regisss/math_qa huggingface dataset:
Problem: if the sum of two numbers is 16 and the sum of their squares is 200 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 88 , e ) 28
Rationale: "according to the given conditions x + y = 16 and x ^ 2 + y ^ 2 = 200 now ( x + y ) ^ 2 = x ^ 2 + y ^ 2 + 2 xy so 16 ^ 2 = 200 + 2 xy so xy = 56 / 2 = 28 answer : e"
Answer: e
Problem: a and b can do a piece of work in 12 days . with the help of c they finish the work in 6 days . c alone can do that piece of work in ?
Options: a ) 33 , b ) 878 , c ) 30 , d ) 88 , e ) 12
Rationale: "c = 1 / 6 â € “ 1 / 12 = 1 / 12 = > 12 days answer : e"
Answer: e
Problem: an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 4000 , what will be the difference between q and r ' s share ?
Options: a ) 2788 , b ) 5000 , c ) 7282 , d ) 2782 , e ) 2729
Rationale: "4 - - - 4000 5 - - - ? = > 5000 answer : b"
Answer: b
Problem: running at the same constant rate , 6 identical machines can produce a total of 390 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2600 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 390 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 390 x = ( 10 x 4 x 390 ) / ( 6 ) x = 2600 . answer : c"
Answer: c
Problem: a certain pair of used shoes can be repaired for $ 14.50 and will last for 1 year . a pair of the same kind of shoes can be purchased new for $ 32.00 and will last for 2 years . the average cost per year of the new shoes is what percent greater than the cost of repairing the used shoes ?
Options: a ) 16 , b ) 10.34 , c ) 12.46 , d ) 11.2 , e ) 14
Rationale: 1 ) cost of repairing = 14.5 ( for one year ) , therefore for 2 years it would be $ 29 . 2 ) cost of new pair which will last for 2 years is $ 32 . percentage change formula = ( final value - initial value ) / ( initial value ) * 100 . in this case the final value would be the price of new shoeinitial value would be the cost of repairing the old shoe . i . e ( 32 - 29 ) / ( 29 ) * 100 = 10.34 % . ans is b
Answer: b
Problem: if length of rectangle is increased by 10 % , and breadth is decreased by 10 % . what will it effect on area of rectangle ?
Options: a ) it will have no effect
b ) 1 % increase
c ) 1 % decrease
d ) 2 % increase
e ) 2 % decrease
Rationale: let initial length = l , and breadth = b area = l * b new length = l * 110 % = [ l * 110 / 100 ] = 11 l / 10 , new breadth = 9 b / 10 new area = 11 l / 10 * 9 b / 10 = 99 / 100 lb decrease in area = [ lb - 99 / 100 lb ] = lb / 100 = % decrease = [ lb / 100 * 1 / lb * 100 ] = 1 % answer c
Answer: c
Problem: what is the ratio of 12 minute to 1 hour ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 1 / 5 , d ) 2 / 2 , e ) 3 / 1
Rationale: c 1 / 5
Answer: c
Problem: 8 * 8 * 8 * 8 = 2 ^ ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "solution : 2 ^ 3 * 2 ^ 3 * 2 ^ 3 * 2 ^ 3 = 2 ^ ( 3 + 3 + 3 + 3 ) = 2 ^ 12 answer : 12 option : e"
Answer: e
Problem: what is the smallest no . which must be added to 53403977 so as to obtain a sum which is divisible by 11 ?
Options: a ) 5 , b ) 4 , c ) 0 , d ) 1 , e ) 2
Rationale: "for divisibility by 11 , the difference of sums of digits at even and odd places must be either zero or divisible by 11 . for 53403977 , difference = ( 5 + 4 + 3 + 7 ) - ( 3 + 0 + 9 + 7 ) = 19 - 19 = 0 . = > 53403977 is also divisible by 11 c"
Answer: c
Problem: each child has 8 crayons and 15 apples . if there are 7 children , how many crayons are there in total ?
Options: a ) 22 , b ) 56 , c ) 12 , d ) 36 , e ) 10
Rationale: 8 * 7 = 56 . answer is b .
Answer: b
Problem: a student took 6 courses last year and received an average ( arithmetic mean ) grade of 100 points . the year before , the student took 5 courses and received an average grade of 60 points . to the nearest tenth of a point , what was the student ’ s average grade for the entire two - year period ?
Options: a ) 79 , b ) 89 , c ) 95 , d ) 81.81 , e ) 97.2
Rationale: "let the 6 courses that were taken last year be a 1 , a 2 , a 3 , a 4 , a 5 , a 6 a 1 + a 2 + a 3 + a 4 + a 5 + a 6 = 100 * 6 = 600 the year before , the 5 courses be b 1 , b 2 , b 3 , b 4 , b 5 b 1 + b 2 + b 3 + b 4 + b 5 = 60 * 5 = 300 student ' s average = ( 600 + 300 ) / 11 = 81.81 answer d"
Answer: d
Problem: a person is traveling at 20 km / hr and reached his destiny in 2.5 hr then find the distance ?
Options: a ) 53 km , b ) 55 km , c ) 52 km , d ) 60 km , e ) 50 km
Rationale: "t = 2.5 hrs = 5 / 2 hrs d = t * s = 20 * 5 / 2 = 50 km answer is e"
Answer: e
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 12 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 22 cm , b ) 47.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 12 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 14 ) = 1 / 2 ( 22 / 7 ) ( 14 ) = 308 / 14 = 22 cm answer : a"
Answer: a
Problem: a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 2 : 8 , b ) 1 : 2 , c ) 2 : 5 , d ) 6 : 9 , e ) 6 : 2
Rationale: b 1 : 2 t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2
Answer: b
Problem: a corporation paid $ 8 million in federal taxes on its first $ 50 million of gross profits and then $ 30 million in federal taxes on the next $ 150 million in gross profits . by approximately what percent did the ratio of federal taxes to gross profits increase from the first $ 50 million in profits to the next $ 150 million in profits ?
