Cheukting/mathqa huggingface dataset:
Question (general): divide rs . 1500 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) 337 , b ) 299 , c ) 375 , d ) 662 , e ) 201
Rationale: "a + b + c = 1500 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1500 = > 375 answer : c"
Answer: c
Question (general): 80 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 28800 , b ) 24000 , c ) 24936 , d ) 25640 , e ) none
Rationale: "answer ∵ 80 % of p = 23040 ∴ p = ( 23040 x 100 ) / 80 = 28800 correct option : a"
Answer: a
Question (physics): a , b and c completed a piece of work , a worked for 6 days , b for 9 days and c for 4 days . their daily wages were in the ratio of 3 : 4 : 5 . find the daily wages of c , if their total earning was rs . 1702 ?
Options: a ) s . 109 , b ) s . 115 , c ) s . 100 , d ) s . 103 , e ) s . 102
Rationale: "3 x 4 x 5 x 6 9 4 18 x + 36 x + 20 x = 1702 74 x = 1702 = > x = 23 5 x = 115 rs . answer : b"
Answer: b
Question (physics): a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 18 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 7.5 , b ) 12.5 , c ) 17.5 , d ) 22.5 , e ) 27.5
Rationale: in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 18 = 1.5 km . the time it takes the hiker to complete this distance is 1.5 / 4 hours = 22.5 minutes the cyclist needs to wait 22.5 - 5 = 17.5 minutes the answer is c .
Answer: c
Question (physics): at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 45 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 40 km / h . if the distance between city p and city q is 300 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 30 , b ) 5 : 00 , c ) 5 : 30 , d ) 6 : 00 , e ) 6 : 30
Rationale: "at 2 : 00 pm , the truck and the car are 255 km apart . the truck and the car complete a distance of 85 km each hour . the time it takes to meet is 255 / 85 = 3 hours . they will meet at 5 : 00 pm . the answer is b ."
Answer: b
Question (physics): two cars are driving toward each other . the first car is traveling at a speed of 75 km / h , which is 25 % slower than the second car ' s speed . if the distance between the cars is 1050 km , how many hours will it take until the two cars meet ?
Options: a ) 4 , b ) 4.5 , c ) 5 , d ) 5.5 , e ) 6
Rationale: "the speed of the first car is 75 km / h . the speed of the second car is 75 / 0.75 = 100 km / h . the two cars complete a total of 175 km each hour . the time it takes the cars to meet is 1050 / 175 = 6 hours . the answer is e ."
Answer: e
Question (physics): an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 26 metre of cloth ?
Options: a ) 175 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 203 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 26 : x = > x = { \ color { blue } \ frac { 26 \ times 1 } { 0.128 } } = > x = 203.13 so time will be approx 203 seconds answer : e"
Answer: e
Question (other): in a class of 38 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 9 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 38 - 29 = 9 play neither answer is c"
Answer: c
Question (geometry): if the diameter of circle r is 80 % of the diameter of circle s , the area of circle r is what percent of the area of circle s ?
Options: a ) 74 % , b ) 64 % , c ) 84 % , d ) 94 % , e ) 34 %
Rationale: "let diameter of circle r , dr = 80 and diameter of circle s , ds = 100 radius of circle r , rr = 40 radius of circle s , rs = 50 area of circle r / area of circle s = ( pi * rr ^ 2 ) / ( pi * rs ^ 2 ) = ( 40 / 50 ) ^ 2 = ( 8 / 10 ) ^ 2 = 64 % answer : b"
Answer: b
Question (geometry): find the perimeter and area of a square of side 9 cm .
Options: a ) 36 , b ) 49 , c ) 64 , d ) 81 , e ) 100
Rationale: "we know that the perimeter of square = 4 ã — side side = 9 cm therefore , perimeter = 4 ã — 9 cm = 36 cm now , area of the square = ( side ã — side ) sq . units = 9 ã — 9 cm â ² = 81 cm â ² answer : d"
Answer: d
Question (geometry): the ratio of the volumes of two cubes is 9261 : 12167 . what is the ratio of their total surface areas ?
