regisss/math_qa huggingface dataset:
Problem: little john had $ 7.10 . he spent $ 1.05 on sweets and gave to his two friends $ 1.00 each . how much money was left ?
Options: a ) $ 4.85 , b ) $ 4.15 , c ) $ 4.65 , d ) $ 4.55 , e ) $ 4.05
Rationale: "john spent and gave to his two friends a total of 1.05 + 1.00 + 1.00 = $ 3.05 money left 7.10 - 3.05 = $ 4.05 answer : e"
Answer: e
Problem: in a class of 32 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 10 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 15
Rationale: "total # of students = 32 avg # of books per student = 2 total # of books = 32 * 2 = 64 # of student borrowed at least 3 books = 32 - 2 - 12 - 10 = 8 # of books borrowed by above 8 students = 60 - ( 12 * 1 ) + ( 10 * 2 ) = 32 considering that 7 out of above 8 students borrowed only 3 books , # of books borrowed = 7 * 3 = 21 so maximum # of books borrowed by any single student = 32 - 21 = 11 option d"
Answer: d
Problem: the average of 10 numbers is calculated as 21 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 21 + 36 – 26 = 220 = > 220 / 10 = 22 d )"
Answer: d
Problem: - 45 * 29 + 108 = ?
Options: a ) 1197 , b ) 1897 , c ) - 1197 , d ) - 1900 , e ) none of these
Rationale: "= > - 45 * ( 30 - 1 ) + 108 ; = > - ( 45 * 30 ) + 45 + 108 ; = > - 1350 + 153 = - 1197 . correct option : c"
Answer: c
Problem: in a family gathering , there is a basket in which there are oranges , bananas and apples . half of the people in the family eat oranges , half of the other half eat bananas and the rest eat apples . if the number of people who eat oranges are 10 less than the total number of people , find the number of people in the gathering .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let the number of people who eat oranges be x . then , total number of people = x + ( x / 2 ) + ( x / 2 ) = 2 x = > 2 x - 10 = x = > x = 10 = > total number of people were 2 x = 20 option d
Answer: d
Problem: excluding stoppages , the average speed of a bus is 60 km / hr and including stoppages , the average speed of the bus is 15 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 22 , b ) 88 , c ) 77 , d ) 20 , e ) 45
Rationale: "in 1 hr , the bus covers 60 km without stoppages and 15 km with stoppages . stoppage time = time take to travel ( 60 - 15 ) km i . e 45 km at 60 km / hr . stoppage time = 45 / 60 hrs = 45 min . answer : e"
Answer: e
Problem: in a garment industry , 12 men working 9 hours per day complete a piece of work in 10 days . to complete the same work in 12 days , working 15 hours a day , the number of men required is :
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "explanation : let the required number of men be x . less days , more men ( indirect proportion ) more working hrs per day , less men ( indirect proportion ) days 8 : 10 working hrs 15 : 9 : : 12 : x = > 12 x 15 x x = 10 x 8 x 12 = > x = 10 x 9 x 12 / ( 12 x 15 ) = > x = 7 answer : d"
Answer: d
Problem: laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 20 kmph and prasanna moves southward at a speed of 30 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 28 , d ) 27 , e ) 18
Rationale: explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 20 kmph x 1 hr = 20 km total southward prasanna ' s distance = 30 kmph x 1 hr = 30 km total distance between prasanna and laxmi is = 20 + 30 = 50 km . answer : b
Answer: b
Problem: there is a train and car . the ratio between the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 4 / 5 th of the speed of the train . how many kilometers will the car cover in 7 hours ?
Options: a ) 375 , b ) 425 , c ) 475 , d ) 525 , e ) 575
Rationale: the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 5 ) / 4 = 80 km / hr the speed of the car is 80 / 16 * 15 = 75 km / hr the distance covered by the car in 7 hours is 75 × 7 = 525 km the answer is d .
Answer: d
Problem: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a then what is the units digit for a / ( ( 13 ! ) ^ 4 ) =
Options: a ) 7 , b ) 8 , c ) 9 , d ) 6 , e ) 5
Rationale: ( ( ( 13 ! ) ^ 16 ) - ( ( 13 ! ) ^ 8 ) ) / ( ( ( 13 ! ) ^ 8 ) + ( ( 13 ! ) ^ 4 ) ) = a solving it , we get a / ( ( 13 ! ) ^ 4 ) = ( ( 13 ! ) ^ 4 - 1 ) last digit of ( 13 ! ) ^ 4 will be 0 . so last digit of ( ( 13 ! ) ^ 4 - 1 ) will be 9 . answer : c
Answer: c
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6358 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2200 , c ) 2000 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6358 = x = 6358 / 2.89 = 2200 therefore , amount invested by raghu is rs . 2200 . answer : b"
Answer: b
Problem: jacob is 16 years old . he is 2 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 24
Rationale: "j = 16 ; j = 2 b ; b = 16 / 2 = 8 ; twice as old so b = 8 ( now ) + ( 8 ) = 16 ; jacob is 16 + 8 = 24 answer : e"
Answer: e
Problem: a bag of potatoes weighs 50 lbs divided by half of its weight . how much does the bag of potatoes weigh ?
