regisss/math_qa huggingface dataset:
Problem: the average weight of 5 person ' s increases by 5.5 kg when a new person comes in place of one of them weighing 68 kg . what might be the weight of the new person ?
Options: a ) 60 kg , b ) 95.5 kg , c ) 80 kg , d ) 85 kg , e ) 90 kg
Rationale: "total weight increased = ( 5 x 5.5 ) kg = 27.5 kg . weight of new person = ( 68 + 27.5 ) kg = 95.5 kg option b"
Answer: b
Problem: in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the rate in the remaining 40 overs to reach the target of 292 runs ?
Options: a ) 6.5 , b ) 6.22 , c ) 6.29 , d ) 6.39 , e ) 6.13
Rationale: "required run rate = [ 292 - ( 3.2 * 10 ) ] / 40 = 260 / 40 = 6.5 answer : a"
Answer: a
Problem: the radius of a semi circle is 5.2 cm then its perimeter is ?
Options: a ) 32.52 , b ) 32.48 , c ) 26.74 , d ) 32.9 , e ) 32.31
Rationale: "36 / 7 r = 5.2 = 26.74 answer : c"
Answer: c
Problem: p and q invested in a business . they earned some profit which they divided in the ratio of 2 : 3 . if p invested rs . 50 , 000 , the amount invested by q is :
Options: a ) rs . 65,000 , b ) rs . 70,000 , c ) rs . 75,000 , d ) rs . 90,000 , e ) rs . 60,000
Rationale: q invested = 50000 / 2 * 3 = 75000 answer : c
Answer: c
Problem: if log 102 = 0.3010 , log 10 3 = 0.4771 , then the number of zeros between the decimal point and the first significant figure in ( 0.0432 ) 10 is ?
Options: a ) 10 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: x = ( 0.0432 ) 10 = ( 432 / 10000 ) 10 = ( 33.24 / 104 ) 10 therefore , log 10 x = 10 ( log 103 + 4 log 102 - 4 ) = 10 ( 1.4313 + 1.2040 - 4 ) = 10 ( - 1.3647 ) = - 13.647 = - 14.353 therefore , x = antilog ( - 14.053 ) thus , number of zeros between the decimal and the first significant figure = 13 answer : b
Answer: b
Problem: eden drove an average speed of 15 miles per hour for the first 20 miles of a tripthen at a average speed of 30 miles / hr for the remaining 20 miles of the trip if she made no stops during the trip what was eden ' s avg speed in miles / hr for the entire trip
Options: a ) 35 , b ) 20 , c ) 45 , d ) 50 , e ) 55
Rationale: avg . speed = total distance / total time total distance = 40 miles total time = 20 / 15 + 15 / 30 = 2 avg . speed = 20 . answer - b
Answer: b
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 44 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 36 degrees , d ) 34 degrees , e ) 74 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 44 tu + w + th = 192 - 44 = 148 f = 184 – 148 = 36 answer : c"
Answer: c
Problem: if w is the set of all the integers between 49 and 88 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 11 , b ) 44 , c ) 48 , d ) 28 , e ) 26
Rationale: "official solution : number of multiples of 3 step 1 . subtract the extreme multiples of 3 within the range ( the greatest is 87 , the smallest is 51 ) : 87 - 51 = 36 step 2 . divide by 3 : 36 / 3 = 12 step 3 . add 1 : 12 + 1 = 13 . so there are 13 multiples of 3 within the range : examples are 51 , 54 , 57 , 60 , etc . number of multiples of 2 step 1 . subtract the extreme multiples of 2 within the range ( the greatest is 88 , the smallest is 50 ) : 88 - 50 = 38 step 2 . divide by 2 : 38 / 2 = 19 step 3 . add 1 : 19 + 1 = 20 . so there are 19 multiples of 2 within the range : examples are 50 , 52 , 54 , 56 , 58 , 60 etc . add the 13 multiples of 3 and the 19 multiples of 2 : 13 + 19 = 32 . however , by adding the multiples of 2 and the multiples of 3 , we are effectively counting several numbers twice : for example , 54 and 60 are parts of both the lists above . so we ca n ' t just take 13 + 19 = 32 . find the number of multiples of 6 ( which are the double counted , as 6 is divisible by both 2 and 3 ) , and subtract it from 32 : step 1 . subtract the extreme multiples of 6 within the range ( the greatest is 72 , the smallest is 54 ) : 84 - 54 = 30 step 2 . divide by 6 : 30 / 6 = 5 step 3 . add 1 : 5 + 1 = 6 . so there are 6 multiples of 6 within the range : we counted 6 numbers twice . subtract the 6 multiples of 6 from the sum of the multiples of 2 and 3 : = 13 + 19 - 6 = 32 - 6 = 26 therefore , the final number of multiples of 2 , 3 or 6 is 26 . hence , this is the correct answer . ( e )"
Answer: e
Problem: in the xy - coordinate plane , the graph of y = - x ^ 2 + 9 intersects line l at ( p , - 5 ) and ( t , - 7 ) . what is the least possible value of the slope of line l ?