Options: a ) 6 % , b ) 14 % , c ) 20 % , d ) 23 % , e ) 86 %
Rationale: "difference in ratios = ( 30 / 150 ) - ( 8 / 50 ) = ( 6 / 50 ) % change = ( change ( 6 / 50 ) / original ratio ( 7 / 50 ) ) * 100 = 86 % answer - e"
Answer: e
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9 , 40 and 41 ?
Options: a ) 6 , b ) 4 , c ) 24.5 , d ) 20.5 , e ) 12.5
Rationale: "explanatory answer 9 , 40 and 41 is pythagorean triplet . so , the triangle is right angled . key property about right triangles in a right angled triangle , the radius of the circle that circumscribes the triangle is half the hypotenuse . in the given triangle , the hypotenuse = 41 . therefore , the radius of the circle that circumscribes the triangle = 41 / 2 = 20.5 units . choice d"
Answer: d
Problem: 70 , 75 , 80 , 85 , 90 , 105 , 105 , 130 , 130 , 130 the list shown consists of the times , in seconds , that it took each of 10 schoolchildren to run a distance of 400 on of meters . if the standard devastation of the 10 running times is 25.4 seconds , 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 ) one , b ) two , c ) three , d ) four , e ) five
Rationale: the most time consuming part in this question is to define the mean . under exam pressure and time pressure it is very easy to make mistake . it is easier to group numbers : 130 * 3 = 390 ; 105 * 2 = 210 ; 75 + 85 = 160 ; 70 + 80 = 150 ; 90 ; next stage combine results , again using more convenient ways to calculate : 390 + 210 = 600 ; 160 + 150 = 310 ; 90 . 600 + 310 + 90 = 1000 . since there are 10 numbers the mean is 100 . questions asks to find the quantity of numbers one sd below the mean , which is 100 - 25,4 = 74,6 . there are only two numbers below 74,6 . the answer is b
Answer: b
Problem: if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 400 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 410 . what is the value of x ?
Options: a ) 8000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000
Rationale: "simple way to solve this question is to use options . from si , we know that x * y = 20,000 . now , put the value of x = 4000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 4000 + 5 % of 4000 = 4200 . 2 nd year , amount = 4200 + 5 % of 4200 = 4410 . we can see after 2 years interest = 4410 - 4000 = 410 . hence , it satisfies the question . hence d is the correct answer"
Answer: d
Problem: a cricket bat is sold for $ 900 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25.5 % , c ) 33.33 % , d ) 36.3 % , e ) 40 %
Rationale: "225 / ( 900 - 225 ) = 33.33 % . answer : c"
Answer: c
Problem: a part of certain sum of money is invested at 16 % per annum and the rest at 12 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 5 : 4 , b ) 1 : 4 , c ) 3 : 1 , d ) 3 : 5 , e ) 3 : 4
Rationale: "12 : 16 = 3 : 4 answer : e"
Answer: e
Problem: reduce 4128 / 4386 to its lowest terms
Options: a ) 14 / 13 , b ) 13 / 17 , c ) 16 / 17 , d ) 13 / 18 , e ) none of these
Rationale: explanation : hcf of 4128 and 4386 4128 ) 4386 ( 1 4128 - - - - - 258 ) 4128 ( 16 4128 - - - - 0 hence hcf of 4128 and 4386 is 258 . 4128 / 258 = 16 4386 / 258 = 17 4128 / 4386 = 16 / 17 answer : option c
Answer: c
Problem: a bag holds 2 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be red ?
Options: a ) 1 / 10 , b ) 1 / 5 , c ) 3 / 10 , d ) 2 / 5 , e ) 1 / 2
Rationale: probability of selecting first red marble = 2 / 5 probability of selecting second red marble without replacement = 1 / 4 final probability = 2 / 5 * 1 / 4 = 1 / 10 correct answer - a
Answer: a
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 40 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 40 4 n < 33 n < 8 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 8 ) combining the two - 1.5 < n < 8.25 n = 1 to 8 ( 48 integers ) and n = - 1 and 0 so 10 integers . a"
Answer: a
Problem: a contractor undertook to do a piece of work in 9 days . he employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days . find the number of men originally employed .
Options: a ) 15 , b ) 6 , c ) 13 , d ) 9 , e ) none of these
Rationale: let the number of men originally employed be x . 9 x = 15 ( x – 6 ) or x = 15 answer a
Answer: a
Problem: the average of 11 results is 42 , if the average of first 5 results is 49 and that of the last 7 is 52 . find the fifth result ?
Options: a ) 145 , b ) 146 , c ) 147 , d ) 148 , e ) 149
Rationale: 1 to 11 = 11 * 42 = 462 1 to 5 = 5 * 49 = 245 5 to 11 = 7 * 52 = 364 5 th = 245 + 364 – 462 = 147 answer : c
Answer: c
Problem: a train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . the length of the platform is
Options: a ) 400 m , b ) 450 m , c ) 560 m , d ) 600 m , e ) 680 m
Rationale: length of the ist train = 2 x m and the length of the other train be x m ( 1 / 2 ) the relative speed of the train ( 48 + 42 ) = 90 kmph or 25 m / s time taken to cross one another = 12 s hence , 12 = 2 x + x / 25 solving , x = 100 m and 200 m now to determine the length of the platform 45 = 100 + length of the platform / speed of the ist train 45 = 100 + l / 240 / 18 ( 48 kmph = 240 / 118 m / s ) solving , we get l = 600 m answer : d
Answer: d
Problem: if x is to be chosen at random from the set { 1 , 2 , 3 } and y is to be chosen at random from the set { 5 , 6 , 7 } , what is the probability that xy will be even ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "probably the best way to solve would be to use 1 - p ( opposite event ) = 1 - p ( odd ) = 1 - p ( odd ) * p ( odd ) = 1 - 2 / 4 * 2 / 3 = 8 / 12 = 5 / 6 . answer : e ."
