Cheukting/mathqa huggingface dataset:
Question (physics): how many pieces of 85 cm length can be cut from a rod of 29.75 meters long ?
Options: a ) 55 , b ) 45 , c ) 35 , d ) 25 , e ) 15
Rationale: "number of pieces = 2975 / 85 = 35 the answer is c ."
Answer: c
Question (general): for every even positive integer m , f ( m ) represents the product of all even integers from 2 to m , inclusive . for example , f ( 12 ) = 2 x 4 x 6 x 8 x 10 x 12 . what is the greatest prime factor of f ( 30 ) ?
Options: a ) 2 , b ) 5 , c ) 11 , d ) 13 , e ) 19
Rationale: "f ( 30 ) = 2 * 4 * 6 * 8 * 10 * 12 * 14 * 16 * 18 * 20 * 22 * 24 * 26 * 28 * 30 the greatest prime factor in this list is 13 . the answer is d ."
Answer: d
Question (general): in a office work is distribute between p persons . if 1 / 3 members are absent then work increased for each person is ?
Options: a ) 13.28 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 50 %
Rationale: "let total % of work is 100 % total person = p 1 / 3 person are absent of total person . so absent person is 1 / 3 p ie p / 3 . left person is , p - p / 3 = 2 p / 3 . p person do the work 100 % 1 person do the work 100 * p % 2 p / 3 person do the work ( 100 * p * 3 ) / 2 p % = 150 % work increased for each person is = ( 150 - 100 ) % = 50 % answer : e"
Answer: e
Question (geometry): find the area of a parallelogram with base 60 cm and height 16 cm ?
Options: a ) 960 cm 2 , b ) 240 cm 2 , c ) 480 cm 2 , d ) 45 cm 2 , e ) 250 cm 2
Rationale: "area of a parallelogram = base * height = 60 * 16 = 960 cm 2 answer : a"
Answer: a
Question (geometry): in front of you lies a figure made up with 20 x 10 square blocks . will you be able to find out the number of unique squares and rectangles that are being formed inside this figure by combining two or more distinct squares ?
Options: a ) 11647
b ) 11550
c ) 12654
d ) 26537
e ) 32651
Rationale: b 11550 there is just one way to find it out and that is the generic computing method . the number of squares and rectangles formed = ( summation of column numbers ) = ( 1 + 2 + 3 + . . . . . . + 19 + 20 ) * ( 1 + 2 + 3 + . . . . . . + 9 + 10 ) = 210 * 55 = 11550
Answer: b
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8400 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) s . 4580 , b ) s . 4570 , c ) s . 4500 , d ) s . 4550 , e ) s . 4900
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8400 = 33600 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 1600 salary of may is rs . 6500 salary of january = rs . 4900 answer : e"
Answer: e
Question (physics): if a light flashes every 6 seconds , how many times will it flash in 2 / 5 of an hour ?
Options: a ) 181 , b ) 211 , c ) 241 , d ) 271 , e ) 301
Rationale: "in 2 / 5 of an hour there are 24 * 60 = 1440 seconds the number of 6 - second intervals = 1440 / 6 = 240 after the first flash , there will be 240 more flashes for a total of 241 . the answer is c ."
Answer: c
Question (geometry): the sides of the triangle are in the ratio 1 / 2 : 1 / 3 : 1 / 4 and its perimeter is 104 cm . the length of the longest side is ?
Options: a ) 32 cm
b ) 48 cm
c ) 50 cm
d ) 28 cm
e ) 30 cm
Rationale: ratio of sides = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 largest side = 104 * 6 / 13 = 48 cm answer is b
Answer: b
Question (gain): what percent of 11 is 11 percent of 1 ?
Options: a ) 1 , b ) 0.01 , c ) 0.1 , d ) 13 , e ) 101 .
Rationale: "11 % of 1 = ( 11 / 100 ) * 1 = 11 / 100 to determine what percentage of 11 this is : [ 11 ] [ / 100 * 11 ] * 100 = 1 % ans : a"
Answer: a
Question (geometry): the area of a square is equal to five times the area of a rectangle of dimensions 20 cm * 16 cm . what is the perimeter of the square ?
