Cheukting/mathqa huggingface dataset:
Question (general): how many integers k greater than 100 and less than 1100 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 9 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 8 . 809 | 908 9 . 910 | 1001 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 9 sets with 10 such number in each set will give 9 x 10 = 90 integers . e"
Answer: e
Question (general): anil had to do a multiplication . instead of taking 35 as one of the multipliers , he took 53 . as a result , the product went up by 540 . what is the new product ?
Options: a ) 1590 , b ) 1600 , c ) 1950 , d ) 1630 , e ) 1760
Rationale: explanation : let the number that anil wanted to multiply be ' y ' . he was expected to find the value of 35 y . instead , he found the value of 53 y . the difference between the value that he got ( 53 y ) and what he was expected to get ( 35 y ) is 540 . = > 53 y - 35 y = 540 = > ( 53 - 35 ) * y = 540 = > y = 30 therefore , the correct product = 53 * 30 = 1590 answer : a
Answer: a
Question (gain): at what rate percent of simple interest will a sum of money double itself in 33 years ?
Options: a ) 6.54 % , b ) 4.54 % , c ) 8 . 2 % , d ) 3.03 % , e ) 5.54 %
Rationale: "let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 33 ) = 100 / 33 = 3.03 % answer : d"
Answer: d
Question (physics): a 360 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 216 , e ) 112
Rationale: "s = 360 / 6 * 18 / 5 = 216 kmph answer : d"
Answer: d
Question (gain): a trader bought a car at 30 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 118 , b ) 110 , c ) 112 , d ) 113 , e ) 98
Rationale: "original price = 100 cp = 70 s = 70 * ( 140 / 100 ) = 98 100 - 112 = 2 % answer : e"
Answer: e
Question (general): one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 25 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 51 , b ) 20 , c ) 40 , d ) 50 , e ) 55
Rationale: "x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 25 x / 10 = 5 x = 50 answer : d"
Answer: d
Question (physics): a train is 310 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 36 seconds , b ) 18 seconds , c ) 40 seconds , d ) 19 seconds , e ) 45 seconds
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 310 + 140 = 500 meter time = distance / speed = 450 * ( 2 / 25 ) = 36 seconds answer : a"
Answer: a
Question (physics): a 49 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 12 , b ) 20 , c ) 88 , d ) 77 , e ) 14
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 49 = 14 answer : e"
Answer: e
Question (general): there are 6 boxes numbered 1 , 2 , . . . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is :
Options: a ) 5 , b ) 21 , c ) 33 , d ) 60 , e ) 6
Rationale: "explanatory answer list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . choice b"
Answer: b
Question (general): the overall age of x and y is 18 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 18
Rationale: "e 18 ( x + y ) â € “ ( y + z ) = 18 x â € “ z = 18"
Answer: e
Question (physics): tom , working alone , can paint a room in 8 hours . peter and john , working independently , can paint the same room in 4 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 ) 4 / 7 , b ) 5 / 7 , c ) 6 / 7 , d ) 1 / 7 , e ) 3 / 7
Rationale: "let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 8 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 4 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 8 * ( t + 4 ) + 1 / 4 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 8 - - > ( t + 4 ) + ( 2 t + 2 ) + 4 t = 8 - - > t = 2 / 7 ; hence peter has done 1 / 4 * ( 2 / 7 + 2 ) = 1 / 4 * 16 / 7 = 16 / 28 = 8 / 14 = 4 / 7 answer : a"
Answer: a
Question (general): a boy rides his bicycle 10 km at an average sped of 12 km / hr and again travels 12 km at an average speed of 10 km / hr . his average speed for the entire trip is approximately .
Options: a ) 10.2 kmph , b ) 10.4 kmph , c ) 10.8 kmph , d ) 11.8 kmph , e ) none
Rationale: sol . total distance travelled = ( 10 + 12 ) km / hr = 22 km / hr . total time taken = [ 10 / 12 + 12 / 10 ] hrs = 61 / 30 hrs ∴ average speed = [ 22 * 30 / 61 ] km / hr = 10.8 km / hr . answer c
Answer: c
Question (general): ( a / 2 ) / ( b / c ) in the expression above , a , b , and c are different numbers and each is one of the numbers 1 , 2 , or 4 . what is the largest possible value of the expression ?
Options: a ) 8 / 2 , b ) 2 / 4 , c ) 1 / 8 , d ) 2 / 4 , e ) 4 / 6
Rationale: ( a / 2 ) / ( b / c ) = ( a * c ) / 2 b the expression will have the largest value when numerator ( a * c ) is the largest . = ( 2 * 4 ) / 2 * 1 = 8 / 2 answer a
Answer: a
Question (other): in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 190 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 494 , e ) 512
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 190 x = 38 total number of students = 13 x = 13 * 38 = 494 answer is d"
Answer: d
Question (general): if the numerator of a fraction be increased by 15 % and its denominator be diminished by 8 % , the value of the fraction is 15 / 16 . find the original fraction ?