Options: a ) 1 : 12 , b ) 85 : 31 , c ) 51 : 45 , d ) 58 : 67 , e ) 53 : 58
Rationale: "ratio of the sides = ³ √ 9261 : ³ √ 12167 = 21 : 23 ratio of surface areas = 212 : 232 = 53 : 58 answer : e"
Answer: e
Question (physics): a and b together can do a work in 3 days . if a alone can do it in 12 days . in how many days can b alone do it ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 25
Rationale: "a 4 1 / 3 â € “ 1 / 12 = 1 / 4 = > 4"
Answer: a
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 18 percent alcohol by volume ?
Options: a ) 100 , b ) 150 , c ) 200 , d ) 250 , e ) 300
Rationale: "18 % is 8 % - points higher than 10 % but 12 % - points lower than 30 % . thus there should be 3 parts of solution x for 2 parts of solution y . we should add 200 ml of solution y . the answer is c ."
Answer: c
Question (gain): if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 100 % of j ?
Options: a ) 0.35 , b ) 3.5 , c ) 35 , d ) 350 , e ) 700
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 100 % of 10 is 10 . . . . ( 70 * 100 ) / 10 = 700 . . . . ans : e"
Answer: e
Question (general): if p is a prime number greater than 5 , what is the remainder when p ^ 2 is divided by 6 .
Options: a ) 4 , b ) can not be determined , c ) 2 , d ) 6 , e ) 1
Rationale: take square of any prime number remainder will be 1 ans e
Answer: e
Question (general): a sum of rs . 2200 has been divided among a , b and c such that a gets 1 / 4 of what b gets and b gets 1 / 5 of what c gets . what is b ' s share ?
Options: a ) 342 , b ) 352 , c ) 322 , d ) 332 , e ) 362
Rationale: "let c ' s share = rs . x then b ' s share = x / 5 a ' s share = x / 5 × 1 / 4 = x / 20 hence , x + x / 5 + x / 20 = 2200 ⇒ x ( 1 + 1 / 5 + 1 / 20 ) = 2200 ⇒ x ( 25 / 20 ) = 2200 ⇒ x ( 5 / 4 ) = 2200 ⇒ x = 2200 × 4 / 5 = 440 × 4 = rs . 1760 b ' s share = x / 5 = 1760 / 5 = rs . 352 answer is b ."
Answer: b
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 9.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 4 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.75 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: "salary grade of 4 is p ( 4 ) = 9.50 + 0.25 ( 4 – 1 ) = 9.50 + 0.25 * 3 ; salary grade of 1 is p ( 1 ) = 9.50 + 0.25 ( 1 – 1 ) = 9.50 ; p ( 4 ) - p ( 1 ) = 9.50 + 0.25 * 4 - 9.50 = 0.75 . answer : a ."
Answer: a
Question (gain): the price of a t . v . set worth rs . 8000 is to be paid in 20 installments of rs . 750 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 7250 , b ) 7200 , c ) 7820 , d ) 6000 , e ) 2799
Rationale: "money paid in cash = rs . 750 balance payment = ( 8000 - 1000 ) = rs . 7250 answer : a"
Answer: a
Question (general): in an examination , 40 % of total students failed in hindi , 40 % failed in english and 15 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "pass percentage = 100 - ( 40 + 45 - 15 ) = 100 - 70 = 30 answer : c"
Answer: c
Question (geometry): some students are standing in a circle in which 6 th and the 16 th student are standing opposite to each other . find how many students were present there .
Options: a ) 10
b ) 15
c ) 20
d ) 25
e ) 30
Rationale: ( n / 2 ) - x = 6 n - x = 16 solving these two = > n = number of students = 20 answer : c
Answer: c
Question (gain): if the annual increase in the population of a town is 10 % and the present number of people is 13000 , what will the population be in 2 years ?