Options: a ) 289 cm , b ) 160 cm , c ) 829 cm , d ) 288 cm , e ) 289 cm
Rationale: "area of the square = s * s = 5 ( 20 * 16 ) = > s = 40 = 40 cm perimeter of the square = 4 * 40 = 160 cm . answer : b"
Answer: b
Question (general): on a race track a maximum of 5 horses can race together at a time . there are a total of 25 horses . there is no way of timing the races . what is the minimum number w of races we need to conduct to get the top 3 fastest horses ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "w = 7 is the correct answer . good solution buneul . b"
Answer: b
Question (gain): what is 66.67 % of 804 of 0.1666 ?
Options: a ) 19.33 , b ) 54.55 , c ) 89.33 , d ) 97.21 , e ) 68.77
Rationale: "66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 536 of 0.166 = 536 * ( 1 / 6 ) = 89.33 . . . . ans - c"
Answer: c
Question (general): find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 870 ?
Options: a ) rs . 700 , b ) rs . 780 , c ) rs . 750 , d ) rs . 1000 , e ) none of these
Rationale: "explanation : 870 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 750 answer : option c"
Answer: c
Question (general): how many multiples of 2 are there between 1 and 60 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 29 , d ) 26 , e ) 28
Rationale: "29 multiples of 2 between 1 and 60 exclusive . from 2 * 1 upto 2 * 29 , ( 1,2 , 3,4 , . . . , 29 ) . hence , 29 multiples ! correct option is c"
Answer: c
Question (gain): the bankers discount of a certain sum of money is rs . 576 and the true discount on the same sum for the same time is rs . 480 . the sum due is :
Options: a ) 2880 , b ) 2870 , c ) 2860 , d ) 2850 , e ) 2840
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 576 * 480 ) / 576 - 480 ; 2880 answer : a"
Answer: a
Question (gain): a pair of articles was bought for $ 50 at a discount of 30 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 17.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 70 % of x = 25 x = 25 * . 7 = $ 17.50 answer is b"
Answer: b
Question (physics): in an intercollegiate competition that lasted for 3 days , 185 students took part on day 1 , 150 on day 2 and 200 on day 3 . if 100 took part on day 1 and day 2 and 110 took part on day 2 and day 3 and 50 took part on all three days , how many students took part only on day 3 ?
Options: a ) 45 , b ) 35 , c ) 55 , d ) 30 , e ) 40
Rationale: "day 1 & 2 = 100 ; only day 1 & 2 ( 100 - 50 ) = 50 , day 2 & 3 = 110 ; only day 2 & 3 ( 110 - 50 ) = 60 , only day 3 = 200 - ( 50 + 60 + 50 ) = 40 answer : e"
Answer: e
Question (physics): express a speed of 46 kmph in meters per second ?
Options: a ) 10.78 mps , b ) 12.78 mps , c ) 97.78 mps , d ) 17.78 mps , e ) 18.78 mps
Rationale: "46 * 5 / 18 = 12.78 mps answer : b"
Answer: b
Question (general): simplify 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 â ˆ ’ 5 â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ â ¯ ) ) ]
Options: a ) 23 , b ) 25 , c ) 89 , d ) 30 , e ) 32
Rationale: explanation : = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ( 7 â ˆ ’ 8 + 5 ) ) ] ( please check due to overline , sign has been changed ) = 80 â ˆ ’ [ 5 â ˆ ’ ( 6 + 2 ã — 4 ) ) ] = 80 â ˆ ’ [ â ˆ ’ 9 ] = 80 + 9 = 89 option c
Answer: c
Question (general): solve the equation for x : 19 ( x + y ) + 17 = 19 ( - x + y ) - 21 ?
Options: a ) - 1 , b ) 77 , c ) 8 , d ) 3 , e ) 2
Rationale: "19 x + 19 y + 17 = - 19 x + 19 y - 21 38 x = - 38 = > x = - 1 answer : a"
Answer: a
Question (gain): if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 5 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 9125 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 5 = 9125 answer : d"
Answer: d
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 204 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 36 , c ) 55 , d ) 77 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 204 = > . 1 x + 3 / 4 x = 204 = > x = 240 240 - 204 = pure gala = 36 . answer b"
Answer: b
Question (general): ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = ?