Options: a ) 6 , b ) - 1 , c ) - 2 , d ) - 6 , e ) - 10
Rationale: we need to find out the value of p and l to get to the slope . line l and graph y intersect at point ( p , - 5 ) . hence , x = p and y = - 5 should sactisfy the graph . soliving 5 = - p 2 + 9 p 2 = 4 p = + or - 2 simillarly point ( t , - 7 ) should satisfy the equation . hence x = t and y = - 7 . - 7 = - t 2 + 9 t = + or - 4 considering p = - 2 and t = 4 , the least slope is ( - 7 + 5 ) / ( 4 - 2 ) = - 1 imo option b is correct answer .
Answer: b
Problem: two numbers n and 16 have lcm = 52 and gcf = 8 . find n .
Options: a ) 35 , b ) 26 , c ) 76 , d ) 87 , e ) 24
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 52 * 8 n = 52 * 8 / 16 = 26 correct answer b"
Answer: b
Problem: an ant walks an average of 1000 meters in 30 minutes . a beetle walks 10 % less distance at the same time on the average . assuming the beetle walks at her regular rate , what is its speed in km / h ?
Options: a ) 1.8 , b ) 1.6 , c ) 2.775 . , d ) 1.9 , e ) 3.5 .
Rationale: the ant walks an average of 1000 meters in 30 minutes 1000 meters in 1 / 2 hours the beetle walks 10 % less distance = 1000 - 10 = 900 meters in 30 minutes 0.900 km in 30 / 60 = 1 / 2 hours speed = 0.900 * 2 = 1.8 km / h i guess option a should be 1.8
Answer: a
Problem: two trains 151 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.18 , c ) 7.16 , d ) 7.84 , e ) 7.12
Rationale: "t = ( 151 + 165 ) / ( 80 + 65 ) * 18 / 5 t = 7.84 answer : d"
Answer: d
Problem: joe has candys on his pocket , 4 of those candies have lemon flavor , and 3 have caramel flavor . if joe take one , what is the probability that he picks one caramel flavor ?
Options: a ) 1 , b ) 2 , c ) none , d ) 3 / 7 , e ) 3 / 4
Rationale: the total number of candies is 7 and the number of candies with lemon flavor is 3 then , in one chance the probability to pick one candie with lemon flavor is 3 / 7 answer d
Answer: d
Problem: john bought a total of 24 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 24 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: "let number of mangoes be x , number of oranges be 24 - x 0.80 x + ( 24 - x ) 0.60 / 24 = 0.65 solving for x , we get x = 6 - - > mangoes 6 , oranges 18 now , number of oranges to be returned be y 0.80 * 6 + ( 18 - y ) * 0.60 / 24 - y = 0.72 solving for y , y = 14 ans : e"
Answer: e
Problem: the difference between the ages of two persons is 10 years . fifteen years ago , the elder one was twice as old as the younger one . the present age of the elder person is
Options: a ) 25 years , b ) 30 years , c ) 35 years , d ) 40 years , e ) none
Rationale: "sol . let their ages of x years and ( x + 10 ) years respectively . then , ( x + 10 ) - 15 = 2 ( x - 15 ) ⇔ x - 5 = 2 x - 30 ⇔ x = 25 . ∴ present age of the elder person = ( x + 10 ) = 35 years . answer c"
Answer: c
Problem: how many 3 - digit numerals begin with a digit that represents a prime and end with a digit that represents a odd prime number ?
Options: a ) 16 , b ) 120 , c ) 160 , d ) 180 , e ) 240
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 3 ways total = 4 * 10 * 3 = 120 ans : b"
Answer: b
Problem: an automobile parts supplier charges $ 20 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 20 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1005 , b ) 1045 , c ) 1075 , d ) 1015 , e ) 1096
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 20 * 4 / 5 = 16 a certain week the supplier sold 60 gasket 1 . he sold 20 % of the gaskets to x = 12 gaskets = 20 * 10 + 16 * 2 = 200 + 32 = 232 2 . he sold 15 % of the gaskets to y = 9 gaskets = 20 * 9 = 180 3 . he sold remaining 65 % to z = 39 gaskets = 20 * 10 = 200 + 16 * 29 = 684 thus , total money earned 232 + 180 + 684 = 1096 answer is e"
Answer: e
Problem: the length of a rectangle is increased by 25 % and its breadth is decreased by 15 % . what is the effect on its area ?
Options: a ) 1288 , b ) 1299 , c ) 10625 , d ) 10000 , e ) 2887
Rationale: "100 * 100 = 10000 125 * 85 = 10625 answer : c"
Answer: c
Problem: suraj has a certain average of runs for 8 innings . in the 9 th innings he scores 90 runs thereby increasing his average by 6 runs . what is his average after the 9 th innings ?
Options: a ) 42 , b ) 64 , c ) 36 , d ) 72 , e ) 27
Rationale: "to improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings . thus , the average after the 9 th innings = 90 - 48 = 42 . answer : a"
Answer: a
Problem: 20 men or 25 women can finish a work in 25 days . how many days 38 men and 15 women will take to finish this job ?
