regisss/math_qa huggingface dataset:
Problem: set v consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set v , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: v = { 3 , - 8 , y , 19 , - 6 } b = { k , - 3 , 016 , - 59 } y > 21 so l = median of v = 3 m = mode of set b z = ( 3 ) ^ m if z is a divisor of 26 , ( 3 ) ^ m = 1 because 26 does not have 3 as a factor = > m = 0 hence k = 0 , as m is mode and 0 will be the most frequently occuring number in set b . answer - c
Answer: c
Problem: in 1982 and 1983 , company b ’ s operating expenses were $ 11.0 million and $ 14.0 million , respectively , and its revenues were $ 15.6 million and $ 18.8 million , respectively . what was the percent increase in company b ’ s profit ( revenues minus operating expenses ) from 1982 to 1983 ?
Options: a ) 3 % , b ) 16 2 / 3 % , c ) 25 % , d ) 4 1 / 3 % , e ) 60 %
Rationale: "profit in 1982 = 15.6 - 11 = 4.6 million $ profit in 1983 = 18.8 - 14 = 4.8 million $ percentage increase in profit = ( 4.8 - 4.6 ) / 4.6 * 100 % = 4 1 / 3 % answer d"
Answer: d
Problem: how many integers between 1 and 1,800 are divisible by 20 , 30,40 ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "lcm of the given numbers = 120 therefore , number of integers = 1800 / 120 = 15 option b is answer"
Answer: b
Problem: a sum of rs . 2704 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1672 , b ) 1664 , c ) 1677 , d ) 1698 , e ) 1679
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2704 - x ) * 3 * 5 ) / 100 24 x / 100 = 40560 / 100 - 15 x / 100 39 x = 40560 = > x = 1040 second sum = 2704 â € “ 1040 = 1664 answer : b"
Answer: b
Problem: 150 is increased by 40 % . find the final number .
Options: a ) 200 , b ) 210 , c ) 180 , d ) 190 , e ) 220
Rationale: "final number = initial number + 40 % ( original number ) = 150 + 40 % ( 150 ) = 150 + 60 = 210 . answer b"
Answer: b
Problem: a person ' s salary is getting reduced by 20 % . what percentage should be added to get back his original salary ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 85 % , e ) 95 %
Rationale: salary he get after reduced 20 % = 100 - 20 % = 80 % so , percentage should be added to get back his salary = ( 20 / 80 ) * 100 = 25 % answer : a
Answer: a
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 18 white marbles . how many red marbles could be in bag a ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 18 = 6 k + 4 p = > k = 1 , p = 3 total red ' s in bag a will be 2 k = 2 a"
Answer: a
Problem: the price of lunch for 10 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 18
Rationale: clearly e is the answer i used poe here lets consider option ( e ) 10 * 18 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo e
Answer: e
Problem: in an office , totally there are 1800 employees and 60 % of the total employees are males . 30 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 756 , b ) 750 , c ) 600 , d ) 760 , e ) none of these
Rationale: "number of male employees = 1800 * 60 / 100 = 1080 required number of male employees who are less than 50 years old = 1080 * ( 100 - 30 ) % = 1080 * 70 / 100 = 756 . answer : a"
Answer: a
Problem: if 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 2300 , b ) 600 , c ) 250 , d ) 300 , e ) none of these
Rationale: "1 st line - 0 points 2 nd line - new 1 point 3 td line - new 2 points + old 1 point 4 th line - new 3 points + old 2 + 1 points 5 th line - new 4 points + old 3 + 2 + 1 points n - th line - ( n - 1 ) points + ( n - 2 ) . . . . 3 + 2 + 1 therefore , s = 1 + 2 + 3 . . . ( n - 1 ) s = ( n - 1 ) n / 2 = 24 * 25 / 2 = 300 ans ; d"
Answer: d
Problem: in a renowned city , the average birth rate is 5 people every two seconds and the death rate is 3 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 85,400 , b ) 86,400 , c ) 87,400 , d ) 88,400 , e ) 89,400
Rationale: "this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 5 - 3 = 2 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 2 = 86,400 . hence b ."
Answer: b
Problem: population is 21000 . population increases by 10 % every year , then the population after 3 years is ?