Options: a ) 10 lb , b ) 20 lb , c ) 30 lb , d ) 40 lb , e ) 50 lb
Rationale: "a 10 lb 50 ÷ 5 = 10 ."
Answer: a
Problem: in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors a ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have a = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Problem: the payment per hour for a daily - wages employee is increased by 33.33 and the working time is reduced by 33.33 % . what is the percentage change in the employee ' s income ?
Options: a ) rs . 0.7889 , b ) rs . 0.8889 , c ) rs . 0.9889 , d ) rs . 1.8889 , e ) rs . 2.8889
Rationale: if payment per hr is increased by 33.33 % , then 11.11 % decrease in income if earlier he is getting rs 1 hr per hr and working for 1 hr , income = rs 1 now he is getting rs 1.3333 per hr and working for 0.66667 hrs , income = rs . 0.8889 answer : b
Answer: b
Problem: the sub - duplicate ratio of 16 : 64 is
Options: a ) 4 : 3 , b ) 1 : 2 , c ) 1 : 3 , d ) 1 : 4 , e ) 2 : 4
Rationale: "root ( 16 ) : root ( 64 ) = 4 : 8 = 2 : 4 answer : e"
Answer: e
Problem: there are 38 students in a certain geometry class . if two thirds of the students are boys and 3 fourths of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 6 , b ) 12 , c ) 19 , d ) 24 , e ) 27
Rationale: 38 * 2 / 3 * 3 / 4 = 19 answer : c
Answer: c
Problem: a boat crossed a lake from north to east at the speed of 7 km / h , entered a river and covered twice as much distance going upstream at 6 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.8 km / h that day , what was its approximate downstream speed ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "one way of solving this is : speed of boat on still water ( lake ) = 7 kmph speed upstream = 6 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 7 + 1 = 8 kmph ans is e"
Answer: e
Problem: a bullet train 120 m long is running with a speed of 50 kmph . in what time will it pass a man who is running at 4 kmph in the direction opposite to that in which the bullet train is going ?
Options: a ) 23 sec , b ) 15 sec , c ) 12 sec , d ) 8 sec , e ) 16 sec
Rationale: "d 8 sec speed of the bullet train relative to man = ( 50 + 4 ) kmph = 54 * 5 / 18 m / sec = 45 / 3 m / sec . time taken by the bullet train to cross the man = time taken by it to cover 120 m at ( 45 / 3 ) m / sec = ( 120 * 3 / 45 ) sec = 8 sec"
Answer: d
Problem: a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 8 is
Options: a ) 189 , b ) 197 , c ) 221 , d ) 227 , e ) 230
Rationale: "in that case , the sophie prime numbers greater than 8 are 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be a ."
Answer: a
Problem: how many digits will be there to the right of the decimal point in the product of 89.635 and . 02218 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "explanation : sum of decimal places = 3 + 5 = 8 the last digit to the extreme right is zero ( since 5 x 8 = 40 ) hence , there will be 7 significant digits to the right of the decimal point . answer : option c"
Answer: c
Problem: 70,76 , 74,85 , 90,105 , 105,130 , 130,130 the list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . if the standard deviation of the 10 running times is 22.4 , rounded to the nearest tenth of a second , how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times .
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: how many of the 10 running times are more than one sd below the meanmeans how many data points from given 10 are less thanmean - 1 sd . we are given that sd = 22.4 , so we should find mean - - > mean = 100 - - > there are only 3 data points below 100 - 22.4 = 77.6 , namely 70 75 , and 74 . answer : c .
Answer: c
Problem: if the cost price of 60 articles is equal to the selling price of 40 articles , then what is the percent profit ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 40 y = 60 x y = 1.5 x the answer is c ."
Answer: c
Problem: john is the owner of a company and for thanksgiving he wants to give a turkey to each employee to celebrate the holiday . each turkey cost him $ 25 . if he has 85 employees , how much would john need to spend ?
Options: a ) $ 2125 , b ) $ 1320 , c ) $ 2000 , d ) $ 1580 , e ) $ 2000.75
Rationale: answer is ( a ) . if john wants to give each of his employees a turkey to help celebrate the thanksgiving holiday and each one costs him $ 25 multiplied by the number of employees ( 85 ) , he would have to pay a total of $ 2125 .
Answer: a
Problem: set a { 3 , 3,3 , 4,5 , 5,5 } has a standard deviation of 1 . what will the standard deviation be if every number in the set is multiplied by 5 ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 8 , e ) e ) 5
Rationale: "points to remember - 1 . if oneadd / subtractthe same amont from every term in a set , sd does n ' t change . 2 . if onemultiply / divideevery term by the same number in a set , sd changes by same number . hence the answer to the above question is e"
Answer: e
Problem: there are 28 balls which are red , blue or green . if 12 balls are green and the sum of red balls and green balls is less than 24 , at most how many red balls are there ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14
Rationale: r + g + b = 28 g = 12 r + g < 24 = > r + 12 < 24 = > r < 12 = > at most 11 red balls answer : c
Answer: c
Problem: a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 480 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 4000 , d ) 2800 , e ) 2791
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 480 = > 36 x / 100 - 24 x / 100 = 480 = > 12 x / 100 = 480 = > x = 4000 . answer : c"
Answer: c
Problem: what is 66.67 % of 804 ?