Options: a ) 12 days , b ) 10 days , c ) 5 days , d ) 6 days , e ) 15 days
Rationale: 20 men = 25 women therefore , 1 women = 20 / 25 men = 4 / 5 men 15 women = 4 / 5 * 15 men = 12 men i . e . 38 men + 15 women = 38 men + 12 men = 50 men 1 work done by men = 20 * 25 20 * 25 = 50 * ? number of days = 20 * 25 / 50 = 10 days . b
Answer: b
Problem: two heavily loaded sixteen - wheeler transport trucks are 940 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 ) 140 , 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 = 940 - 90 = 850 k ratio of speeds 9 : 8 - > 850 / 17 = 50 truck a = 90 + 50 * 9 = 540 truck b = 50 * 8 = 400 delta = 140 km answer d"
Answer: d
Problem: in an examination , 32 % of total students failed in hindi , 56 % failed in english and 12 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 24 , b ) 37 , c ) 28 , d ) 40 , e ) 81
Rationale: "explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 32 + 56 â € “ 12 = 76 therefore students who passed = 100 â € “ 76 = 24 . answer : a"
Answer: a
Problem: of the 250 employees at company x , 80 are full - time , and 175 have worked at company x for at least a year . there are 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 25 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "250 employees 80 are full - time 175 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 250 - 80 = 170 employees not full time 170 - 20 = 150 employees not full time who worked over a year 175 employees have worked at company x for at least a year - 150 employees not full time who worked over a year = 25 full - time employees of company x have worked at the company for at least a year ans a"
Answer: a
Problem: a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 221 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 33 , c ) 55 , d ) 77 , e ) 39
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 221 = > . 1 x + 3 / 4 x = 221 = > x = 260 260 - 221 = pure gala = 39 . e"
Answer: e
Problem: the ratio between the perimeter and the breadth of a rectangle is 5 : 1 . if the area of the rectangle is 216 sq . cm , what is the length of the rectangle ?
Options: a ) 18 cm
b ) 20 cm
c ) 22 cm
d ) 24 cm
e ) 25 cm
Rationale: 2 ( l + b ) = 5 b 1 2 l + 2 b = 5 b 3 b = 2 l b = 2 l 3 then , area = 216 cm 2 l x b = 216 l x 2 l = 216 3 l 2 = 324 l = 18 cm . a
Answer: a
Problem: 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 50 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 44 ( 44 - 12 ) must be those with four screens or more e is the answer"
Answer: e
Problem: on a two - dimensional coordinate plane , the line q = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s q = x ^ 2 - x ^ 3 instead of q = x ^ 2 - q ^ 3 . in this case : the x - intercept is the value ( s ) of x for q = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Problem: if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value w of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers w ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value . hence , answer choice c is the one to go ."
Answer: c
Problem: there is 60 lit of milk and water in which milk forms 84 % . howmuch water must be added to this solution to make it solution in which milk forms 60 %
Options: a ) 18.75 , b ) 19.75 , c ) 20.75 , d ) 21.75 , e ) 24
Rationale: "60 * 84 / 100 = 50.40 lit milk that is 9.60 lit water let x lit water will be added then ( 60 + x ) * 60 / 100 = 50.40 so x = 18.75 answer : e"
Answer: e
Problem: the average ( arithmetic mean ) of the 5 positive integers k , m , r , s , and t is 10 , and k < m < r < s < t . if t is 20 , what is the greatest possible value of the median of the 5 integers ?
Options: a ) 16 , b ) 18 , c ) 13 , d ) 20 , e ) 22
Rationale: "we need to find the median which is the third value when the numbers are in increasing order . since k < m < r < s < t , the median would be r . the average of the positive integers is 10 which means that in effect , all numbers are equal to 10 . if the largest number is 20 , it is 10 more than 20 . we need r to be maximum so k and m should be as small as possible to get the average of 10 . since all the numbers are positive integers , k and m can not be less than 1 and 2 respectively . 1 is 9 less than 10 and 2 is 8 less than 10 which means k and m combined are 17 less than the average . 20 is already 10 more than 10 and hence we only have 17 - 10 = 7 extra to distribute between r and s . since s must be greater than r , r can be 10 + 3 = 13 and s can be 10 + 4 = 14 . so r is 13 . answer ( c )"
Answer: c
Problem: if a person walks at 15 km / hr instead of 10 km / hr , he would have walked 15 km more . the actual distance traveled by him is ?
Options: a ) 30 , b ) 50 , c ) 15 , d ) 12 , e ) 20
Rationale: "let the actual distance traveled be x km . then , x / 10 = ( x + 15 ) / 15 x - 30 = > x = 30 km . answer : a"
Answer: a
Problem: the population of a bacteria culture doubles every 1 minutes . approximately how many minutes will it take for the population to grow from 1,000 to 500,000 bacteria
Options: a ) 9 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "this one ' s easy . 1000 * 2 ^ t = 500,000 2 ^ t = 500 now gauging , since 2 ^ 8 = 256 , then 2 ^ 9 = 512 so t = 9 but be careful , ' t ' is in time intervals of 1 minutes so answer is 9 * 1 = 9 minutes answer ( a )"
Answer: a
Problem: a rectangular tiled patio is composed of 48 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 48 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 48 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 48 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 48 ( 2 r - 4 ) * r = 48 2 r ^ 2 - 4 r - 48 = 0 r can not be negative so r = 6 and c = 8 so , answer will be b"
Answer: b
Problem: what is the units digit of 28 ! + 50 ! + 3 ! + 4 ! ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "for all n greater than 4 , the units digit of n ! is 0 . the sum of the four units digits is 0 + 0 + 6 + 4 = 10 the units digit is 0 . the answer is a ."
