Cheukting/mathqa huggingface dataset:
Question (general): each week , harry is paid x dollars per hour for the first 21 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "42 x = 21 x + 1.5 x ( h - 21 ) = = > 42 = 21 + 1.5 ( h - 21 ) = = > h - 21 = 21 / 1.5 = 14 = > h = 35 answer is a"
Answer: a
Question (geometry): the volume of a cube is 729 cc . find its surface .
Options: a ) 486 , b ) 556 , c ) 255 , d ) 287 , e ) 267
Rationale: "a 3 = 729 = > a = 9 6 a 2 = 6 * 9 * 9 = 486 answer : a"
Answer: a
Question (probability): a bag contains 4 white marbles and 4 black marbles . if each of 4 girls and 4 boys randomly selects and keeps a marble , what is the probability that all of the girls select the same colored marble ?
Options: a ) 1 / 35 , b ) 1 / 9 , c ) 1 / 10 , d ) 1 / 20 , e ) 1 / 30
Rationale: "first , total ways to select for all boys and girls , i . e 8 ! / ( 4 ! * 4 ! ) = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / 4 * 3 * 2 * 1 * 4 * 3 * 2 * 1 = 70 then there are one two way girls can have all same colors , either white or black . the number of ways in which 4 girls can select 4 white balls = 4 c 4 = 1 the number of ways in which 4 girls can select 4 black balls = 4 c 4 = 1 therefore , total favorable outcomes / total outcomes = 2 / 70 = 1 / 35 a"
Answer: a
Question (physics): a can knit a pair of socks in 3 days . b can knit the same thing in 6 days . if they are knitting together , in how many days will they knit two pairs of socks ?
Options: a ) 4 days , b ) 2 days , c ) 4 1 ⁄ 2 days , d ) 3 days , e ) none of these
Rationale: explanationa ’ s one day ’ s work = 1 ⁄ 3 rd work . b ’ s one day ’ s work = 1 ⁄ 6 rd work . ( a + b ) ’ s one day ’ s work = 1 ⁄ 3 + 1 ⁄ 6 = 1 ⁄ 2 nd work . ∴ a and b together can complete the work ( knit a pair of socks ) in 2 days . ∴ they together knit two pair of socks in 4 days . answer a
Answer: a
Question (gain): the difference between c . i . and s . i . on an amount of $ 20,000 for 2 years is $ 72 . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 9 %
Rationale: "$ 72 is the interest on the first year of interest . let x be the interest rate . the interest after the first year is 20000 * x . the interest on the first year ' s interest is 20000 * x * x 20000 * x ^ 2 = 72 x = 0.06 the answer is b ."
Answer: b
Question (general): running at their respective constant rates , machine x takes 6 days longer to produce w widgets than machine y . at these rates , if the two machines together produce 5 / 4 w widgets in 3 days , how many days would it take machine x alone to produce 2 w widgets ?
Options: a ) 8 , b ) 6 , c ) 4 , d ) 10 , e ) 12
Rationale: "together they make 5 / 4 w widgets in 3 days . so they make w widgets in 3 * 4 / 5 = 12 / 5 days . 1 / ( t + 2 ) + 1 / t = 5 / 12 now , calculating this is really cumbersome so try to plug in options to get to the answer . if machine x takes 12 days to produce 2 w widgets , it would take 6 days to make w widgets , t would be 4 . 1 / 6 + 1 / 4 = 5 / 12 it works so t = 4 . answer : a"
Answer: a
Question (general): find the ones digit of 73 ^ 353
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "the units digit of 73 ^ 353 will be the same as the units digit of 3 ^ 353 . 3 ^ 1 = 3 - - > the units digit is 3 ; 3 ^ 2 = 9 - - > the units digit is 9 ; 3 ^ 3 = 27 - - > the units digit is 7 ; 3 ^ 4 = 81 - - > the units digit is 1 ; 3 ^ 5 = 243 - - > the units digit is 3 again ; . . . so , as you can see the units digit repeats in blocks of 4 : { 3 , 9 , 7 , 1 } , { 3 , 9 , 7 , 1 } , . . . now , since 353 = 352 + 1 = ( multiple of 4 ) + 1 , then the units digit of 3 ^ 353 will be the first number in the pattern thus 3 . answer : a ."
