Cheukting/mathqa huggingface dataset:
Question (general): x is a positive integer of t less than 500 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: took me more than 2 mins to solve . that ' s how i did it . x is between 1 - 499 included . smallest number that can be written as 7 n + 1 ( 7 * 0 + 1 ) is 1 largest number that can be written as 7 n + 1 is ( 7 * 71 + 1 ) is 498 so there are total 72 numbers that can be written as 7 n + 1 because x can also be written as 3 m + 2 , we have to see how many numbers that can be written as 7 n + 1 also can be written as 3 m + 2 7 * 0 + 1 can not be written in the form 3 m + 2 7 * 1 + 1 can be written in the form 3 m + 2 7 * 2 + 1 can not be written in the form 3 m + 2 7 * 3 + 1 can not be written in the form 3 m + 2 7 * 4 + 1 can be written in the form 3 m + 2 here we see a sequence that one out of every 4 numbers can be written as 3 m + 1 72 / 4 = 24 numbers can be written as 3 m + 1 d is the answer
Answer: d
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paving the floor by slabs at the rate of rs . 1400 per sq . metre .
Options: a ) rs . 15000 , b ) rs . 15550 , c ) rs . 15600 , d ) rs . 28875 , e ) none of these
Rationale: "solution area of the floor = ( 5.5 × 3.75 ) m 2 = 20.625 m 2 ∴ cost of paving = rs . ( 1400 × 20.625 ) = 28875 . answer d"
Answer: d
Question (general): in a rectangular box measuring 12 inches by 14 inches by 16 inches if small rectangular boxes measuring 3 inches by 7 inches by 2 inches are arranged in it , what is the max number of boxes that fit into it ?
Options: a ) 23 , b ) 32 , c ) 44 , d ) 15 , e ) 64
Rationale: the 3 inch side should be aligned to the 12 inch side ( 4 layer ) 7 inch side should be aligned to the 14 inch side . ( 2 layer ) and 2 inch side should be aligned to the 16 inch side . ( 8 layer ) maximum number of rectangles = 4 * 2 * 8 = 64 answer is e
Answer: e
Question (general): ashis ' s height is 25 % more than babji , by how much percent babji ' s height is less than ashis .
Options: a ) 30 % , b ) 25 % , c ) 75 % , d ) 20 % , e ) none of these
Rationale: explanation : solution : babji is less than ashis by ( 25 / ( 100 + 25 ) * 100 ) % = 20 % answer : d
Answer: d
Question (general): what is the difference between the place value and the face value of 7 in the numeral 297832 ?
Options: a ) none of these , b ) 5993 , c ) 994 , d ) 5994 , e ) 995
Rationale: explanation : place value of 6 = 7000 face value of 6 = 7 difference = 6000 - 7 = 5993 answer : b
Answer: b
Question (general): in a graduating class , 40 percent of the students are male . in this class , 40 percent of the male students and 20 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) 0.9 , b ) 0.72 , c ) 0.45 , d ) 0.35 , e ) 0.28
Rationale: "let x be the total number of students . the number students who are younger than 25 is 0.6 * 0.4 x + 0.8 * 0.6 x = 0.72 x the answer is b ."
Answer: b
Question (general): what is the least number to be subtracted from 696 to make it a perfect square ?
Options: a ) 1 , b ) 16 , c ) 20 , d ) 71 , e ) 60
Rationale: "the numbers less than 696 and are squares of certain numbers are 676 , 625 . the least number that should be subtracted from 696 to make it perfect square = 696 - 676 = 20 . answer : c"
Answer: c
Question (general): if the remainder is 12 when the integer n is divided by 22 , what is the remainder when 2 n is divided by 11 ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: "n = 22 k + 12 2 n = 2 ( 22 k + 12 ) = 4 * 11 k + 24 = 4 * 11 k + 2 * 11 + 2 = 11 j + 2 . the answer is b ."
