Cheukting/mathqa huggingface dataset:
Question (general): a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 10 . if he got 230 marks in two subjects together how many marks did he got in english ?
Options: a ) 140,90 , b ) 180,60 , c ) 160,90 , d ) 150,80 , e ) none of them
Rationale: "let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 10 2 x - 3 y = 60 â € ¦ â € ¦ > ( 1 ) x + y = 230 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 150 and y = 80 answer is d ."
Answer: d
Question (physics): how many times are the hands of a clock at right angle in 5 days ?
Options: a ) 202 , b ) 220 , c ) 210 , d ) 212 , e ) 222
Rationale: in 1 day , they are at right angles 44 times . in 5 days , they are at right angles 220 times . answer : option b
Answer: b
Question (general): sebastian bought a meal at a restaurant and left a 15 % tip . with the tip , he paid exactly $ 36.57 . how much did the meal cost without the tip ?
Options: a ) $ 31.80 , b ) $ 29.91 , c ) $ 30.15 , d ) $ 30.60 , e ) $ 30.85
Rationale: the tip is a percent increase of 15 % , which is 115 % . let x equal the price before the tip . thus , 115 % of this price equals $ 36.57 : 1.15 x = 36.57 divide both sides by 1.15 : = > x = 36.57 / 1.15 = 31.80 correct answer a ) $ 31.80
Answer: a
Question (general): what should be the least number to be added to the 4499 number to make it divisible by 9 ?
Options: a ) 1 , b ) 17 , c ) 18 , d ) 77 , e ) 26
Rationale: "answer : 1 option : a"
Answer: a
Question (general): let c be defined as the sum of all prime numbers between 0 and 28 . what is c / 3
Options: a ) 155 , b ) 100 / 3 , c ) 61 , d ) 47 , e ) 43
Rationale: "prime numbers between 0 and 30 - 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 sum , c = 100 c / 3 = 11 / 3 answer b"
Answer: b
Question (general): we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value e of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "e - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Question (geometry): how many books each of volume 100 meter cube can be packed into a crate of volume 4000 meter cube ?
Options: a ) 100
b ) 120
c ) can not be determined
d ) 180
e ) 200
Rationale: gud question with a simple concept . in geo if we want to insert one shape into another we need to know the dimensions of the two shapes . in above with volume given , we can come up with different shapes , so we cant know the answer for ex : 4000 m 3 can be 400 * 10 or 40 * 100 or just 4000 * 1 we do n ' t know , so we cant calculate answer : c
Answer: c
Question (general): jane started baby - sitting when she was 20 years old . whenever she baby - sat for a child , that child was no more than half her age at the time . jane is currently 32 years old , and she stopped baby - sitting 10 years ago . what is the current age of the oldest person for whom jane could have baby - sat ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: check two extreme cases : jane = 20 , child = 10 , years ago = 32 - 20 = 12 - - > child ' s age now = 10 + 12 = 22 ; jane = 22 , child = 11 , years ago = 32 - 22 = 10 - - > child ' s age now = 11 + 10 = 21 . answer : c .
Answer: c
Question (general): if integer k is equal to the sum of all even multiples of 25 between 295 and 615 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: if we break down what the stem is asking what is the sum of all mult of 50 between 300 and 600 . using arithmetic progression to find n : 600 = 300 + ( n - 1 ) 50 300 + 50 = 50 n 350 = 50 n = > n = 7 the sum would be : 11 * mean mean = [ 600 + 300 ] / 2 = 450 7 * 450 = 4950 b
Answer: b
Question (gain): sonika deposited rs . 8000 which amounted to rs . 9200 after 3 years at simple interest . had the interest been 2 % more . she would get how much ?
Options: a ) 9680 , b ) 4280 , c ) 2789 , d ) 7892 , e ) 2792
Rationale: "( 8000 * 3 * 2 ) / 100 = 480 9200 - - - - - - - - 9680 answer : a"
Answer: a
Question (general): a certain city with a population of 60,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district what is the minimum possible population that the least populated district could have ?
Options: a ) a ) 10,700 , b ) b ) 10,800 , c ) c ) 10,900 , d ) d ) 11,000 , e ) e ) 5,000
Rationale: "let x = number of people in smallest district x * 1.1 = number of people in largest district x will be minimised when the number of people in largest district is maximised 10 * x * 1.1 = 11 x = total number of people in other districts so we have 11 x + x = 60 k x = 5,000 answer : e"
Answer: e
Question (geometry): the perimeter of a rectangular yard is completely surrounded by a fence that measures 10 meters . what is the length of the yard if the area of the yard is 6 meters squared ?