Answer: e
Problem: if seven machines working at the same rate can do 3 / 4 of a job in 30 minutes , how many minutes would it take two machines working at the same rate to do 3 / 5 of the job ?
Options: a ) 45 , b ) 60 , c ) 75 , d ) 84 , e ) 100
Rationale: "using the std formula m 1 d 1 h 1 / w 1 = m 2 d 2 h 2 / w 2 substituting the values we have 7 * 1 / 2 * 4 / 3 = 2 * 5 / 3 * x ( converted 30 min into hours = 1 / 2 ) 14 / 3 = 10 / 3 * x x = 7 / 5 hour so 84 minutes answer : d"
Answer: d
Problem: what is the % change in the area of a rectangle when its length increases by 60 % and its width decreases by 60 % ?
Options: a ) 0 % , b ) 20 % increase , c ) 36 % decrease , d ) 1 % decrease , e ) insufficient data
Rationale: "( 16 / 10 ) * ( 4 / 10 ) = 64 / 100 of original area 64 / 100 is a 36 % decrease from 100 / 100 - > c"
Answer: c
Problem: initially two cups of same volume are present with milk filled upto 3 / 5 th and 4 / 5 th of their volumes . water is then filled . then two mixtures are mixed . find the ratio of water to milk in the mixture
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: water content can b in 1 st and second is 2 / 5 and 1 / 5 total : 3 / 5 . the total milk content is 7 / 5 . the ratio is ( ( 3 / 5 ) / ( 7 / 5 ) ) = 3 / 7 . answer : c
Answer: c
Problem: convert 600 miles into meters ?
Options: a ) 784596 , b ) 845796 , c ) 965604 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 600 mile = 600 * 1609.34 = 965604 meters answer is c"
Answer: c
Problem: heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 30 litres of tomato juice ?
Options: a ) 3.75 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 30 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 3.75 liters . answer : a"
Answer: a
Problem: if x < y < z and y - x > 3 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
Options: a ) 7 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "we have : 1 ) x < y < z 2 ) y - x > 3 3 ) x = 2 k ( x is an even number ) 4 ) y = 2 n + 1 ( y is an odd number ) 5 ) z = 2 p + 1 ( z is an odd number ) 6 ) z - x = ? least value z - x = 2 p + 1 - 2 k = 2 p - 2 k + 1 = 2 ( p - k ) + 1 - that means that z - x must be an odd number . we are asked to find the least value , so we have to pick the least numbers since y is odd and x is even , y - x must be odd . since y - x > 3 , the least value for y - x must be 5 , the least value for x must be 2 , and , thus , the least possible value for y must be 7 ( y - 2 = 5 , y = 7 ) 2 < 7 < z , since z is odd , the least possible value for z is 9 z - x = 9 - 2 = 7 answer a"
Answer: a
Problem: if an amount of rs 42900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Problem: six bells commence tolling together and toll at intervals of 2 , 4 , 6 , 8 10 and 12 seconds respectively . in 50 minutes , how many times do they toll together ?
Options: a ) 4 , b ) 10 , c ) 15 , d ) 16 , e ) 26
Rationale: "l . c . m of 2,4 , 6,8 , 10,12 is 120 . i . e after each 2 min they will toll together . so in 50 min they will toll 25 times . as they have initially tolled once , the answer will be 25 + 1 = 26 . answer : e"
Answer: e
Problem: what least number must be subtracted from 9671 so that the remaining number is divisible by 5 ?
Options: a ) 5 , b ) 4 , c ) 3 , d ) 2 , e ) 1
Rationale: "on dividing 9671 by 5 , we get remainder = 1 . required number be subtracted = 1 answer : e"
Answer: e
Problem: find the average of all prime numbers between 50 and 70
Options: a ) 90 , b ) 45 , c ) 60 , d ) 90 , e ) 26
Rationale: "prime numbers between 50 and 70 are 53 , 59 , 61 , 67 required average = ( 53 + 59 + 61 + 67 ) / 4 = 240 / 4 = 60 answer is c"
Answer: c
Problem: the sum of ages of 5 children born at the intervals of 3 years each is 70 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 70 5 x = 40 x = 8 . age of the youngest child = x = 8 years . e )"
Answer: e
Problem: for how many integer values of n will the value of the expression 4 n + 7 be an integer greater than 1 and less than 120 ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "4 n + 7 > 1 4 n > - 6 n > - ( 3 / 2 ) n > - 1.5 ( n = - 1 , 0 , 1 , 2 3 . . . . . . . . upto infinity ) from second constraint 4 n + 7 < 120 4 n < 113 n < 28 . 25 n = ( - infinity , . . . . . . . - 3 , - 2 , - 1 , 0 , 1 , 2 , . . . . . . . . . upto 48 ) combining the two - 1.5 < n < 48.25 n = 1 to 28 ( 48 integers ) and n = - 1 and 0 so 30 integers . e is the answer"
Answer: e
Problem: the average of thirteen numbers is 9 . the average of first 6 numbers is 5 and the average of last 6 numbers is 7 . what is the middle number ?