Answer: a
Question (general): if 2 x + y = 26 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 26 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 36 divide both sides by 3 to get : x + y = 12 so , ( x + y ) / 3 = 12 / 3 = 4 answer : e"
Answer: e
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 16 per cubic meter ?
Options: a ) 2998 , b ) 2799 , c ) 2890 , d ) 1485 , e ) 1584
Rationale: "22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 16 = 1584 answer : e"
Answer: e
Question (general): alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1015 . find the cost of each ice - cream cup ?
Options: a ) 34 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1015 96 + 225 + 490 + 6 x = 1015 6 x = 204 = > x = 34 . answer : a"
Answer: a
Question (general): a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more thanc . out of a total profit of rs . 35000 , a receives :
Options: a ) 14700 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 35000 * 21 / 50 ) = rs . 14,700 . answer : a ) 14700
Answer: a
Question (gain): a certain car ' s price decreased by 2.5 % ( from the original price ) each year from 1996 to 2002 , during that time the owner of the car invested in a new carburetor and a new audio system for the car , which increased car ' s price by $ 2,000 . if the price of the car in 1996 was $ 22,000 , what is the car ' s price in 2002 ?
Options: a ) $ 18,400 , b ) $ 19,500 , c ) $ 20,200 , d ) $ 20,700 , e ) $ 21,100
Rationale: "price in 96 = 22000 price decrease each year = 2.5 / 100 * 22000 = 550 price in 97 = 22000 - 550 price in 98 = 22000 - 2 * 550 price in 99 = 22000 - 3 * 550 price in 00 = 22000 - 4 * 550 price in 01 = 22000 - 5 * 550 price in 02 = 22000 - 6 * 550 = 18700 investment in the car = 1500 net price of the car in 02 = 18700 + 2000 = $ 20700 correct option : d"
Answer: d
Question (physics): a , b and c can do a piece of work in 24 days , 30 days and 40 days respectively . they began the work together but c left 6 days before the completion of the work . in how many days was the work completed ?
Options: a ) 12 days , b ) 16 days , c ) 18 days , d ) 11.5 days , e ) 38 days
Rationale: "one day work of a , b and c = 1 / 24 + 1 / 30 + 1 / 40 = 1 / 10 work done by a and b together in the last 6 days = 6 * ( 1 / 24 + 1 / 30 ) = 9 / 20 remaining work = 11 / 20 the number of days required for this initial work = 5.5 days . the total number of days required = 6 + 5.5 = 11.5 days . answer : d"
Answer: d
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
Options: a ) $ 1200 , b ) $ 1300 , c ) $ 1400 , d ) $ 1800 , e ) $ 1900
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 300 . so 1 / 4 of her savings is $ 300 . so her original savings are 4 times $ 300 = $ 1200 correct answer a"
Answer: a
Question (gain): walking 7 / 6 of his usual rate , a boy reaches his school 6 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 42 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 6 - - - - - - - - - ? = 42 m answer : d"
Answer: d
Question (physics): a jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
Options: a ) 3.6 sec , b ) 18 sec , c ) 35 sec , d ) 72 sec , e ) none of these
Rationale: "speed of train relative to jogger = ( 45 – 9 ) km / h = 36 km / h = ( 36 × 5 ⁄ 18 ) m / sec = 10 m / sec distance to be covered = ( 230 + 120 ) m = 350 m . ∴ time taken = ( 350 ⁄ 10 ) sec = 35 sec . answer c"
Answer: c
Question (physics): a train covers a distance of 36 km in 12 min . if it takes 10 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 300 m , b ) 1000 m , c ) 120 m , d ) 200 m , e ) 500 m
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 10 = 500 m . answer : e"
Answer: e
Question (general): 8 people decided to split the restaurant bill evenly . if the bill was $ 214.18 dollars , how much money did they 1 cent is the smallest unit ?
