Cheukting/mathqa huggingface dataset:
Question (general): a wholesaler wishes to sell 100 pounds of mixed nuts at $ 2.50 a pound . she mixes peanuts worth $ 1.50 a pound with cashews worth $ 4.00 a pound . how many pounds of cashews must she use ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "cashews / peanuts = ( mean price - peanuts price ) / ( cashew price - mean price ) = ( 2.5 - 1.5 ) / ( 4 - 2.5 ) = 2 / 3 cashew = ( 2 / 5 ) * 100 = 40 kg answer is a ."
Answer: a
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 44 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "annie earned 40 x + 4 ( 2 x ) = 48 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 48 x ( 1.5 x ) ( h ) = 63 x h = 42 hours the answer is b ."
Answer: b
Question (physics): two pipes a and b can fill a cistern in 9 and 18 minutes respectively , and a third pipe c can empty it in 24 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 6 min , b ) 7 min , c ) 8 min , d ) 10 min , e ) 17 min
Rationale: "1 / 9 + 1 / 18 - 1 / 24 = 1 / 8 8 / 1 = 8 answer : c"
Answer: c
Question (general): laura took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 36.75 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.80
Rationale: "principal that is amount taken by laura at year beginning = 35 $ rate of interest = 5 % interest = ( 5 / 100 ) * 35 = 1.75 $ total amount that laura owes a year later = 35 + 1.75 = 36.75 $ answer b"
Answer: b
Question (general): a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 56 %
Rationale: "first $ 20 million : royalties / sales ratio = 3 / 20 = 36 / 240 next $ 108 million : royalties / sales ratio = 9 / 108 = 1 / 12 = 20 / 240 answer : c"
Answer: c
Question (general): what is the sum of the integers from - 194 to 195 inclusive ?
Options: a ) 0 , b ) 5 , c ) 195 , d ) 875 , e ) 965
Rationale: "sum / n = average . sum = ( average ) ( n ) average = a + b / 2 = 194 + 195 / 2 = 0.5 number of items ( n ) = b - a + 1 = 195 - ( - 194 ) + 1 = 195 + 195 = 390 . sum = average * n = 0.5 * 390 = 195 . answer is c"
Answer: c
Question (general): if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value q of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value q . hence , answer choice c is the one to go ."
Answer: c
Question (general): the average of first seven prime numbers which are between 30 and 70 is
Options: a ) 35.4 , b ) 42 , c ) 44.4 , d ) 57 , e ) 67
Rationale: "explanation : first seven prime numbers which are between 30 and 70 = 31 , 37 , 41 , 43 , 47 , 53 , 59 average = ( 31 + 37 + 41 + 43 + 47 + 53 + 59 ) / 7 = 44.4 answer : c"
Answer: c
Question (general): a batsman makes a score of 90 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
Options: a ) 25 , b ) 31 , c ) 27 , d ) 29 , e ) 42
Rationale: "let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 90 = total runs scored in 17 innings = > 16 ( x - 3 ) + 90 = 17 x = > 16 x - 48 + 90 = 17 x = > x = 42 answer is e ."
Answer: e
Question (general): if x / y = 3 / z , then 4 x ^ 2 =
Options: a ) y / z , b ) xy , c ) y ² / z ² , d ) 36 y ² / z ² , e ) 15 y ² / z ²
Rationale: "this question is most easily solved by isolating y in the equation and substituting into the expression 4 x ² : x / y = 3 / z x = 3 y / z if we substitute 3 y / z into the expression for x , we get : 4 ( 3 y / z ) ² = 4 ( 9 y ² / z ² ) = 36 y ² / z ² . the correct answer is choice ( d ) ."
Answer: d
Question (general): the captain of a cricket team of 11 members is 25 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 25 + 28 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 44 2 x = 44 x = 22 . so , average age of the team is 22 years . answer c"
Answer: c
Question (general): on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.90 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.6
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.9 = 3 * x - - > x = $ 0.6 . answer : e ."
Answer: e
Question (general): if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 31 km more . the actual distance traveled by him is ?
Options: a ) 30 , b ) 25 , c ) 20.67 , d ) 12.33 , e ) 19.48
Rationale: "let the actual distance traveled is ' x ' km then by given conditions , we have x / 10 = ( x + 31 ) / 25 25 x = 10 x + 310 x = 20.67 km ans - c"
Answer: c
Question (physics): the speed of a boat in still water is 8 kmph . if it can travel 1 km upstream in 1 hr , what time it would take to travel the same distance downstream ?