Options: a ) 47 , b ) 45 , c ) 25 , d ) 37 , e ) 44
Rationale: the total of thirteen numbers = 13 x 9 = 117 the total of first 6 and last 6 numbers is = 6 x 5 + 6 x 7 = 72 so , the middle number is ( 117 - 72 ) = 45 b
Answer: b
Problem: two heavily loaded sixteen - wheeler transport trucks are 1025 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 130 , c ) 150 , d ) 320 , e ) 145
Rationale: "i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 1025 - 90 = 935 k ratio of speeds 9 : 8 - > 935 / 17 = 55 truck a = 90 + 55 * 9 = 585 truck b = 55 * 8 = 440 delta = 145 km answer e"
Answer: e
Problem: find the sum of all 2 digit numbers divisible by 3 .
Options: a ) 1565 , b ) 1665 , c ) 1300 , d ) 1448 , e ) 1465
Rationale: "all 2 digit numbers divisible by 3 are 12,15 , 18,21 , … … … . . 99 this is an a . p with a = 12 , and d = 3 , let it contain n terms then , 12 + ( n – 1 ) * 3 = 99 , or n = ( 99 - 12 ) / 3 + 1 = 30 required sum = 30 / 2 * ( 12 + 99 ) = 15 * 111 = 1665 answer : b"
Answer: b
Problem: 2 , 3 , 6 , 0 , 10 , - 3 , 14 , ( . . . )
Options: a ) - 6 , b ) 8 , c ) - 2 , d ) 4 , e ) 10
Rationale: "there are two series 2 , 6 , 10 , 14 , . . . ( adding 4 ) 3 , 0 , - 3 , . . . ( subtracting 3 ) hence , next term is - 3 - 3 = - 6 answer is a"
Answer: a
Problem: a man can row downstream at the rate of 12 km / hr and upstream at 8 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 10,2 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 8 ) = 10 km / hr rate of current = 1 / 2 ( 12 - 8 ) = 2 km / hr answer : option d"
Answer: d
Problem: the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town after 2 years ?
Options: a ) 1000 , b ) 2000 , c ) 1563 , d ) 2153 , e ) 1245
Rationale: "p = 1000 r = 25 % required population of town = p ( 1 + r / 100 ) ^ t = 1000 ( 1 + 25 / 100 ) ^ 2 = 1000 ( 5 / 4 ) ^ 2 = 1563 ( approximately ) answer is c"
Answer: c
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 2.0 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) s . 1014 , b ) s . 1332 , c ) s . 999 , d ) s . 1085 , e ) s . 1020
Rationale: "a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 – 6 = 666 * 2.0 = 1332 answer : b"
Answer: b
Problem: two employees m and n are paid a total of $ 605 per week by their employer . if m is paid 120 percent of the salary paid to n , how much is n paid per week ?
Options: a ) $ 245 , b ) $ 255 , c ) $ 265 , d ) $ 275 , e ) $ 285
Rationale: "1.2 n + n = 605 2.2 n = 605 n = 275 the answer is d ."
Answer: d
Problem: the weight of 4 dogs is determined to be 25 pounds , 31 pounds , 35 pounds and 33 pounds respectively . the weight of a fifth dog is determined to be y pounds . if the average ( arithmetic mean ) weight of the first 4 dogs is the same as that of all 5 dogs what is the value of y ?
Options: a ) 31 , b ) 33 , c ) 35 , d ) 37 , e ) 39
Rationale: total weight of the 4 dogs = ( 25 + 31 + 35 + 33 ) = 124 avg = 124 / 4 = 31 total weight of 5 dogs = 124 + y or 4 ( 31 ) + y average of 5 dogs as per question = 31 equation : 4 ( 31 ) + y = 5 ( 31 ) , or y = 31 . choose a
Answer: a
Problem: how many ounces of a 60 % salt solution must be added to 40 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 40 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 40 + . 6 x = . 4 ( 40 + x ) x = 40 amswer b"
Answer: b
Problem: car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 60 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
Options: a ) 3 : 7 , b ) 4 : 9 , c ) 13 : 7 , d ) 5 : 3 , e ) 6 : 11
Rationale: "car a travels 50 × 8 = 400 km car b travels 60 × 4 = 240 km the ratio is 400 : 240 = 40 : 24 = 5 : 3 the answer is d ."
Answer: d
Problem: if the cost price of 50 articles is equal to the selling price of 46 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 65 , c ) 78 , d ) 33 , e ) 8.69
Rationale: given that , cost price of 50 article is equal to selling price of 46 articles . let cost price of one article = rs . 1 selling price of 46 articles = rs . 50 but cost price of 46 articles = rs . 46 therefore , the trader made profit . \ percentage of profit = 4 / 46 * 100 = 8.69 % answer : e
Answer: e
Problem: johnny travels a total of one hour to and from school . on the way there he jogs at 5 miles per hour and on the return trip he gets picked up by the bus and returns home at 21 miles per hour . how far is it to the school ?
Options: a ) 2 miles , b ) 4 miles , c ) 6.5 miles , d ) 8 miles , e ) 10 miles
Rationale: "answer : c ) 6.5 miles . average speed for round trip = 2 * a * b / ( a + b ) , where a , b are speeds so , average speed was = 2 * 5 * 21 / ( 5 + 21 ) = 6.5 m / hr the distance between schoolhome should be half of that . ie . 6.5 miles answer c"
Answer: c
Problem: if 3 x + y = 40 , 2 x - y = 20 , for integers of x and y , 3 y ^ 2 = ?