Options: a ) 26630 , b ) 27951 , c ) 36621 , d ) 26621 , e ) 26821
Rationale: "population after 1 st year = 21000 * 10 / 100 = 2100 = = = > 21000 + 2100 = 23100 population after 2 nd year = 23100 * 10 / 100 = 2310 = = = > 23100 + 2310 = 25410 population after 3 rd year = 254100 * 10 / 100 = 2541 = = = > 25410 + 2541 = 27951 answer : b"
Answer: b
Problem: a , b , c hired a car for rs . 720 and used it for 9 , 10 and 13 hours respectively . hire charges paid by b are :
Options: a ) rs 220 , b ) rs . 225 , c ) rs . 230 , d ) rs . 235 , e ) rs . 255
Rationale: "a : b : c = 9 : 10 : 13 . hire charges paid by b = rs . 720 * 10 / 32 = rs . 225 . answer : b"
Answer: b
Problem: at what price must an book costing $ 47.50 be marked in order that after deducting 12 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 67.5 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 88 / 100 ) = 59.375 mp = 67.5 c"
Answer: c
Problem: the average of 45 results is 13 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 480 , c ) 750 , d ) 650 , e ) 695
Rationale: "23 th result = sum of 45 results - sum of 44 results 13 * 45 - 15 * 22 + 20 * 22 = 585 - 330 + 440 = 695 answer is e"
Answer: e
Problem: if log 1087.5 = 5.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 30 , b ) 70 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 1087.5 + 1 ) = 10 ( 5.9421 + 1 ) = 10 ( 6.9421 ) = 69.421 x = antilog ( 69.421 ) therefore , number of digits in x = 70 . answer : b"
Answer: b
Problem: a japanese rock band made ¥ 3 million on their first album with sales of ¥ 12 million , and made ¥ 5 million on their second album with sales of ¥ 30 million . by approximately what percent did the ratio of profit to sales decrease from the first album to second album ?
Options: a ) 24 % , b ) 27 % , c ) 30 % , d ) 33 % , e ) 36 %
Rationale: solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of profits to sales . the first ratio will be for the first album , and the second ratio will be for the next album . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first album profit / sales = 3 / 12 = 1 / 4 second album profit / sales = 5 / 30 = 1 / 6 we can simplify each ratio by multiplying each by the lcm of the two denominators , which is 12 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first album profit / sales = ( 1 / 4 ) x 12 = 3 next 2 million profit / sales = ( 1 / 6 ) x 12 = 2 we can plug 3 and 2 into our percent change formula : ( 2 – 3 ) / 3 x 100 = - 1 / 3 x 100 so approximately a 33 % decrease . answer d .
Answer: d
Problem: an inspector rejects 0.05 % of the meters as defective . how many will he examine to reject 2 ?
Options: a ) a ) 1500 , b ) b ) 2000 , c ) c ) 2500 , d ) d ) 3000 , e ) e ) 4000
Rationale: "let the number of meters to be examined be x then , 0.05 % of x = 2 ( 5 / 100 ) * ( ( 1 / 100 ) * x = 2 x = 4000 answer is e"
Answer: e
Problem: a number is doubled and 9 is added . if resultant is trebled , it becomes 69 . what is that number
Options: a ) 7 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 69 = > 2 x + 9 = 23 = > x = 7 answer : option a"
Answer: a
Problem: a motor boat takes 12 hours to go downstream and it takes 24 hours to return the same distance . what is the time taken by boat in still water ?
Options: a ) 26 h , b ) 16 h , c ) 86 h , d ) 96 h , e ) 66 h
Rationale: explanation : if t 1 and t 2 are the upstream and down stream times . then time taken in still water is given by \ inline \ frac { 2 \ times t 1 \ times t 2 } { t 1 + t 2 } = \ frac { 2 \ times 12 \ times 24 } { 36 } = 16 h answer : b
Answer: b
Problem: if x is a positive integer , then the least value of x for which x ! is divisible by 100000 is ? can someone please explain intuitively what the question is asking ?
Options: a ) 5 , b ) 9 , c ) 12 , d ) 20 , e ) 30
Rationale: in order x ! to be divisible by 1,000 , it should have at least 3 trailing zeros . a trailing 0 in factorial of a number is produced by 2 and 5 in it : 2 * 5 = 10 . so , we need 10 to be in x ! at least in power of 3 . 5 ! = 120 has 1 trailing zeros . 10 ! will have 2 trailing zeros . 15 ! will have 3 trailing zeros . 20 ! will have 5 trailing zeros . answer : d .
Answer: d
Problem: a certain sum of money is divided among a , b and c such that a gets one - third of what b and c together get and b gets two - seventh of what a and c together get . if the amount received by a is $ 30 more than that received by b , find the total amount shared by a , b and c .
Options: a ) $ 1080 , b ) $ 1180 , c ) $ 1280 , d ) $ 1380 , e ) $ 1480
Rationale: a = 1 / 3 ( b + c ) = > c = 3 a - b - - - ( 1 ) b = 2 / 7 ( a + c ) = > c = 3.5 b - a - - ( b ) a - b = $ 30 a = 30 + b ( 1 ) = = = > c = 90 + 3 b - b = 2 b + 90 = = > 2 b - c = - 90 - - - ( 3 ) ( 2 ) = = = > c = 3.5 b - b - 30 = 2.5 b - 30 = = > 2.5 b - c = 30 - - - ( 4 ) from ( 4 ) and ( 3 ) 0.5 b = 120 b = $ 240 a = $ 270 c = 810 - 240 = $ 570 total amount = 270 + 240 + 570 = $ 1080 answer : a
Answer: a
Problem: if 0.25 of a number is equal to 0.05 of another number , the ratio of the numbers is :
Options: a ) 2 : 5 , b ) 3 : 4 , c ) 1 : 5 , d ) 20 : 5 , e ) 30 : 7
Rationale: "0.25 a = 0.05 b - > a / b = 0.05 / 0.25 = 5 / 25 = 1 / 5 : . a : b = 1 : 5 answer : c"
Answer: c
Problem: what is the compound interest on rs : 50,000 for 4 months at the rate of 5 % per annum
Options: a ) 1058.24 , b ) 2006.24 , c ) 838.55 , d ) 848.55 , e ) 858.55
Rationale: "it is monthly compound rate = 5 / 12 % per month 50000 * ( 1 + 5 / 1200 ) ^ 4 - 50000 = 838.55 answer : c"
Answer: c
Problem: if k and w are the dimensions of a rectangle that has area 20 and if k and w are integers such that k > w , what is the total number of possible values of k ?