Answer: b
Question (general): the average marks of a class of 30 students is 40 and that of another class of 50 students is 80 . find the average marks of all the students ?
Options: a ) 52.5 , b ) 52.9 , c ) 52.1 , d ) 52.3 , e ) 65
Rationale: "sum of the marks for the class of 30 students = 30 * 40 = 1200 sum of the marks for the class of 50 students = 50 * 80 = 4000 sum of the marks for the class of 80 students = 1200 + 4000 = 5200 average marks of all the students = 5200 / 80 = 65 answer : e"
Answer: e
Question (geometry): a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( - 1 , - 4 ) . what is the smallest possible area of that circle ?
Options: a ) 13 π
b ) 26 π
c ) 262 √ π
d ) 52 π
e ) 4 π
Rationale: the distance between the two points is sqrt ( 8 ) radius = sqrt ( 8 ) / 2 area = pi * ( sqrt ( 8 ) / 2 ) ^ 2 e . 4 π
Answer: e
Question (other): a jar contains a mixture of a & b in the ratio 4 : 1 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 16 , d ) 20 , e ) 25
Rationale: 10 litres of mixture that is replaced will contain 8 litres of a and 2 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 8 ] / [ k - 2 + 10 ] = 2 / 3 solve for k which is k = 4 so initial volume of liquid a = 4 k = 16 litres answer : c
Answer: c
Question (other): at an m & m factory , two types of m & ms are produced , red and blue . the m & ms are transported individually on a conveyor belt . anna is watching the conveyor belt , and has determined that 4 out of every 5 red m & ms are followed by a blue one , while one out of every 6 blue m & ms is followed by a red one . what proportion of the m & ms are red ?
Options: a ) 1 / 29 , b ) 2 / 29 , c ) 3 / 29 , d ) 4 / 29 , e ) 5 / 29
Rationale: suppose that the fraction of red m & ms is fr and the fraction of blue m & ms is fb . then the probability that anna sees a red one emerge next is fr . this probabil - ity can also be expressed using conditional probabilities as fr = p ( blue ) p ( red after blue ) + p ( red ) p ( red after red ) , or fr = fb ( 1 = 6 ) + fr ( 1 = 5 ) . likewise , we find fb = fr ( 4 = 5 ) + fb ( 5 = 6 ) . solving the system of equations gives fb = 24 29 and fr = 5 / 29 correct answer e
Answer: e
Question (other): in a certain corporation , there are 300 male employees and 150 female employees . it is known that 50 % of the male employees have advanced degrees and 40 % of the females have advanced degrees . if one of the 450 employees is chosen at random , what is the probability this employee has an advanced degree or is female ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "p ( female ) = 150 / 450 = 1 / 3 p ( male with advanced degree ) = 0.5 * 300 / 450 = 150 / 450 = 1 / 3 the sum of the probabilities is 2 / 3 the answer is b ."
Answer: b
Question (gain): ravi and kavi start a business by investing â ‚ ¹ 5000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 72 , b ) 5 : 72 , c ) 7 : 72 , d ) 1 : 72 , e ) 3 : 72
Rationale: "ratio of profit = ratio of investments = 5000 : 72000 = 5 : 72 answer : b"
Answer: b
Question (general): if a ( a + 2 ) = 99 and b ( b + 2 ) = 99 , where a ≠ b , then a + b =
Options: a ) - 2 , b ) - 5 , c ) - 8 , d ) - 10 , e ) - 12
Rationale: "i . e . if a = 9 then b = - 11 or if a = - 11 then b = 9 but in each case a + b = - 11 + 9 = - 2 answer : a"
Answer: a
Question (general): three numbers are in the ratio 5 : 4 : 6 and their average is 750 . the largest number is :
Options: a ) 30 , b ) 98 , c ) 900 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be 5 x , 4 x and 6 x , then , ( 5 x + 4 x + 6 x ) / 3 = 750 = > 15 x = 750 * 3 = > x = 150 largest number 6 x = 6 * 150 = 900 answer : c"
Answer: c
Question (gain): by selling 18 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 8 , b ) 12 , c ) 6 , d ) 4 , e ) 9
Rationale: "80 % - - - 18 120 % - - - ? 80 / 120 * 18 = 12 answer : b"
Answer: b
Question (general): find the average of all numbers between 3 and 69 which are divisible by 5
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 ) / 13 = 455 / 13 = 35 answer : option e"
Answer: e
Question (general): if x is a sum of all even integers on the interval 13 . . . 63 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 13 , c ) 26 , d ) 25 , e ) 1014
Rationale: x = 14 + 16 + . . . + 62 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 62 ) / 2 * 25 = 38 * 25 . gcd of 25 and 39 * 25 is 25 . answer : d .
