regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the average age of students of a class is 15.8 years . the average age of boys in the class is 16.2 years and that of the girls is 15.4 years . the ration of the number of boys to the number of girls in the class is :
Options: a ) 2 : 5 , b ) 2 : 3 , c ) 2 : 4 , d ) 1 : 1 , e ) 2 : 9
Rationale: "let the ratio be k : 1 . then , k * 16.2 + 1 * 15.4 = ( k + 1 ) * 15.8 = ( 16.2 - 15.8 ) k = ( 15.8 - 15.4 ) = k = 0.4 / 0.4 = 1 / 1 required ratio = 1 / 1 : 1 = 1 : 1 . answer : d"
Answer: d
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 75 . what is that number
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 75 = > 2 x + 9 = 25 = > x = 8 answer : option a"
Answer: a
Problem: a batsman scored 210 runs which included 3 boundaries and 8 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 65 % , d ) 71.4 % , e ) 75 %
Rationale: "number of runs made by running = 210 - ( 3 x 4 + 8 x 6 ) = 210 - ( 60 ) = 150 now , we need to calculate 60 is what percent of 120 . = > 150 / 210 * 100 = 71.4 % d"
Answer: d
Problem: ( 112 x 5 ^ 4 ) = ?
Options: a ) 70000 , b ) 80000 , c ) 90000 , d ) 90090 , e ) 100000
Rationale: "( 112 x 54 ) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 a )"
Answer: a
Problem: x + ( 1 / x ) = 2 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2 , b ) 3.25 , c ) 4.25 , d ) 5.25 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 2 ^ 2 x ^ 2 + 1 / x ^ 2 = 4 - 2 x ^ 2 + 1 / x ^ 2 = 2 answer : a"
Answer: a
Problem: what least no . must be subtracted from 427398 so that remaining no . is divisible by 15 ?
Options: a ) 344545629 , b ) 723437481 , c ) 354595321 , d ) 964564944 , e ) 458449909
Rationale: "explanation : on dividing 427398 by 15 we get the remainder 3 , so 3 should be subtracted option b"
Answer: b
Problem: in a box of 12 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 9 , c ) 6 / 11 , d ) 9 / 16 , e ) 3 / 4
Rationale: "# defective pens = 3 # good pens = 9 probability of the 1 st pen being good = # of favorable outcomes / # of total outcomes = 9 / 12 probability of the 2 nd pen being good = # of remaining favorable outcomes / # of total remaining outcomes = 8 / 11 total probability = 9 / 12 * 8 / 11 = 6 / 11 answer will be c"
Answer: c
Problem: if a sum of money doubles itself in 15 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 6.67 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 15 ) = 6.67 option c"
Answer: c
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 883 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 76 , c ) 29 , d ) 12 , e ) 20
Rationale: "explanation : let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 883 96 + 225 + 490 + 6 x = 883 6 x = 72 = > x = 12 . answer : d"
Answer: d
Problem: if a person walks at 16 km / hr instead of 8 km / hr , he would have walked 20 km more . the distance traveled by him if he walked at 16 km / hr ?
Options: a ) 50 km , b ) 58 km , c ) 60 km , d ) 70 km , e ) 40 km
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 16 2 x - x = 20 = > x = 20 km . the required distance is = ( 20 + 20 ) km = 40 km answer : e"
Answer: e
Problem: drum x is 1 / 2 full of oil and drum y , which has twice the capacity of drum x , is 1 / 3 full of oil . if all of the oil in drum x is poured into drum y , then drum y will be filled to what capacity ?
Options: a ) 2 / 3 , b ) 5 / 6 , c ) 7 / 12 , d ) 11 / 12 , e ) 17 / 24
Rationale: "( 1 / 2 ) x = ( 1 / 4 ) y ( 1 / 4 ) y + ( 1 / 3 ) y = ( 7 / 12 ) y the answer is c ."
