regisss/math_qa huggingface dataset:
Problem: a man buys a cycle for rs . 1400 and sells it at a loss of 5 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1160 , c ) s . 1190 , d ) s . 1202 , e ) s . 1330
Rationale: "since , c . p = 1400 loss % = ( c . p - s . p ) / c . p * 100 5 = ( 1400 - s . p ) / 1400 * 100 so , after solving answer = 1330 . answer : e"
Answer: e
Problem: the population of a bacteria colony doubles every day . if it was started 5 days ago with 2 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 64 , d ) 2048 , e ) 4096
Rationale: "2 ^ 5 ( 2 ) = 2 ^ 6 = 64 the answer is c"
Answer: c
Problem: a goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 36 seconds . what is the length of the goods train ?
Options: a ) 470 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) none of these
Rationale: "explanation : speed = [ 72 x ( 5 / 18 ) ] m / sec = 20 m / sec . time = 36 sec . let the length of the train be x metres . then , [ ( x + 250 ) / 36 ] = 20 = > x + 250 = 720 = > x = 470 . answer : a"
Answer: a
Problem: if an integer n is to be selected at random from 1 to 900 , inclusive , what is probability n ( n + 1 ) will be divisible by 9 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 2 / 3
Rationale: for n ( n + 1 ) to be a multiple of 9 , either n or n + 1 has to be a multiple of 9 . thus n must be of the form 9 k or 9 k - 1 . the probability is 2 / 9 . the answer is d .
Answer: d
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 100 of money ?
Options: a ) 1500 , b ) 6000 , c ) 2500 , d ) 1400 , e ) 2000
Rationale: "p = 100 ( 100 / 10 ) 2 = > p = 2000 answer : e"
Answer: e
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 45 meters deep by working for 6 hours ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 45 x = 90 total workers 90 - 45 = 45 new workers the answer is c ."
Answer: c
Problem: if p / q = 4 / 5 , then the value of 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: "answer given exp . = 4 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 4 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 4 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 4 / 7 + 6 / 14 = 4 / 7 + 3 / 7 = 7 / 7 = 1 . correct option : c"
Answer: c
Problem: patrick purchased 70 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 70 pencils is how many times the selling price of 70 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.28 , e ) 1.35
Rationale: "say the cost price of 70 pencils was $ 70 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 70 - 70 p = 20 p - - > p = 7 / 9 . ( cost price ) / ( selling price ) = 1 / ( 7 / 9 ) = 9 / 7 = 1.28 . answer : d ."
Answer: d
Problem: 3 men and 8 women complete a task in same time as 6 men and 2 women do . how much fraction of work will be finished in same time if 4 men and 5 women will do that task .
Options: a ) 13 / 14 , b ) 13 / 10 , c ) 13 / 18 , d ) 13 / 16 , e ) 13 / 11
Rationale: 3 m + 8 w = 6 m + 2 w 3 m = 6 w 1 m = 2 w therefore 3 m + 8 w = 14 w 4 m + 5 w = 13 w answer is 13 / 14 answer : a
Answer: a
Problem: 40 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 1100 , b ) 2100 , c ) 1300 , d ) 1650 , e ) 1400
Rationale: "4 x / 10 - x / 3 = 110 1 x / 15 = 110 x = 1650 answer : d"
Answer: d
Problem: the ratio of boarders to day students at a school was originally 5 to 12 . however , after a number of new boarders join the initial 330 boarders , the ratio changed to 1 to 2 . if no boarders became day students and vice versa , and no students left the school , how many new boarders joined the school ?
Options: a ) 48 , b ) 66 , c ) 72 , d ) 80 , e ) 84
Rationale: let x be the number of new boarders . the ratio changed from 5 : 12 up to 1 : 2 = 6 : 12 . 330 / ( 330 + x ) = 5 / 6 x = 66 the answer is b .
Answer: b
Problem: a flagpole 18 meters high casts a shadow of length 45 meters . if a building under similar conditions casts a shadow of length 70 meters , what is the height of the building ( in meters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "the height : length ratio will be equal in both cases . 18 / 45 = x / 70 x = 28 the answer is c ."
Answer: c
Problem: the average weight of a group of boys is 20 kg . after a boy of weight 33 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 12 , b ) 14 , c ) 18 , d ) 24 , e ) 10
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 20 x after the boy weighing 33 kg joins the group , total weight of boys = 20 x + 33 so 20 x + 33 = 21 ( x + 1 ) = > x = 12 . answer : a"
Answer: a
Problem: presently the ratio between the ages of dan and james is 6 : 5 . after 4 years dan will be 28 . what is the present age of james ?