Options: a ) 587.69 , b ) 536 , c ) 627 , d ) 300.87 , e ) 567.67
Rationale: "66.67 % = 2 / 3 2 / 3 of 804 = 2 / 3 * 804 = 536 . . . . ans - b"
Answer: b
Problem: a 7 - meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point ?
Options: a ) 4 / 5 , b ) 6 / 7 , c ) 5 / 8 , d ) 7 / 9 , e ) 9 / 10
Rationale: "the longer wire will form a square with an area more than 1 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 7 . the answer is b ."
Answer: b
Problem: a train 200 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 987 , b ) 271 , c ) 72 , d ) 27 , e ) 36
Rationale: "length = speed * time speed = l / t s = 200 / 20 s = 10 m / sec speed = 10 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 36 kmph answer : e"
Answer: e
Problem: a fair coin is tossed 5 times . what is the probability that it lands heads up at least twice ?
Options: a ) 1 / 16 , b ) 5 / 16 , c ) 2 / 5 , d ) 13 / 16 , e ) 27 / 32
Rationale: fair coin is tossed 5 times . hence total number of outcomes = 2 ^ 5 = 32 . problem asks for probability of getting atleast heads twice . hence if we calculate probability of getting heads exactly once and probability of not getting heads at all and subract it from the total probability of the event which is 1 ( as total probability of certain event will be always 1 ) we can get the probability of getting atleast heads twice . probability of getting exactly one head and no heads = ( number of possible outcomes [ htttt , thttt , tthtt , tttht , tttth , ttttt ] = 6 ) / ( total possible outcomes = 32 ) = > 6 / 32 = 3 / 16 hence probability of getting atleast heads twice = 1 - ( 3 / 16 ) = 13 / 16 = > choice [ d ]
Answer: d
Problem: there are 50 students in a class . if 6 % are absent on a particular day , find the number of students present in the class .
Options: a ) 47 , b ) 36 , c ) 28 , d ) 12 , e ) 11
Rationale: "number of students absent on a particular day = 6 % of 50 i . e . , 6 / 100 × 50 = 3 therefore , the number of students present = 50 - 3 = 47 students . answer : a"
Answer: a
Problem: what is 3 / 4 of 4 / 5 of 2 / 3 ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "3 / 4 * 4 / 5 * 2 / 3 = 2 / 5 answer : b"
Answer: b
Problem: if the numerator of a fraction is increased by 20 % and its denominator is diminished by 25 % value of the fraction is 2 / 15 . find the original fraction ?
Options: a ) 1 / 12 , b ) 1 / 16 , c ) 1 / 19 , d ) 1 / 14 , e ) 1 / 13
Rationale: "x * ( 120 / 100 ) - - - - - - - - - - - - - - - - = 2 / 15 y * ( 75 / 100 ) x / y = 1 / 12 answer : a"
Answer: a
Problem: when w is divided by 13 , the reminder is 0 . if w is 3 more than it value and when divided by 11 its remainder is 0 . what is the value of w ?
Options: a ) 13 , b ) 52 , c ) 39 , d ) 26 , e ) 35
Rationale: w is divided by 13 so that is multiple of 14 as 13 , 26,39 . . . w + 3 is divided by 11 the remainder is 0 so it is divisible by 11 . consider from option let us take the number is 13 it is divisible by 14 but 13 + 3 is not divisible by 11 so it is not answers so let us take 2 nd option 52 which is divisible by 13 and 52 + 3 = 55 is divisible by 11 so ans is b
Answer: b
Problem: which is the least number that must be subtracted from 1828 so that the remainder when divided by 8 , 12 , 16 is 4 ?
Options: a ) 0 , b ) 4 , c ) 8 , d ) 6 , e ) 2
Rationale: "first we need to figure out what numbers are exactly divisible by 8 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 8 , 12,16 ) = 48 = 48 number is to be subtracted is 0 the largest such number less than or equal to 1828 is 48 * 38 + 4 a"
Answer: a
Problem: a high school has 400 students 1 / 2 attend the airthmetic club , 5 / 8 attend the biology club and 3 / 4 attend the chemistry club . 1 / 8 attend all 3 clubs . if every student attends at least one club how many students attend exactly 2 clubs .
Options: a ) 300 , b ) 200 , c ) 250 , d ) 150 , e ) 160
Rationale: basically , this question is asking you to figure out how many students are being double - counted . a - club has 200 members ( 1 / 2 of 400 ) b - club has 250 members ( 5 / 8 of 400 ) c - club has 300 members ( 3 / 4 of 400 ) we can create an equation to solve this : 200 + 250 + 300 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 50 ) . 750 = 400 + x + 100 x = 250 c
Answer: c
Problem: the difference between the place values of two eights in the numerical 38140482 is
Options: a ) 7999920 , b ) 799920 , c ) 7920 , d ) 79920 , e ) none of them
Rationale: "required difference = ( 8000000 - 80 ) = 7999920 . answer is a"
Answer: a
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b nd c be 27 , then how old is b ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "solution let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ∴ ( 2 x + 2 ) + 2 x + x = 27 ⇔ 5 x = 25 ⇔ x = 5 . hence , b ' s age = 2 x = 10 years . answer d"
Answer: d
Problem: last year elaine spent 20 % of her annual earnings on rent . this year she earned 35 % more than last year and she spent 30 % of her annual earnings on rent . the amount she spent on rent this year is what percent of the amount spent on rent last year ?