Options: a ) $ 214.16 , b ) $ 214.17 , c ) $ 214.18 , d ) $ 214.19 , e ) $ 214.24
Rationale: "if the last three digits of a whole number are divisible by 8 , then the entire number is divisible by 8 the last 3 digit 418 not divisible by a hence , we need to add 6 to this number for it to be divisible by 8 correct option : e"
Answer: e
Question (physics): if 4 women can color 48 m long cloth in 2 days , then 6 women can color 36 m long cloth in
Options: a ) 2 days , b ) 3 days , c ) 1 day , d ) 4 days , e ) 5 days
Rationale: "the length of cloth painted by one woman in one day = 48 / 4 × 2 = 6 m no . of days required to paint 36 m cloth by 6 women = 36 / 6 × 6 = 1 day . c"
Answer: c
Question (geometry): a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of 4 cubic feet . if a large block has twice the width , twice the depth , and twice the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 16
b ) 20
c ) 36
d ) 32
e ) 28
Rationale: volume of cube = lbh = 4 new cube l , b , h are increases of 2 l , 2 b , 2 h new volume of cube = 2 l * 2 b * 2 h = 8 * lbh = 8 * 4 = 32 answer : d
Answer: d
Question (general): a man is 32 years older than his son . in six years , his age will be twice the age of his son . the present age of this son is
Options: a ) 26 years , b ) 27 years , c ) 28 years , d ) 29 years , e ) 30 years
Rationale: "explanation : let ' s son age is x , then father age is x + 32 . = > 2 ( x + 6 ) = ( x + 32 + 6 ) = > 2 x + 12 = x + 38 = > x = 26 years answer : option a"
Answer: a
Question (geometry): the monthly rent of a shop of dimension 20 feet × 18 feet is rs . 1440 . what is the annual rent per square foot of the shop ?
Options: a ) 48
b ) 56
c ) 68
d ) 87
e ) 92
Rationale: sol . monthly rent per square feet = 1440 / ( 20 * 18 ) = 4 & annual rent per square feet = 12 * 4 = 48 answer : a
Answer: a
Question (gain): ashley and betty start a business with $ 9000 each , and after 3 months , betty adds another $ 5000 . how should they share the profits at the end of the 24 months ?
Options: a ) 72 : 107 , b ) 4 : 5 , c ) 17 : 23 , d ) 3 : 4 , e ) 68 : 95
Rationale: ashley invests $ 9000 for 24 months , but betty invests $ 9000 for the first 3 months and then adds $ 5000 . so , the investment of betty for remaining 21 months is $ 14000 . ashley : betty 9000 * 24 : ( 9000 * 3 ) + ( 14000 * 21 ) 216000 : 321000 a : b = 72 : 107 answer : a
Answer: a
Question (general): in an examination , 25 % of total students failed in hindi , 50 % failed in english and 25 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 28 , d ) 40 , e ) 50
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 25 + 50 â € “ 25 = 50 therefore students who passed = 100 â € “ 50 = 50 . answer : e"
Answer: e
Question (geometry): the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 12 units ?
Options: a ) 140 sq . units , b ) 170 sq . units , c ) 190 sq . units , d ) 168 sq . units , e ) 149 sq . units
Rationale: "explanation : given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 12 units area of the rectangle = lb = 14 * 12 = 168 sq . units answer : option d"
Answer: d
Question (general): a pineapple costs rs 9 each and a watermelon costs rs . 6 each . if i spend rs 51 on total what is the number of pineapple i purchased ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 3 , e ) 2
Rationale: "5 * 9 + 6 = 51 5 pineapples answer : c"
Answer: c
Question (general): a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 4000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 34000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 4000 = > total profit = 4000 * 7 = 28000 . answer : option a"
Answer: a
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 26 years . what is deepak present age ?
Options: a ) 22 , b ) 15 , c ) 77 , d ) 266 , e ) 182
Rationale: "present age is 4 x and 3 x , = > 4 x + 6 = 26 = > x = 5 so deepak age is = 3 ( 5 ) = 15 answer : b"
Answer: b
Question (general): a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability j that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability j of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e .
Answer: e
Question (general): how many multiples of 7 are there between 14 and 343 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 44
Rationale: "7 * 2 = 14 7 * 49 = 343 total multiples = ( 49 - 2 ) + 1 = 48 exclude 7 343 = 48 - 2 = 46 answer is ( c )"
Answer: c
Question (physics): the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 10.8 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5 / 18 = 50 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 50 = 10.8 seconds . answer : c"
Answer: c
Question (geometry): find the cube root of 185193 .