Options: a ) 54210 , b ) 54250 , c ) 52150 , d ) none of these , e ) 521500
Rationale: "its speed and accuracy which decides the winner . you can use various methods including vedic mathematics to do complex calculations quickly . ( 32323 + 7344 + 41330 ) - ( 317 x 91 ) = 80997 - 28847 = 52150 answer is c"
Answer: c
Question (general): an amount of rs . 1560 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) rs . 390 , b ) rs . 368 , c ) rs . 380 , d ) rs . 360 , e ) rs . 311
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 1560 = rs . 360 . answer : d"
Answer: d
Question (physics): 42 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 28 , b ) 77 , c ) 36 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 42 : : 18 : x [ please pay attention , we have written 27 : 42 rather than 42 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 42 \ times 18 } { 27 } } x = 28 so 28 days will be required to get work done by 27 men . answer : a"
Answer: a
Question (general): how many three - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "the possible number n can be written as follow : n = multiple of lcm ( 6,10 ) + 1 st such number n = 30 x + 1 possible values = 1 , 31 , 61 , 91 , 121,151 , 181,211 , 241,271 . . . . . 991 answer : none : a"
Answer: a
Question (geometry): find the area of a parallelogram with base 32 cm and height 18 cm ?
Options: a ) 576 cm 2 , b ) 384 cm 2 , c ) 672 cm 2 , d ) 267 cm 2 , e ) 286 cm 2
Rationale: "area of a parallelogram = base * height = 32 * 18 = 576 cm 2 answer : a"
Answer: a
Question (general): the number 91 is equal to the sum of the cubes of two integers . what is the product of those integers ?
Options: a ) 8 , b ) 12 , c ) 21 , d ) 27 , e ) 39
Rationale: "3 ^ 3 + 4 ^ 3 = 91 therefore number is 3 * 4 = 12 b"
Answer: b
Question (general): a student multiplied a number by 3 / 5 instead of 5 / 3 . what is the percentage error in the calculation ?
Options: a ) 54 , b ) 48 , c ) 65 , d ) 25 , e ) 64
Rationale: let the number be x . then , error = 5 / 3 x - 3 / 5 x = 16 / 15 x . error % = ( 16 x / 15 * 3 / 5 x * 100 ) % = 64 % answer e ) 64 %
Answer: e
Question (physics): angelina walked 250 meters from her home to the grocery at a constant speed . she then walked 360 meters to the gym at double the speed . she spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 250 / x . . the speed to gym = 2 x . . so time taken = 360 / 2 x = 180 / x . . its given 250 / x - 180 / x = 70 . . 70 / x = 70 . . x = 1 m / secs . . so grocery to gym = 2 * 1 = 2 m / s . . . answer : a"
Answer: a
Question (general): 2 + 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + 2 ^ 5 + 2 ^ 6 + 2 ^ 7 + 2 ^ 8 =
Options: a ) 2 ^ 9 , b ) 2 ^ 10 , c ) 2 ^ 12 , d ) 2 ^ 16 , e ) 2 ^ 20
Rationale: let ' s see that : 2 + 2 is 2 ^ 2 , then : 2 ^ 2 + 2 ^ 2 becomes 2 x 2 ^ 2 that is 2 ^ 3 . you follow with the next : 2 ^ 3 + 2 ^ 3 is equal to 2 x 2 ^ 3 that is 2 ^ 4 . then is assumed right before 2 ^ 8 : 2 ^ 8 x 2 ^ 8 becomes 2 x 2 ^ 8 that is 2 ^ 9 . option a , 2 ^ 9 .
Answer: a
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 400 before any discount ?
Options: a ) $ 230.00 , b ) $ 224.00 , c ) $ 263.80 , d ) $ 282.00 , e ) $ 210.00
Rationale: "since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 400 would be . . . . . ( $ 400 ) ( . 7 ) ( . 8 ) = ( $ 400 ) ( . 56 ) = 224 final answer : b"
Answer: b
Question (general): logx 16 = 0.8 then what is the value of x ?
Options: a ) 32 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: x ^ 0.8 = 16 x = ( 2 ^ 4 ) ^ ( 10 / 8 ) x = 2 ^ 5 x = 32 answer : a
Answer: a
Question (gain): a 16 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 200
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 16 , money invested = 100 × 16 / 8 = rs . 175 ie , market value of the stock = rs . 200 answer is e ."
