Cheukting/mathqa huggingface dataset:
Question (general): a company that ships boxes to a total of 12 distribution centers uses color coding to identify each center . if either a single color or a pair of two different colors is chosen to represent each center and if each center is uniquely represented by that choice of one or two colors , what is the minimum number of colors needed for the coding ? ( assume that the order of the colors in a pair does not matter )
Options: a ) 4 , b ) 5 , c ) 6 , d ) 12 , e ) 24
Rationale: "back - solving is the best way to solve this problem . you basically need 12 combinations ( including single colors ) if we start from option 1 - > 1 = > 4 c 2 + 4 = 10 ( not enough ) 2 = > 5 c 2 + 5 = 15 ( enough ) since the minimum number is asked . it should be 5 . answer - b"
Answer: b
Question (physics): 10 binders can bind 1400 books in 21 days . how many binders will be required to bind 1800 books in 20 days ?
Options: a ) 87 , b ) 18 , c ) 17 , d ) 16 , e ) 12
Rationale: "binders books days 10 1400 21 x 1600 20 x / 10 = ( 1800 / 1400 ) * ( 21 / 20 ) = > x = 12 answer : 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 27 metre of cloth ?
Options: a ) 211 seconds , b ) 195 seconds , c ) 155 seconds , d ) 115 seconds , e ) 115 seconds
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 27 : x = > x = { \ color { blue } \ frac { 27 \ times 1 } { 0.128 } } = > x = 210.94 so time will be approx 211 seconds answer : a"
Answer: a
Question (gain): a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 11 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 22.38 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 11 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 89 / 100 = ( 1 + p % ) profit % = 22.38 % b"
Answer: b
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 11 kmph ?
Options: a ) 21.23 , b ) 52.85 , c ) 23.26 , d ) 41.67 , e ) 25.15
Rationale: "distance covered in 1 min = ( 66 * 1000 ) / 60 = 183.33 cm circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 183.33 / 4.4 = 41.67 answer : d"
Answer: d
Question (general): 1 * 2 + 2 * 2 ^ 2 + 3 * 2 ^ 3 + 4 * 2 ^ 4 … … … … … … … … + 2012 * 2 ^ 2012
Options: a ) 8100312 , b ) 8100313 , c ) 8100412 , d ) 8200312 , e ) 8300312
Rationale: take 2 outside as common we get 2 ( 1 + 2 * 1 ^ 2 + 3 * 1 ^ 3 + . . . . . . . . . 2012 * 1 ^ 2012 ) then 2 ( 1 + 2 + . . . . . 2012 ) we get 8100312 answer : a
Answer: a
Question (general): stock / number of shares v - - - - - - - - - - - - 68 w - - - - - - - - - - 112 x - - - - - - - - - - - - 56 y - - - - - - - - - - - - 94 z - - - - - - - - - - - - 45 the table shows the number of shares of each of the 5 stocks owned by mr sami . if mr . sami was to sell 20 shares of stock x and buy 23 shares of stock y , what would be the increase in the range of the numbers of shares of the 5 stocks owned by mr . sami ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 14 , e ) 20
Rationale: based on the original number of shares , the range would be : 112 - 45 = 67 however , the prompt tells us that two of the values in the table are going to change . after the changes , the values will be : v 68 w 112 x 36 y 117 z 45 now the range is 117 - 36 = 81 the increase in the range requires us to compare thenewrange to theoldrange : 81 - 67 = 14 d
Answer: d
Question (gain): if the cost price of 20 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 20 % loss , c ) 25 % profit , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be rs . 1 . therefore , cost price of 20 articles = 20 * 1 = rs . 20 the selling price of 25 articles = cost price of 20 articles = rs . 20 . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = rs . 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 20 - 25 = - rs . 5 . because the profit is in the negative , the merchant has made a loss of rs . 5 . therefore , % loss = loss / cost price ∗ 100 % loss = 5 / 25 ∗ 100 = 20 % loss . answer : b"
Answer: b
Question (general): the mean of 50 observations was 32 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 32.5 , c ) 36.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 32 × 50 + 48 – 23 ) = 1625 . therefore correct mean = 1625 / 50 = 32.5 . answer b"
Answer: b
Question (general): 0.009 / x = 0.05 . find the value of x
Options: a ) 0.00018 , b ) 0.09 , c ) 0.018 , d ) 0.18 , e ) 90
Rationale: "x = 0.009 / 0.18 = 0.05 answer : d"
Answer: d
Question (gain): by selling an article at rs . 700 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 25 % ?