Options: a ) 33 , b ) 57 , c ) 99 , d ) 17 , e ) 01
Rationale: "observe unit digit here is 3 so unit digit of the answer is 7 . now omit 193 . now find after which perfect cube 193 lies . it is 125 . so our tenth place is 5 . so answer is 57 . answer : b"
Answer: b
Question (physics): david and lewis leave chennai for hyderabad simultaneously at 8 p . m in the night driving in two cars at speeds of 50 mph and 70 mph respectively . as soon as lewis reaches hyderabad he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 350 miles , how far from chennai did david and lewis meet ?
Options: a ) 250 miles , b ) 240 miles , c ) 230 miles , d ) 235 miles , e ) 75 miles
Rationale: time taken by lewis to reach hyderabad = 350 / 70 = 5 hours in 5 hours , david travels 50 * 5 = 250 miles so distance at which they meet should be greater than 250 miles . only a satisfies . answer is a .
Answer: a
Question (other): divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e
Answer: e
Question (general): how many three digit numbers w are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples w - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Question (general): cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 5
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 4 ) / ( 10 - 5 ) = 1 / 5 so they should be mixed in the ratio 1 : 5 answer - e"
Answer: e
Question (general): what is the hcf of 2 / 3 , 4 / 9 and 6 / 18
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 1 / 9 , d ) 8 / 45 , e ) 9 / 45
Rationale: explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 18 ) = 2 / 18 = 1 / 9 answer : option c
Answer: c
Question (general): the mean proportional between 234 and 104 is
Options: a ) 12 , b ) 39 , c ) 54 , d ) 156 , e ) none
Rationale: "sol . required mean proportional = √ 234 x 104 = √ 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d"
Answer: d
Question (gain): a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 6.30 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 6.30 when c . p = ( 100 * 6.30 ) / 21 = 30 answer : a"
Answer: a
Question (general): a bus starts from city x . the number of women in the bus is half of the number of men . in city y , 16 men leave the bus and 8 women enter . now , number of men and women is equal . in the beginning , how many passengers entered the bus ?
Options: a ) 15 , b ) 30 , c ) 36 , d ) 72 , e ) 46
Rationale: explanation : originally , let number of women = x . then , number of men = 2 x . so , in city y , we have : ( 2 x - 16 ) = ( x + 8 ) or x = 24 . therefore total number of passengers in the beginning = ( x + 2 x ) = 3 x = 72 . answer : d
Answer: d
Question (physics): at tea factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at tea factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Question (gain): there are two concentric circles with radii 6 and 4 . if the radius of the outer circle is increased by 50 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 160 , b ) 210 , c ) 260 , d ) 310 , e ) 360
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 36 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 20 pi . when the big circle ' s radius increases , the new area is 81 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 72 pi . the ratio of a 2 / a 1 is 72 / 20 = 3.6 which is an increase of 260 % . the answer is c ."
Answer: c
Question (general): john works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 8 , b ) 1 / 7 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 6
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 6 x total tips for all months = 6 * x + 6 x = 12 x tips for august / total tips for all months = 6 x / 12 x = 1 / 2 answer : c
Answer: c
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 192,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,500 , d ) $ 2,050 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 192,000 / ( 8 * 10 * 12 ) = 200 one box costs 7.50 , so 200 box will cost = 200 * 7.5 = 1500 c is the answer"
Answer: c
Question (physics): x does a work in 15 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 11.25 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 45 ) = 1 / 11.25 both together will finish the work in 11.25 days . correct option is d"
Answer: d
Question (other): in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 75 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 3 : 2 = = 60 : 40 represents the number ratio of republicans : democrats . if 75 % of republicans ( which is ( 60 * 0.75 ) = 45 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 51 ( 45 + 6 ) voters voted for candidate x and 49 voted for candidate y . thus we can infer that candidate x is expected to win the election by 2 ( 51 - 49 ) votes . therefore candidate x is expected to win the election by ( 2 / 100 ) votes which is equivalent to 2 % . i think the answer is a ."
Answer: a