Options: a ) 202.5 , b ) 194.5 , c ) 197.5 , d ) 182.5 , e ) 177.5
Rationale: "for this it is easiest to use simple numbers . let ' s assume that elaine ' s annual earnings last year were $ 100 . she would ' ve spent $ 20 of this on rent . this year she earned 15 % more , or $ 135 . she would ' ve spent 30 % of this on rent , or $ 40.5 do $ 40.5 / $ 20 this will give you 202.5 % a is the correct answer ."
Answer: a
Problem: i chose a number and divide it by 4 . then i subtracted 24 from the result and got 10 . what was the number i chose ?
Options: a ) 170 , b ) 700 , c ) 800 , d ) 900 , e ) none
Rationale: "solution : let x be the number i chose , then x / 4 â ˆ ’ 24 = 10 x / 5 = 34 x = 170 answer : a"
Answer: a
Problem: an agent , gets a commission of 2.5 % on the sales of cloth . if on a certain day , he gets rs . 21 as commission , the cloth sold through him on that day is worth
Options: a ) 333 , b ) 500 , c ) 840 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 2.5 % . of x = 21 < = > ( 25 / 10 * 1 / 100 * x ) = 21 < = > x = 840 . answer : c"
Answer: c
Problem: the average temperature for tuesday , wednesday and thursday was 32 ° c . the average temperature for wednesday , thursday and friday was 34 ° c . if the temperature on friday be 44 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 38 ° c , d ) 42 ° c , e ) none of these
Rationale: "explanation : t + w + t = 32 × 3 = 96 ° c w + t + f = 34 × 3 = 102 ° c also , temperature on friday = 44 ° c temperature on tuesday = 96 + 44 - 102 = 38 ° c answer : option c"
Answer: c
Problem: a cyclist bikes x distance at 10 miles per hour and returns over the same path at 9 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 8.6 , d ) 8.9 , e ) 9.5
Rationale: "distance = d 1 = x miles speed = s 1 = 10 miles per hour time = t 1 = distance / speed = x / 10 2 . going from b to a distance = d 2 = x miles speed = s 2 = 9 miles per hour time = t 2 = distance / speed = x / 9 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 9 = x ( 1 / 10 + 1 / 9 ) = x ( 4 + 5 ) / 40 = 19 x / 90 speed = 2 x / ( 19 x / 90 ) = ( 2 x * 90 ) / 9 x = 180 x / 19 x = 180 / 19 = 9.5 answer : e"
Answer: e
Problem: the diagonal of a cube is 8 √ 3 . find its volume and surface area .
Options: a ) 354
b ) 384
c ) 324
d ) 344
e ) 364
Rationale: √ 3 . a = 8 √ 3 = > a = 8 volume = a ( power ) 3 = > ( 8 × 8 × 8 ) cm ( power ) 3 = > 512 cm ( power ) 3 surface area = > 6 a ( power ) 2 = > ( 6 × 8 × 8 ) cm ( power ) 2 = > 384 cm ( power ) 2 answer is b .
Answer: b
Problem: a certain rectangular crate measures 8 feet by 14 feet by 16 feet . a cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces . what should the radius of the tank be if it is to be of the largest possible volume ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
Rationale: "ans is ` ` b ' ' . for max volume of cylinder ( pi * r ^ 2 * h ) we need to max out r ^ 2 * h . we do n ' t know what the dimensions of the crate refer to . . therefore for max vol base should be 14 x 20 i . e . of radius 12 / 2 = 6 c"
Answer: c
Problem: a group of boy scouts and girls scouts is going on a rafting trip . 70 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 75 % of the boy scouts arrived with signed permission slips , then what percentage of the girl scouts arrived with signed permission slips ? round to the nearest percent .