Answer: a
Problem: a shopkeeper loses 15 % , if an article is sold for rs . 119 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 177 , b ) s . 168 , c ) s . 144 , d ) s . 129 , e ) s . 112
Rationale: "given that sp = rs . 119 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 119 ) / 85 = rs . 140 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 140 * 120 ) / 100 = rs . 168 answer : b"
Answer: b
Problem: eight women can do a work in 10 days . ten men can complete the same work in 6 days . what is the ratio between the capacity of a man and a woman ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 2 : 3 , d ) 4 : 3 , e ) none of these
Rationale: "explanation : ( 8 ã — 10 ) women can complete the work in 1 day . â ˆ ´ 1 woman ' s 1 day ' s work = 1 / 80 ( 10 ã — 6 ) men can complete the work in 1 day . â ˆ ´ 1 man ' s 1 day ' s work = 1 / 60 so , required ratio = 1 / 80 : 1 / 60 = 4 : 3 answer : d"
Answer: d
Problem: x , y and z , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2350 , what will be z ' s share of the earnings ?
Options: a ) $ 525 , b ) $ 550.50 , c ) $ 1080.02 , d ) $ 522.3 , e ) $ 1020.2
Rationale: "the dollars earned will be in the same ratio as amount of work done 1 day work of z is 1 / 12 ( or 2 / 24 ) 1 day work of the combined workforce is ( 1 / 6 + 1 / 8 + 1 / 12 ) = 9 / 24 z ' s contribution is 2 / 9 of the combined effort translating effort to $ = 2 / 9 * 2350 = $ 522.3 hence : d"
Answer: d
Problem: the sides of a cube measures 6.5 cm . if the surface area of the cube is the same as a ball , what is the radius of the ball ? round to the nearest whole number .
Options: a ) 9
b ) 7
c ) 4
d ) 8
e ) 6
Rationale: first calculate the surface area of the cube . the cube is made of 6 squares with the sides measuring 6.5 cm each . the surface area of 1 side of the cube is 42.25 cm . multiply the surface area of the 1 side by 6 will give you the cube ' s total surface area . the cubes surface area is 253.5 cm . now we know that the surface area of the ball is 253.5 cm . to find out the surface area of a sphere you need to square the radius , then multiply by pi , and multiply by the number 4 . going backwards to find the radius - you will need to dived the surface area by 4 . then divide by pi . then determine the square root of the answer . the radius is 4.460 . rounding to the nearest whole number the radius is 4 . the correct answer is ( c ) .
Answer: c
Problem: ratio of two numbers x and y is 5 : 7 . if x is increased by 20 % and y is increased by 2 then the new ratio becomes 2 : 3 . what is the ratio 3 y : ( x + 6 )
Options: a ) 7 : 8 , b ) 8 : 7 , c ) 6 : 7 , d ) 7 : 6 , e ) 2 : 7
Rationale: "let : x = 5 n y = 7 n 6 n / ( 7 n + 2 ) = 2 / 3 18 n = 2 * ( 7 n + 2 ) n = 1 so , x = 5 ; y = 7 y / ( x + 3 ) = 7 / 8 answer = a"
Answer: a
Problem: if a = { 9 , 17 , 25 , 28 , 29 , 30 } , how much less is the mean of the numbers in a than the median of the numbers in s ?
Options: a ) 1.0 , b ) 9.6 , c ) 3.5 , d ) 3.2 , e ) 5.1
Rationale: "this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 9 + 17 + 25 + 28 + 29 + 30 ) / 6 = 23 median = ( 25 + 28 ) / 2 = 26.5 difference = 3.5 option c"
Answer: c
Problem: a , b and c have rs . 1000 between them , a and c together have rs . 700 and b and c rs . 600 . how much does c have ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 400 , e ) 500
Rationale: "a + b + c = 1000 a + c = 700 b + c = 600 - - - - - - - - - - - - - - a + b + 2 c = 1300 a + b + c = 1000 - - - - - - - - - - - - - - - - c = 300 answer : c"
Answer: c
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 10 more than 1 / 4 of the fine and peter paid $ 10 less than 1 / 3 of the fine , leaving pay $ 25 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 120 , b ) $ 125 , c ) $ 130 , d ) $ 135 , e ) $ 140
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 10 ] + [ ( 1 / 3 ) f – 10 ] + [ ( 1 / 2 ) f – 25 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 25 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 300 12 f = 13 f – 300 – f = – 300 f = 300 well , if the fine cost $ 300 , then sam paid the part not covered by joe or peter . half the fine is $ 150 , and sam paid $ 25 less than this : $ 125 answer = b"
Answer: b
Problem: from a pack of 52 cards , 1 card is drawn at random . what is the probability that a king is drawn ?