Answer: e
Question (gain): at an elementary school , 70 % of the faculty members are women and 40 % of the faculty members are married . if 1 ⁄ 3 of the men are single , what fraction of the men are married ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 3 / 5 , e ) 2 / 7
Rationale: "- - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - - 20 - - - - - 20 - - - - - - - - - 40 not married - - - - - 10 - - - - - 50 - - - - - - - - - 60 total - - - - - - - - - - - - - 30 - - - - - 70 - - - - - - - - 100 need married man / total man , so 20 / 30 = 2 / 3 c"
Answer: c
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 12 of money ?
Options: a ) 1200 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 12 ( 100 / 10 ) 2 = > p = 1200 answer : a"
Answer: a
Question (general): a man whose bowling average is 12.4 , takes 3 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "12.4 * x + 26 = ( 3 + x ) 12 solve equation x = 25 answer : c"
Answer: c
Question (general): a 40 - liter solution of alcohol and water is 5 percent alcohol . if 3.5 liters of alcohol and 6.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 8 % , b ) 11 % , c ) 14 % , d ) 17 % , e ) 20 %
Rationale: "the percent of alcohol in the solution is ( 0.05 ( 40 ) + 3.5 ) / 50 = 5.5 / 50 = 11 % the answer is b ."
Answer: b
Question (physics): how long does a train 110 m long traveling at 90 kmph takes to cross a bridge of 170 m in length ?
Options: a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
Rationale: "d = 110 + 170 = 280 m s = 90 * 5 / 18 = 50 / 2 t = 280 * 2 / 50 = 11.2 sec answer : d"
Answer: d
Question (physics): if 12 men can reap 80 hectares in 24 days , then how many hectares can 36 men reap in 30 days ?
Options: a ) 127 , b ) 237 , c ) 300 , d ) 450 , e ) 281
Rationale: "explanation : let the required no of hectares be x . then men - - - hectares - - - days 12 - - - - - - - - - 80 - - - - - - - - - 24 36 - - - - - - - - - x - - - - - - - - - 30 more men , more hectares ( direct proportion ) more days , more hectares ( direct proportion ) x = 36 / 12 * 30 / 24 * 80 x = 300 answer : c"
Answer: c
Question (physics): a martian bat flies at 60 yards per second from its nest to a dry lake . when it arrives there , it immediately continues at 45 yards per second to a nearby cave . if the distance between the lake and the cave is half the distance between the nest and the lake , what is the average speed , in yards per second , of the bat during the whole flight ?
Options: a ) 36 , b ) 40 , c ) 42 , d ) 54 , e ) 65
Rationale: distance from nest to lake = d , speed = 60 , time = d / 60 distance from lake to cave = d / 2 , speed = 45 , time = d / 90 average speed = ( d + d / 2 ) / ( d / 60 + d / 90 ) = ( 3 / 2 ) / ( 1 / 36 ) = 54 answer : d
Answer: d
Question (general): the sum of all the integers k such that – 20 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 37
Rationale: "- 19 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 19 - 18 sum of which is - 37 . hence option d . e"
Answer: e
Question (gain): a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8000 = 1 / 16 = 6.25 % the answer is c ."
Answer: c
Question (physics): a tank is filled in 10 hours by 3 pipes a , b and c . pipe a is twice as fast as pipe b , and b is twice as fast as c . how much time will pipe b alone take to fill the tank ?
Options: a ) 56 hours , b ) 28 hours , c ) 35 hours , d ) 66 hours , e ) 47 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 10 ( given ) also given that a = 2 b and b = 2 c = > 1 / 2 b + 1 / b + 2 / b = 1 / 10 = > ( 1 + 2 + 4 ) / 2 b = 1 / 10 = > 2 b / 7 = 10 = > b = 35 hours . answer : c
Answer: c
Question (general): the sum of the first 50 positive even integers is 2550 . what is the sum e of even integers from 102 to 200 inclusive ?