Options: a ) two
b ) three
c ) four
d ) five
e ) six
Rationale: kw = 20 = 20 * 1 = 10 * 2 = 5 * 4 - - > k can take 3 values , answer : b
Answer: b
Problem: danny is sitting on a rectangular box . the area of the front face of the box is half the area of the top face , and the area of the top face is 1.5 times the area of the side face . if the volume of the box is 648 , what is the area of the side face of the box ?
Options: a ) 32
b ) 78
c ) 84
d ) 90
e ) 72
Rationale: lets suppose length = l , breadth = b , depth = d front face area = l * w = 1 / 2 w * d ( l = 1 / 2 d or d = 2 l ) top face area = w * d side face area = w * d = 1.5 d * l ( w = 1.5 l ) volume = l * w * d = 648 l * 1.5 l * 2 l = 648 l = 6 side face area = l * d = l * 2 l = 6 * 2 * 6 = 72 e is the answer
Answer: e
Problem: the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 30 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 492 kms , d ) 752 kms , e ) 152 kms
Rationale: "explanation : total distance travelled in 12 hours = ( 30 + 32 + 34 + . . . . . upto 12 terms ) this is an a . p with first term , a = 30 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 30 + { 12 - 1 ) x 2 ] = 6 ( 82 ) = 492 kms . answer : c"
Answer: c
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 54 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 16.7 sec , d ) 18 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 54 * 5 / 18 = 15 mps t = 250 / 15 = 16.7 sec answer : c"
Answer: c
Problem: if x and g are integers and 2 x – g = 11 , then 4 x + g can not be
Options: a ) – 5 , b ) 1 , c ) 13 , d ) 17 , e ) 551
Rationale: 2 x - g = 11 . . . . g = 2 x - 11 4 x + g = 4 x + 2 x - 11 = 6 x - 11 6 x - 11 = - 5 . . . x = 1 6 x - 11 = 1 . . . x = 2 6 x - 11 = 13 . . . x = 4 6 x - 11 = 17 . . x is not integer 6 x - 11 = 551 . . x is not integer i think the choice e is 55 not 551 . otherwise both de can not be solution = d
Answer: d
Problem: a fair 8 - sided dice labeled 1 to 8 is tossed 3 times . what is the probability the value of the dice shown is 3 at least once ?
Options: a ) 57 / 512 , b ) 7 / 512 , c ) 55 / 512 , d ) 9 / 512 , e ) 11 / 512
Rationale: this is a fair dice with 8 fair sides , so the probability of the dice landing on any sides is equal . the question ask if the value of the dice is shown 3 at least once so the calculation of the first possible outcomes is 1 / 8 * 1 / 8 * 1 / 8 ( all of the dice thrown shown the value of 3 ) this is follow by the second possible outcomes if the dice thrown show the value of 3 2 times ( 1 / 8 * 1 / 8 * 7 / 8 ) * 7 here referring to any number besides 3 the third possible outcomes is that the dice show the value 3 one time ( 1 / 8 * 7 / 8 * 7 / 8 ) so the answer is 1 / 512 + 7 / 512 + 49 / 512 = 57 / 512 answer : a
Answer: a
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 216 km / hr ?
Options: a ) 2.5 sec , b ) 2.9 sec , c ) 1.7 sec , d ) 7.5 sec , e ) 2.4 sec
Rationale: "speed = 215 * 5 / 18 = 60 m / sec time taken = 100 / 60 = 1.7 sec . answer : c"
Answer: c
Problem: consider below info to be a table : amount of bacteria time - amount 1 pm - 10 gms 4 pm - x gms 7 pm - 12.1 gms data for a certain biology experiment are given in the table above . if the amount of bacteria present increased by the same factor during each of the two 3 - hour periods shown , how many grams of bacteria were present at 4 pm ?