Options: a ) 1 / 4 , b ) 4 / 13 , c ) 1 / 13 , d ) 3 / 26 , e ) 7 / 52
Rationale: "the total number of cards is 52 . the number of kings is 4 . p ( king ) = 4 / 52 = 1 / 13 the answer is c ."
Answer: c
Problem: if ( 1 / 2 ) ^ 18 ( 1 / 81 ) ^ k = 1 / 18 ^ 18 , then k =
Options: a ) 9 , b ) 12 , c ) 16 , d ) 24 , e ) 36
Rationale: "i ' m going to focus on denominator only . . ( 2 ^ 18 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 18 ( 2 ^ 18 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 18 hence 4 k = 36 k = 9 answer a i hope it ' s quite clear"
Answer: a
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 300 girls , the total number of students in the college is
Options: a ) 420 , b ) 520 , c ) 620 , d ) 780 , e ) 820
Rationale: "explanation : let the boy are 8 x and girls are 5 x = > 5 x = 300 = > x = 60 total students = 8 x + 5 x = 13 x = 13 ( 60 ) = 780 option d"
Answer: d
Problem: the sale price sarees listed for rs . 390 after successive discount is 15 % and 25 % is ?
Options: a ) 298 , b ) 237 , c ) 248 , d ) 876 , e ) 291
Rationale: "390 * ( 85 / 100 ) * ( 75 / 100 ) = 248 answer : c"
Answer: c
Problem: a student finds the average of 9 positive integers . each integer contains two digits . by mistake , the boy interchanges the digits of one number say pq for qp . due to this , the average becomes 1 less than the previous one . what was the difference of the two digits p and q ?
Options: a ) 8 , b ) 6 , c ) 1 , d ) 4 , e ) 2
Rationale: explanation : let the original number be pq i . e . , ( 10 p + q ) . after interchanging the digits , the new number becomes qp i . e . , ( 10 q + p ) . the question states that the average of 9 numbers has become 1 less than the original average . therefore , the sum of the original 9 numbers will be 9 * 1 more than the sum of the 9 numbers with the digits interchanged . i . e . , 10 p + q = 10 q + p + 9 = > 9 a - 9 b = 9 = > a - b = 1 . answer : c
Answer: c
Problem: a man can row a distance of 5 km in 60 min with the help of the tide . the direction of the tide reverses with the same speed . now he travels a further 25 km in 10 hours . how much time he would have saved if the direction of tide has not changed ?
Options: a ) 2 , b ) 5 , c ) 1 , d ) 6 , e ) 7
Rationale: "explanation : he covered 5 km in 1 hour , so he might cover 25 km in 5 hours . but he took 10 hours . he would have saved 10 â € “ 5 = 5 hours . answer : b"
Answer: b
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 7000 ?
Options: a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 7000 * 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 . answer : e"
Answer: e
Problem: during the first two weeks of january , the total rainfall in springdale was 30 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 18 inches
Rationale: "total rainfall in 2 weeks = 18 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 18 inches x = 12 and 1.5 x = 18 rainfall during second week = 18 inches option e"
Answer: e
Problem: let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 45 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 32 , b ) 35 , c ) 39 , d ) 40 , e ) 42
Rationale: "the question is finding y such that ( 45 - y ) ! is a multiple of 45 . that means we need to have 5 * 3 ^ 2 in ( 45 - y ) ! 6 ! is the smallest factorial number with 5 * 3 ^ 2 as a factor . 45 - y = 6 y = 39 the answer is c ."
Answer: c
Problem: what is the minimum value of | x - 4 | + | x + 2 | + | x - 5 | ?
Options: a ) - 3 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "a can not be the answer as all the three terms are in modulus and hence the answer will be non negative . | x - 4 | > = 0 - - > minimum occurs at x = 4 | x + 2 | > = 0 - - > minimum occurs at x = - 2 | x - 5 | > = 0 - - > minimum occurs at x = 5 x = - 2 - - > result = 6 + 0 + 7 = 13 . also any negative value will push the combined value of | x - 4 | + | x - 5 | to a value > 9 . x = 4 - - > result = 0 + 6 + 1 = 7 x = 5 - - > result = 1 + 7 + 0 = 8 x = 2 - - > result = 2 + 4 + 3 = 9 so minimum value of the expression occurs at x = 4 and the resultant value = 7 answer : d"
Answer: d
Problem: the average weight of 8 persons increases by 4 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 97 kg , e ) 25 kg
Rationale: "total weight increased = ( 8 x 4 ) kg = 32 kg . weight of new person = ( 65 + 32 ) kg = 97 kg . answer : d"
Answer: d
Problem: a train 120 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 54 kmph , d ) 18 kmph , e ) 27 kmph
Rationale: "s = 120 / 16 * 18 / 5 = 27 kmph answer : e"
Answer: e
Problem: subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 25 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 30 page ' s copy = ( 25 / 2.5 ) = 10 hrs answer : b"
Answer: b
Problem: if p and q are positive integers each greater than 1 , and 17 ( p + 1 ) = 25 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 40 , d ) 46 , e ) none
Rationale: "17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 25 , so the least value of p is 24 and the least positive value of q + 1 is 17 , so the least value of q is 16 - - > the least value of p + q is 24 + 16 = 40 . answer : c ."