Options: a ) 14 minutes , b ) 4 minutes , c ) 24 minutes , d ) 28 minutes , e ) 23 minutes
Rationale: "speed of the boat in still water = 8 km / hr speed upstream = 1 ⁄ 1 = 1 km / hr speed of the stream = 8 - 1 = 7 km / hr speed downstream = ( 8 + 7 ) = 15 km / hr answer is b time taken to travel 1 km downstream = 1 / 15 hr = ( 1 × 60 ) / 15 = 4 minutes"
Answer: b
Question (general): # p is defined as 2 p - 20 for any number p . what is p , if # ( # ( # p ) ) = 12 ?
Options: a ) – 108 , b ) 19 , c ) 10 , d ) 16 , e ) 18
Rationale: # p = 2 p - 20 - - - > # ( # p ) = 2 ( 2 p - 20 ) - 20 = 4 p - 60 and thus # ( 4 p - 60 ) = 2 ( 4 p - 60 ) - 20 = 8 p - 140 = 12 - - - > 8 p = 152 - - - > p = 19 , b is the correct answer .
Answer: b
Question (general): if 90 percent of 600 is 50 percent of x , then x = ?
Options: a ) 100 , b ) 1000 , c ) 1080 , d ) 1020 , e ) 1200
Rationale: "0.9 * 600 = 0.5 * x x = 9 / 5 * 600 = 1080"
Answer: c
Question (gain): a number increased by 20 % gives 1080 . the number is ?
Options: a ) 800 , b ) 700 , c ) 500 , d ) 900 , e ) 600
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 1080 ( 120 ã — 9 = 1080 ) 100 % - - - - - - - > 900 ( 100 ã — 9 = 900 ) option ' d '"
Answer: d
Question (physics): a train 500 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 87 kmph , b ) 97 kmph , c ) 72 kmph , d ) 90 kmph , e ) 19 kmph
Rationale: "length = speed * time speed = l / t s = 500 / 20 s = 25 m / sec speed = 25 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 90 kmph answer : d"
Answer: d
Question (general): if 5 < x < 12 and y = x + 3 , what is the greatest possible integer value of x + y ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "x + y = x + x + 3 = 2 x + 3 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 11.5 then x + y = 11.5 + 14.5 = 26 . the answer is d ."
Answer: d
Question (general): on dividing a number by 357 , we get 42 as remainder . on dividing the same number by 17 , what will be the remainder ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 7 , e ) 2
Rationale: "let x be the number and y be the quotient . then , x = 357 * y + 42 = ( 17 * 21 * y ) + ( 17 * 2 ) + 8 = 17 * ( 21 y + 2 ) + 8 . required number = 8 . answer is c"
Answer: c
Question (general): evaluate : 20 - 16 ÷ 4 × 3 =
Options: a ) 16 , b ) 10 , c ) 4 , d ) 8 , e ) 6
Rationale: "according to order of operations , 16 ÷ 4 × 3 ( division and multiplication ) is done first from left to right 16 ÷ 4 × 3 = 4 × 3 = 12 hence 20 - 16 ÷ 4 × 3 = 20 - 12 = 8 correct answer d ) 8"
Answer: d
Question (physics): a train 1020 m long running at 102 kmph crosses a platform in 50 sec . what is the length of the platform ?
Options: a ) 287 , b ) 298 , c ) 396 , d ) 726 , e ) 267
Rationale: "d = 102 * 5 / 18 = 50 = 1416 â € “ 1020 = 396 answer : c"
Answer: c
Question (general): a seller of used cars has 15 cars to sell and each of his clients selected 3 cars that he liked most . if each car was selected exactly thrice , how many clients visited the garage ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "ifno caris selected more than once then the number of clients = 15 / 3 = 5 but since every car is being selected three times so no . of clients must be thrice as well = 5 * 3 = 15 answer : option e"
Answer: e
Question (geometry): if a rectangular room measures 11 meters by 6 meters by 4 meters , what is the volume of the room in cubic centimeters ? ( 1 meter = 100 centimeters )
Options: a ) 24,000 , b ) 240,000 , c ) 2 , 400,000 , d ) 24 , 000,000 , e ) 264 , 000,000
Rationale: "e . 264 , 000,000 11 * 100 * 6 * 100 * 4 * 100 = 264 , 000,000"
Answer: e
Question (physics): a rock is dropped into a well and the distance traveled is 16 t 2 feet , where t is the time . if the water splash is heard 3 seconds after the rock was dropped , and that the speed of sound is 1100 ft / sec , approximate the height of the well
Options: a ) 134.8 feet , b ) 136.2 feet , c ) 132.7 feet , d ) 132.2 feet , e ) 115.3 feet
Rationale: let t 1 be the time it takes the rock to reach the bottom of the well . if h is the height of the well , we can write h = 16 t 1 2 let t 2 be the time it takes sound wave to reach the top of the well . we can write h = 1100 t 2 the relationship between t 1 and t 2 is t 1 + t 2 = 3 eliminate h and combine the equations h = 16 t 1 2 and h = 1100 t 2 to obtain 16 t 1 2 = 1100 t 2 we now substitute t 2 by 3 - t 1 in the above equation 16 t 1 2 = 1100 ( 3 - t 1 ) the above is a quadratic equation that may be written as 16 t 1 2 + 1100 t 1 - 3300 = 0 the above equations has two solutions and only one of them is positive and is given by t 1 = 2.88 seconds ( 2 decimal places ) we now calculate the height h of the well h = 16 t 1 2 = 16 ( 2.88 ) 2 = 132.7 feet answer c
Answer: c
Question (gain): a man can row his boat with the stream at 18 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 3 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 18 us = 4 s = ? s = ( 18 - 4 ) / 2 = 7 kmph answer : d"
Answer: d
Question (gain): how is 2 % expressed as a decimal fraction ?
