Cheukting/mathqa huggingface dataset:
Question (general): in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 81 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8100 , c ) 6000 , d ) 5000 , e ) 4000
Rationale: state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 81 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 81 = > total appeared candidates in state b = 81 x 100 = 8100 = > total appeared candidates in state a = total appeared candidates in state b = 8100
Answer: b
Question (other): find the compound ratio of ( 3 : 2 ) , ( 4 : 3 ) and ( 1 : 4 ) is
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 3 : 2
Rationale: "required ratio = 3 / 2 * 4 / 3 * 1 / 4 = 1 / 2 = 1 : 2 answer is a"
Answer: a
Question (general): a ( 5 , w ^ 2 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 11 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9 .
Rationale: "y = x ^ 2 + 11 w ^ 2 = 5 ^ 2 + 11 w ^ 2 = 36 w = 6 answer d"
Answer: d
Question (general): how many positive integers less than 5,000 are evenly divisible by neither 16 nor 21 ?
Options: a ) 4,514 , b ) 4,475 , c ) 4,521 , d ) 4,428 , e ) 4,349
Rationale: "integers less than 5000 divisible by 16 5000 / 16 = 333 . something , so 333 integers less than 5000 divisible by 21 5000 / 21 = 238 . # # , so 238 we have double counted some , so take lcm of 16 and 21 = 105 and divide by 5000 , we get 47 . so all numbers divisible by 16 and 21 = 333 + 238 - 47 = 524 now subtract that from 4999 . 4999 - 524 = 4514 answer a ."
Answer: a
Question (physics): a girl walks at a speed of 5 kmph . how much time does he take to walk a distance of 30 km ?
Options: a ) 10 hrs , b ) 2 hrs , c ) 3 hrs , d ) 5 hrs , e ) 6 hrs
Rationale: time = distance / speed = 30 / 5 = 6 hours . answer is e
Answer: e
Question (general): a man â € ™ s current age is ( 2 / 5 ) of the age of his father . after 10 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: "let , father â € ™ s current age is a years . then , man â € ™ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 10 ] = ( 1 / 2 ) ( a + 10 ) 2 ( 2 a + 50 ) = 5 ( a + 10 ) a = 50 d"
Answer: d
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 34 ?
Options: a ) 3 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "n = 5 p + 1 = 6,11 , 16,21 , 26,31 n = 7 q + 3 = 3 , 10,17 , 24,31 = > n = 34 m + 31 to get this , we need to take lcm of co - efficients of p and q and first common number in series . so we need to add 3 more to make it 34 m + 34 answer - a"
Answer: a
Question (general): a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4 . the number of wickets taken by him till the last match was :
Options: a ) 64 , b ) 72 , c ) 80 , d ) 85 , e ) none of the above
Rationale: "let the number of wickets taken till the last match be x . then , 12.4 x + 26 / x + 5 = 12 ⇒ 12.4 x + 26 = 12 x + 60 ⇒ 0.4 x = 34 ⇒ x = 34 ⁄ 0.4 = 340 ⁄ 4 = 85 . answer d"
Answer: d
Question (physics): working together , tim and tom can type 12 pages in one hour . if they would be able to type 14 pages in one hour if tom increases his typing speed by 25 % , what is the ratio of tom ' s normal typing speed to that of tim ?
Options: a ) 2 / 1 , b ) 1 / 2 , c ) 1 / 3 , d ) 4 / 1 , e ) 1 / 4
Rationale: "lets say tim types x pages an hour and tom types y pages an hour . we know that x + y = 12 tom increase speed by 25 % means he will type 1.25 y pages an hour . so we get x + 1.25 y = 14 we need to know the ratio of tom ' s speed to tim ' s speed . this is going to be proportional to the number of pages each can type in an hour , hence ( y / x ) . subtracting both : 0.25 y = 2 so y = 8 . . . so x = 4 ( y / x ) = 8 / 4 = 2 / 1 answer is ( a )"
Answer: a
Question (general): in a bus left side are 15 seats available , 3 few seats in right side because in rear exit door . each seat hold 3 people . in addition , there is a seat back can sit 9 people all together . how many people can sit in a bus ?