Options: a ) 12.0 , b ) 12.1 , c ) 12.2 , d ) 12.3 , e ) 11.0
Rationale: let say the factor is x , the at 7 pm quantity = 10 ( i . e . quantity @ 1 pm ) * x ^ 2 = 12.1 = > x ^ 2 = 1.21 or x = 1.1 = > @ 4 pm quantity = 10 x = 10 * 1.1 = 11 . answer e
Answer: e
Problem: every day daniel drives 120 miles back from work . on sunday , daniel drove all the way back from work at a constant speed of x miles per hour . on monday , daniel drove the first 32 miles back from work at ( 2 x ) miles per hour , and the rest of the way at ( x / 2 ) miles per hour . the time it took daniel to drive back from work on monday is longer than the time it took him to drive back from work on sunday by what percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 60 %
Rationale: let ' s test x = 4 . . . . on sunday , daniel drove 120 miles at 4 miles / hour . d = ( r ) ( t ) 120 = ( 4 ) ( t ) 120 / 4 = 30 = t it takes 30 hours to drive home on monday , daniel drove the first 32 miles at ( 2 ) ( 4 ) = 8 miles / hour and the rest of the way ( 88 miles ) at 4 / 2 = 2 miles / hour d = ( r ) ( t ) 32 = ( 8 ) ( t ) 32 / 8 = 4 = t it takes 4 hours for the first part d = ( r ) ( t ) 88 = ( 2 ) ( t ) 88 / 2 = 44 = t it takes 44 hours for the second part total time to drive home on monday = 4 + 44 = 48 hours we ' re asked by what percent 48 hours is greater than 30 hours . 48 / 30 = 1.6 , so it is 60 % greater . answer : e
Answer: e
Problem: how many multiples of 4 are there between 1 and 100 , inclusive ?
Options: a ) 25 , b ) 22 , c ) 23 , d ) 30 , e ) 36
Rationale: "25 multiples of 4 between 1 and 100 inclusive . from 4 * 1 upto 4 * 25 , ( 1,2 , 3,4 , . . . , 25 ) . hence , 25 multiples ! correct option is a"
Answer: a
Problem: caleb spends $ 66.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 33 , c ) 20 , d ) 40 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 66.50 . by solving the equations y = 33 . ans b ."
Answer: b
Problem: a pump can fill a tank with water in 2 hours . because of a leak , it took hours to fill the tank . the leak can drain all the water of the tank in :
Options: a ) 33 , b ) 37 , c ) 76 , d ) 14 , e ) 29
Rationale: explanation : work done by the leak in 1 hour = { \ color { black } \ left ( \ frac { 1 } { 2 } - \ frac { 3 } { 7 } \ right ) = \ frac { 1 } { 14 } } { \ color { black } \ therefore } leak will empty the tank in 14 hrs answer : d ) 14 hours
Answer: d
Problem: rectangular tile each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 900 cm by 600 cm , such that the tiles do not overlap and they are placed with edges jutting against each other on all edges . a tile can be placed in any orientation so long as its edges are parallel to the edges of floor . no tile should overshoot any edge of the floor . the maximum number of tiles that can be accommodated on the floor is :
Options: a ) 50 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "area of tile = 90 * 30 = 2700 area of floor = 900 * 300 = 270000 no of tiles = 270000 / 2700 = 100 so , the no of tile = 100 answer : e"
Answer: e
Problem: a merchant has selected two items to be placed on sale , one of which currently sells for 45 percent less than the other . if he wishes to raise the price of the cheaper item so that the two items are equally priced , by what percentage must he raise the price of the less expensive item ?
Options: a ) 100 % , b ) 90 % , c ) 80 % , d ) 70 % , e ) 60 %
Rationale: "expensive item = $ 100 ; cheap item = $ 55 ; we must increase $ 55 to $ 100 , so by $ 45 , which is approximately 80 % increase : ( 100 - 55 ) / 55 = 3 / 7 = ~ 0.81 . answer : c ."
Answer: c
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 15 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 6300 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: "8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 15 machine produce 560 * 6 * ( 15 / 8 ) in 6 minutes 560 * 6 * 15 / 8 = 6300 answer is b ."
Answer: b
Problem: in how many ways 3 boys and 3 girls can be seated in a row so that boys and girls are alternate ?
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Rationale: "number of ways = 2 * 3 ! * 3 ! = 72 answer is d"
Answer: d
Problem: if 7 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 42 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 7 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 7 = > ( 3 / 20 ) c = 7 = > c = ( 7 * 20 ) / 3 = 46.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 7 = 34.99 + 7 = 41.99 = 42 answer d"
Answer: d
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 6 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 28 , e ) e . 24
Rationale: "rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 28 hours d"
Answer: d
Problem: speed of a boat in standing water is 9 kmph and the speed of the stream is 6 kmph . a man rows to place at a distance of 170 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 68 hours , c ) 36 hours , d ) 58 hours , e ) none
Rationale: "sol . speed upstream = 3 kmph ; speed downstream = 15 kmph . ∴ total time taken = [ 105 / 7.5 + 105 / 10.5 ] hours = 68 hours . answer b"
Answer: b
Problem: if the cost price of 17 articles is equal to the selling price of 16 articles , what is the percentage of profit or loss that the merchant makes ?
Options: a ) 20 % loss , b ) 6.25 % profit , c ) 33.33 % loss , d ) 30.33 % loss , e ) none of these
Rationale: "explanation : let cost price of 1 article be re . 1 . therefore , cost price of 17 articles = rs . 17 . selling price of 16 articles = rs . 17 therefore , selling price of 17 articles is : - = > 17 / 16 ã — 17 = > 18.06 therefore , profit = selling price - cost price . = > 18.06 â ˆ ’ 17 = 1.06 hence , the percentage of profit = profit x 100 / c . p . = > 1.06 / 17 ã — 100 . = > 6.25 % profit . answer : b"
Answer: b
Problem: according to a recent student poll , 4 / 5 out of 20 members of the finance club are interested in a career in investment banking . if two students are chosen at random , what is the probability that at least one of them is interested in investment banking ?