Options: a ) 0.2 , b ) 0.02 , c ) 0.002 , d ) 0.0002 , e ) 2
Rationale: 2 / 100 = 0.02 answer : b
Answer: b
Question (general): for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers v are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Question (general): 25.25 / 3000 is equal to :
Options: a ) 0.008416667 , b ) 0.110773333 , c ) 0.12526234 , d ) 0.01072333 , e ) 0.12725002
Rationale: "25.25 / 3000 = 2525 / 300000 = 0.008416667 answer : a"
Answer: a
Question (physics): a man can row downstream at 28 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 2 , 9 , b ) 4 , 9 , c ) 8 , 9 , d ) 19 , 9 , e ) 7 , 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 28 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 38 = > x = 19 , y = 9 . answer : d"
Answer: d
Question (physics): two bullet trains of equal lengths take 8 seconds and 15 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 10.4 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: speed of the first bullet train = 120 / 8 m / sec = 15 m / sec . speed of the second bullet train = 120 / 15 m / sec = 8 m / sec . relative speed = ( 15 + 8 ) = 23 m / sec . required time = ( 120 + 120 ) / 23 sec = 10.4 sec . b
Answer: b
Question (general): how many even number in the range between 10 to 170 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 33 , e ) 54
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 170 using ap formula , we can say 170 = 10 + ( n - 1 ) * 2 or n = 81 . for 6 , 12,18 , . . . 168 using ap formula , we can say 168 = 12 + ( n - 1 ) * 6 or n = 27 . hence , only divisible by 2 but not 3 = 81 - 27 = 54 . hence , answer e"
Answer: e
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 80 feet , b ) 70 feet , c ) 60 feet , d ) 50 feet , e ) 20 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 20 * breadth = 600 = > breadth = 30 feet area to be fenced = 2 b + l = 2 * 30 + 20 = 80 feet answer : option a"
Answer: a
Question (general): when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.16 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 8 / y . the remainder in decimal form is given as . 16 therefore , 8 / y = . 16 solve for y and get 50 . c"
Answer: c
Question (general): the mean of 30 values was 140 . it was detected on rechecking that one value 145 was wrongly copied as 135 for the computation of the mean . find the correct mean .
Options: a ) 151 , b ) 140.33 , c ) 152 , d ) 148 , e ) none of the above
Rationale: "corrected mean = 140 × 30 − 135 + 145 / 30 = 4200 − 135 + 145 / 30 = 4210 / 30 = 140.33 answer b"
Answer: b
Question (physics): two trains 110 meters and 180 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.2 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 110 + 180 ) / ( 80 + 65 ) * 18 / 5 t = 7.20 answer : a"
Answer: a
Question (geometry): the perimeter of a triangle is 20 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 28 cm 2 , b ) 27 cm 2 , c ) 29 cm 2 , d ) 25 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 20 / 2 = 25 cm 2 answer : d"
Answer: d
Question (geometry): you buy a piece of land with an area of √ 900 , how long is one side of the land plot ?
Options: a ) 28
b ) 29
c ) 30
d ) 31
e ) 32
Rationale: try filling the numbers into the answer y x y = find the closest to 900 . answer c
Answer: c
Question (general): a large box contains 21 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 450 , d ) 550 , e ) 525
Rationale: "the number of chocolate bars is equal to 21 * 25 = 525 correct answer e"
Answer: e
Question (gain): a typist uses a sheet measuring 20 cm by 30 cm lenghtwise . if a margin of 2 cm is left on each side and a 3 cm margin on the top and bottom , then what is the percentage of page used by the typist ?