Options: a ) 8 , b ) 1 , c ) 5 , d ) 7 , e ) 3
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 10 - - > l + b = 5 area = l * b = 6 b = 5 - l l ( 5 - l ) = 6 5 l - l ^ 2 = 6 l ^ 2 - 5 l + 6 = 0 upon simplifying we get l = 2 or 3 . only 3 is there in the answer choice . answer : e"
Answer: e
Question (physics): how long does a train 150 m long traveling at 50 kmph takes to cross a bridge of 250 m in length ?
Options: a ) 28.8 sec , b ) 16.8 sec , c ) 15.2 sec , d ) 25.4 sec , e ) 16.2 sec
Rationale: "d = 150 + 250 = 400 m s = 50 * 5 / 18 = 125 / 9 t = 400 * 125 / 9 = 28.8 sec answer : a"
Answer: a
Question (other): if 7 and 6 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 7 * 6 should be integer = > 2 * 2 * 3 * 5 * n / 7 * 2 * 3 = 2 * 5 * n / 7 must be an integer for this to be true n must multiple of 7 , thus min of n = 7 hence c"
Answer: c
Question (physics): a train 50 m long passes a platform 100 m long in 10 seconds . the speed of the train in m / sec is ?
Options: a ) 150 , b ) 50 , c ) 10 , d ) 15 , e ) 12
Rationale: speed of train = distance covered / time . = ( 50 + 100 ) / 10 = 15 m / sec . answer : d
Answer: d
Question (gain): how many liters of water must be evaporated from 50 liters of a 4 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 30 , b ) 32 , c ) 34 , d ) 36 , e ) 38
Rationale: "4 % of a 50 liter solution is 2 l which is 10 % of the solution at the end . the solution at the end must be 20 l . we need to evaporate 30 liters . the answer is a ."
Answer: a
Question (other): in a class of 70 students , 10 did not opt for math . 5 did not opt for science and 3 did not opt for either . how many students of the class opted for both math and science ?
Options: a ) 23 , b ) 25 , c ) 27 , d ) 37 , e ) 38
Rationale: "70 students total 10 did not opt for math 5 did not opt for science 3 did not opt for either total of 40 students in math and 2 did not opt for sci but did for math 40 - 2 = 38 38 students of the class opted for both math and science answer : e"
Answer: e
Question (general): 562 ã — 99 = ?
Options: a ) 55684 , b ) 55432 , c ) 55638 , d ) 44530 , e ) 44538
Rationale: "562 ã — ( 100 - 1 ) 56200 - 562 = 55638 answer c"
Answer: c
Question (gain): the sale price sarees listed for rs . 550 after successive discount is 18 % and 12 % is ?
Options: a ) 298 , b ) 237 , c ) 342 , d ) 396 , e ) 291
Rationale: "550 * ( 88 / 100 ) * ( 82 / 100 ) = 396 answer : d"
Answer: d
Question (gain): an empty wooden vessel weighs 12 % of its total weight when filled with paint . if the weight of a partially filled vessel is one half that of a completely filled vessel , what fraction of the vessel is filled .
Options: a ) 3 / 5 , b ) 5 / 11 , c ) 1 / 24 , d ) 4 / 9 , e ) 2 / 5
Rationale: "an empty wooden vessel weighs 12 % of its total weight when filled with paint : vessel = 0.12 ( vessel + paint ) ; 12 v = v + p ( so the weight of completely filled vessel is 12 v ) p = 11 v ( so the weight of the paint when the vessels is completely filled is 11 v ) . the weight of a partially filled vessel is one half that of a completely filled vessel : v + p ' = 1 / 2 * 12 v ; p ' = 5 v ( so the weight of the paint when the vessels is partially filled is 5 v ) . what fraction of the vessel is filled ? so , we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled : p ' / p = 5 v / 11 v = 5 / 11 . answer : b ."
Answer: b
Question (gain): a side of beef lost 50 percent of its weight in processing . if the side of beef weighed 750 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 840 , e ) 1,500
Rationale: "let weight of side of beef before processing = x ( 50 / 100 ) * x = 750 = > x = ( 750 * 100 ) / 50 = 1500 answer e"
Answer: e
Question (general): 50 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 70 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 50 % of companies which offer wireless internet also offer snacks . the answer is d ."