Options: a ) 62 / 95 , b ) 52 / 95 , c ) 92 / 95 , d ) 42 / 95 , e ) 32 / 95
Rationale: "16 students are interested , 4 are not interested prob = 1 - 4 c 2 / 20 c 2 = 1 - ( 4 * 3 / ( 20 * 19 ) ) = 1 - 3 / 95 = 92 / 95 answer : c"
Answer: c
Problem: let p be a prime number . if n = 8 p , how many distinct even divisors does n have ?
Options: a ) 1 , b ) 4 , c ) 5 , d ) 2 , e ) 3
Rationale: "the correct answer is d . there are two : 2 and 2 p . 8 p = 2 * 2 * 2 p = ( 2 * 2 ) * 2 p . since we care only about distinct divisors , we ignore the fact that 2 appears three times ."
Answer: d
Problem: a candidate who gets 30 % of the marks fails by 30 marks . but another candidate who gets 45 % marks gets 15 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 200 marks , c ) 280 marks , d ) 371 marks , e ) 120 marks
Rationale: "30 % - - - - - - - - - - - - 30 45 % - - - - - - - - - - - - 15 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 45 30 % - - - - - - - - - - - - - - ? 90 + 30 = 120 marks answer : e"
Answer: e
Problem: in a forest 190 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
Options: a ) 150 , b ) 750 , c ) 1,250 , d ) 1,900 , e ) 2,500
Rationale: "the percentage of tagged deer in the second sample = 5 / 50 * 100 = 10 % . so , 190 tagged deers comprise 10 % of total # of deers - - > total # of deers = 190 * 10 = 1,900 . answer : d ."
Answer: d
Problem: a person ' s present age is two - fifth of the age of his mother . after 6 years , he will be one - half of the age of his mother . how old is the mother at present ?
Options: a ) a ) 25 , b ) b ) 40 , c ) c ) 32 , d ) d ) 45 , e ) e ) 30
Rationale: "let the mother ' s present age be x years then the person ' s present age = 2 x / 5 ( 2 x / 5 ) + 6 = 1 / 2 ( x + 6 ) 2 ( 2 x + 30 ) = 5 ( x + 6 ) x = 30 answer is e"
Answer: e
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 20 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 , b ) 88 , c ) 48 , d ) 99 , e ) 72
Rationale: "relative speed = 20 + 30 = 50 km / hr . 50 * 5 / 18 = 125 / 9 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 9 / 125 = 72 sec answer : e"
Answer: e
Problem: find the circumference and area of radius 11 cm .
Options: a ) 124 cm ² , b ) 144 cm ² , c ) 380 cm ² , d ) 284 cm ² , e ) 394 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 11 × 11 cm ² = 154 cm ² answer : c"
Answer: c
Problem: the average of marks obtained by 120 boys was 37 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 120 , d ) 130 , e ) 140
Rationale: let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 37 24 x = 4440 - 1800 = > x = 2640 / 24 x = 110 . hence , the number of boys passed = 110 . answer : b
Answer: b
Problem: a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 105 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 220 , b ) 250 , c ) 280 , d ) 300 , e ) 340
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 105 x = 300 therefore there are a total of 300 ounces in the drink . the answer is d ."
Answer: d
Problem: find the least number which when divided by 5 , 6,7 , and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder
Options: a ) 1683 , b ) 1684 , c ) 1685 , d ) 1582 , e ) 1584
Rationale: "explanation : l . c . m . of 5,6 , 7,8 = 840 . required number is of the form 840 k + 3 least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . required number = ( 840 x 2 + 3 ) = 1683 answer is a"
Answer: a
Problem: it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she does yoga for 25 minutes , how much time will she spend in the gym ?
Options: a ) 35 min , b ) 5 min , c ) 15 min , d ) 25 min , e ) 20 min
Rationale: "the ratio is 2 : 3 = yoga : exer , so ( 25 ) ( 3 / 2 ) = 37.5 minutes for exercise , and 2 : 3 = gym : ride , and ( 2 / 3 ) ( 37.5 ) = 25 minutes in the gym . answer : d"
Answer: d
Problem: find the compound interest accrued on an amount of rs . 14,800 at 13.5 % p . a at the end of two years . ( round off your answer to nearest integer ?
Options: a ) 2828 , b ) 2338 , c ) 377 , d ) 4266 , e ) 288
Rationale: "ci = 14800 { [ 1 + 13.5 / 100 ] 2 - 1 } = 14800 { [ 1 + 27 / 200 ] 2 - 1 = 14800 { 2 + 27 / 200 } { 27 / 200 } = ( 74 ) [ 2 + 27 / 200 ] ( 27 ) = 1998 [ 2 + 27 / 200 ] = 3996 + 269.73 = rs . 4266 . answer : d"
Answer: d
Problem: the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 150 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 150 2 l ^ 2 / 3 = 150 l ^ 2 = 225 l = 15 cm the answer is a ."