Options: a ) s . 600 , b ) s . 480 , c ) s . 500 , d ) s . 450 , e ) s . 420
Rationale: "sp = 700 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 700 * [ 100 / 125 ] = 560 loss = 25 % = 25 % of 560 = rs . 140 sp = cp - loss = 560 - 140 = rs . 420 answer : e"
Answer: e
Question (general): in a office work is distribute between p persons . if 1 / 6 members are absent then work increased for each person is ?
Options: a ) 10 % , b ) 14.28 % , c ) 15 % , d ) 16 % , e ) 20 %
Rationale: let total % of work is 100 % total person = p 1 / 6 person are absent of total person . so absent person is 1 / 6 p ie p / 6 . left person is , p - p / 6 = 5 p / 6 . p person do the work 100 % 1 person do the work 100 * p % 5 p / 6 person do the work ( 100 * p * 6 ) / 5 p % = 120.00 % work increased for each person is = ( 120 - 100 ) % = 20 % answer : e
Answer: e
Question (physics): a cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom . if the cistern is full , in what time will the leak empty it ?
Options: a ) 50 hours , b ) 62 hours , c ) 90 hours , d ) 75 hours , e ) 100 hours
Rationale: "let the leak empty the full cistern in x hours 9 x / x - 9 = 9 + 1 x = 90 hours answer is c"
Answer: c
Question (general): the total marks obtained by a student in mathematics and physics is 60 and his score in chemistry is 10 marks more than that in physics . find the average marks scored in mathamatics and chemistry together .
Options: a ) 35 , b ) 30 , c ) 25 , d ) data inadequate , e ) none of these .
Rationale: "let the marks obtained by the student in mathematics , physics and chemistry be m , p and c respectively . given , m + c = 60 and c - p = 10 m + c / 2 = [ ( m + p ) + ( c - p ) ] / 2 = ( 60 + 10 ) / 2 = 35 . answer : a"
Answer: a
Question (other): mrs . evans gave a test to her freshmen economics class , which has 50 students enrolled and 25 of them answered question 1 correctly . if 20 answered question 2 correctly and 20 did not take the test then how many answered both questions correctly ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 20 , e ) 19
Rationale: "total number of enrolled students = 50 number of students who did not take test = 20 hence , number of students who took test = 50 - 20 = 30 number of students who answered q 2 correctly = 20 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 20 . number of students who answered both q 1 & q 2 correctly = 20 . answer : d"
Answer: d
Question (physics): carl can wash all the windows of his house in 8 hours . his wife maggie can wash all the windows in 4 hours . how many hours will it take for both of them working together to wash all the windows ?
Options: a ) 2 , b ) 2 1 / 4 , c ) 3 2 / 2 , d ) 4 1 / 2 , e ) 5
Rationale: "work hrs = ab / ( a + b ) = 32 / 12 = 3 2 / 2 answer is c"
Answer: c
Question (gain): in a certain parking lot , 3 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what % of cars in the parking lot are parked illegally . '
Options: a ) 11 , b ) 13 , c ) 15 , d ) 60 , e ) 75
Rationale: "so total no . of cars parked illegally : 300 total no . of cars : 2000 300 / 2000 * 100 , so 15 % answer : c"
Answer: c
Question (gain): if the given two numbers are respectively 5 % and 25 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 30 % , e ) none of these
Rationale: "here , l = 5 and m = 25 therefore , first number = l / m x 100 % of second number = 5 / 25 x 100 % of second number = 20 % of second number answer : a"
Answer: a
Question (general): if the radius of a cylinder is doubled and height 4 times , what is the new volume of the cylinder divided by the old one ?