Options: a ) 2 , b ) 48 , c ) 0 , d ) 10 , e ) 3
Rationale: 3 x + y = 40 2 x - y = 20 5 x = 60 x = 12 y = 4 3 y ^ 2 = 3 * 16 = 48 answer is b
Answer: b
Problem: how many distinct 3 digit number less than 10
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "000,001 , 002,003 , 004,005 , 006,007 , 008,009 . 10 distinct 3 digit numbers less than 10 . answer : c"
Answer: c
Problem: the average age of a group of persons going for picnic is 16 years . 20 new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years . the number of persons initially going for picnic is ?
Options: a ) 10 , b ) 20 , c ) 37 , d ) 26 , e ) 22
Rationale: let the initial number of persons be x . then , 16 x + 20 * 15 = 15.5 ( x + 20 ) < = > 0.5 x = 10 < = > x = 20 . answer : b
Answer: b
Problem: in an election between two candidates , the winner has a margin of 10 % of the votes polled . if 2000 people change their mind and vote for the loser , the loser would have won by a margin of 10 % of the votes polled . find the total number of votes polled in the election ?
Options: a ) 20000 , b ) 25000 , c ) 24000 , d ) 23000 , e ) 22000
Rationale: "winner - looser 55 % - 45 % if 2000 people change their mind and vote for the loser : winner - looser 45 % - 55 % thus 2,000 people compose 10 % of all voters , which means that the total number of votes is 20,000 . answer : a ."
Answer: a
Problem: if 99 < x < 199 and 10 < y < 100 , then the product xy can not be equal to :
Options: a ) 19,104 , b ) 19,903 , c ) 19 , 356.732 , d ) 19,502 , e ) 19,880
Rationale: correct answer : ( b ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 99 * 10 . the largest value must be less than 199 * 100 . this means that 990 < xy < 19,900 . ( b ) is outside of this range , so it is not a possible product of xy .
Answer: b
Problem: a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 39,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 14500 , c ) 14900 , d ) 16380 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 39000 × 21 / 50 = 16380 answer is d"
Answer: d
Problem: if the operation € is defined for all x and y by the equation x € y = 3 * x * y , then 3 € ( 4 € 5 ) =
Options: a ) 80 , b ) 120 , c ) 160 , d ) 540 , e ) 660
Rationale: "working inside out , ( 4 € 5 ) = 3 * 4 * 5 = 60 3 € 60 = 3 * 3 * 60 = 540 hence , answer is d"
Answer: d
Problem: a person can swim in still water at 8 km / h . if the speed of water 4 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "m = 8 s = 4 us = 8 - 4 = 4 d = 4 t = 8 / 4 = 2 answer : a"
Answer: a
Problem: thomas and matt has some money with them in the ratio of 3 : 4 . if their father gives rs . 30 to each of them then the ratio becomes 4 : 5 . what would be the ratio if thomas spend rs . 40 and matt spend rs . 20 from what they have now ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: let money of thomas and matt be x and y respectively . x / y = 3 / 4 = > x = 3 / 4 y ( x + 30 ) / ( y + 30 ) = 4 / 5 = > 5 x + 150 = 4 y + 120 = > 5 x = 4 y - 30 but x = 3 / 4 y 5 * 3 / 4 y = 4 y - 30 15 y = 16 y - 120 = > y = 120 = > x = 3 * 120 / 4 = > x = 90 ratio of their money , if thomas spend rs . 40 and matt spend rs . 20 = > ( 90 - 40 ) / ( 120 - 20 ) = 50 / 100 . = > 1 : 2 answer : a
Answer: a
Problem: if the integer n has exactly 5 positive divisors , including 1 and n , how many positive divisors does √ n have ?
Options: a ) 6 , b ) 5 , c ) 2 , d ) 3 , e ) 4
Rationale: take the example of 16 . . . it has 3 positive divisors ( 1 , 2,4 , 8,16 ) now , take the example of 4 . . . it has only 3 divisors . . so d is the ans
Answer: d
Problem: a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 480 ?
Options: a ) 249 , b ) 498 , c ) 239 , d ) 823 , e ) 1,002
Rationale: "slope of 2 and a y - intercept of 2 y - coordinate is 480 y = 2 x + 2 478 = 2 x x = 239 answer : c . 239"
Answer: c
Problem: bruce purchased 7 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 985 , b ) b ) 1050 , c ) c ) 1055 , d ) d ) 1065 , e ) e ) 1075
Rationale: cost of 7 kg grapes = 70 × 7 = 490 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 490 + 495 = 985 a
Answer: a
Problem: if the sum of two positive integers is 26 and the difference of their squares is 52 , what is the product of the two integers ?
Options: a ) 108 , b ) 119 , c ) 128 , d ) 135 , e ) 168
Rationale: let the 2 positive numbers x and y x + y = 26 - - 1 x ^ 2 - y ^ 2 = 52 = > ( x + y ) ( x - y ) = 52 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 14 y = 12 product = 14 * 12 = 168 answer e
Answer: e
Problem: fonzie , aunt bee and lapis paid $ 7000 , $ 8000 and $ 9000 respectively to buy a map to capt . plaidstache ' s treasure . when they found it , the treasure turned out to be worth a cool $ 900000 . how much of it should lapis get ?
Options: a ) $ 300000 , b ) $ 320000 , c ) $ 335000 , d ) $ 336500 , e ) $ 337500
Rationale: a = 7000 b = 8000 c = 9000 a share 7 parts , b share 8 parts & c share 9 parts total 24 parts - - - - - > 900000 - - - - > 1 part - - - - - - - > 37500 c share = 9 parts - - - - - > 337500 e
Answer: e
Problem: for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 9 ] * [ 4 ] equivalent to ?
Options: a ) [ 108 ] , b ) [ 54 ] , c ) [ 36 ] , d ) [ 27 ] , e ) [ 18 ]
Rationale: "[ 9 ] * [ 4 ] = 27 * 2 = 54 = ( 1 / 2 ) ( 108 ) = [ 108 ] the answer is a ."