Answer: a
Problem: how many odd numbers between 10 and 1500 are the squares of integers ?
Options: a ) 11 , b ) 14 , c ) 17 , d ) 20 , e ) 23
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 37 which includes 17 numbers . the answer is c ."
Answer: c
Problem: gold is 11 times as heavy as water and copper is 5 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 11 w c = 5 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 11 w + 5 wx = x + 1 * 8 w 11 + 5 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"
Answer: b
Problem: if a car went the first third of the distance at 80 kmh , the second third at 24 kmh , and the last third at 30 kmh , what was the average speed of the car for the entire trip ?
Options: a ) 36 kmh , b ) 40 kmh , c ) 42 kmh , d ) 44 kmh , e ) 34 kmh
Rationale: "assume d / 3 = 240 ( this number is convenient because it is divisible by 80 , 24 and 30 ) so : 240 = 80 * t 1 = 3 hrs 240 = 24 * t 2 = 10 hrs 240 = 30 * t 3 = 8 hrs t = t 1 + t 2 + t 3 = 21 hrs d = rt ( 240 * 3 ) = r * 21 r = 34 answer : e"
Answer: e
Problem: how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 63 kmph ?
Options: a ) 22 sec , b ) 77 sec , c ) 25 sec , d ) 14.3 sec , e ) 17 sec
Rationale: "d = 100 + 150 = 250 s = 63 * 5 / 18 = 17.5 mps t = 250 / 17.5 = 14.3 sec answer : d"
Answer: d
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase i in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase i = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 15000 , then find his savings ?
Options: a ) 3600 , b ) 3607 , c ) 3608 , d ) 3602 , e ) 3000
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 15000 = > x = 3000 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3000 . answer : e"
Answer: e
Problem: salesperson a ' s compensation for any week is $ 280 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 5000 , b ) $ 7000 , c ) $ 9000 , d ) $ 11,000 , e ) $ 13,000
Rationale: "280 + 0.06 ( x - 1000 ) = 0.08 x 0.02 x = 220 x = $ 11,000 the answer is d ."
Answer: d
Problem: rashmi walks to her bus stop at 5 kmph and reaches there late by 10 minutes . on the next day , she increases her speed to 6 kmph and reaches the bus stop 10 minutes early . how far is the bus stop ?
Options: a ) 13 , b ) 12 , c ) 11 , d ) 10 , e ) 9
Rationale: let the distance to the bus stop is ` ` d ' ' km time taken by her ( at 5 kmph ) = d / 5 hour , and time taken by her ( at 6 kmph ) = d / 6 hour as per given condition , d / 5 - d / 6 = 20 / 60 d = 10 kms answer : d
Answer: d
Problem: the amount of principal rs . 8000 at compound interest at the ratio of 5 % p . a . for 2 years is
Options: a ) s . 9621 , b ) s . 6921 , c ) s . 8820 , d ) s . 6261 , e ) s . 6361
Rationale: "c . i = p ( 1 + r / 100 ) ^ n = 8000 ( 1 + 5 / 100 ) ^ 2 = rs 8820 answer : c"
Answer: c
Problem: a cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 , b ) 50 , c ) 53.5 , d ) 55 , e ) 57
Rationale: "explanation : area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 6 x 1.25 ) + 6 x 4 ] m 2 = 49 m 2 answer : a"
Answer: a
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 152 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1216 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 152 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 152 = 3 k + 152 = > 2 k = 304 = > k = 152 the initial quantity of milk in a = 8 k = 8 * 152 = 1216 liters .
Answer: a
Problem: the average expenditure of a labourer for 7 months was 85 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income is
Options: a ) 70.11 , b ) 72.02 , c ) 86.5 , d ) 78.2 , e ) none of the above
Rationale: "income of 7 months = ( 7 × 85 ) – debt = 595 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 865 average monthly income = 865 ÷ 10 = 86.5 answer c"
Answer: c
Problem: a man leaves a point p at 6 a . m . and reaches the point q at 10 a . m . another man leaves the point give at 8 a . m . and reaches the point p at 12 noon . at what time do they meet ?
Options: a ) 2 a . m , b ) 6 a . m , c ) 9 a . m , d ) 5 a . m , e ) 1 a . m
Rationale: 9 a . m . answer : c
Answer: c
Problem: 35 % of major airline companies equip their planes with wireless internet access . 70 % of major airlines offer passengers free on - board snacks . what is the greatest possible percentage of major airline companies that offer both wireless internet and free on - board snacks ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: "to maximize the percentage of companies offering both , let ' s assume that all 35 % of companies which offer wireless internet also offer snacks . the answer is b ."
Answer: b
Problem: the batting average of a particular batsman is 59 runs in 46 innings . if the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs , find his highest score .