Options: a ) 50 % , b ) 60 % , c ) 63 % , d ) 66 % , e ) 70 %
Rationale: 60 % were boy scouts so 40 % ( 100 - 60 = 40 ) were girl scouts . # of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed ( 75 % of 60 % of the total going ) + ( ? % of 40 % of the total going ) = 70 % of the total going we can let the ` ` total going ' ' = 1,000 arbitrarily since we only care about the percent ( of girl scouts w / permission signed ) . 75 * . 60 * 1,000 + x * . 40 * 1,000 = . 70 * 1,000 450 + x * 400 = 700 400 x = 250 x = 250 / 400 x = . 625 converting this to a percent , we have 62.5 % . rounding , we have 63 % . c
Answer: c
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 216 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 60 %
Rationale: "answer : e 216 ° divided by 360 ° equals 0.6 , therefore the sector is equal to 60 % of the total"
Answer: e
Problem: in a school of 850 boys , 34 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) a ) 125 , b ) b ) 627 , c ) c ) 153 , d ) d ) 238 , e ) e ) 159
Rationale: "34 + 28 + 10 = 72 % 100 – 72 = 28 % 850 * 28 / 100 = 238 answer : d"
Answer: d
Problem: if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a third circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 12,000 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 120 degrees = 12000 anglets answer - c"
Answer: c
Problem: 2 ^ 46655 mod 9 = ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: by remainder theorem remainder = { [ ( 2 ^ 3 ) ^ 1551 * 2 ^ 2 ] / 9 } = [ { ( - 1 ) ^ 1551 * 4 } / 9 ] = 5 answer : b
Answer: b
Problem: a cube has five of its faces painted half red and half white . the other face is completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 6 : 11
b ) 2 : 5
c ) 3 : 4
d ) 5 : 7
e ) 2 : 3
Rationale: let x be the area of each face of the cube . the area painted red is 5 ( x / 2 ) = 5 x / 2 the area painted white is 5 ( x / 2 ) + x = 7 x / 2 x the ratio of red to white is 5 x / 2 : 7 x / 2 which is 5 : 7 . the answer is d .
Answer: d
Problem: the h . c . f . of two numbers is 25 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 322 , d ) 345 , e ) 350
Rationale: "clearly , the numbers are ( 25 x 13 ) and ( 25 x 14 ) . larger number = ( 25 x 14 ) = 350 . answer : option e"
Answer: e
Problem: increasing the original price of a certain item by 25 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 62.5
Rationale: we ' re told that the original price of an item is increased by 25 % and then that price is increased by 30 % . . . . if . . . . starting value = $ 100 + 25 % = 100 + . 25 ( 100 ) = 125 + 30 % = 125 + . 30 ( 125 ) = 125 + 37.5 = 162.5 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 62.5 / 100 = 62.50 % final answer : e
Answer: e
Problem: the population of a bacteria colony doubles every day . if it was started 10 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 1024 , d ) 2048 , e ) 4096
Rationale: "2 ^ 10 ( 2 ) = 2 ^ 11 = 2048 the answer is d ."
Answer: d
Problem: a computer manufacturer produces a certain electronic component at a cost of $ 80 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 16,200 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 150 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) $ 28 , b ) $ 82 , c ) $ 110 , d ) $ 190 , e ) $ 192
Rationale: "this question can be solved easily using a equation model . 150 * p = 16200 ( fixed cost ) + 150 * 80 + 150 * 2 . = 16200 + 12000 + 300 = 28500 p = $ 190 . d"
Answer: d
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 6 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 3 / 13 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 6 * x hence , a 1 + a 2 + . . + a 20 + n = 26 x so , the fraction asked = 6 x / 26 x = 6 / 26 = 3 / 13 d"
Answer: d
Problem: in a sports club with 42 members , 20 play badminton and 23 play tennis and 6 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "20 + 23 = 43 but where as total number is 42 - 6 = 36 therefore answer is 43 - 36 = 7 hence answer is d"
Answer: d
Problem: a tempo , while travelling at 70 kmph , uses 30 % more petrol than it uses while travelling at 50 kmph for travelling a certain distance . using one litre of petrol , it can travel 19.5 km at 50 kmph . how far can the tempo travel on 10 litres of petrol at a speed of 70 kmph ?
Options: a ) 150 kms , b ) 160 kms , c ) 170 kms , d ) 180 kms , e ) 190 kms
Rationale: @ 50 kmph , one km distance uses 1 / 19.5 ltr petrol . @ 70 kmph , one km dist . uses 1.3 / 19.5 ltr petrol distance travelled with 10 ltrs @ 70 kmph = 10 * 19.5 / 1.3 = 150 kms . answer : a
Answer: a
Problem: in an examination it is necessary for a candidate to get 45 % of the maximum marks to pass . a candidate who gets 180 marks , fails by 45 marks . find the maximum marks .
Options: a ) 450 , b ) 600 , c ) 500 , d ) 550 , e ) 650
Rationale: let max . mark = x pass mark = 45 x / 100 180 = 45 x / 100 - 45 x = 180 * 100 - 4500 / 45 = 500 answer : c
Answer: c
Problem: in a box of 9 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 ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Rationale: p ( neither pen is defective ) = 6 / 9 * 5 / 8 = 5 / 12 the answer is c .
Answer: c
Problem: 265.124 x 11.98 ã · 8.001 + 32.28 = ?
Options: a ) 983.578 , b ) 659.121 , c ) 781.189 , d ) 429.966 , e ) 456.512
Rationale: "explanation : ? = 265.124 x 11.98 ã · 8.001 + 32.28 â ‰ ˆ ( 265.124 x 12 / 8 ) + 32.28 â ‰ ˆ 397.686 + 32.28 â ‰ ˆ 429.966 answer : option d"
Answer: d
Problem: find a two digit number , given that the sum of the digits is 9 and the difference of the digits is 3 . ?
Options: a ) 75 , b ) 63 , c ) 83 , d ) 94 , e ) 39
Rationale: using elimination method find which of the options fit the description of the number . . . from the option only 63 meets this description sum of digits - - - 6 + 3 = 9 difference of digits - - - 6 - 3 = 3 answer b .