Options: a ) 1 / 2 , b ) 3 / 5 , c ) 5 / 7 , d ) 9 / 11 , e ) 3 / 4
Rationale: "let the original fraction be x / y then , 115 % of x / 92 % of y = 15 / 16 115 x / 92 y = 15 / 16 x / y = 3 / 4 answer is e"
Answer: e
Question (general): simplify : 32 ÷ 8 × 24 + 16 =
Options: a ) 130 , b ) 124 , c ) 120 , d ) 115 , e ) 112
Rationale: "32 ÷ 8 × × 24 + 16 = > 4 × × 24 + 16 = 96 + 16 = 112 option e"
Answer: e
Question (general): a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"
Answer: b
Question (general): the tax on a commodity is diminished by 32 % but its consumption is increased by 12 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 15 % , d ) 12 % , e ) 24 %
Rationale: "100 * 100 = 10000 68 * 112 = 7616 10000 - - - - - - - 2384 100 - - - - - - - ? = 24 % answer : e"
Answer: e
Question (general): 106 x 106 - 94 x 94 = ?
Options: a ) 2400 , b ) 2000 , c ) 1904 , d ) 1906 , e ) none of them
Rationale: "= ( 106 ) ^ 2 - ( 94 ) ^ 2 = ( 106 + 94 ) ( 106 - 94 ) = ( 200 x 12 ) = 2400 answer is a"
Answer: a
Question (other): of the 90 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 90 - 50 - ( 40 - 35 ) = 90 - 55 = 35 answer e"
Answer: e
Question (physics): how many cuboids of length 5 m , width 6 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 4 , b ) 6 , c ) 10 , d ) 8 , e ) 11
Rationale: "( 18 ã — 15 ã — 12 ) / ( 5 ã — 3 ã — 2 ) = 6 answer is b ."
Answer: b
Question (general): when x is multiplied by 3 , the result is 26 more than the result of subtracting x from 26 . what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
Rationale: "the equation that can be formed is : 3 x - 26 = 26 - x or , 4 x = 52 or , x = 13 . d answer ."
Answer: d
Question (general): the sum of digits of a two digit number is 11 , the difference between the digits is 5 . find the number
Options: a ) 85 , b ) 94 , c ) 83 , d ) 72 , e ) none
Rationale: "description : = > x + y = 11 , x - y = 5 adding these 2 x = 16 = > x = 8 , y = 3 . thus the number is 83 answer c"
Answer: c
Question (general): if x , y , and z are positive integers and 3 x = 7 y = 5 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 25 , c ) 71 , d ) 35 , e ) 45
Rationale: "given 3 x = 7 y = 5 z x + y + z in terms of x = x + ( 3 x / 7 ) + ( 3 x / 5 ) = 71 x / 35 now checking with each of the answers and see which value gives a minimum integer value . a x = 35 / 71 * 15 , not an integer b , d , e can be ruled out similarly . c is minimum value as x = 71 * 35 / 71 = 35 answer is c"
Answer: c
Question (general): a sports retailer ordered white and yellow tennis balls in equal number but the dispatch clerk of the tennis ball company erred and dispatched 90 extra yellow balls and making ratio of white balls to yellow balls 8 / 13 . how many tennis balls did the retailer order originally .
Options: a ) 180 , b ) 130 , c ) 140 , d ) 160 , e ) 288
Rationale: "white : yellow = x : ( x + 90 ) = 8 : 13 - - > 13 x = 8 x + 720 - - > x = 144 . the total # of balls originally x + x = 144 + 144 = 288 . answer : e ."
Answer: e
Question (general): a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Question (physics): if two girls starting from same point , walking in the opposite directions with 5 km / hr and 10 km / hr as average speeds respectively . then the distance between them after 5 hours is ?
Options: a ) 45 , b ) 55 , c ) 65 , d ) 75 , e ) 85
Rationale: "explanation : total distance = distance traveled by person a + distance traveled by person b = ( 5 ã — 5 ) + ( 10 ã — 5 ) = 25 + 50 = 75 km answer : d"
Answer: d
Question (general): in the junior basketball league there are 15 teams , 1 / 3 of them are bad and ½ are rich . what ca n ' t be the number of teams that are rich and bad ?
Options: a ) 4 . , b ) 6 . , c ) 7 . , d ) 8 . , e ) 9 .
Rationale: "total teams = 15 bad teams = ( 1 / 3 ) * 15 = 5 rich teams = 8 so maximum value that the both rich and bad can take will be 8 . so e = 9 can not be that value . ans e ."