Answer: d
Question (gain): joe invested a certain sum of money in a simple interest bond whose value grew to $ 260 at the end of 3 years and to $ 360 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 6 % , b ) 8 % , c ) 10 % , d ) 12 % , e ) 15 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 260 - $ 60 = 200 . the interest rate is $ 20 / $ 200 = 10 % the answer is c ."
Answer: c
Question (general): a cuban cigar would cost 3 dollar less than 1.5 times a french cigar , had the french cigar cost 0.7 dollar less than it does now . an arabian cigar costs 50 cents more than 1.5 times the cuban cigar . the 3 cigars together cost 74.7 dollars . what is the price of the french cigar ?
Options: a ) 19.7 $ . , b ) 23 $ . , c ) 14.7 $ . , d ) 35 $ . , e ) 37.4 $ .
Rationale: the three cigars together cost 74.7 dollars . if each cost the same , they would have cost a little less than 25 dollars each . from the given data we know french cigar < cuban cigar < arabic cigar and each is more expensive 1.5 times . therefore eliminate options a , d , e straightaway . since french cigar is at least 1.5 times cheaper we know b can not be the answer . therefore c is the answer .
Answer: c
Question (gain): the salary of a worker is first increased by 15 % and afterwards reduced by 15 % . what is the net change in the worker ' s salary ?
Options: a ) 5.25 % increase , b ) 5.25 % decrease , c ) 2.25 % increase , d ) 2.25 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.85 ( 1.15 x ) = 0.9775 x the answer is d ."
Answer: d
Question (general): a company decreased the price of its main product by 25 % . subsequently , the number of units sold increased such that the total revenue remained unchanged . what was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product ?
Options: a ) 2.0 , b ) 4.0 , c ) 5.0 , d ) 6.0 , e ) 8.0
Rationale: "for the total revenue to remain the same when the price is one fourth , the number of products sold must four times . therefore increase in the number of products sold is 100 % = > the required ratio = 100 % / 25 % = 4.0 answer : b"
Answer: b
Question (other): a firm is comprised of partners and associates in a ratio of 2 : 63 . if 35 more associates were hired , the ratio of partners to associates would be 1 : 34 . how many partners are currently in the firm ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the ratio 1 : 34 = 2 : 68 so the ratio changed from 2 : 63 to 2 : 68 . 68 - 63 = 5 which is 1 / 7 of the increase in 35 associates . the ratio changed from 14 : 441 to 14 : 476 . thus the number of partners is 14 . the answer is b ."
Answer: b
Question (geometry): carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 9 inches long , how wide is jordan ' s rectangle , in inches ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: "area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d"
Answer: d
Question (other): x starts a business with rs . 45000 . y joins in the business after 6 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 3 : 1 , d ) 2 : 3 , e ) 5 : 3
Rationale: "ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 30000 × 6 = 45 × 12 : 30 × 6 = 3 × 12 : 2 × 6 = 3 : 1 answer is c"
Answer: c
Question (gain): sam invested $ 1000 @ 20 % per annum for one year . if the interest is compounded half yearly , then the amount received by sam at the end of the year will be ?