Answer: c
Problem: what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 54 ?
Options: a ) 3672 , b ) 920 , c ) 7290 , d ) 6928 , e ) 3729
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 54 = rs . 3672 . answer : option a"
Answer: a
Problem: excluding stoppages , the speed of a train is 45 kmph and including stoppages it is 33 kmph . of how many minutes does the train stop per hour ?
Options: a ) 73 , b ) 83 , c ) 16 , d ) 83 , e ) 28
Rationale: "explanation : t = 12 / 45 * 60 = 16 answer : option c"
Answer: c
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long should it take both a and b , working together but independently , to do the same job ?
Options: a ) 70 hours , b ) 40 / 9 hours , c ) 9 hours , d ) 16 hours , e ) 20 hours
Rationale: "a ’ s 1 hour ' s work = 1 / 8 b ' s 1 hour ' s work = 1 / 10 ( a + b ) ' s 1 hour ' s work = ( 1 / 8 ) + ( 1 / 10 ) = 9 / 40 both a and b will finish the work in 40 / 9 days . answer b 40 / 9 hours"
Answer: b
Problem: rectangle dimensions were given , 2 doors dimensions given , 2 windows dimensions given . 70 cm wide wallpaper to be covered on the walls of this room . cost of wallpaper is 60 per meter . . calculate total cost
Options: a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 70
Rationale: area of room = ( l * b ) m ^ 2 area of door + window = ( d + w ) m ^ 2 remaining area = ( ( l * b ) - ( d + w ) ) m ^ 2 so length = remaining area / 0.70 m total cost = length * 60 - - - ans and total cost = 60 answer : d
Answer: d
Problem: set s consists of integers { 12 , 34 } . if two numbers are chosen from set s at random , what is the probability that the sum of 2 numbers is more than 6 ?
Options: a ) 1 / 3 , b ) 1 / 6 , c ) 2 / 3 , d ) 2 / 5 , e ) 3 / 7
Rationale: number of ways you can choose 2 from 4 = 4 c 2 = 6 e = event of getting the 2 numbers is more than 6 = ( 3,4 ) = 1 probability = 1 / 6 answer is b
Answer: b
Problem: in a sample of 800 high school students in which all students are either freshmen , sophomores , juniors , or seniors , 23 percent are juniors and 75 percent are not sophomores . if there are 160 seniors , how many more freshmen than sophomores are there among the sample of students ?
Options: a ) 42 , b ) 48 , c ) 56 , d ) 64 , e ) 72
Rationale: 200 are sophomores . the number of freshmen is 600 - 160 - 0.23 ( 800 ) = 256 the answer is c .
Answer: c
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 9 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.97 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.09 * 80 90 x - 80 = 7.2 90 x = 87.2 x = 87.2 / 90 = 0.968 x is slightly under 0.9688 = 0.97 answer : b"
Answer: b
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.25 , c ) 0.75 , d ) 0.375 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 h thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : d"
Answer: d
Problem: the average weight of 10 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 50 kg . what might be the weight of the new person ?
Options: a ) 76 kg , b ) 76.5 kg , c ) 75 kg , d ) data inadequate , e ) none of these
Rationale: "explanation : total weight increased = ( 10 x 2.5 ) kg = 25 kg . weight of new person = ( 50 + 25 ) kg = 75 kg . answer : c"
Answer: c
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hourr . the distance travelled downstream in 24 mins is ?
Options: a ) 6 km , b ) 7 km , c ) 7.2 km , d ) 8 km , e ) 8.4 km
Rationale: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = 2460 × 18 = 2 × 185 = 7.2 km c"
Answer: c
Problem: if 1 tic equals 4 tacs and 5 tacs equal 8 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 32 / 5 , e ) 1 / 15
Rationale: "tic = 4 * tac and 5 * tac = 8 * toc ; 5 * tic = 20 * tac and 20 * tac = 32 * toc - - > 5 * tic = 32 * toc - - > tic / toc = 32 / 5 . answer : d ."
Answer: d
Problem: a man can row upstream at 22 kmph and downstream at 42 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 23
Rationale: "us = 22 ds = 42 m = ( 42 + 22 ) / 2 = 32 answer : d"
Answer: d
Problem: if the side length of square b is five times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 5 , b ) 15 , c ) 25 , d ) 35 , e ) 45
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( 5 x ) ^ 2 = 25 x ^ 2 . the answer is c ."
Answer: c
Problem: the average weight of 20 oarsmen in a boat is increased by 2 kg when one of the crew , who weight 40 kg is replaced by a new man . find the weight of the new man .
