 9 + 1 + 2 + 4 = 16 ( ii ) ( i ) - ( ii ) = 16 + x - 16 = x - 0 hence x should be = 0 to make this a multiple of 11 ( 0 ) option e
Answer: e
Question (general): in kaya ' s teacher ' s desk there are 9 pink highlighters , 8 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 22 , c ) 77 , d ) 33 , e ) 88
Rationale: add the numbers of highlighters . 9 + 8 + 5 = 22 . answer is b .
Answer: b
Question (physics): a metal company ' s old machine makes bolts at a constant rate of 100 bolts per hour . the company ' s new machine makes bolts at a constant rate of 150 bolts per hour . if both machines start at the same time and continue making bolts simultaneously , how many minutes will it take the two machines to make a total of 500 bolts ?
Options: a ) 36 , b ) 72 , c ) 120 , d ) 144 , e ) 180
Rationale: "old machine 100 bolts in 60 mins so , 5 / 3 bolts in 1 min new machine 150 bolts in 60 mins so , 5 / 2 bolts in 1 min together , 5 / 3 + 5 / 2 = 25 / 6 bolts in 1 min so , for 500 bolts 500 * 6 / 25 = 120 mins ans c"
Answer: c
Question (general): the average mark of a class of thirty two students is 75 . if 3 students whose marks are 28 and 34 are removed , then find the approximate average mark of the remaining students of the class .
Options: a ) 71 , b ) 74 , c ) 78 , d ) 70 , e ) 80
Rationale: exp . total mark of 32 students = 75 * 32 = 2400 , total mark after the removal of 2 students = 2400 – ( 28 + 34 ) = 2400 – 62 = 2338 approximate average mark = 2338 / ( 32 - 2 ) = 2338 / 30 = 78 answer : c
Answer: c
Question (physics): a can do a piece of work in 6 days , and b can do it in 5 days . if c , who can do the work in 12 days , joins them , how long will they take to complete the work ?
Options: a ) 2 days , b ) 3.5 days , c ) 2.2 days , d ) 4 days , e ) 5.7 days
Rationale: a , b , and c do the work in = 6 * 5 * 12 / 6 * 5 + 5 * 12 + 6 * 12 = 360 / 162 = 2.2 days answer is c
Answer: c
Question (geometry): the perimeter of a triangle is 39 cm and the inradius of the triangle is 1.5 cm . what is the area of the triangle ?
Options: a ) 22 , b ) 35 , c ) 77 , d ) 54 , e ) 29
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 1.5 * 39 / 2 = 29 cm 2 answer : e"
Answer: e
Question (general): the average age of 20 students of a class is 20 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 20 th student is
Options: a ) 186 , b ) 120 , c ) 152 , d ) 220 , e ) 220
Rationale: "explanation : age of the 20 th student = [ 20 * 20 - ( 14 * 5 + 16 * 9 ) ] = ( 400 - 214 ) = 186 years . answer : a"
Answer: a
Question (physics): tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 5 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 19 / 35 , b ) 23 / 42 , c ) 27 / 55 , d ) 31 / 63 , e ) 35 / 74
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 21 / 30 ) = 10 / 21 hours peter worked for 31 / 21 hours so he painted 31 / 21 * 1 / 3 = 31 / 63 of the room . the answer is d ."
Answer: d
Question (general): little roshini had $ 10.50 . he spent some money on sweets and gave to his two friends $ 3.40 each . how much money was spent for sweets ?
Options: a ) $ 4.70 , b ) $ 4.80 , c ) $ 3.85 , d ) $ 3.80 , e ) $ 3.70
Rationale: roshini spent and gave to his two friends a total of x + 3.40 + 3.40 = $ 3.65 money spent for sweet = 10.50 - 6.80 = $ 3.70 correct answer is e ) $ 3.70
Answer: e