Options: a ) $ 1542 , b ) $ 1145 , c ) $ 1210 , d ) $ 1642 , e ) $ 1020
Rationale: "p = $ 1000 r = 20 % p . a . = 10 % t = 2 half years amount = 1000 * ( 1 + 10 / 100 ) ^ 2 = 1000 * 11 / 10 * 11 / 10 = $ 1210 answer is c"
Answer: c
Question (general): solve below question 3 x - 5 = - 20
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 1
Rationale: 1 . subtract 1 from both sides : 3 x - 5 + 5 = - 20 + 5 2 . simplify both sides : 3 x = - 15 3 . divide both sides by 3 : 4 . simplify both sides : x = - 5 c
Answer: c
Question (general): the average of runs of a cricket player of 10 innings was 30 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 74 , c ) 10 , d ) 76 , e ) 17
Rationale: "average after 11 innings = 34 required number of runs = ( 34 * 11 ) - ( 30 * 10 ) = 374 - 300 = 74 . answer : b"
Answer: b
Question (general): if 30 % of a number is equal to one - fourth of another number , what is the ratio of first number to the second number ?
Options: a ) 4 : 7 , b ) 6 : 5 , c ) 1 : 2 , d ) 2 : 3 , e ) 5 : 6
Rationale: let 30 % of a = 1 / 4 b . then , 30 a / 100 = 1 b / 4 = > 3 a / 10 = 1 b / 4 a / b = ( 1 / 4 * 10 / 3 ) = 5 / 6 a : b = 5 : 6 . answer : e
Answer: e
Question (physics): a cistern is two - third full of water . pipe a can fill the remaining part in 12 minutes and pipe b in 8 minutes . once the cistern is emptied , how much time will they take to fill it together completely ?
Options: a ) 12 minutes , b ) 12.5 min , c ) 14.4 min , d ) 10.2 min , e ) 14.66 min
Rationale: as pipe a takes 12 min . to fill remaining one - third it takes 36 min . to fill completely . similarly pipe b takes 24 min . to fill completely so , total time taken by both together is reciprocal of : ( 1 / 36 ) + ( 1 / 24 ) = 5 / 72 ans : 14.4 min . answer : c
Answer: c
Question (geometry): what should be added to 5021 so that it may become a perfect square ?
Options: a ) 20 , b ) 23 , c ) 26 , d ) 27 , e ) 29
Rationale: "71 x 71 = 5041 5041 - 5021 = 20 if added to 20 get perfect square answer = a"
Answer: a
Question (general): when a student joe , weighing 44 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 36.5 kg , e ) 7 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 44 + 30 = 74 so , the average the two persons = 37 that gives the answer 44 - 37 = 7 answer e"
Answer: e
Question (gain): 70 is what percent of 125 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 56 %
Rationale: 70 / 125 × 100 = 56 % answer : e
Answer: e
Question (general): ( 525 + 275 ) ã — 4 ã — ( 3 + 2 ) = ?
Options: a ) 12000 , b ) 24000 , c ) 16000 , d ) 14000 , e ) 16200
Rationale: "( 525 + 275 ) ã — 4 ã — ( 3 + 2 ) = ? or , ? = 800 ã — 4 ã — 5 = 16000 answer c"
Answer: c
Question (general): if a 2 - b 2 = 8 and a * b = 2 , find a 4 + b 4 .
Options: a ) 62 , b ) 72 , c ) 82 , d ) 92 , e ) 62
Rationale: "a 2 - b 2 = 8 : given a 4 + b 4 - 2 a 2 b 2 = 82 : square both sides and expand . a * b = 2 : given a 2 b 2 = 22 : square both sides . a 4 + b 4 - 2 ( 4 ) = 82 : substitute a 4 + b 4 = 72 correct answer b"
Answer: b
Question (general): when positive integer x is divided by positive integer y , the remainder is 5.76 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 5.76 - - > x = qy + 5.76 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 5.76 - - > y = 48 . answer : c ."