Options: a ) 62 % , b ) 63 % , c ) 64 % , d ) 65 % , e ) 66 %
Rationale: area of the sheet = ( 20 * 30 ) cm 2 = 600 cm 2 area used for typing = ( [ 20 - 4 ] * [ 30 - 6 ] ) cm 2 = 384 cm 2 therefore required percentage = ( 384 / 600 ) * 100 = 64 % answer c
Answer: c
Question (gain): an association of mathematics teachers has 1,260 members . only 525 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 62 percent of the votes cast ?
Options: a ) 75 % , b ) 58 % , c ) 42 % , d ) 34 % , e ) 25.83 %
Rationale: "total number of members = 1260 number of members that cast votes = 525 since , winning candidate received 62 percent of the votes cast number of votes for winning candidate = ( 62 / 100 ) * 525 = 325.5 percent of total membership that voted for winning candidate = ( 325.5 / 1260 ) * 100 = 25.83 % answer e"
Answer: e
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 161 ?
Options: a ) 2670 , b ) 2980 , c ) 3550 , d ) 4030 , e ) 4540
Rationale: "100 + 102 + . . . + 160 = 100 * 31 + ( 2 + 4 + . . . + 60 ) = 100 * 31 + 2 * ( 1 + 2 + . . . + 30 ) = 100 * 31 + 2 ( 30 ) ( 31 ) / 2 = 100 * 31 + 30 * 31 = 130 ( 31 ) = 4030 the answer is d ."
Answer: d
Question (physics): a clock shows the time as 11 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 45 minutes , b ) 55 minutes , c ) 35 minutes , d ) 25 minutes , e ) 40 minutes
Rationale: "there are 7 hours in between 11 a . m . to 6 p . m . 7 * 5 = 35 minutes . answer : c"
Answer: c
Question (general): a man is 26 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 24 years , d ) 20 years , e ) 19 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 26 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 26 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 24 answer : c"
Answer: c
Question (physics): a and b can do a piece of work in 6 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 15.5 days , b ) 19.5 days , c ) 17.5 days , d ) 16.5 days , e ) 30 days
Rationale: "c = 1 / 5 – 1 / 6 = 1 / 30 = > 30 days answer : e"
Answer: e
Question (physics): an aeroplane covers a certain distance at a speed of 120 kmph in 5 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 520 , b ) 620 , c ) 820 , d ) 740 , e ) 720
Rationale: "distance = ( 120 x 5 ) = 600 km . speed = distance / time speed = 600 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 600 x 3 / 5 ) km / hr = 360 km / hr answer a ) 360 km / hr"
Answer: a
Question (physics): a man swims downstream 18 km and upstream 12 km taking 3 hours each time , what is the speed of the man in still water ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 8
Rationale: "18 - - - 3 ds = 6 ? - - - - 1 12 - - - - 3 us = 4 ? - - - - 1 m = ? m = ( 6 + 4 ) / 2 = 5 answer : b"
Answer: b
Question (physics): amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.3 km ?
Options: a ) 600 m , b ) 325 m , c ) 300 m , d ) 400 m , e ) 100 m
Rationale: "b 325 m distance covered by amar = 18 / 4.8 ( 1.3 km ) = 3 / 8 ( 1300 ) = 325 m answer is b"
Answer: b
Question (gain): a sum of rs . 2678 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1629 , b ) 1648 , c ) 2677 , d ) 2986 , e ) 2679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2678 - x ) * 3 * 5 ) / 100 24 x / 100 = 40170 / 100 - 15 x / 100 39 x = 40170 = > x = 1030 second sum = 2678 â € “ 1030 = 1648 answer : b"
Answer: b
Question (general): the sum of two numbers is 24 and their product is 148 . find the sum of the squares of that numbers .
Options: a ) 250 , b ) 280 , c ) 230 , d ) 290 , e ) 250
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 24 ab = 148 so , 24 ^ 2 = a ^ 2 + b ^ 2 + 2 * 148 576 = a ^ 2 + b ^ 2 + 296 a ^ 2 + b ^ 2 = 280 ans b
Answer: b
Question (physics): two numbers n and 12 have lcm = 54 and gcf = 8 . find n .
Options: a ) 24 , b ) 34 , c ) 36 , d ) 54 , e ) 64
Rationale: the product of two integers is equal to the product of their lcm and gcf . hence . 12 × n = 54 × 8 n = 54 × 8 / 12 = 36 correct answer c
Answer: c