Answer: e
Question (geometry): the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 2028 sq m , then what is the breadth of the rectangular plot ?
Options: a ) 11 , b ) 17 , c ) 26 , d ) 101 , e ) 1322
Rationale: "let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 2028 3 b 2 = 2028 b 2 = 676 = 26 ( b > 0 ) b = 26 m . answer : c"
Answer: c
Question (general): find the least number which when divided by 5 , 67 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a
Answer: a
Question (general): xavier , yvonne , and zelda each try independently to solve a problem . if their individual probabilities for success are 1 / 6 , 1 / 2 and 5 / 8 , respectively , what is the probability that xavier and yvonne , but not zelda , will solve the problem ?
Options: a ) 1 / 32 , b ) 7 / 8 , c ) 9 / 64 , d ) 5 / 64 , e ) 3 / 64
Rationale: "p ( xavier will solve ) = 1 / 6 p ( yvonne will solve ) = 1 / 2 p ( zelda will not solve ) = 1 - 5 / 8 = 3 / 8 . now , we need to multiply all this ps to find an answer : p = ( 1 / 6 ) * ( 1 / 2 ) * ( 3 / 8 ) = 1 / 32 . ans . a ."
Answer: a
Question (general): for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.267 ] = 1 and [ 1.999 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 0 , c ) 27 , d ) 54 , e ) can not be determined
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . b"
Answer: b
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 22 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 166 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 22 = 40 5 * quotient = 40 quotient = 8 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 8 ) + 6 = 166 . b )"
Answer: b
Question (gain): a sum fetched total simple interest of 4016.25 at the rate of 11 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 8925 , b ) 8032.5 , c ) 7302.3 , d ) 8900 , e ) none of these
Rationale: "let the sums be p . now , 55 % of p = 4016.25 or , p = 7302.3 answer c"
Answer: c
Question (physics): a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , three boggies were detached . the train now crosses a telegraph post in
Options: a ) 18 sec , b ) 12 sec , c ) 15 sec , d ) 20 sec , e ) 13.5 sec
Rationale: "length of train = 12 ã — 15 = 180 m . then , speed of train = 180 â  „ 18 = 10 m / s now , length of train = 9 ã — 15 = 135 m â ˆ ´ required time = 135 â  „ 10 = 13.5 sec . answer e"
Answer: e
Question (gain): what is the cp of rs 100 stock at 8 discount , with 1 / 5 % brokerage ?
Options: a ) 92.9 , b ) 96.3 , c ) 92.2 , d ) 96.7 , e ) 92.8
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 8 + 1 / 5 92.2 thus the cp is rs 92.2 . answer : c"
Answer: c
Question (general): zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 27 kg of zinc has been consumed in it ?
Options: a ) 58 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 27 kg zinc , mixture , melted = [ 20 / 9 x 27 ] kg = 60 kg . answer b"
Answer: b
Question (general): if x is an integer such that 3 < x < 10 , 5 < x < 18 , 9 > x > – 2 , 8 > x > 0 , and x + 1 < 9 , then x is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "3 < x < 10 , 6 < x < 18 , - 2 < x < 9 0 < x < 8 x < 8 from above : 6 < x < 8 - - > x = 7 . answer : c ."
Answer: c
Question (general): if n is a positive integer greater than 1 , then p ( n ) represents the product of all the prime numbers less than or equal to n . the second smallest prime factor of p ( 12 ) + 11 is
Options: a ) 2 , b ) 11 , c ) 13 , d ) 17 , e ) 211
Rationale: p ( 12 ) + 11 = 2 ∗ 3 ∗ 5 ∗ 7 ∗ 11 + 11 = 11 ( 2 ∗ 3 ∗ 5 ∗ 7 + 1 ) = 11 ∗ 211 . both 11 and 211 are primes : 11 is the smallest prime of p ( 12 ) + 11 and 211 is the second smallest prime of p ( 12 ) + 11 . answer : e .
Answer: e
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 140 marks , the no of questions he attempts correctly is :
Options: a ) a ) 35 , b ) b ) 38 , c ) c ) 90 , d ) d ) 88 , e ) e ) 40
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 140 = > 5 x = 200 = > x = 40 answer : e"
Answer: e
Question (general): the average ( arithmetic mean ) of 4 different integers is 70 . if the largest integer is 90 , what is the least possible value of the smallest integer ?
Options: a ) 1 , b ) 19 , c ) 29 , d ) 13 , e ) 33
Rationale: "total of integers = 70 * 4 = 280 lowest of the least possible integer is when the middle 2 intergers are at the maximum or equal to the highest possible integer . but all integers are distinct . so if the largest integer is 90 , then the middle 2 will be 88 and 89 lowest of least possible integer = 280 - ( 90 + 89 + 88 ) = 280 - 267 = 13 answer : d"
Answer: d
Question (gain): double of quarter of 6 percent written as a decimal is :
Options: a ) 0.03 , b ) 0.0005 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 6 % = 0.03 answer : a"
Answer: a
Question (physics): p and q can complete a work in 20 days and 12 days respectively . p alone started the work and q joined him after 4 days till the completion of the work . how long did the work last ?