Answer: c
Problem: find the area of trapezium whose parallel sides are 26 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 330 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 26 + 18 ) * ( 15 ) = 330 cm 2 answer : c"
Answer: c
Problem: a train 160 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 90 kmph
Rationale: "speed of train relative to man : 160 / 6 * 18 / 5 km / hr = 96 km / hr let speed of train = x therefore x + 6 = 96 x = 96 - 6 x = 90 km / hr answer : e"
Answer: e
Problem: an aeroplane covers a certain distance at a speed of 240 kmph in 6 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 ) 864
Rationale: "distance = ( 240 x 6 ) = 1440 km . speed = distance / time speed = 1440 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = ( 1440 x 3 / 5 ) km / hr = 864 km / hr answer e ) 864 km / hr"
Answer: e
Problem: if 9 engines consume 24 metric tonnes of coal , when each is working 8 hoursday , bow much coal will be required for 8 engines , each running 13 hours a day , it being given that 3 engines of former type consume as much as 4 engines of latter type ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) none of them
Rationale: let 3 engines of former type consume 1 unit in 1 hour . then , 4 engines of latter type consume 1 unit in 1 hour . therefore 1 engine of former type consumes ( 1 / 3 ) unit in 1 hour . 1 engine of latter type consumes ( 1 / 4 ) unit in 1 hour . let the required consumption of coal be x units . less engines , less coal consumed ( direct proportion ) more working hours , more coal consumed ( direct proportion ) less rate of consumption , less coal consumed ( direct prportion ) number of engines 9 : 8 working hours 8 : 13 } : : 24 : x rate of consumption ( 1 / 3 ) : ( 1 / 4 ) [ 9 x 8 x ( 1 / 3 ) x x ) = ( 8 x 13 x ( 1 / 4 ) x 24 ) = 24 x = 624 = x = 26 . hence , the required consumption of coal = 26 metric tonnes . answer is c .
Answer: c
Problem: the value of log 2 ( log 5625 ) is
Options: a ) 2 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: solution let log 5625 = x . then , 5 x = 625 = 54 ‹ = › x = 4 . let log 2 ( log 5625 ) = y . then , log 24 = y ‹ = › 2 y = 4 y ; 2 . answer a
Answer: a
Problem: if 16 percent of the students at a certain school went to a camping trip and took more than $ 100 , and 75 percent of the students who went to the camping trip did not take more than $ 100 , what percentage of the students at the school went to the camping trip ?
Options: a ) 95 , b ) 90 , c ) 85 , d ) 80 , e ) 64
Rationale: "let x be the number of students in the school . 0.16 x students went to the trip and took more than 100 $ . they compose ( 100 - 75 ) = 25 % of all students who went to the trip . therefore the toal of 0.16 x / 0.25 = 0.64 x students went to the camping which is 64 % . the answer is e"
Answer: e
Problem: a man sitting in a train which is traveling at 55 kmph observes that a goods train , traveling in opposite direction , takes 10 seconds to pass him . if the goods train is 320 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 60 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 320 / 10 m / sec = ( ( 320 / 10 ) × ( 18 / 5 ) ) kmph = 115 kmph . speed of goods train = ( 115 - 55 ) kmph = 60 kmph answer : option c"
Answer: c
Problem: a man invests some money partly in 10 % stock at 90 and partly in 5 % stock at 90 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 1 : 2 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 10 % stock at 90 , investment = rs . ( 90 / 10 ) = rs . 9 . for an income of rs . 1 in 5 % stock at 90 , investment = rs . ( 90 / 5 ) = rs . 18 . ∴ ratio of investments = 9 : 18 = 1 : 2 answer a"
Answer: a
Problem: average of 10 matches is 32 , how many runs one should should score to increase his average by 6 runs .
Options: a ) a ) 70 , b ) b ) 76 , c ) c ) 78 , d ) d ) 98 , e ) e ) 88
Rationale: "explanation : average after 11 innings should be 38 so , required score = ( 11 * 38 ) - ( 10 * 32 ) = 418 - 320 = 98 answer : option d"
Answer: d
Problem: solve below question 2 x + 1 = - 23
Options: a ) - 8 , b ) - 9 , c ) - 12 , d ) - 4 , e ) 12
Rationale: 1 . subtract 1 from both sides : 2 x + 1 - 1 = - 23 - 1 2 . simplify both sides : 2 x = - 24 3 . divide both sides by 2 : 4 . simplify both sides : x = - 12 c
Answer: c
Problem: calculate 85184 ÷ ? = 352
Options: a ) 241 , b ) 242 , c ) 244 , d ) 247 , e ) 240
Rationale: "answer let 85184 ÷ x = 242 then x = 85184 / 242 = 352 . option : b"
Answer: b
Problem: 7.51 8.22 7.86 8.36 8.09 7.83 8.30 8.01 7.73 8.25 7.96 8.53 a vending machine is designed to dispense 8 ounces of coffee into a cup . after a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine , the 12 listed amounts , in ounces , were selected from the data above . if the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.4 ounces , how many of the 12 listed amounts are within 1.5 standard deviation of the mean ?
Options: a ) four , b ) six , c ) nine , d ) ten , e ) twelve
Rationale: mean = 8.1 standard deviation = 0.4 within 1.5 standard deviation of the mean i . e . 1.5 standard deviation above the mean = 8.1 + 1.5 * 0.4 = 8.7 and 1.5 standard deviation below the mean = 8.1 - 1.5 * 0.4 = 7.5 all values are within the range hence , 12 values fall within 1.5 sd from mean answer : option e
Answer: e