Options: a ) 156 , b ) 208 , c ) 210 , d ) 223 , e ) 229
Rationale: "explanation : total runs scored by the batsman = 59 * 46 = 2714 runs now excluding the two innings the runs scored = 58 * 44 = 2552 runs hence the runs scored in the two innings = 2714 – 2552 = 162 runs . let the highest score be x , hence the lowest score = x – 150 x + ( x - 150 ) = 162 2 x = 312 x = 156 runs answer a"
Answer: a
Problem: find the simple interest on $ 3000 for 3 years at 10 % per annum ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 1000
Rationale: "si = ptr / 100 = 3000 * 3 * 10 / 100 = $ 900 answer is a"
Answer: a
Problem: if 9 ^ y = 3 ^ 12 , what is y ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "3 ^ 2 y = 3 ^ 12 2 y = 12 , therefore y = 6 e"
Answer: e
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 150 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 400 , e ) 480
Rationale: "easy 400 is the answer . 3 / 4 ( x / 2 ) = 150 x = 150 * 8 / 3 = 400 . answer d"
Answer: d
Problem: with a uniform speed a car covers the distance in 8 hours . had the speed been increased by 1 km / hr , the same distance could have been covered in 7 1 / 2 hours . what is the distance covered ?
Options: a ) 187 km , b ) 480 km , c ) 278 km , d ) 120 km , e ) 671 km
Rationale: "let the distance be x km . then , x / ( 7 1 / 2 ) - x / 8 = 1 2 x / 15 - x / 8 = 1 = > x = 120 km . answer : d"
Answer: d
Problem: the ratio of the present age of sandy to that of molly is 7 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 42
Rationale: "let the present age of sandy be 7 x years and that of molly be 2 x years . ( 7 x + 8 ) / ( 2 x + 8 ) = 5 / 2 4 x = 24 x = 6 six years ago , sandy ' s age was 7 ( 6 ) - 6 = 36 the answer is d ."
Answer: d
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 420 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 600 , c ) 287 , d ) 780 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 420 = 3780 salary of the new supervisor = 3780 â ˆ ’ 3000 = 780 answer : d"
Answer: d
Problem: the average of 6 no . ' s is 3.95 . the average of 2 of them is 3.6 , while the average of the other 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 3.6 * 2 ) + ( 3.85 * 2 ) ] = 8.8 . required average = ( 8.8 / 2 ) = 4.4 . b"
Answer: b
Problem: two trains 121 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 55 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.62 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 121 + 165 ) / ( 80 + 55 ) * 18 / 5 t = 7.62 answer : c"
Answer: c
Problem: 24 oz of juice p and 25 oz of juice q are mixed to make smothies x and y . the ratio of p to q in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: easy way to solve this question is start from the answer and then conform the information provided in the question . we can start from option d i . e 20 . . . as a quantity of juice p in x because it is the only one option that gets divided by 4 is 20 . . . since in the x the juice p to q ratio is 4 : 1 this gives us that quantity of juice p in x = 20 therefore quantity of juice v will be 5 . . . hence ratio = 4 : 1 this will lead to quantity of juice p in x = 4 and quantity of juice v = 20 . . . hence ratio 1 : 5 if we calculate total juice p = 24 and total of juice q = 25 it fits because totals are same as what mentioned in the question . . . thus ans is d
Answer: d
Problem: a shirt goes on sale for 90 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 81 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 90 then it is marked down by 10 % = 90 - 9 = 81 . hence it is 81 % od the original price . hence answer is b ."
Answer: b
Problem: in a certain parking lot , 2 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 4 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: let x be the number of cars and let y be the number of cars parked illegally . 2 % * x = 20 % * y y / x = 1 / 10 = 10 % the answer is d .
Answer: d
Problem: the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 145 , what is the difference between the ages of patrick and monica ?
Options: a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18
Rationale: "ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 145 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"
Answer: b
Problem: a is an integer greater than 29 but less than 41 , b is an integer greater than 39 but less than 51 , what is the range of a / b ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 2 / 5 , d ) 1 , e ) 5 / 4
Rationale: "min value of a / b will be when b is highest and a is lowest - - - > a = 30 and b = 50 so , a / b = 3 / 5 max value of a / b will be when b is lowest and a is highest - - - > a = 40 and b = 40 so , a / b = 1 range is 1 - ( 3 / 5 ) = 2 / 5 answer should be c ."
Answer: c
Problem: in one year , the population , of a village increased by 5 % and in the next year , it decreased by 5 % . if at the end of 2 nd year , the population was 9975 , what was it in the beginning ?
Options: a ) 7787 , b ) 10000 , c ) 1988 , d ) 1277 , e ) 2081
Rationale: "x * 105 / 100 * 95 / 100 = 9975 x * 0.9975 = 9975 x = 9975 / 0.9975 = > 10000 answer : b"
Answer: b
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 1 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "2 ^ ( 2 w ) = 8 ^ ( w − 1 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 1 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 3 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 3 w = 3 the answer is a ."