Options: a ) 52 , b ) 49 , c ) 95 , d ) 90 , e ) 66
Rationale: "right side = 15 seat left side = 15 - 3 ( 3 few seat in right side ) = 12 seat total = 15 + 12 = 27 people can seat in 27 seat = 27 * 3 = 81 people can seat in last seat = 9 total people can seat = 81 + 9 = 90 answer : d"
Answer: d
Question (general): the average of temperatures at noontime from monday to friday is 25 ; the lowest one is 15 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 50 , d ) 45 , e ) 75
Rationale: average = 25 , sum of temperatures = 25 * 5 = 125 as the min temperature is 15 , max would be 125 - 4 * 15 = 65 - - > the range = 65 ( max ) - 15 ( min ) = 50 answer : c
Answer: c
Question (gain): what will be the compound interest on a sum of rs . 27,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s . 10123.77 , b ) s . 10123.21 , c ) s . 10933.05 , d ) s . 10123.28 , e ) s . 10123.21
Rationale: "amount = [ 27000 * ( 1 + 12 / 100 ) 3 ] = 27000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 37933.0 c . i . = ( 37933.056 - 27000 ) = rs . 10933.05 answer : c"
Answer: c
Question (gain): a merchant marks goods up by 75 % and then offers a discount on the marked price . the profit that the merchant makes after offering the discount is 22.5 % . what % discount did the merchant offer ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: let p be the original price of the goods and let x be the rate after the markup . ( 1.75 p ) * x = 1.225 p x = 1.225 / 1.75 = 0.7 which is a discount of 30 % . the answer is c .
Answer: c
Question (general): a , b and c rents a pasture for rs . 1130 . 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 ) 199 , c ) 351 , d ) 156 , e ) 122
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 1130 = 351 answer : c"
Answer: c
Question (general): how many multiples of 2 are there between 1 and 54 , exclusive ?
Options: a ) 21 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "26 multiples of 2 between 1 and 54 exclusive . from 2 * 1 upto 2 * 26 , ( 1,2 , 3,4 , . . . , 26 ) . hence , 26 multiples ! correct option is d"
Answer: d
Question (gain): at what rate percent per annum will a sum of money double in 2 years .
Options: a ) 34 % , b ) 50 % , c ) 11.5 % , d ) 20 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 2 ) ] % = 50 % per annum . answer : b"
Answer: b
Question (physics): the sum of 2 consecutive numbers is definitely :
Options: a ) positive . , b ) divisible by 2 . , c ) divisible by 3 . , d ) divisible by 4 . , e ) divisible by 5 .
Rationale: "if 1 st term is x : x + ( x + 1 ) = 2 x + 1 - - - > positive if 2 nd term is x : ( x - 1 ) + x = 2 x - 1 - - - > positive a"
Answer: a
Question (geometry): four concentric circles r given . the radius of 1 st circle is x . next is 2 x , then 3 x and 4 x . given that area b / w 2 nd and 1 st is a and 4 th and 3 rd circles being b . find ratio of a to b
Options: a ) 2 : 7
b ) 1 : 7
c ) 3 : 5
d ) 3 : 7
e ) 3 : 4
Rationale: area of first circle = pi * ( x ) ^ 2 = pi * x ^ 2 area of second circle = pi * ( 2 x ) ^ 2 = 4 * pi * x ^ 2 area of third circle = pi * ( 3 x ) ^ 2 = 9 * pi * x ^ 2 area of fourth circle = pi * ( 4 x ) ^ 2 = 16 * pi * x ^ 2 area b / w 1 st and 2 nd circles = 3 * pi * x ^ 2 area b / w 3 rd and 4 th circles = 7 * pi * x ^ 2 so ratio = 3 : 7 answer : d
Answer: d
Question (general): a grocery shop has a sale of rs . 6335 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 5091 , e ) 5291
Rationale: "let the sale in the sixth month = x then ( 6335 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6335 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 33909 + x = 39000 = > x = 39000 − 33909 = 5091 answer : d"
Answer: d
Question (physics): two numbers have a h . c . f of 9 and a product of two numbers is 1800 . find the l . c . m of the two numbers ?