Options: a ) 15730 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 10002
Rationale: the required population is = 13000 ( 1 + 10 / 100 ) ^ 2 = 13000 * 11 / 10 * 11 / 10 = 15730 answer is a
Answer: a
Question (gain): find the compound interest on $ 46,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.05 , b ) 2552.32 , c ) 2524.34 , d ) 7250.75 , e ) 9012.55
Rationale: "principal = $ 46000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 46000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 53250.75 ci . = $ ( 53250.75 - 46000 ) = $ 7250.75 answer d ."
Answer: d
Question (general): lagaan is levied on the 60 percent of the cultivated land . the revenue department collected total rs . 3 , 44000 through the lagaan from the village of mutter . mutter , a very rich farmer , paid only rs . 480 as lagaan . the percentage of total land of mutter over the total taxable land of the village is :
Options: a ) 0.23255 , b ) 0.14544 , c ) 0.25632 , d ) 0.35466 , e ) 0.63435
Rationale: total land of sukhiya = \ inline \ frac { 480 x } { 0.6 } = 800 x \ therefore cultivated land of village = 344000 x \ therefore required percentage = \ inline \ frac { 800 x } { 344000 } \ times 100 = 0.23255 a
Answer: a
Question (general): how many positive integer solutions does the equation 5 x + 10 y = 100 have ?
Options: a ) 2 , b ) 33 , c ) 38 , d ) 35 , e ) 14
Rationale: formula : ( constant ) / ( lcm of two nos ) = 100 / ( 5 * 10 ) = 2 answer : a
Answer: a
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 3025 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 220
Rationale: "given that the area of the square = 3025 sq . units = > side of square = √ 3025 = 55 units the radius of the circle = side of the square = 55 units length of the rectangle = 2 / 5 * 55 = 22 units given that breadth = 10 units area of the rectangle = lb = 22 * 10 = 220 sq . units answer : option e"
Answer: e
Question (gain): what is the difference between the ci on rs . 5000 for 1 years at 4 % per annum ci yearly and half yearly ?
Options: a ) rs . 2.04 , b ) rs . 2.12 , c ) rs . 2.23 , d ) rs . 3 , e ) rs . 3.04
Rationale: c . i . when interest compounded yearly = rs . 5000 x 1 + 4 x 1 + x 4 100 100 = rs . 5000 x 26 x 51 25 50 = rs . 5304 . c . i . when interest is compounded half - yearly = rs . 5000 x 1 + 2 3 100 = rs . 5000 x 51 x 51 x 51 50 50 50 = rs . 5306.04 difference = rs . ( 5306.04 - 5304 ) = rs . 2.04 a
Answer: a
Question (gain): 140 is what percent of 40 ?
Options: a ) 5 % , b ) 20 % , c ) 50 % , d ) 350 % , e ) 500 %
Rationale: "40 * x = 140 - - > x = 3.5 - - > 3.5 expressed as percent is 350 % . answer : d ."
Answer: d
Question (gain): tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 56 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 740 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 26 tickets = 20 * 26 = 520 revenue generated from sales of 56 tickets = 120 + 340 + 520 = 980 $ answer d"
Answer: d
Question (general): in the annual cultural programme of indra prastha there was this math quiz going on . yudhisthir faced this last question that will bring the champion ' s trophy . what will be thesolution for the given problem ? the function f is defined is defined asf ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) what is f ( 29 ) ?
Options: a ) 200 , b ) 230 , c ) 140 , d ) 170 , e ) none of these
Rationale: explanation : f ( 2 x + 3 ) = ( x - 3 ) ( x + 4 ) put x = 13 f ( 2 * 13 + 3 ) = ( 13 - 3 ) * ( 13 + 4 ) = 10 * 17 f ( 29 ) = 170 answer : d
Answer: d
Question (physics): a driver goes on a trip of 70 kilometers , the first 35 kilometers at 48 kilometers per hour and the remaining distance at 24 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 30 , b ) 32 , c ) 35 , d ) 36 , e ) 40
Rationale: "the time for the first part of the trip was 35 / 48 hours . the time for the second part of the trip was 35 / 24 hours . the total time fro the trip was 35 / 48 + 35 / 24 = 105 / 48 = 35 / 16 hours . the average speed for the trip was 70 / ( 35 / 16 ) = 32 kph the answer is b ."