Answer: b
Problem: fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 25 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 25 %
Rationale: "x discount on pony jeans , ( 0.25 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.25 - x ) + 2 * 18 x = 9 - - > x = 0.25 = 25 % answer : e ."
Answer: e
Problem: eight identical machines can produce 360 aluminum cans per hour . if all of the machines work at the same constant rate , how many cans could 5 such machines produce in 7 hours ?
Options: a ) 675 , b ) 750 , c ) 1,800 , d ) 5,900 , e ) 1,575
Rationale: "8 machines / 360 cans = 5 machines / x cans 8 x = 1800 x = 225 ( 225 ) ( 7 hours ) = 1575 cans . the answer is e ."
Answer: e
Problem: if x is an integer and 2.13 × 10 ^ x is less than 2100 , what is the greatest possible value for x ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "if x = 3 2.13 × 10 ^ 3 = 2130 > 2,100 so , x = 2 answer : a"
Answer: a
Problem: if 5 % more is gained by selling an article for rs . 360 than by selling it for rs . 340 , the cost of the article is ?
Options: a ) 127 , b ) 688 , c ) 400 , d ) 121 , e ) 123
Rationale: "let c . p . be rs . x . then , 5 % of x = 360 - 340 = 20 x / 20 = 20 = > x = 400 answer : c"
Answer: c
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 525 what is the least possible value of k ?
Options: a ) 10 , b ) 14 , c ) 15 , d ) 21 , e ) 25
Rationale: "525 = 3 * 5 * 5 * 7 thus k must include numbers at least up to the number 10 so that there are two appearances of 5 . the answer is a ."
Answer: a
Problem: find the area of trapezium whose parallel sides are 28 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 227 , b ) 299 , c ) 345 , d ) 161 , e ) 212
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 28 + 18 ) * ( 15 ) = 345 cm 2 answer : c"
Answer: c
Problem: joshua and jose work at an auto repair center with 4 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "1 ) probability of chosing josh first = 1 / 6 probability of chosing jose second = 1 / 5 total = 1 / 30 probability of chosing jose first = 1 / 6 probability of choosing josh second = 1 / 5 total = 1 / 30 final = 1 / 30 + 1 / 30 = 1 / 15 2 ) number of ways two persons can be chosen 6 c 2 = 15 number of ways josh and jose are the two persons = 1 total = 1 / 15 answer will be a ."
Answer: a
Problem: 3 candidates in an election and received 6136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 46 % , b ) 49 % , c ) 57 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 6136 + 7636 + 11628 ) = 25400 so , required percentage = 11628 / 25400 * 100 = 46 % a"
Answer: a
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - fourth of the males and one - half of the females in the class ?
Options: a ) 128
b ) 136
c ) 144
d ) 152
e ) 160
Rationale: 1 / 4 * 2 / 5 + 1 / 2 * 3 / 5 = 2 / 20 + 6 / 20 = 2 / 5 the number of degrees is 2 / 5 * 360 = 144 degrees the answer is c .
Answer: c
Problem: 4 liters of a 20 percent solution of alcohol in water are mixed with 5 liters of a 10 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 14.4 % , b ) 14.8 % , c ) 15.2 % , d ) 15.6 % , e ) 16.0 %
Rationale: "the total amount of alcohol is 0.2 ( 4 ) + 0.1 ( 5 ) = 1.3 liters . the percentage is 1.3 / 9 = 13 / 90 which is about 14.4 % the answer is a ."
Answer: a
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 45 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 15 , b ) 25 , c ) 13 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 45 % = 81 responded as satisfied , so remaining satisfied are 120 - 81 = 39 so 39 is what percentage of 300 - 13 % so the answer should be c"
Answer: c
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "soln : - original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.2 c ( 20 % profit ) x = 1.2 / . 8 * c x = 3 / 2 c original selling price is 1.5 c which is 50 % profit answer : c"
Answer: c
Problem: solution a is 30 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 2
Rationale: "forget the volumes for the time being . you have to mix 30 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 30 ) = 3 / 2 so the volume of the two solutions will be equal . answer has to be 3 : 2 e"
Answer: e
Problem: a question paper has 2 parts , a & b , each containing 8 questions . if a student has to choose 8 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 110 , b ) 70 , c ) 120 , d ) 130 , e ) 140
Rationale: "there 8 questions in part a out of which 8 question can be chosen as = 8 c 8 . similarly , 4 questions can be chosen from 8 questions of part b as = 8 c 4 . hence , total number of ways , = 8 c 8 * 8 c 4 = [ 8 ! / ( 0 ! 8 ! ) ] * [ 8 ! / ( 4 ! * 4 ! ) ] = { 1 } * { 8 * 7 * 6 * 5 / ( 4 ! ) } = 70 . b"
Answer: b
Problem: a can do a piece of work in 80 days . he works at it for 10 days b alone finishes the remaining work in 42 days . in how much time will a and b working together , finish the work ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 32 , e ) none of them
Rationale: "work done by a in 10 days = ( 1 / 80 * 10 ) = 1 / 8 remaining work = ( 1 - 1 / 8 ) = 7 / 8 now , 7 / 8 work is done by b in 42 days . whole work will be done by b in ( 42 x 8 / 7 ) = 48 days . a ’ s 1 day ' s work = 1 / 80 and b ' s 1 day ' s work = 1 / 48 ( a + b ) ' s 1 day ' s work = ( 1 / 80 + 1 / 48 ) = 8 / 240 = 1 / 30 hence , both will finish the work in 30 days . answer is b ."