Options: a ) 200 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "l . c . m of two numbers is given by ( product of the two numbers ) / ( h . c . f of the two numbers ) = 1800 / 9 = 200 . answer : a"
Answer: a
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 4 eggs . if the cost of each pound of rice is $ 0.33 , then how many cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.22 , b ) 0.44 , c ) 0.55 , d ) 22 , e ) 55
Rationale: a dozen eggs cost as much as a pound of rice - - > 12 eggs = 1 pound of rice = 33 cents ; a half - liter of kerosene costs as much as 8 eggs - - > 4 eggs = 1 / 2 liters of kerosene . how many cents does a liter of kerosene cost - - > 1 liter of kerosene = 8 eggs = 8 / 12 * 33 = 22 cents . answer : d .
Answer: d
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 14000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 28
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 14000 x 7 ) + 6000 ( x - 7 ) x = 28 . answer e"
Answer: e
Question (gain): a man buys rs . 48 shares paying 9 % dividend . the man wants to have an interest of 12 % on his money . the market value of each share is :
Options: a ) s . 12 , b ) s . 15 , c ) s . 18 , d ) s . 21 , e ) s . 36
Rationale: "dividend on rs . 48 = rs . 9 / 100 x 48 = rs . 4.32 . rs . 12 is an income on rs . 100 . rs . 4.32 is an income on rs . 100 / 12 x 4.32 = rs . 36 . answer : option e"
Answer: e
Question (physics): a can do a piece of work in 20 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 18 , b ) 77 , c ) 66 , d ) 55 , e ) 10
Rationale: "8 / 20 + 6 / x = 1 x = 10 days answer : e"
Answer: e
Question (other): the ratio of three numbers is 3 : 4 : 5 and the sum of their squares is 1250 . the sum of the numbers is :
Options: a ) 30 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let the numbers be 3 x , 4 x and 5 x then , 9 x 2 + 16 x 2 + 25 x 2 = 1250 50 x 2 = 1250 x = 5 sum of numbers = 3 x + 4 x + 5 x = 12 x = 60 answer c 60"
Answer: c
Question (general): elena ’ s bread recipe calls for 8 ounces of butter for each 14 cups of flour used . she needs to make 4 times the original recipe . if 12 ounces of butter is used , then how many cups of flour are needed ?
Options: a ) 1 , b ) 4 , c ) 9 , d ) 13 , e ) 56
Rationale: "solving through algebra route : 8 b + 14 f = x amount if we multiply this equation with 4 we get : 32 b + 56 f = 4 x therefore , we got 32 ounces of butter and 4 x amount of quantity when we use 56 ounces of floor . ans : e"
Answer: e
Question (other): solution a is 20 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: "let : x = ounces taken from solution a ( 20 % salt ) y = ounces taken from solution b ( 80 % salt ) to prepare 50 ounce 50 % salt . first equation is simple : x + y = 50 to get another equation so as to be able to solve , compute salt contents . 20 % of x + 80 % of y = 50 % of 50 or x / 5 + 4 / 5 * y = 25 or x + 4 y = 125 solve two equations to get : x = 25 y = 25 so solutions has to mix in 1 : 1 oops 4 : 4 answer : c"
Answer: c
Question (physics): a man can row at 6 kmph in still water . if the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 2.6 km , c ) 2.9 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 6 kmph speed of the current = 1 kmph speed downstream = ( 6 + 1 ) = 7 kmph speed upstream = ( 6 - 1 ) = 5 kmph let the required distance be x km total time taken = 1 hour â ‡ ’ x / 7 + x / 5 = 1 â ‡ ’ 5 x + 7 x = 35 â ‡ ’ 12 x = 35 â ‡ ’ x = 2.9 km answer : option c"
Answer: c
Question (general): 5 kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ?
Options: a ) 30 , b ) 25 , c ) 15 , d ) 10 , e ) 5
Rationale: five kilograms of oranges contained 95 % of water . if the next day the concentration of water decreased by 5 % , what was the new weight of the oranges , in kilograms ? ( a ) 30 ( b ) 25 ( c ) 15 ( d ) 10 ( e ) 5 if b is the answer , then the question means that the concentration of water the newt day became 90 % . out of 5 kilograms 95 % , or 4.75 kilograms was water and 0.25 kilograms was non - water . the next day , after some water evaporated , oranges became 90 % water and 10 % of non - water , so the next day 0.25 kilograms of non - water composed 10 % of oranges , which means that the new weight of the oranges was x * 0.10 = 0.25 - - > x = 25 kilograms . answer : b .