Answer: b
Question (general): one day a car rental agency rented 2 / 3 of its cars , including 3 / 5 of its cars with cd players . if 3 / 4 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 10 % , b ) 35 % , c ) 45 % , d ) 66.7 % , e ) 90 %
Rationale: let us try to solve this by getting some number for total cars . let there be 3,4 and 5 = 60 cars . . . ( we have taken denominators of 2 / 3,3 / 4 and 3 / 5 least common number ) . 2 / 3 ( 60 ) = 40 cars . . . total rented cars , then 1 / 3 ( 60 ) = 20 cars were not rented . 3 / 4 ( 60 ) = 45 cars with cd players . . . total cdp cars now 3 / 5 ( 3 / 4 ) = 3 / 5 ( 45 ) = 27 cdp cars and these are cars that we rented . non rented cdp = total cdp - rented cdp = 45 - 27 = 18 . 18 / 20 = 90 % . answer : e
Answer: e
Question (general): if 183 is divisible by 11 , find the value of the smallest natural no . n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 10 , e ) 12
Rationale: in aptitude tests , we get questions on divisibility by 11 . a number is divisible by 11 , when the difference between the sum of digits at even places and at odd places is 0 or multiple of 11 the given number is n 183 . ( sum of digits at even places ) – ( sum of digits at odd places ) = 0 ( 8 + n ) - ( 3 + 1 ) = 0 ( 8 + n ) - 4 = 0 here the value of n must be 7 b
Answer: b
Question (physics): joshua and jose work at an auto repair center with 3 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 10 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: two methods 1 ) probability of chosing josh first = 1 / 5 probability of chosing jose second = 1 / 4 total = 1 / 20 probability of chosing jose first = 1 / 5 probability of chosing josh second = 1 / 4 total = 1 / 20 final = 1 / 20 + 1 / 20 = 1 / 10 b
Answer: b
Question (physics): a can do a piece of work in 40 days ; b can do the same in 40 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 20 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 40 + 10 / x = 1 x = 20 days answer : a"
Answer: a
Question (physics): in a 280 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 22 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 280 m in 7 / 56 * 280 = 35 seconds since a beats b by 7 seconds , a runs 280 m in ( 35 - 7 ) = 28 seconds hence , a ' s time over the course = 28 seconds answer : e"
Answer: e
Question (general): in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what z percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Question (physics): in a kilometer race , a beats b by 80 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 176 sec , d ) 115 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 80 = 125 sec . time taken by a = 125 - 10 = 115 sec . answer : d"
Answer: d
Question (geometry): if n is the smallest integer such that 144 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "144 can written as = 2 * 2 * 2 * 2 * 3 * 3 - - > 2 ^ 4 * 3 ^ 2 - - - ( 1 ) so for 144 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Question (general): claire has a total of 86 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
Options: a ) 39 , b ) 50 , c ) 60 , d ) 54 , e ) 60
Rationale: "g + h = 86 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 86 - h or 3 ( 86 - h ) + 4 h = 300 h = 300 - 258 = 42 then g = 96 - 42 = 54 d"
Answer: d
Question (gain): jackie has two solutions that are 4 percent sulfuric acid and 12 percent sulfuric acid by volume , respectively . if these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 5 percent sulfuric acid , approximately how many liters of the 12 percent solution will be required ?
Options: a ) 18 , b ) 20 , c ) 24 , d ) 33.75 , e ) 42
Rationale: "let a = amount of 4 % acid and b = amount of 12 % acid . now , the equation translates to , 0.04 a + . 12 b = . 05 ( a + b ) but a + b = 60 therefore . 04 a + . 12 b = . 05 ( 60 ) = > 4 a + 12 b = 300 but b = 60 - a therefore 4 a + 12 ( 60 - a ) = 300 = > 16 a = 420 hence a = 26.25 . b = 60 - 26.25 = 33.75 answer : d"
Answer: d
Question (geometry): how much space , in cubic units , is left vacant when maximum number of 4 x 4 x 4 cubes are fitted in a rectangular box measuring 10 x 12 x 16 ?