Answer: a
Problem: two pipes p and q can fill a cistern in 10 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 5 , e ) 5.5
Rationale: "let x be the total time it takes for the cistern to fill . 4 / 10 + x / 15 = 1 x / 15 = 3 / 5 x = 9 after the first pipe is turned off , it takes 5 more minutes to fill the cistern . the answer is d ."
Answer: d
Problem: express 20 mps in kmph ?
Options: a ) 23 , b ) 88 , c ) 90 , d ) 72 , e ) 21
Rationale: 20 * 18 / 5 = 72 kmph answer : d
Answer: d
Problem: you hold some gold in a vault as an investment . over the past year the price of gold increases by 40 % . in order to keep your gold in the vault , you must pay 5 % of the total value of the gold per year . what percentage has the value of your holdings changed by over the past year .
Options: a ) 35 % , b ) 33 % , c ) 36 % , d ) 38 % , e ) 40 %
Rationale: "( 100 % + 40 % ) * ( 100 % - 5 % ) = 140 * 0.95 = 133 % an increase of 33 % your gold holdings have increased in value by 33 % . the answer is b"
Answer: b
Problem: a large tanker can be filled by two pipes a and b in 60 and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 30 , b ) 15 , c ) 20 , d ) 25 , e ) 50
Rationale: suppose the tank is filled in x minutes . then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 = > x = 30 min answer a
Answer: a
Problem: the captain of a cricket team of 11 members is 27 years old and the wicket keeper is 1 year older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "let the average age of the whole team be x years . 11 x - ( 27 + 28 ) = 9 ( x - 1 ) 11 x - 9 x = 46 2 x = 46 x = 23 . the average age of the team is 23 years . the answer is d ."
Answer: d
Problem: if log 1087.5 = 6.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 28 , c ) 80 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 6.9421 + 1 ) = 10 ( 7.9421 ) = 79.421 x = antilog ( 79.421 ) therefore , number of digits in x = 80 . answer : c"
Answer: c
Problem: two heavily loaded sixteen - wheeler transport trucks are 787 kilometers apart , sitting at two rest stops on opposite sides of the same highway . driver a begins heading down the highway driving at an average speed of 90 kilometers per hour . exactly one hour later , driver b starts down the highway toward driver a , maintaining an average speed of 80 kilometers per hour . how many kilometers farther than driver b , will driver a have driven when they meet and pass each other on the highway ?
Options: a ) 90 , b ) 131 , c ) 150 , d ) 320 , e ) 450
Rationale: i ' ve been reading the website for a while and i ' m always keen to see different approaches so i would like to share one that works for me : short version : truck a travels for an hour . distance remaining = 787 - 90 = 697 k ratio of speeds 9 : 8 - > 697 / 17 = 41 truck a = 90 + 41 * 9 = 459 truck b = 41 * 8 = 328 delta = 131 km answer b
Answer: b
Problem: in a group of 800 people , 1 / 5 play at least one instrument , 64 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 3 / 25 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: "p ( playing 2 or more instruments ) = 64 / 800 = 2 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 2 / 25 = 3 / 25 . answer a ."
Answer: a
Problem: what is the angle between the hands of a clock when time is 8 : 30 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 30 h - 11 / 2 m = 30 * 8 - 30 * 11 / 2 = 240 - 165 = 75 deg answer : b"
Answer: b
Problem: if the difference between compound interest ( interest compounded yearly ) and simple interest on a certain sum at the rate 20 % p . a . after 3 years is rs . 1280 then what is the principal ?
Options: a ) 7900 , b ) 8,000 , c ) 10,000 , d ) 8,300 , e ) 9,300
Rationale: "let p is the principal , so p ( [ 120 / 100 ] ^ 3 - 1 ) - p * 20 / 100 * 3 = 1280 p [ 728 / 1000 - 3 / 5 ] = 1280 p = 1280 * 5 * 1000 / 728 * 5 - 3000 = 10000 answer : c"
Answer: c
Problem: in the xy - coordinate system , if ( m , n ) and ( m + 4 , n + k ) are two points on the line with the equation x = 2 y + 5 , then k =
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 5 / 2 , e ) 4
Rationale: "since ( m , n ) and ( m + 2 , n + k ) are two points on the line with the equation x = 2 y + 5 they should satisfy m = 2 n + 5 and m + 4 = 2 * ( n + k ) + 5 . by 1 st equation we have m - 2 n = 5 and by 2 nd equation m - 2 n = 2 k + 1 - - - > 5 = 2 k + 1 - - - > k = 2 . the answer is , therefore , ( c ) ."
Answer: c
Problem: during the first week of performances of a certain play , 5400 tickets were sold , all at reduced price . during the remaining weeks of performances , 5 times as many tickets were sold at full price as were sold at reduced price . if the total number of tickets r sold was 25200 , how many of them were sold at full price ?
Options: a ) 21000 , b ) 19800 , c ) 16500 , d ) 15800 , e ) 8700
Rationale: given : the question tells us about the number of tickets sold in the first week at reduced price = 5400 . it also tells us that during the remaining weeks , the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price . the total tickets sold was 25200 , and we are asked to find the number of tickets that where sold at full price . approach : the question asks us to find the number of ticket sold at full price . we know that the number of tickets sold at full price was 5 times the no . of tickets sold at reduced price in remaining weeks . hence , assuming tickets sold at reduced price in remaining weeks to be x would give us the no . of tickets sold at full price to be 5 x . tickets sold in first week + tickets sold in remaining weeks = total no . of tickets soldi . e . tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold we know the no . of tickets sold during first week and the total no . of tickets sold . we will use this relation to get to our answer . working out : tickets sold in first week + tickets sold at full price in remaining weeks + tickets sold at reduced price in remaining weeks = total no . of tickets sold substituting values in the equation , we get 5400 + 5 x + x = 25200 x = 3300 tickets sold at full price = 5 x = 16500 answer : option c
Answer: c
Problem: income and expenditure of a person are in the ratio 10 : 4 . if the income of the person is rs . 19000 , then find his savings ?