Options: a ) 5100 , b ) 7550 , c ) 10100 , d ) 15500 , e ) 20100
Rationale: "my solution is : first 50 even integers : 2 4 6 8 < . . . > integers from 102 to 200 102 104 106 108 < . . . > we notice that each integer from the second set is 100 more than the respective integer in the first set . since we have 50 even integers from 102 to 200 , then : e = 2550 + ( 100 * 50 ) = 7550 . b"
Answer: b
Question (general): a , b and c rents a pasture for rs . 928 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 288 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 928 = 288 answer : c"
Answer: c
Question (general): in a class of 28 students in an examination in maths 4 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47.3 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 4 * 95 + 3 * 0 + 21 * 45 = 1325 average marks of whole class = 1325 / 28 = 47.3 answer : option a"
Answer: a
Question (general): gopi gives rs . 90 plus one turban as salary to his servant for one year . the servant leaves after 9 months and receives rs . 65 and the turban . find the price of the turban .
Options: a ) 27 , b ) 36 , c ) 29 , d ) 10 , e ) 11
Rationale: "let the price of turban be x . thus , for one year the salary = ( 90 + x ) for 9 months he should earn 3434 ( 90 + x ) . now he gets one turban and rs . 65 . thus , 3434 ( 90 + x ) = 65 + x or 270 + 3 x = 260 + 4 x or x = 10 answer : d"
Answer: d
Question (general): the temperature of a certain cup of coffee 30 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 120 , c ) 80 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 30 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 30 a ) + 60 60 = 120 * ( 2 ^ - 30 a ) 60 / 120 = 2 ^ - 30 a 1 / 2 = 2 ^ - 30 a 2 ^ - 1 = 2 ^ - 30 a - 1 = - 30 a 1 / 30 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 30 * 30 ) + 60 f = 120 * ( 2 ^ - 1 ) + 60 f = 120 * ( 1 / 2 ^ 1 ) + 60 f = 120 * 1 / 2 + 60 f = 60 + 60 = 120 answer b !"
Answer: b
Question (physics): the sum of three consecutive even numbers is 246 . what are the numbers ?
Options: a ) 80 , 82,84 , b ) 65 , 68,71 , c ) 45 , 47,42 , d ) 100 , 102,49 , e ) 87 , 88,89
Rationale: "first x make the first x second x + 2 even numbers , sowe add 2 to get the next third x + 4 add 2 more ( 4 total ) to get the third f + s + t = 246 summeansaddfirst ( f ) plussecond ( s ) plusthird ( t ) ( x ) + ( x + 2 ) + ( x + 4 ) = 246 replace each f , s , and t withwhatwe labeled them x + x + 2 + x + 4 = 246 here the parenthesis are not needed 3 x + 6 = 246 combine like terms x + x + x and 2 + 4 − 6 − 6 subtract 6 fromboth sides 3 x = 240 the variable ismultiplied by 3 3 3 divide both sides by 3 x = 80 our solution for x first 80 replace x in the origional listwith 80 . second ( 80 ) + 2 = 82 the numbers are 80 , 82 , and 84 . third ( 80 ) + 4 = 84 correct answer a"
Answer: a
Question (physics): two pipes a and b can separately fill a cistern in 60 minutes and 120 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 60 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 100 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 60 - ( 1 / 60 + 1 / 120 ) = - 1 / 120 third pipe can empty in 120 minutes answer : d"
Answer: d
Question (general): if the average of 10 consecutive integers is 23.5 then the 10 th integer is : -
Options: a ) 15 , b ) 20 , c ) 23 , d ) 28 , e ) 25
Rationale: "the average falls between the 5 th and 6 th integers , integer 5 = 23 , integer 6 = 24 . counting up to the tenth integer we get 28 . answer : d"
Answer: d
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 7.2 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 9 ) = 5 / 36 the cistern will be filled in 36 / 5 hrs i . e . , 7.2 hrs . answer : d"
Answer: d
Question (physics): the distance between west - town to east - town is 16 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 5 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 7 . , c ) 10 . , d ) 12 . , e ) 16 .
Rationale: "time taken by the birds to meet = 16 / ( 5 + 1 ) = 4 mins distance traveled by the bird traveling from west - town = 4 * 4 = 16 answer : e"
Answer: e
Question (general): which 2 digit number has its digits reversed when you double it and take 1 ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: reverse it and you get 73 which is 2 * 37 - 1 . answer : e
Answer: e