Options: a ) 5 days , b ) 10 days , c ) 14 days , d ) 22 days , e ) 26 days
Rationale: "explanation : work done by p in 1 day = 1 / 20 work done by q in 1 day = 1 / 12 work done by p in 4 days = 4 × ( 1 / 20 ) = 1 / 5 remaining work = 1 – 1 / 5 = 4 / 5 work done by p and q in 1 day = 1 / 20 + 1 / 12 = 8 / 60 = 2 / 15 number of days p and q take to complete the remaining work = ( 4 / 5 ) / ( 2 / 15 ) = 6 total days = 4 + 6 = 10 answer : option b"
Answer: b
Question (physics): if in one hour , a canoe rows at 16 km / hr downstream and 9 km / hr upstream , calculate the speed of a boat in still water ( in km / hr ) .
Options: a ) 18 kmph , b ) 15.5 kmph , c ) 12.5 kmph , d ) 13.5 kmph , e ) 22.5 kmph
Rationale: speed in still water = ( 16 + 9 ) 1 / 2 kmph = 12.5 kmph . answer : c
Answer: c
Question (physics): a rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it . one parallel to the length and the other parallel to breadth . the cost of graveling the roads at 75 paise per sq meter is ?
Options: a ) rs . 259 , b ) rs . 252 , c ) rs . 258 , d ) rs . 251 , e ) rs . 252
Rationale: "area of cross roads = 55 * 4 + 35 * 4 - 4 * 4 = 344 sq m cost of graveling = 344 * ( 75 / 100 ) = rs . 258 answer : c"
Answer: c
Question (general): a salesman ` s commission is 5 % on all sales upto rs . 10000 and 4 % on all sales exceeding this . he remits rs . 31100 to his parent company after deducing his commission . find the total sales .
Options: a ) 32500 , b ) 2500 , c ) 22500 , d ) 30000 , e ) 40000
Rationale: let his total sales be rs . x . now ( total sales ) – ( commission ) = rs . 31100 x - [ ( 5 % of 10000 + 4 % of ( x - 10000 ) ] = 31100 x - [ ( ( 5 / 100 ) * 10000 + ( 4 / 100 ) * ( x - 10000 ) ] = 31100  x - 500 - ( ( x - 10000 ) / 25 ) = 31100  x - ( x / 25 ) = 31200  24 x / 25 = 31200  x = [ ( 31200 * 25 ) / 24 ) = 32500 . total sales = rs . 32500 answer a
Answer: a
Question (general): approximately how many revolutions will be made by a car tire with a 15 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 669 , b ) 660 , c ) 360 , d ) 720 , e ) 1,440
Rationale: diameter of car tire = 15 inches radius of car tire = 7.5 inches = 7.5 * 2.54 cm = 19.05 cm circumference of the car tire = 2 * pi * 19.05 = 2 * 3.14 * 19.05 = 119.63 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 119.63 = 668.73 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer a
Answer: a
Question (geometry): the area of an isosceles trapezoid with sides of length 5 and bases of length 7 and 13 is ?
Options: a ) 40
b ) 41
c ) 42
d ) 43
e ) 44
Rationale: isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 13 will be divided into 3 parts = 7 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 20 * 4 = 40 a
Answer: a
Question (general): 16 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 240
Rationale: 2 * 16 c 2 = 2 * 120 = 240 the answer is e .
Answer: e
Question (general): the grade point average of one third of the classroom is 30 ; the grade point average of the rest is 33 . what is the grade point average of the whole class ?
Options: a ) 44 , b ) 41 , c ) 38 , d ) 35 , e ) 32
Rationale: "let n = total students in class total points for 1 / 3 class = 30 n / 3 = 10 n total points for 2 / 3 class = 33 * 2 n / 3 = 22 n total points for whole class = 10 n + 22 n = 32 n 32 n total class points / n total students = 32 grade point average for total class answer : e"
Answer: e
Question (geometry): in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 4,4 ) , ( 7,4 ) , ( 5,9 ) , ( 8,9 ) ?
Options: a ) 21 .
b ) 28 .
c ) 5 .
d ) 49 .
e ) 52 .
Rationale: delta x will give us the dimension of one side of the parallelogram = 5 - 4 = 1 unit delta y will give us the dimension of the other side of parallelogram = 9 - 4 = 5 unit area of parallelogram = 1 * 5 = 5 answer is c
Answer: c