Options: a ) 60 kg , b ) 50 kg , c ) 92 kg , d ) 80 kg , e ) 70 kg
Rationale: total weight increased = 2 * 20 = 40 kg weight of the new man = 40 + 40 = 80 kg answer is d
Answer: d
Problem: in a club with 310 peopl , 138 play tennis , 255 play baseball , and 94 people play both sports . how many people do not pla a sport ?
Options: a ) 9
b ) 8
c ) 4
d ) 10
e ) 11
Rationale: take 94 off the baseball players - - > 161 then 161 + 138 = 299 play either baseball or tennis 310 - 299 = 11 answer is e
Answer: e
Problem: a 14 % stock yielding 8 % is quoted at ?
Options: a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 185
Rationale: "assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 14 , money invested = 100 × 14 / 8 = rs . 175 ie , market value of the stock = rs . 175 answer is c ."
Answer: c
Problem: at present the ratio between the ages of arun and deepak is 4 : 3 . after 6 years , arun ' s age will be 26 years . what is the age of deepak at present ?
Options: a ) 15 , b ) 21 , c ) 23 , d ) 12 , e ) 25
Rationale: let the present ages of arun and deepak be 4 x years and 3 x years respectively 4 x + 6 = 26 4 x = 20 x = 5 deepak ' s age = 3 x = 15 years answer is a
Answer: a
Problem: working together , jose and jane can complete an assigned task in 5 days . however , if jose worked alone and complete half the work and then jane takes over the task and completes the second half of the task , the task will be completed in 15 days . how long will jose take to complete the task if he worked alone ? assume that jane is more efficient than jose
Options: a ) 26 days , b ) 15 days , c ) 60 days , d ) 65 days , e ) 36 days
Rationale: "assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 5 5 ( x + y ) = xy next , we ' re told 1 job takes 15 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 15 x + y = 30 so xy = 150 the answer choices are : 26 days 15 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 15 days for jose and 10 days for jane . answer : b"
Answer: b
Problem: two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1,000 ?
Options: a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
Rationale: "investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %"
Answer: e
Problem: a gets 3 times as much money as b gets , b gets only rs . 25 more then what c gets . the 3 gets rs . 645 in all . find the share of b ?
Options: a ) 134 , b ) 120 , c ) 218 , d ) 140 , e ) 145
Rationale: a + b + c = 645 a = 3 b 3 b + b + b - 25 = 645 5 b = 670 b = 134 answer : a
Answer: a
Problem: if ( a - b - c + d = 13 ) and ( a + b - c - d = 3 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 8 . , c ) 12 . , d ) 25 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 13 eq 2 : a + b - c - d = 3 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 13 - a + b - c - d = 3 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 10 ( 2 ) simplify - b + d = 5 b - d = - 5 ( b - d ) ^ 2 = ( - 5 ) ^ 2 = 25 my answer : d"
Answer: d
Problem: dhoni spent 20 percent of his earning last month on rent and 5 percent less than what he spent on rent to purchase a new dishwasher . what percent of last month ' s earning did dhoni have left over ?
Options: a ) 61 % , b ) 62 % , c ) 65 % , d ) 64 % , e ) 50 %
Rationale: say dhoni ' s earning last month was $ 100 . dhoni spent 20 percent of his earning last month on rent - - > $ 20 on rent ; 5 percent less than what he spent on rent to purchase a new dishwasher - - > $ 20 * 0.95 = $ 19 on the dishwasher . left over amount 100 - ( 20 + 19 ) = $ 61 answer : a
Answer: a
Problem: if a ' s height is 20 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 25 %
Rationale: "excess of b ' s height over a ' s = [ ( 20 / ( 100 - 20 ) ] x 100 % = 25 % answer : e )"
Answer: e
Problem: a set of football matches is to be organized in a ` ` round - robin ' ' fashion , i . e . , every participating team plays a match against every other team once and only once . if 15 matches are totally played , how many teams participated ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: 2 ways to solve this problem . . summation ( x ) = n ( n - 1 ) / 2 n ( n - 1 ) / 2 = 15 ; n ^ 2 - n - 30 = 0 ans : 6 answer : c
Answer: c
Problem: the average weight of 8 sailors in a boat is increased by 1 kg if one of them weighing 56 kg is replaced by a new sailor . the weight of the new sailor is ?
Options: a ) 57 kg , b ) 60 kg , c ) 64 kg , d ) 62 kg , e ) 66 kg
Rationale: the sailor weighing 56 kg is replaced and the average is increased by 1 kg . hence , the weight of the new sailor is ( 56 + increase in total weight ) = 56 + 1 x 8 = 56 + 8 = 64 kg . answer : c
Answer: c
Problem: there are some sweets in party , 1 / 3 rd eaten by kids . then 2 / 5 th of the remaining by men , then 2 / 3 rd of the remaining by women . at last 2 were remaining . how many sweets were in total ?
Options: a ) 45 , b ) 27 , c ) 15 , d ) 26 , e ) 91
Rationale: sol : if x sweets were there in total , then x × ( 1 – 1 / 3 ) × ( 1 – 2 / 5 ) × ( 1 – 2 / 3 ) = 2 x × 2 / 3 × 3 / 5 × 1 / 3 = 2 x = 15 answer : c
Answer: c
Problem: the cost of 100 articles is equal to selling price of 90 . find the gain or loss percent ?