Options: a ) 79754 , b ) 87689 , c ) 59875 , d ) 11400 , e ) 87648
Rationale: "let the income and the expenditure of the person be rs . 10 x and rs . 4 x respectively . income , 10 x = 19000 = > x = 1900 savings = income - expenditure = 10 x - 4 x = 6 x = 6 ( 1900 ) so , savings = rs . 11400 . answer : d"
Answer: d
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 2000 . the difference between the profit shares of a and c is ?
Options: a ) 621 , b ) 276 , c ) 236 , d ) 800 , e ) 211
Rationale: "explanation : ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 2000 = > 5 parts out of 15 parts is rs . 2000 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 2000 ) = rs . 800 answer : d"
Answer: d
Problem: if a card is drawn from a well shuffled deck of cards , what is the probability of drawing a black card or a face card ?
Options: a ) 7 / 13 , b ) 15 / 26 , c ) 9 / 12 , d ) 8 / 13 , e ) 29 / 52
Rationale: "p ( b á ´ œ f ) = p ( b ) + p ( f ) - p ( b â ˆ © f ) , where b denotes black cards and f denotes face cards . p ( b á ´ œ f ) = 26 / 52 + 12 / 52 - 6 / 52 = 8 / 13 answer : d"
Answer: d
Problem: a cistern 4 m long and 2 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 23 m 2 , b ) 20 m 2 , c ) 52 m 2 , d ) 24 m 2 , e ) 55 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 2 x 1.25 + 4 x 1.25 ) + 4 x 2 ] m 2 = 23 m 2 . answer : a"
Answer: a
Problem: jane makes toy bears . when she works with an assistant , she makes 62 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 100 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 64.8 bears per 36 hours a week or 1.8 bears / hr ( [ 40 bears * 1.62 ] / [ 40 hrs * . 90 ] ) . [ ( 1.8 - 1 ) / 1 ] * 100 % = 80 % answer : b"
Answer: b
Problem: find the average of all numbers between 5 and 37 which are divisible by 4
Options: a ) 25 , b ) 20 , c ) 45 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 4 + 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 ) / 4 ) = 180 / 4 = 45 option c"
Answer: c
Problem: uncle bruce is baking chocolate chip cookies . he has 36 ounces of dough ( with no chocolate ) and 18 ounces of chocolate . how many ounces of chocolate are left over if he uses all the dough but only wants the cookies to consist of 20 % chocolate ?
Options: a ) 3 , b ) 6 , c ) 7.2 , d ) 7.8 , e ) 9
Rationale: "answer is e . x / x + 36 = 1 / 5 x = 9 18 - 9 = 9"
Answer: e
Problem: a broker invested her own money in the stock market . during the first year , she increased her stock market wealth by 50 percent . in the second year , largely as a result of a slump in the stock market , she suffered a 30 percent decrease in the value of her stock investments . what was the net increase or decrease on her overall stock investment wealth by the end of the second year ?
Options: a ) − 5 % , b ) 5 % , c ) 15 % , d ) 20 % , e ) 80 %
Rationale: "assume the broker invested $ 100 . after year 1 ( 50 % increase in wealth ) : $ 100 * 0.5 = $ 50 increase + $ 100 = $ 150 after year 2 ( 30 % decrease in wealth ) : $ 150 * 0.3 = $ 45 ; $ 150 - $ 45 decrease = $ 105 net increase = $ 105 / $ 100 - 1 = 5 % answer is b ."
Answer: b
Problem: the sum of the squares of three numbers is 225 , while the sum of their products taken two at a time is 200 . their sum is :
Options: a ) 10 , b ) 30 , c ) 40 , d ) 25 , e ) none of these
Rationale: "x ^ + y ^ 2 + z ^ 2 = 225 xy + yz + zx = 200 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 225 + ( 2 * 200 ) ( x + y + z ) ^ 2 = 625 so x + y + z = 25 answer : d"
Answer: d
Problem: a train travels from new york to chicago , a distance of approximately 480 miles , at an average rate of 40 miles per hour and arrives in chicago at 6 : 00 in evening , chicago time . at what hour in the morning , new york time , did the train depart for chicago ? ( note : chicago time is one hour earlier than new york time )
Options: a ) 3 : 00 , b ) 4 : 00 , c ) 5 : 00 , d ) 6 : 00 , e ) 7 : 00
Rationale: "6 : 00 in evening in chicago = 7 : 00 in evening in new york . so , the train was in chicago 7 : 00 in the evening , new york time . the trip took t = d / r = 480 / 40 = 12 hours . therefore , the train depart from new york at 7 : 00 - 12 hours = 7 : 00 in the morning , new york time . answer : e ."
Answer: e
Problem: if m is the set of all consecutive multiples of 9 between 100 and 500 , what is the median of m ?
Options: a ) 300 , b ) 301 , c ) 301.5 , d ) 302.5 , e ) 306
Rationale: since 100 / 9 = 11.11 , 500 / 9 = 55.55 , m can be written as { 9 * 12 , 9 * 13 , . . . . , 9 * 54 , 9 * 55 } . the number of elements of m is , therefore , 44 ( = 55 - 12 + 1 ) . since the number of elements is even number the median is the average of the 22 nd element ( = 9 * 33 ) and 23 rd element ( = 9 * 34 ) . so the median is ( 9 * 33 + 9 * 34 ) / 2 = 301.5 . the answer is c .