Answer: a
Problem: a person travels equal distances with speeds of 7 km / hr , 8 km / hr and 9 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 6 km , b ) 3 km , c ) 7 km , d ) 9 km , e ) 2 km
Rationale: "let the total distance be 3 x km . then , x / 7 + x / 8 + x / 9 = 47 / 60 36 x / 95 = 47 / 60 = > x = 2.07 . total distance = 3 * 2.07 = 6.2 km . answer : a"
Answer: a
Problem: a leak in the bottom of a tank can empty the full tank in 9 hours . an inlet pipe fills water at the rate of 6 litres a minute . when the tank is full , the inlet is opened and due to the leak , the tank is empty in 12 hours . how many litres does the cistern hold ?
Options: a ) 7580 , b ) 12960 , c ) 8290 , d ) 8640 , e ) none
Rationale: "solution work done by the inlet in 1 hour = ( 1 / 9 - 1 / 12 ) = 1 / 36 work done by the inlet in 1 min . = ( 1 / 36 × 1 / 60 ) = 0.000463 volume of 0.000463 part = 6 litres . therefore , volume of whole = 1 / 0.000463 x 6 ‹ = › 12960 litres . answer b"
Answer: b
Problem: if k ^ 2 is divisible by 240 what is the least possible value of integer k ?
Options: a ) 60 , b ) 30 , c ) 12 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 2 to be divisible by 240 it should contain at least 2 ^ 4 and 3 and 5 in its factors . we can leave out option c because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 2 will have 2 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 2 = ( 2 ^ 4 ) * ( 3 ^ 2 ) * ( 5 ^ 2 ) . so it shows that 60 ^ 2 is divisible by 240 and hence the answer . answer : a"
Answer: a
Problem: you enter a weight loss challenge game and manage to lose 11 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 11 % ) * ( 100 % + 2 % ) = 0.89 * 1.02 = 9.22 % the weigh in records your weight loss at 9.22 % ! the answer is b"
Answer: b
Problem: in a certain game , a large bag is filled with blue , green , purple and red chips worth 1 , 5 , x and 11 points each , respectively . the purple chips are worth more than the green chips , but less than the red chips . a certain number of chips are then selected from the bag . if the product of the point values of the selected chips is 2200 , how many purple chips were selected ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "2200 = 1 * 5 ^ 2 * 8 * 11 the factor of 8 must come from the purple point value , so there is 1 purple chip . the answer is a ."
Answer: a
Problem: solution a is 40 % salt and solution b is 80 % salt . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % salt solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 1
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 40 ) = 3 / 1 so the volume of the two solutions will be equal . answer has to be 3 : 1 . e
Answer: e
Problem: a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 40 as remainder . find the no . is ?
Options: a ) 220044 , b ) 145778 , c ) 220400 , d ) 220014 , e ) 220040
Rationale: "( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220040 e"
Answer: e
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 . 1500 . the difference between the profit shares of a and c is ?
Options: a ) 8867 , b ) 299 , c ) 279 , d ) 600 , e ) 2612
Rationale: "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 . 1500 = > 5 parts out of 15 parts is rs . 1500 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1500 ) = rs . 600 . answer : d"
Answer: d
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 3 of the mixture is sand , 1 / 2 of the mixture is water , and the remaining 8 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 46 , e ) 48
Rationale: "let the total weight be x . sand content = ( 1 / 3 ) x water content = ( 1 / 2 ) x gravel = x - ( 1 / 3 ) x - ( 1 / 2 ) x = ( 1 / 6 ) x = 8 x = 48 then answer will be e = 48"
Answer: e
Problem: machine a and machine b are each used to manufacture 330 sprockets . it takes machine a 10 hours longer to produce 330 sprockets than machine b . machine b produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machineaproduce ?
Options: a ) 3.3 , b ) 6.6 , c ) 60 , d ) 100 , e ) 110
Rationale: "time taken by b = t time taken by a = t + 10 qty produced by a = q qty produced by b = 1.1 q for b : t ( 1.1 q ) = 330 qt = 300 for a : ( t + 10 ) ( q ) = 330 qt + 10 q = 330 300 + 10 q = 330 q = 3 so a can produce 3 / hour . then b can produce = 3 ( 1.1 ) = 3.3 / hour . a"
Answer: a
Problem: albert is 2 times mary ’ s age and 4 times as old as betty . mary is 14 years younger than albert . how old is betty ?
Options: a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 18
Rationale: "a = 2 m = m + 14 m = 14 a = 28 a = 4 b , and so b = 7 the answer is b ."
Answer: b
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 35 % solution ?
Options: a ) a ) 6.7 , b ) b ) 38.5 , c ) c ) 9.6 , d ) d ) 12.5 , e ) e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 35 / 100 200 + 20 x = 700 + 7 x 13 x = 500 x = 28.5 answer is b"
Answer: b
Problem: when y is divided by 276 , the remainder is 42 . what is the remainder when the same y is divided by 23 ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "y = 276 * a + 42 = ( 23 * 12 ) * a + 23 + 19 the answer is d ."
Answer: d
Problem: when 200 is divided by positive integer x , the remainder is 2 . what is the remainder when 398 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 200 / x leaves a reminder 2 then ( 200 - 2 ) i . e . 198 is divisible by x so ( 200 + 198 ) / x leaves a reminder rem ( 200 / x ) + rem ( 198 / x ) = > 2 + 0 = 2 answer : a"
Answer: a