Answer: b
Question (general): the mean of 20 values was 150 . it was detected on rechecking that one value 160 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 149 , c ) 151.25 , d ) 148 , e ) none of the above
Rationale: corrected mean = 150 × 20 − 135 + 160 / 20 = 3000 − 135 + 160 / 20 = 3025 / 20 = 151.25 answer c
Answer: c
Question (gain): the present population of a town is 200 . population increase rate is 10 % p . a . find the population of town after 1 years ?
Options: a ) 100 , b ) 120 , c ) 200 , d ) 220 , e ) 250
Rationale: "p = 200 r = 10 % required population of town = p * ( 1 + r / 100 ) ^ t = 200 * ( 1 + 10 / 100 ) = 200 * ( 11 / 10 ) = 220 ( approximately ) answer is d"
Answer: d
Question (physics): at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 2 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 19 + 18 + 12 - 2 - 2 x 2 x = 19 + 18 + 12 - 2 - 39 = 45 - 37 = 8 x = 4 c"
Answer: c
Question (general): if n is a prime number greater than 7 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 7 , square it and see what would be the remainder upon division of it by 12 . n = 11 - - > n ^ 2 = 121 - - > remainder upon division 121 by 12 is 1 . answer : b ."
Answer: b
Question (physics): if sushi rows 27 km upstream and 81 km down steam taking 9 hours each , then the speed of the stream
Options: a ) 12 kmph , b ) 13 kmph , c ) 22 kmph , d ) 20 kmph , e ) 15 kmph
Rationale: speed upstream = 27 / 9 = 3 kmph speed down stream = 81 / 3 = 27 kmph speed of stream = ½ ( 27 - 3 ) = 12 kmph answer : a
Answer: a
Question (general): a rich aristocrat decided that he would give every man rs . 45 and every women rs . 60 . only one nineth of the man and only one twelfth of the women collected their dues . can u tell me how much money thath aristocrat spent if their were 3552 people in total
Options: a ) 17760 , b ) 18540 , c ) 16320 , d ) 14640 , e ) 15640
Rationale: iman = 45 and 1 women = 60 then 1 / 9 man = 1 / 9 * 45 = 5 and 1 / 12 of women = 1 / 12 * 60 = 5 total people 3552 = 3552 * 5 = 17760 answer : a
Answer: a
Question (physics): 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 8 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour slower than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 8 m / h - - > 4 m in 1 / 2 hr side 2 = 6 m / h - - > 3 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option a
Answer: a
Question (physics): a fill pipe can fill 1 / 3 of cistern in 20 minutes in how many minutes , it can fill 3 / 4 of the cistern ?
Options: a ) 15 min , b ) 45 min , c ) 25 min , d ) 40 min , e ) 50 min
Rationale: "1 / 3 of the cistern can fill in 20 min 3 / 4 of the cistern can fill in = 20 * 3 * 3 / 4 = 45 min answer is b"
Answer: b
Question (physics): the length of the bridge , which a train 145 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 230 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 145 + x ) / 30 = 25 / 2 = > 2 ( 145 + x ) = 750 = > x = 230 m . answer : c"
Answer: c
Question (geometry): a cube is divided into 125 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: "each side of the cube has 5 x 5 = 25 cubelets . only the interior cubelets are painted one colour . on each side , 3 x 3 = 9 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 9 = 54 the answer is d ."
Answer: d
Question (gain): indu gave bindu rs . 3750 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 4 , e ) 9
Rationale: "3750 = d ( 100 / 4 ) 2 d = 6 answer : c"
Answer: c
Question (general): for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 37 , the mean is how much greater than the median ?