Answer: b
Problem: working together , printer a and printer b would finish the task in 24 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 6 pages a minute more than printer a ?
Options: a ) 600 , b ) 800 , c ) 1000 , d ) 720 , e ) 1500
Rationale: answer : d .
Answer: d
Problem: the monthly rent of a shop of dimension 18 feet × 22 feet is rs . 2244 . what is the annual rent per square foot of the shop ? ( a ) rs . 5 ( 2 / 3 )
Options: a ) 43 , b ) 56 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 2244 / ( 18 * 22 ) & annual rent per square feet = 12 * ( 2244 / ( 18 * 22 ) ) = 68 c"
Answer: c
Problem: a grocer has a sale of rs . 5255 , rs . 5840 , rs . 5921 , rs . 6022 and rs . 6499 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5500 ?
Options: a ) 3463 , b ) 4463 , c ) 5463 , d ) 4063 , e ) 5063
Rationale: "total sale for 5 months = rs . ( 5255 + 5840 + 5921 + 6022 + 6499 ) = rs . 29537 . required sale = rs . [ ( 5500 x 6 ) - 29537 ] = rs . ( 33000 - 29537 ) = rs . 3463 . answer : b"
Answer: b
Problem: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 135 mangoes .
Options: a ) 360 , b ) 380 , c ) 400 , d ) 450 , e ) 412
Rationale: mr . john used to purchase certain number of mangoes for $ 360 since the price of mangoes is reduced by 10 % he got 12 more mangoes today . find the original price of 120 mangoes . method 1 : let price per mango = x . let number of mangoes be n . then , nx = 360 . now price = 0.9 x ; number of mangoes = n + 12 . total amount = 0.9 x * ( n + 12 ) = 360 . nx = 0.9 nx + 10.8 x = > 0.1 nx = 10.8 x = > n = 108 = > x = 360 / 108 = 3.33 original price of 135 mangoes = 135 * 3.33 = 450 . answer d
Answer: d
Problem: a gambler has won 40 % of his 20 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 20 ) + 0.8 x = 0.6 ( x + 20 ) 0.2 x = 4 x = 20 the answer is a ."
Answer: a
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 100 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1000 , b ) 1400 , c ) 1200 , d ) 800 , e ) 1000
Rationale: "volume of pool = 60 * 100 * 10 cu . ft , 80 % full = 60 * 100 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 100 * 10 * 0.8 / 60 min = 800 min d"
Answer: d
Problem: walking at 4 / 5 of her normal speed , a worker is 10 minutes later than usual in reaching her office . the usual time ( in minutes ) taken by her to cover the distance between her home and her office is
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "let v be her normal speed and let t be her normal time . d = ( 4 / 5 ) v * ( t + 10 ) since the distance is the same we can equate this to a regular day which is d = v * t v * t = ( 4 / 5 ) v * ( t + 10 ) t / 5 = 8 t = 40 the answer is c ."
Answer: c
Problem: find the length of the longest pole that can be placed in a room 12 m long , 8 m broad and 9 m high .
Options: a ) 10 m , b ) 12 m , c ) 17 m , d ) 19 m , e ) none
Rationale: solution length of longest pole = length of the diagonal of the room = √ ( 12 ) 2 + 82 + 92 ‹ = › √ 289 = 17 m . answer c
Answer: c
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 4 m , the volume of the box ( in m 3 ) is :
Options: a ) 4480 , b ) 5120 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 8 ) m = 40 m , b = ( 36 - 8 ) m = 28 m , h = 8 m . volume of the box = ( 40 x 28 x 4 ) m 3 = 4480 m 3 . answer : option a"
Answer: a
Problem: find the value of x in ( x + 1 ) / ( x + 3 ) = 5
Options: a ) 2.5 , b ) - 2.5 , c ) 3.0 , d ) 3.5 , e ) - 3.5
Rationale: "( x - 1 ) / ( x + 3 ) = 5 multiplying both sides with x + 3 gives x + 1 = 5 ( x + 3 ) = x + 1 = 5 x + 15 subtracting x from both sides gives 4 x + 15 = 1 subtracting 15 from both sides gives 4 x = - 14 dividing by 4 on both sides gives x = - 3.5 answer : e"
Answer: e
Problem: a and b can together finish a work in 40 days . they worked together for 10 days and then b left . after another 15 days , a finished the remaining work . in how many days a alone can finish the job ?
Options: a ) 10 , b ) 25 , c ) 60 , d ) 30 , e ) 20
Rationale: "a + b 10 days work = 10 * 1 / 40 = 1 / 4 remaining work = 1 - 1 / 4 = 3 / 4 3 / 4 work is done by a in 15 days whole work will be done by a in 15 * 4 / 3 = 20 days answer is e"
Answer: e
Problem: if the radius of a cylinder is made 3 times and height is doubled , what is the new volume of the cylinder divided by the old one ?