Options: a ) 8 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 16 .
Rationale: "let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 2 r ) ^ 2 ( 4 h ) v ' = 16 v e ) 16"
Answer: e
Question (physics): starting from his house one day , a student walk at a speed of 2 kmph and reaches his school 10 minutes late . next he increased his speed by 1 kmph and reaches the school 10 minutes early . how far is the school from his house ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: let the distance be x km difference in timings = 20 min = 20 / 60 = 1 / 3 hr x / 2 - x / 3 = 1 / 3 x = 2 km answer is b
Answer: b
Question (physics): if 23 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 176 , b ) 253 , c ) 342 , d ) 458 , e ) 560
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 23 lines is 23 c 2 = 253 the answer is b ."
Answer: b
Question (gain): what is the compound interest on rs . 6500 at 5.5 % p . a . compounded half - yearly for 1 year .
Options: a ) 369.42 , b ) 762.42 , c ) 162.42 , d ) 362.42 , e ) 333.42
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 6 , 862.42 c . i . > > 6 , 862.42 - 6500 > > rs . 362.42 answer : d"
Answer: d
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 6 units ?
Options: a ) 140 , b ) 84 , c ) 88 , d ) 72 , e ) 12
Rationale: "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 = 6 units area of the rectangle = lb = 14 * 6 = 84 sq . units answer : b"
Answer: b
Question (general): the sum of the non - prime numbers between 20 and 30 , non - inclusive , is
Options: a ) 173 , b ) 185 , c ) 197 , d ) 209 , e ) 221
Rationale: "sum of consecutive integers from 21 to 29 , inclusive = = = = > ( a 1 + an ) / 2 * # of terms = ( 21 + 29 ) / 2 * 9 = 25 * 9 = 225 sum of non - prime numbers b / w 20 and 30 , non inclusive = = = > 225 - 52 ( i . e . , 23 + 29 , being the prime # s in the range ) = 173 answer : a"
Answer: a
Question (general): there are 60 supermarkets in the fgh chain . all of them are either in the us or canada . if there are 22 more fgh supermarkets in the us than in canada , how many fgh supermarkets are there in the us ?
Options: a ) 20 , b ) 31 , c ) 41 , d ) 53 , e ) 64
Rationale: "x + ( x - 22 ) = 60 - - > x = 41 . answer : c ."
Answer: c
Question (general): a salt manufacturing company produced a total of 1000 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 51 , b ) 53 , c ) 55 , d ) 56 , e ) 57
Rationale: total production of salt by the company in that year = 1000 + 1100 + 1200 + . . . . + 2100 = 18600 . average monthly production of salt for that year = 18600 / 365 â ‰ ˆ 51 answer : a
Answer: a
Question (general): how much water should be added to 15 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 15 + x ) ) ) 2 = 5 % * ( 15 + x ) - - - - - - - - > x = 25 ans a"
Answer: a
Question (general): the sum of ages of 5 children born 3 years different each is 70 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . x + 12 = 8 + 12 = 20 e"
Answer: e
Question (gain): in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 27 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 30 , e ) 36
Rationale: "200 are sophomores . the number of freshmen is 600 - 160 - 0.27 ( 800 ) = 224 the answer is c ."
Answer: c
Question (general): find the average of all the numbers between 6 and 36 which are divisible by 5 .