Answer: d
Question (physics): a work which could be finished in 12 days was finished 3 days earlier after 10 more men joined . the number of men employed was ?
Options: a ) 22 , b ) 20 , c ) 88 , d ) 71 , e ) 10
Rationale: x - - - - - - - 12 ( x + 10 ) - - - - 6 x * 12 = ( x + 10 ) 6 x = 10 \ answer : e
Answer: e
Question (gain): a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 23 per kg , then his gain percent is
Options: a ) 12 % , b ) 23 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 23 ) = rs . 184 . profit = 184 - 150 = 34 so , profit % = ( 34 / 150 ) * 100 = 23 % option b
Answer: b
Question (physics): a can run 4 times as fast as b and gives b a start of 69 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 92 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 69 m he gains 69 * ( 4 / 3 ) i . e 92 m answer : e"
Answer: e
Question (general): a car travels uphill at 30 km / hr and downhill at 40 km / hr . it goes 100 km uphill and 50 km downhill . find the average speed of the car ?
Options: a ) 32 kmph , b ) 33 kmph , c ) 34 kmph , d ) 35 kmph , e ) 36 kmph
Rationale: "avg speed = total distance / total time . total distance traveled = 100 + 50 = 150 km ; time taken for uphill journey = 100 / 30 = 10 / 3 ; time taken for down hill journey = 50 / 40 = 5 / 4 ; avg speed = 150 / ( 10 / 3 + 5 / 4 ) = 33 kmph answer : b"
Answer: b
Question (general): the price of a bushel of corn is currently $ 3.20 , and the price of a peck of wheat is $ 7.80 . the price of corn is increasing at a constant rate of 5 x cents per day while the price of wheat is decreasing at a constant rate of x ( 2 ^ 1 / 2 ) - x cents per day . what is the approximate price when a bushel of corn costs the same amount as a peck of wheat ?
Options: a ) $ 4.50 , b ) $ 5.10 , c ) $ 5.30 , d ) $ 7.50 , e ) $ 5.60
Rationale: "i tried using time / rate approach : - initial price difference = 7.80 - 3.20 = 4.60 price of corn increasing by 5 x price of wheat decreasing by x ( 1.4 ) - x = . 4 x since both the quantities are moving towards reducing the price gap hence : - relative increase = 5 x + . 4 x let t be the time by which gap is filled so , 4.6 = t ( 5.4 x ) - > t = ( 4.6 ) / 5.4 x final price = 3.20 + 5 x * t - > 3.20 + 5 * 4.6 / 5.4 = 7.5 answer d ."
Answer: d
Question (general): a person saved $ 10 in buying an item on sale . if he spent $ 400 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 2.4 % , e ) 6 %
Rationale: "actual price = 400 + 10 = $ 410 saving = 10 / 410 * 100 = 100 / 41 = 2.4 % approximately answer is d"
Answer: d
Question (geometry): the diagonals of the two squares are in the ratio of 7 : 9 find the ratio of their area
Options: a ) 78 : 89
b ) 5 : 48
c ) 49 : 81
d ) 74 : 36
e ) 25 : 49
Rationale: let the diagonals of the square be 7 x and 9 x respectively . ratio of their areas = 1 / 2 ( 7 x ) ^ 2 : 1 / 2 ( 9 x ) = 49 x ^ 2 : 81 x ^ 2 = 49 : 81 answer ( c )
Answer: c
Question (gain): in a certain parking lot , 10 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 10 % * x = 20 % * y y / x = 1 / 2 = 50 % the answer is c ."
Answer: c
Question (general): for what value of â € œ k â €  will the equation ( 2 kx 2 + 7 kx + 2 ) = 0 have equal roots ?
Options: a ) 2 / 7 , b ) 16 / 49 , c ) 16 / 25 , d ) 7 / 1 , e ) 7 / 2
Rationale: "for a 2 nd degree equation ax 2 + bx _ c = 0 has equal roots the condition is b 2 - 4 ac = 0 in the given equation ( 7 k ) ^ 2 - 4 * 2 k * 2 = 0 by solving this equation we get k = 0 , k = 16 / 49 answer : b"
Answer: b
Question (general): in how many ways can 5 different rings be worn in 4 particular fingers ? ( some fingers may get more than one ring and some may get no rings . ) can somebody explain ?