Options: a ) 0
b ) 36
c ) 180
d ) 216
e ) 384
Rationale: no of cubes that can be accommodated in box = ( 10 * 12 * 16 ) / ( 4 * 4 * 4 ) 12 * 16 in numerator can be perfectly divided by 4 * 4 in denominator . side with length 10 ca n ' t be perfectly divided by 4 and hence is the limiting factor . closet multiple of 4 less that 10 is 8 . so vacant area in cube = = 12 * 16 * ( 10 - 8 ) = 12 * 16 * 2 = 384 answer : e
Answer: e
Question (physics): it is currently 8 : 34 pm . at what time in the morning was it exactly 39,668 minutes ago ?
Options: a ) 7 : 22 , b ) 7 : 24 , c ) 7 : 26 , d ) 7 : 28 , e ) 7 : 30
Rationale: divide 39,668 by 60 to convert to minutes : 39,668 / 60 = 661 r 8 . that is 661 hours , 8 minutes . all of the answer choices are during the same hour before : 34 , so we can assume the 661 hours takes the time back into the 7 am hour to 7 : 34 am . going back 8 more minutes yields the time 7 : 26 am . c
Answer: c
Question (general): a palindrome is a number that reads the same forward and backward . for example . 2442 and 111 are palindromes . if 5 - digit palindromes are formed using one or more of the digits , 1 , 2 , 3 , how many such palindromes are possible ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 24 , e ) 27
Rationale: xyzyx x can be 1 , 2 , or 3 , thus 3 options . y can be 1 , 2 , or 3 , thus 3 options . z can be 1 , 2 , or 3 , thus 3 options . total 3 ^ 3 = 27 . answer : e .
Answer: e
Question (physics): a train 125 m long passes a man , running at 20 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 28 , d ) 26 , e ) 65
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 20 ) km / hr . x - 20 = 45 = = > x = 65 km / hr answer : e"
Answer: e
Question (general): if 20 % of ( x - y ) = 14 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 17.6 % , e ) 25 %
Rationale: "20 % of ( x - y ) = 14 % of ( x + y ) 20 / 100 ( x - y ) = 14 / 100 ( x + y ) 6 x = 34 y required percentage = y / x * 100 = 6 y / 34 y * 100 = 17.64 % answer is d"
Answer: d
Question (general): if rs . 510 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively :
Options: a ) rs . 260 , b ) rs . 360 , c ) rs . 350 , d ) rs . 364 , e ) rs . 362
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 510 * 2 / 17 = rs . 60 b ' s share = 510 * 3 / 17 = rs . 90 c ' s share = 510 * 12 / 17 = rs . 360 . answer : b"
Answer: b
Question (general): what is the dividend . divisor 15 , the quotient is 9 and the remainder is 5 ?
Options: a ) a ) 140 , b ) b ) 134 , c ) c ) 148 , d ) d ) 158 , e ) e ) 160
Rationale: "d = d * q + r d = 15 * 9 + 5 d = 135 + 5 d = 140 answer a"
Answer: a
Question (other): an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases .
Options: a ) 4 : 3 , b ) 8 : 7 , c ) 4 : 1 , d ) 6 : 5 , e ) none of these
Rationale: "explanation : let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer is b"
Answer: b
Question (physics): stacy and heather are 10 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 6.0 mile , b ) 3.0 mile , c ) 4.0 mile , d ) 3.45 mile , e ) 12 mile
Rationale: "ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 10 - 2.4 = 7.6 time taken = distance / speed = 7.6 / 11 = 0.69 hrs heather will cover = 5 * 0.69 = 3.45 miles . answer d"
Answer: d
Question (physics): a man can row upstream at 26 kmph and downstream at 40 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 33 , e ) 18
Rationale: "us = 26 ds = 40 m = ( 40 + 26 ) / 2 = 33 answer : d"
Answer: d