Answer: c
Problem: a 300 meter long train crosses a platform in 42 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 289 , c ) 350 , d ) 882 , e ) 400
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 42 = 50 / 3 3 ( x + 300 ) = 2100 è x = 400 m . answer : e"
Answer: e
Problem: shop offered 20 % offer for every shirt , smith bought a shirt at rs . 780 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 700 , e ) 975
Rationale: "sp * ( 80 / 100 ) = 780 sp = 9.75 * 100 = > cp = 975 answer : e"
Answer: e
Problem: two positive integers differ by 4 , and sum of their reciprocals is 1 . then one of the numbers is
Options: a ) 2 , b ) b ) 1 , c ) c ) 5 , d ) d ) 21 , e ) e ) 28
Rationale: algebraic approach : let n be the smaller integer = > 1 / n + 1 / ( n + 4 ) = 1 or ( ( n + 4 ) + n ) / n ( n + 4 ) = 1 or n ^ 2 + 4 n = 2 n + 4 or n = 2 as n can not be - negative solve for n = > n = 2 . hence , a
Answer: a
Problem: john has rs 360 for his expenses . if he exceeds his days by 4 days he must cut down daily expenses by rs 3 . the number of days of john ' s tour program is
Options: a ) 10 , b ) 15 , c ) 20 , d ) 24 , e ) 27
Rationale: let john under takes a tour of x days . then , expenses for each day = 360 x 360 x + 4 = 360 x − 3 x = 20 and − 24 hence , x = 20 days . c
Answer: c
Problem: three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1200 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 1200 x = 20 the numbers are 3 * 20 , 4 * 20 , 5 * 20 hence required h . c . f . = 20 answer is a"
Answer: a
Problem: the price of food in the area where the sims family lives is scheduled to increase by 50 % next year . since the sims family can not afford an increase in their food bill , how much will they have to reduce consumption to keep their cost the same ?
Options: a ) 17 % , b ) 25.6 % , c ) none % , d ) 33.3 % , e ) 50 %
Rationale: solution : let the current food expense be represented by rs . 100 . the cost of food rises 50 % . so , to buy same amount of food , they need to increase their expense , = ( 100 + 50 % of 100 ) = rs . 150 . but , they want to keep food expense the same , so they have to cut rs . by 50 to keep it to rs . = 100 . the % decrease in consumption is , ( 50 / 150 ) * 100 = 33.3 % . mental calculation method ; 100 - - - - - 50 % ↑ - - - → 150 - - - - - - x % ↓ - - - → 100 . here , x = ( 50 / 125 ) * 100 = 33.3 % . answer : option d
Answer: d
Problem: find the simple interest on $ 10000 at 5 % per annum for 12 months ?
Options: a ) $ 410 , b ) $ 500 , c ) $ 650 , d ) $ 710 , e ) $ 1000
Rationale: "p = $ 10000 r = 5 % t = 12 / 12 years = 1 year s . i . = p * r * t / 100 = 10000 * 5 * 1 / 100 = $ 500 answer is b"
Answer: b
Problem: if the given two numbers are respectively 8 % and 16 % of a third number , then what percentage is the first of the second ?
Options: a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
Rationale: "here , l = 8 and m = 16 therefore , first number = l / m x 100 % of second number = 8 / 16 x 100 % of second number = 50 % of second number answer : d"
Answer: d
Problem: if you keep rolling a pair of dice together till a sum of 5 or 7 is obtained , then what is the probability that a sum of 5 comes before a sum of 7 ?
Options: a ) 5 / 5 , b ) 4 / 5 , c ) 3 / 5 , d ) 2 / 5 , e ) 1 / 5
Rationale: this can be solved in a generic and complex way but let us not go into all that . there can be four ways through which the pair of dice results in a sum of 5 . there can be six ways through which the pair of dice can result in a sum of 7 . now , we want the probability of the pair of dice resulting in a sum of 5 before a sum of 7 . thus probability = 4 / ( 4 + 6 ) = 4 / 10 or 2 / 5 . correct answer is d ) 2 / 5
Answer: d
Problem: a pupil ' s marks were wrongly entered as 73 instead of 63 . due to the average marks for the class got increased by half . the number of pupils in the class is ?
Options: a ) 18 , b ) 82 , c ) 20 , d ) 27 , e ) 29
Rationale: "let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 x / 2 = ( 73 - 63 ) = > x / 2 = 10 = > x = 20 . answer : c"
Answer: c
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 4 , 2 ) , what is the area of that square ?
Options: a ) 196 , b ) 125 , c ) 140 , d ) 128 , e ) 134
Rationale: "one point ( - 3 - 4 ) , intersection ( 4,2 ) so the distance from the first point - 3 - 4 = - 7 is the midpoint of the square - - > whole side 14 , 14 * 14 = 196 a"
Answer: a
Problem: a sports equipment store sold ping pong rackets for a total of $ 588 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
Options: a ) 50 , b ) 60 , c ) 490 , d ) 500 , e ) 980
Rationale: "average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 588 x = 60 pairs were sold . answer : b"
Answer: b
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 1 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "if the units digit of a ^ 2 is 1 , then the units digit of a is either 1 or 9 . if the units digit of ( a + 1 ) ^ 2 is 4 , then the units digit of a + 1 is either 2 or 8 . to satisfy both conditions , the units digit of a must be 1 . then a + 2 has the units digit of 3 , thus the units digit of ( a + 2 ) ^ 2 will be 9 . the answer is e ."
Answer: e