Options: a ) 6720 , b ) 7720 , c ) 7820 , d ) 7950 , e ) 8120
Rationale: first ring can be worn in 4 ways ( on any of the four fingers ) ; second ring can be worn in 5 ways ( as it can go on any of four fingers - 4 ways ; plus it can go below the first one - 1 ) ; third ring can be worn in 6 ways ( the same logic as for the second ring ) ; fourth ring can be worn in 7 ways ; fifth ring can be worn in 8 ways ; total : 4 * 5 * 6 * 7 * 8 = 6720 . ans : a
Answer: a
Question (other): bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 50 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 6 , e ) 8
Rationale: 6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 50 = 6 k + 4 k = > k = 5 total red ' s in bag a will be 2 k = 10 b
Answer: b
Question (general): a box contains 6 pairs of shoes ( 12 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 11 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: the problem with your solution is that we do n ' t choose 1 shoe from 12 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 11 as after taking one at random there are 11 shoes left and only one is the pair of the first one ) = 1 / 11 answer : a .
Answer: a
Question (other): the number of stamps that kaye and alberto had were in the ration of 5 : 3 respectively . after kaye gave alberto 12 of her stamps , the ration of the number of kaye had to the number of alberto had was 8 : 6 . as a result of the gift , kaye had how many more stamps than alberto ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 32 , e ) 90
Rationale: c k 1 = 5 x a 1 = 3 x k 2 = 5 x - 12 a 2 = 3 x + 12 k 2 / a 2 = 8 / 6 ( 5 x - 12 ) / ( 3 x + 12 ) = 8 / 6 6 * ( 5 x - 12 ) = 8 * ( 3 x + 12 ) 30 x - 72 = 24 x + 96 6 x = 168 x = 28 k 2 = 5 * 28 - 12 = 128 a 2 = 3 * 28 + 12 = 96 k 2 - a 2 = 32 answer : d
Answer: d
Question (gain): you hold some gold in a vault as an investment . over the past year the price of gold increases by 30 % . in order to keep your gold in the vault , you must pay 2 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 27.5 % , b ) 27.4 % , c ) 27.6 % , d ) 27.7 % , e ) 28.4 %
Rationale: "( 100 % + 30 % ) * ( 100 % - 2 % ) = 130 * 0.98 = 127.4 % an increase of 27.4 % your gold holdings have increased in value by 27.4 % . the answer is b"
Answer: b
Question (general): a number x is 11 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 90.9 , c ) 91.7 , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 11 . then y = 1 is less than x = 11 by ( 11 - 1 ) / 11 * 100 = 10 / 11 * 100 = 90.9 % . answer : b ."
Answer: b
Question (general): ravi ' s 4 days average income is 1025.68 . but in a form he should write his average income as the greatest positive even integer less than or equal to his 4 days average income . what is the difference between his real average and form filling average ?
Options: a ) 2 , b ) 4.3 , c ) 1.68 , d ) 1.5 , e ) 3.2
Rationale: since ravi ' s 4 days average income for form filling is defined as the greatest positive even integer less than or equal to his avg income , then avg income for form filling = 1024 ( the greatest positive even integer less than or equal to 1025.68 is 1024 ) . hence the difference = 1025.68 - 1024 = 1.68 answer : c .
Answer: c
Question (general): roy was suffering from severe headaches . he went to see his doctor and the doctor gave him 5 tablets asking him to take one tablet every 15 minutes . how much time will it take roy to consume all the 5 tablets ?
Options: a ) 60 min , b ) 50 min , c ) 70 min , d ) 65 min , e ) 80 min
Rationale: a 60 min roy will be able to consume all the five tablets in an hour . tablet 1 will be taken in 0 min . tablet 2 will be taken in 15 min . tablet 3 will be taken in 30 min . tablet 4 will be taken in 45 min . tablet 5 will be taken in 60 min .
Answer: a
Question (general): if one root of the equation 2 x ^ 2 + 3 x – k = 0 is 7 , what is the value of k ?