Options: a ) 18 . , b ) 2 . , c ) 6 . , d ) 4 . , e ) 10 .
Rationale: let v and v ' be the original and the changed volume now v = pir ^ 2 h v ' = pi ( 3 r ) ^ 2 ( 2 h ) v ' = 18 v a ) 18
Answer: a
Problem: a train 110 m long is running with a speed of 82 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 ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.5 sec , e ) 2 sec
Rationale: "speed of train relative to man = 82 + 6 = 88 km / hr . = 88 * 5 / 18 = 24.44 m / sec . time taken to pass the men = 110 / 24.44 = 4.5 sec . answer : d"
Answer: d
Problem: the average marks of a class of 35 students is 40 and that of another class of 45 students is 60 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 51.2 , e ) 52.9
Rationale: "sum of the marks for the class of 35 students = 35 * 40 = 1400 sum of the marks for the class of 45 students = 45 * 60 = 2700 sum of the marks for the class of 80 students = 1400 + 2700 = 4100 average marks of all the students = 4100 / 80 = 51.2 . answer : d"
Answer: d
Problem: abcd is a square where ab = √ 2016 . let x be a point on ab and y be a point on cd such that ax = cy . compute the area of trapezoid axyd .
Options: a ) 3008 , b ) 2002 , c ) 1008 , d ) 2016 , e ) 3000
Rationale: note that trapezoids axy d and bxy c are congruent , so the area of axy d is always 2016 / 2 = 1008 . correct answer c
Answer: c
Problem: chris age after 9 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 16
Rationale: "chris present age = x after 9 years = x + 9 5 years back = x - 5 x + 9 = 5 ( x - 5 ) x = 16 answer is e"
Answer: e
Problem: the owner of a furniture shop charges his customer 20 % more than the cost price . if a customer paid rs . 8600 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6289 , b ) rs . 6298 , c ) rs . 6290 , d ) rs . 7166 , e ) rs . 7708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8600 ( 100 / 120 ) = rs . 7166 . answer : d"
Answer: d
Problem: what is the perimeter , in meters , of a rectangular garden 16 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 60 , d ) 56 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 16 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 12 meters . perimeter of garden = 2 * ( 12 + 16 ) = 56 meter . answer is d"
Answer: d
Problem: mrs . evans gave a test to her freshmen economics class , which has 29 students enrolled and 19 of them answered question 1 correctly . if 24 answered question 2 correctly and 5 did not take the test then how many answered both questions correctly ?
Options: a ) 3 , b ) 9 , c ) 11 , d ) 17 , e ) 19
Rationale: "total number of enrolled students = 29 number of students who did not take test = 5 hence , number of students who took test = 29 - 5 = 24 number of students who answered q 2 correctly = 24 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also answered q 2 correctly = 19 . number of students who answered both q 1 & q 2 correctly = 19 . answer : e"
Answer: e
Problem: the distance between west - town to east - town is 10 kilometers . two birds start flying simultaneously towards one another , the first leaving from west - town at a speed of 4 kilometers per minute and the second bird , leaving from east - town , at a speed of 1 kilometers per minute . what will be the distance , in kilometers , between the meeting point and west - town ?
Options: a ) 3 . , b ) 8 . , c ) 10 . , d ) 12 . , e ) 15 .
Rationale: "time taken by the birds to meet = 10 / ( 4 + 1 ) = 2 mins distance traveled by the bird traveling from west - town = 4 * 2 = 8 answer : b"
Answer: b
Problem: if m is a positive integer and m ^ 2 is divisible by 33 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 11 , e ) 16
Rationale: "m ^ 2 is divisible by 33 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 11 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 33 then answer should be 16 . is the question right ? or am i missing some thing ? d"
Answer: d
Problem: √ 2 percent of 2 √ 2 =
Options: a ) 5.0 , b ) 0.05 , c ) 1.0 , d ) 2.0 , e ) 4.0
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 so , √ 2 percent of 2 √ 2 ≈ 1.4 percent of ( 2 ) ( 1.4 ) ≈ ( 1.4 / 100 ) ( 2.8 ) ≈ 3.92 / 100 ≈ 0.03 check the answer choices to see that b is the only answer that ' s close . answer : b"
Answer: b
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 6 : 3 and b : c = 6 : 5 . if the total runs scored by all of them are 118 , the runs scored by b are ?
Options: a ) 24 , b ) 20.13 , c ) 30.93 , d ) 20.93 , e ) 10.93
Rationale: "a : b = 6 : 3 b : c = 6 : 5 a : b : c = 36 : 18 : 15 12 / 59 * 118 = 24 answer : a"
Answer: a
Problem: a man swims downstream 90 km and upstream 55 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 3.8 , b ) 3.5 , c ) 3.3 , d ) 3.2 , e ) 1.6
Rationale: "90 - - - 5 ds = 18 ? - - - - 1 55 - - - - 5 us = 11 ? - - - - 1 s = ? s = ( 18 - 11 ) / 2 = 3.5 answer : b"
Answer: b