Options: a ) 11 % , b ) 20 % , c ) 27 % , d ) 32 % , e ) 49 %
Rationale: "c . p . of each article be $ 1 c . p . of 90 articles = 100 gain % = 10 / 90 * 100 = 11 % approximately answer is a"
Answer: a
Problem: a bag contains 5 green balls and 9 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 11 / 21 , b ) 17 / 42 , c ) 23 / 42 , d ) 46 / 91 , e ) 51 / 91
Rationale: "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 5 c 2 = 10 the number of ways to draw two white balls is 9 c 2 = 36 p ( two balls of the same colour ) = 46 / 91 the answer is d ."
Answer: d
Problem: a no . when divided by 223 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 17 ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 15
Rationale: "223 + 43 = 266 / 17 = 11 ( remainder ) d"
Answer: d
Problem: find the 25 % of rs . 400 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 80 , e ) s . 60
Rationale: "explanation : 25 % of 400 = > 25 / 100 * 400 = rs . 100 answer : c"
Answer: c
Problem: a shop owner sells 40 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 33.33 % , b ) 40 % , c ) 50 % , d ) 66.67 % , e ) 70 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 40 m cloth ) – ( c . p . of 40 m cloth ) selling price of 30 m cloth = selling price of 40 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 30 m cloth = rs . 3000 and s . p . of 30 m cloth = rs . rs . 4000 profit % = 10 / 30 × 100 = 33.33 % profit of 33.33 % was made by the merchant . a"
Answer: a
Problem: ajay spends 50 % of his monthly income on household items , 25 % of his monthly income on buying cloths , 15 % of his monthly income on medicines and saves the remaining amount which is rs . 9000 . find his monthly income .
Options: a ) rs . 90000 , b ) rs . 36000 , c ) rs . 50000 , d ) rs . 45000 , e ) none of these
Rationale: savings 10 % - 9000 expenditure 90 % - 81000 total - 90000 answer : a
Answer: a
Problem: the measurement of a rectangular box with lid is 50 cmx 30 cmx 38 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 4500 , c ) 7200 , d ) 864 , e ) 9640
Rationale: "d = 30 , r = 15 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 15 * 15 * 15 = 4500 π cm 3 answer : b"
Answer: b
Problem: if an article is sold at 12 % profit instead of 16 % profit , then the profit would be rs . 105 less . what is the cost price ?
Options: a ) rs . 3000 , b ) rs . 4000 , c ) rs . 3500 , d ) rs . 4500 , e ) rs . 6000
Rationale: "explanation : let the cost price of an article be rs . x . ( 16 % of x ) - ( 12 % of x ) = 105 16 x / 100 - 12 x / 100 = 105 = > 4 x = 160 * 100 = > x = 1500 cost price = rs . 4000 answer : b"
Answer: b
Problem: gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 16 times as heavy as water ?
Options: a ) 1 : 2 , b ) 7 : 3 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 16 w 19 + 9 x = 16 ( x + 1 ) x = 3 / 7 ratio of gold with copper = 1 : 3 / 7 = 7 : 3 answer is b"
Answer: b
Problem: a question paper has 2 parts , a & b , each containing 7 questions . if a student has to choose 5 from part a & 4 from part b , in how many ways can he choose the questions ?
Options: a ) 1100 , b ) 1200 , c ) 1235 , d ) 1354 , e ) 735
Rationale: "there 7 questions in part a out of which 5 question can be chosen as = 7 c 5 . similarly , 4 questions can be chosen from 7 questions of part b as = 7 c 4 . hence , total number of ways , = 7 c 5 * 7 c 4 = [ 7 ! / ( 2 ! 5 ! ) ] * [ 7 ! / ( 3 ! * 4 ! ) ] = { 21 } * { 7 * 6 * 5 * 4 / ( 4 * 3 * 2 * 1 ) } = 735 . e"
Answer: e
Problem: a man has some hens and cows . if the number of heads be 60 and the number of feet equals 200 , then the number of hens will be :
Options: a ) 22 , b ) 25 , c ) 24 , d ) 20 , e ) 28
Rationale: "explanation : let the number of hens be x and the number of cows be y . then , x + y = 60 . . . . ( i ) and 2 x + 4 y = 200 x + 2 y = 100 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 40 . the required answer = 20 . answer : d"
Answer: d
Problem: what is the difference between 62 % of 150 nd 20 % of 250 .
Options: a ) 16 , b ) 17 , c ) 43 , d ) 19 , e ) 20
Rationale: ( 62 / 100 ) * 150 â € “ ( 20 / 100 ) * 250 93 - 50 = 43 answer : c
Answer: c
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 25 percent on food , and 25 percent on other items . if jill paid a 10 percent tax on the clothing , no tax on the food , and an 20 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 10.00 food = 25 % = $ 50 = $ 0.00 items = 25 % = $ 50 = $ 10.00 total tax = $ 20.00 % of total amount = 20 / 200 * 100 = 10 % answer b"
Answer: b