Options: a ) 6 , b ) 1 , c ) 2 , d ) 4 , e ) 7
Rationale: "mean = ( x + x + 2 + x + 4 + x + 7 + x + 37 ) / 5 = ( 5 x + 50 ) / 5 = x + 10 median = x + 4 thus mean - median = x + 10 - ( x + 4 ) = 6 answer = a"
Answer: a
Question (general): the flow of water through a drainage pipe was monitored for a 3 - hour period . in the second hour , the rate of flow was 36 gallons per hour , which was 50 percent faster than the rate of flow for the first hour . if 25 percent more water flowed through the pipe in the third hour than it did in the second , how many gallons of water flowed through the pipe during the entire 3 hours ?
Options: a ) 106.25 , b ) 105.5 , c ) 105.75 , d ) 106 , e ) 105.0
Rationale: rate of flow of water in second hour = 36 gallons per hour rate of flow of water in first hour = 36 / ( 3 / 2 ) = 24 gallons per hour rate of flow of water in third hour = ( 125 / 100 ) * 36 = ( 5 / 4 ) * 36 = 45 gallons per hour number of gallons of water that flowed through the pipe during the entire 3 hours = 24 + 36 + 45 = 105 gallons answer e
Answer: e
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 330 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2200 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 330 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 330 x = ( 10 x 4 x 330 ) / ( 6 ) x = 2200 . answer : c"
Answer: c
Question (physics): if a light flashes every 6 seconds , how many times will it flash in 1 / 4 of an hour ?
Options: a ) 51 , b ) 151 , c ) 251 , d ) 351 , e ) 451
Rationale: "in 1 / 4 of an hour there are 15 * 60 = 900 seconds the number of 6 - second intervals = 900 / 6 = 150 after the first flash , there will be 150 more flashes for a total of 151 . the answer is b ."
Answer: b
Question (general): a sum of rs . 1360 has been divided among a , b and c such that a gets of what b gets and b gets of what c gets . b ’ s share is :
Options: a ) rs . 120 , b ) rs . 160 , c ) rs . 240 , d ) rs . 300 , e ) none
Rationale: "explanation let c ’ s share = rs . x then , b ’ s share = rs . x / 4 , a ’ s share = rs . ( 2 / 3 x x / 4 ) = rs . x / 6 = x / 6 + x / 4 + x = 13660 = > 17 x / 12 = 13660 = > 13660 x 12 / 17 = rs . 960 hence , b ’ s share = rs . ( 960 / 4 ) = rs . 240 . answer c"
Answer: c
Question (gain): find the compound interest on $ 20000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 1648.64 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 20000 rate = 2 % half yearly = 4 half years amount = 20000 * ( 1 + 2 / 100 ) ^ 4 = 20000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 21648.64 c . i . = 21648.64 - 20000 = $ 1648.64 answer is b"
Answer: b
Question (physics): 78 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 13 , c ) 26 , d ) 15 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 78 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 78 x 5 x 12 x = ( 78 x 5 x 12 ) / ( 30 x 6 ) x = 26 . answer : c"
Answer: c
Question (general): can you find a 6 digit number under 5 lakh such that the sum of it ' s digits is 43 ?
Options: a ) 588338 , b ) 499449 , c ) 399826 , d ) 788392 , e ) 622975
Rationale: b the required number is 499449 . the maximum sum of a number under 5 lakh will be of the number 499999 i . e . 49 . thus the required number must be close to 499999 . the root of 499999 ~ 707.106 by calculating the square of 707 , we get 499849 which is the answer .
Answer: b
Question (gain): a real estate agent received a 6 % commission on the selling price of a house . if his commission was $ 8880 , what was the selling price of the house ?
Options: a ) $ 234000 , b ) $ 227000 , c ) $ 148000 , d ) $ 479000 , e ) $ 337,000
Rationale: 6 % x = 8,880 : x = selling price of house . x = $ 148,000 : solve for x correct answer c .
Answer: c
Question (general): there is a total of 84 marbles in a box , each of which is red , green , blue , or white . if one marble is drawn from the box at random , the probability that it will be white is 1 / 4 and the probability that it will be green is 2 / 7 . what is the probability that the marble will be either red or blue ?
Options: a ) 3 / 7 , b ) 11 / 14 , c ) 13 / 28 , d ) 19 / 28 , e ) 29 / 42
Rationale: p ( red or blue ) = 1 - p ( white ) - p ( green ) = 28 / 28 - 7 / 28 - 8 / 28 = 13 / 28 the answer is c .
Answer: c