Options: a ) 100 , b ) 110 , c ) 119 , d ) 120 , e ) 112
Rationale: we just enter this root into the equation in order to recieve an equation to find the answer ! 2 * 7 ^ 2 + 3 * 7 - k = 0 k = 98 + 21 = 119 the answer is c
Answer: c
Question (gain): what will be the compound interest on a sum of rs . 24,500 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 9920.736 , b ) s . 10823.20 , c ) s . 10123.20 , d ) s . 10123.29 , e ) s . 10123.28
Rationale: "explanation : amount = [ 24500 * ( 1 + 12 / 100 ) 3 ] = 24500 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 35123.20 c . i . = ( 34420.74 - 24500 ) = rs . 9920.736 answer : a"
Answer: a
Question (other): at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 14 th highest price and the 21 st lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 33 , b ) 34 , c ) 35 , d ) 36 , e ) 37
Rationale: there were 13 items sold at a higher price than the radio and 20 items sold at a lower price than the radio . including the radio , there were 13 + 20 + 1 = 34 items sold . the answer is b .
Answer: b
Question (physics): what distance will be covered by a city bus moving at 72 kmph in 30 seconds ?
Options: a ) 200 m , b ) 300 m , c ) 600 m , d ) 500 m , e ) 400 m
Rationale: 72 kmph = 72 * 5 / 18 = 20 mps dist = speed * time = 20 * 30 = 600 m . answer c
Answer: c
Question (other): the cost of 3 pens and 5 pencils is rs . 260 . also the cost of one pen and one pencil is in the ratio of 5 : 1 respectively . what is the cost of one dozen pens ?
Options: a ) rs . 200 , b ) rs . 250 , c ) rs . 300 , d ) rs . 780 , e ) none of these
Rationale: explanation : let the cost of one pen is ‘ 5 x ’ and pencil is ‘ x ’ 3 x 5 x + 5 x = rs . 260 15 x + 5 x = rs . 260 x = 260 / 20 = 13 : . cost of 1 pen = 5 x = 5 x 13 = 65 : . cost of 12 pens , i . e . ( one dozen ) = 65 x 12 = rs . 780 answer : option d
Answer: d
Question (general): in a certain archery competition , points were awarded as follows : the first place winner receives 11 points , the second place winner receives 7 points , the third place winner receives 5 points and the fourth place winner receives 2 points . no other points are awarded . john participated several times in the competition and finished first , second , third , or fourth each time . the product of all the points he received was 107800 . how many times did he participate in the competition ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "107800 = 2 * 2 * 2 * 5 * 5 * 7 * 7 * 11 john participated 8 times . the answer is e ."
Answer: e
Question (gain): according to a recent student poll , 4 / 5 out of 25 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 29 / 30 , b ) 4 / 49 , c ) 2 / 7 , d ) 45 / 49 , e ) 13 / 14
Rationale: "20 students are interested , 5 are not interested prob = 1 - 5 c 2 / 25 c 2 = 1 - ( 5 * 4 / ( 25 * 24 ) ) = 1 - 1 / 30 = 29 / 30 answer : a"
Answer: a
Question (geometry): one side of a rectangular field is 16 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100 , b ) 120 , c ) 91.2 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 17 ) 2 - ( 16 ) 2 = √ 289 - 256 = √ 33 = 5.7 m . ∴ area = ( 16 x 5.7 ) m 2 = 91.2 m 2 . answer c"
Answer: c
Question (general): a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 11 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 72 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 23
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 11 seconds . thus x = 1 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 23 seconds . answer e"
Answer: e
Question (general): - 24 x 29 + 36 = ?
Options: a ) 2436 , b ) 2801 , c ) - 2801 , d ) - 660 , e ) none of them
Rationale: "given exp . = - 24 x ( 30 - 1 ) + 36 = - ( 24 x 30 ) + 24 + 36 = - 720 + 60 = - 660 answer is d"
Answer: d
Question (gain): an alloy weighing 20 ounces is 70 percent gold . how many ounces of pure gold must be added to create an alloy that is 70 percent gold ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 24 , e ) 48
Rationale: "in 24 ounces , gold is 20 * ( 70 / 100 ) = 14 ounces . now we add x ounces of pure gold to make it 90 % gold . so 14 + x = ( 24 + x ) * 70 / 100 = > x = 9 . answer is b ."
Answer: b
Question (physics): a can do a piece of work in 10 days . he works at it for 4 days and then b finishes it in 9 days . in how many days can a and b together finish the work ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 4 , e ) 1
Rationale: "4 / 10 + 9 / x = 1 = > x = 15 1 / 10 + 1 / 15 = 1 / 6 = > 6 days answer : a"
Answer: a