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 22.5
Rationale: "solution average = ( 10 + 15 + 20 + 25 + 30 + 35 ) / 6 ) = 135 / 6 = 22.5 answer e"
Answer: e
Question (physics): tom , working alone , can paint a room in 10 hours . peter and john , working independently , can paint the same room in 5 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 10 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 5 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 10 * ( t + 4 ) + 1 / 5 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 10 - - > ( t + 4 ) + ( 2 t + 2 ) + 5 t = 10 - - > t = 1 / 2 ; hence peter has done 1 / 5 * ( 1 / 2 + 2 ) = 1 / 5 * 5 / 2 = 1 / 2 answer : b"
Answer: b
Question (physics): a train 440 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 80 , b ) 26 , c ) 24 , d ) 54 , e ) 15
Rationale: "speed of train relative to man = 60 + 6 = 66 km / hr . = 66 * 5 / 18 = 55 / 3 m / sec . time taken to pass the men = 440 * 3 / 55 = 24 sec . answer : c"
Answer: c
Question (physics): a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 2 days and b leaves after 4 days from the beginning . how long will work lost ?
Options: a ) 09 2 / 3 , b ) 10 2 / 3 , c ) 11 2 / 3 , d ) 12 2 / 3 , e ) 16 2 / 3
Rationale: "b 10 2 / 3 2 / 10 + 4 / 15 + x / 20 = 1 x = 32 / 3 = 10 2 / 3"
Answer: b
Question (general): find two integers , neither of which ends in a zero , and whose product is exactly 1 , 00,000
Options: a ) 64 and 15,625 , b ) 32 and 3,125 , c ) 64 and 15,620 , d ) 64 and 15,635 , e ) 64 and 16,625
Rationale: 1 , 00,000 = 10 ^ 5 = 10 x 10 x 10 x 10 x 10 = ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) x ( 2 x 5 ) = ( 2 ^ 5 ) x ( 5 ^ 5 ) = 32 x 3125 so the numbers are 32 and 3,125 answer : b
Answer: b
Question (physics): a man starts walking at 3 pm . ha walks at a speed of 4 km / hr on level ground and at a speed of 3 km / hr on uphill , 6 km / hr downhill and then 4 km / hr on level ground to reach home at 9 pm . what is the distance covered on one way
Options: a ) 10 km , b ) 12 km , c ) 14 km , d ) 16 km , e ) 18 km
Rationale: avg speed = 2 * 3 * 6 / ( 3 + 6 ) = 4 so speed of man = 4 km / hr distance = 4 * 6 = 24 km since we want one way distance it will be 24 / 2 = 12 km answer : b
Answer: b
Question (physics): a train 175 m long running at 36 kmph crosses a platform in 40 sec . what is the length of the platform ?
Options: a ) 271 , b ) 266 , c ) 225 , d ) 277 , e ) 232
Rationale: "length of the platform = 36 * 5 / 18 * 40 = 400 – 175 = 225 answer : c"
Answer: c
Question (gain): the population of a town increases 22 % and 25 % respectively in two consecutive years . after the growth the present population of the town is 1220 . then what is the population of the town 2 years ago ?
Options: a ) a ) 600 , b ) b ) 700 , c ) c ) 800 , d ) d ) 900 , e ) e ) 1000
Rationale: "explanation : formula : ( after = 100 denominator ago = 100 numerator ) 1220 * 100 / 122 * 100 / 125 = 800 answer : option c"
Answer: c
Question (general): in how many v ways can a 4 - letter password be chosen , using the letters a , b , c , d , e , and / or f , such that at least one letter is repeated within the password ?
Options: a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 1296
Rationale: total number of four letter passwords = 6 * 6 * 6 * 6 = 1296 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 6 c 4 * 4 ! = 15 * 24 = 360 - - - - - - ( 2 ) therefore required value v = ( 1 ) - ( 2 ) = 1296 - 360 = 936 . d
Answer: d
Question (general): the average expenditure of a labourer for 6 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) none of the above
Rationale: "income of 6 months = ( 6 × 85 ) – debt = 510 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 780 average monthly income = 780 ÷ 10 = 78 answer d"
Answer: d
Question (general): what is the greatest positive integer x such that 7 ^ x is a factor of 343 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "343 ^ 10 = ( 7 ^ 3 ) ^ 10 = 7 ^ 30 answer : e"
Answer: e
Question (general): in the xy - coordinate system , what is the slope of the line that goes through the point ( 4 , 4 ) and is equidistant from the two points p = ( 0 , 2 ) and q = ( 12 , 8 ) ?