Answer: c
Question (physics): timothy leaves home for school , riding his bicycle at a rate of 6 miles per hour . fifteen minutes after he leaves , his mother sees timothy ’ s math homework lying on his bed and immediately leaves home to bring it to him . if his mother drives at 36 miles per hour , how far ( in terms of miles ) must she drive before she reaches timothy ? i think is a 700 level problem but i tag it as 600 / 700 , let me know . either way i hope in an explanationthanks
Options: a ) 1 / 3 , b ) 9 / 5 , c ) 4 , d ) 9 , e ) 12
Rationale: in 15 mins , timothy travels = 6 / 4 miles . now , let his mother takes x hours to reach him , traveling at 36 mph . so , 36 x = 6 x + 6 / 4 x = 1 / 20 hrs . thus , the distance traveled by his mother to reach = 36 * 1 / 20 = 9 / 5 miles . ans b
Answer: b
Question (general): in a group of cows and hens , the number of legs are 20 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 10 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 20 2 x = 20 x = 10 . answer : d"
Answer: d
Question (physics): two trains of equal length , running with the speeds of 60 and 40 kmph , take 55 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 13 sec , d ) 67 sec , e ) 11 sec
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 55 d = 55 * 100 / 18 = 2750 / 9 rs = 60 + 40 = 100 * 5 / 18 t = 2750 / 9 * 18 / 500 = 11 sec answer : e"
Answer: e
Question (general): the instructions state that cheryl needs 5 / 9 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 8 / 24 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 5 / 9 , e ) 2 1 / 9
Rationale: "total bought = 5 / 9 + 1 / 3 left part 8 / 24 - - - > 1 / 3 so used part 5 / 9 + 1 / 3 - 1 / 3 = 5 / 9 answer : d"
Answer: d
Question (general): what is the value of n if the sum of the consecutive odd intergers q from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Question (general): how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 30 % solution ?
Options: a ) a ) 6.7 , b ) b ) 1.3 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 28.6
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 30 / 100 100 + 10 x = 300 + 3 x 7 x = 200 x = 28.6 answer is e"
Answer: e
Question (gain): the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 3600 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2699 , c ) 3000 , d ) 6725 , e ) 2601
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 3600 ( 100 / 120 ) = rs . 3000 answer : c"
Answer: c
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 12 miles per gallon , and from town b to town c , the car averaged 11 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 13.5 , c ) 14 , d ) 14.5 , e ) 15.3
Rationale: "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 12 ) + ( x / 11 ) ) = 15.3 ( formula avg speed = total distance / total time )"
Answer: b
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 30 % on his income , while mindy pays a rate of only 20 % on hers . if mindy earned 3 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 22.5 %
Rationale: say morks income is - 100 so tax paid will be 30 say mindys income is 3 * 100 = 300 so tax paid is 20 % * 300 = 60 total tax paid = 30 + 60 = 90 . combined tax % will be 90 / 100 + 300 = 22.5 %
Answer: e
Question (gain): sahil purchased a machine at rs 9000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22500 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 9000 + 5000 + 1000 = 15000 150 % of 15000 = 150 / 100 * 15000 = 22500 option a"
Answer: a
Question (geometry): find the surface area of a 10 cm * 4 cm * 3 cm brick .
Options: a ) 154 cm square
b ) 156 cm square
c ) 160 cm square
d ) 164 cm square
e ) none of these
Rationale: explanation : surface area of a cuboid = 2 ( lb + bh + hl ) cm square so , surface area of a brick = 2 ( 10 * 4 + 4 * 3 + 3 * 10 ) cm square = 2 ( 82 ) cm square = 164 cm square option d
Answer: d
Question (gain): if a lends rs . 3500 to b at 10 % per annum and b lends the same sum to c at 15 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 525 , b ) 500 , c ) 510 , d ) 530 , e ) 550
Rationale: "( 3500 * 5 * 3 ) / 100 = > 525 answer : a"
Answer: a