Options: a ) 0.1 , b ) 0.3 , c ) 0.5 , d ) 0.7 , e ) 0.9
Rationale: "first , get the middle coordinate between ( 0,2 ) and ( 12,8 ) . . . x = 0 + ( 12 - 0 ) / 2 = 6 y = 2 + ( 8 - 2 ) / 2 = 5 second , get the slope of ( 6,5 ) and ( 4,4 ) . m = 5 - 4 / 6 - 4 = 1 / 2 = 0.5 answer : c"
Answer: c
Question (general): a sum of money is sufficient to pay b ' s wages for 12 days and c ' s wages for 24 days . the same money is sufficient to pay the wages of both for ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let the total money be $ x b ' s 1 day work = $ x / 12 c ' s 1 day work = $ x / 24 a + b 1 day work = $ x / 8 money is sufficient to pay the wages of both for 8 days answer is c
Answer: c
Question (general): jonathan , matthew and zac are picking strawberries from their yard . together they have picked a total of 550 strawberries . jonathan and matthew have picked 350 strawberries together . matthew and zac have picked 250 strawberries together . how many strawberries has zac picked by himself ?
Options: a ) 100 , b ) 200 , c ) 350 , d ) 50 , e ) 250
Rationale: jonathan = matthew + zac = 550 strawberries j + m = 350 m + z = 250 use j + m = 350 to plug into the original formula ( j + m ) + z = 550 350 + z = 550 subtract 350 from each side z = 200 answer : b
Answer: b
Question (geometry): in a certain parallelogram the degree measure of one angle exceeds that of the other by 70 what is the degree measure of the smaller angle ?
Options: a ) 55 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 70 ) = 180 - - > x = 55 . answer : a .
Answer: a
Question (gain): a candidate got 35 % of the votes and lost to the rival by 1350 votes . how many votes were cast ?
Options: a ) 4000 , b ) 4500 , c ) 5000 , d ) 5500 , e ) 6000
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1350 10 % = 450 100 % of the votes = 4500 answer : b"
Answer: b
Question (general): the product of two numbers is 2028 and their h . c . f . is 13 . the number of such pairs is :
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "explanation : let the numbers be 13 a and 13 b . then , 13 a * 13 b = 2028 = > ab = 12 . now , co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) . so , the required numbers are ( 13 * 1 , 13 * 12 ) and ( 13 * 3 , 13 * 4 ) . clearly , there are 2 such pairs . answer is b"
Answer: b
Question (physics): a train 140 m long crosses a platform 160 m long in 16 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 68 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 140 + 160 = 300 t = 16 s = 300 / 16 * 18 / 5 = 67.5 kmph answer : c"
Answer: c
Question (physics): a zeebra chases a tiger 5 hours after the tiger runs . zeebra takes 6 hours to reach the tiger . if the average speed of the zeebra is 55 kmph , what s the average speed of the tiger ?
Options: a ) 35 kmph , b ) 32 kmph , c ) 30 kmph , d ) 31 kmph , e ) 20 kmph
Rationale: tiger take 11 hours and zeebra take 6 hours . . . then distance chased by them is 55 * 6 . so speed of tiger is ( 55 * 6 ) / 11 = 30 kmph . answer is c
Answer: c
Question (probability): if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land heads up on the first 4 flips but not on the last flip ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 1 / 32
Rationale: p ( hhhht ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 32 the answer is e .
Answer: e
Question (gain): a fruit seller had some apples . he sells 40 % and still has 420 apples . originally , he had ?
Options: a ) 588 apples , b ) 600 apples , c ) 672 apples , d ) 700 apples , e ) none
Rationale: "answer ∵ 60 % of n = 420 ∴ n = ( 420 x 100 ) / 60 = 700 correct option : d"
Answer: d