Options: a ) 20 , b ) 19 , c ) 21 , d ) 18 , e ) 22
Rationale: let the present ages dan and james be 6 x years and 5 x years respectively 6 x + 4 = 28 6 x = 24 x = 4 kim ' s age = 5 x = 20 years answer is a
Answer: a
Problem: the sum of two numbers is 62 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 36 - 48 , b ) 50 - 34 , c ) 60 - 24 , d ) 42 - 42 , e ) 25 - 37
Rationale: "in this problem , we are asked to find two numbers . therefore , we must let x be one of them . let x , then , be the first number . we are told that the other number is 12 more , x + 12 . the problem states that their sum is 62 : word problem = 62 the line over x + 12 is a grouping symbol called a vinculum . it saves us writing parentheses . we have : 2 x = 62 â ˆ ’ 12 = 50 . x = 50 / 2 = 25 . this is the first number . therefore the other number is x + 12 = 25 + 12 = 37 . the sum of 25 + 37 is 62 . e"
Answer: e
Problem: a tank is filled by 3 pipes a , b , c in 5 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 50 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 5 7 / x = 1 / 5 x = 35 hours answer is b"
Answer: b
Problem: if 12 men and 16 boys can do a piece of work in 5 days ; 13 men and 24 boys can do it in 4 days , then the ratio of the daily work done by a man to that of a boy is ?
Options: a ) 2 : 1 , b ) 2 : 8 , c ) 2 : 9 , d ) 2 : 5 , e ) 2 : 2
Rationale: "let 1 man ' s 1 day work = x and 1 boy ' s 1 day work = y . then , 12 x + 16 y = 1 / 5 and 13 x + 24 y = 1 / 4 solving these two equations , we get : x = 1 / 100 and y = 1 / 200 required ratio = x : y = 1 / 100 : 1 / 200 = 2 : 1 . answer : a"
Answer: a
Problem: a certain company ’ s profit in 1996 was 20 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 33 % , d ) 44 % , e ) 38 %
Rationale: "profit in 1995 - 100 profit in 1996 - 120 % increae profit in 1997 in comparison to 1995 = 20 + 120 * 20 % = 44 correct option : d"
Answer: d
Problem: a cycle is bought for rs . 670 and sold for rs . 880 , find the gain percent ?
Options: a ) 31 % , b ) 35 % , c ) 54 % , d ) 38 % , e ) 80 %
Rationale: "explanation : 670 - - - - 210 100 - - - - ? = > 31 % answer : a"
Answer: a
Problem: a certain no . when divided by 20 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 20 + 25 = 45 / 15 = 3 ( remainder ) a"
Answer: a
Problem: the s . i . on a certain sum of money for 6 years at 14 % per annum is half the c . i . on rs . 7000 for 2 years at 7 % per annum . the sum placed on s . i . is ?
Options: a ) 603.75 , b ) 555.75 , c ) 569.55 , d ) 256.25 , e ) 563.23
Rationale: c . i . = [ 7000 * ( 1 + 7 / 100 ) 2 - 7000 ] = ( 7000 * 11 / 10 * 11 / 10 - 7000 ) = rs . 1014.3 . sum = ( 507.15 * 100 ) / ( 6 * 14 ) = rs . 603.75 answer : a
Answer: a
Problem: selling an kite for rs . 30 , a shop keeper gains 20 % . during a clearance sale , the shopkeeper allows a discount of 10 % on the marked price . his gain percent during the sale is ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 20 %
Rationale: explanation : marked price = rs . 30 c . p . = 100 / 120 * 30 = rs . 25 sale price = 90 % of rs . 30 = rs . 27 required gain % = 0.2 / 25 * 100 = 8 % . answer : a
Answer: a
Problem: a fruit seller sells mangoes at the rate of rs . 10 per kg and thereby loses 15 % . at what price per kg , he should have sold them to make a profit of 5 %
Options: a ) rs 8.81 , b ) rs 9.35 , c ) rs 10.35 , d ) rs 12.35 , e ) none of these
Rationale: "explanation : 85 : 10 = 105 : x x = ( 10 × 105 / 85 ) = rs 12.35 option d"
Answer: d
Problem: a certain galaxy is known to comprise approximately 3 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 6,000 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 3 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 3 * 10 ^ 11 / 50 * 10 ^ 6 = 30 * 10 ^ 3 / 5 = 6000 therefore answer is b"
Answer: b
Problem: a hostel had provisions for 250 men for 32 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 32 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 32 250 × 32 = 200 x 5 × 32 = 4 x x = 5 × 8 = 40 answer b"
Answer: b
Problem: a cube has a volume of 216 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24 , b ) 1728 , c ) 64 , d ) 80 , e ) 100
Rationale: "volume = 216 = side ^ 3 i . e . side of cube = 6 new cube has dimensions 12 , 12 , and 12 as all sides are twice of teh side of first cube volume = 12 * 12 * 12 = 1728 square feet answer : option b"
Answer: b
Problem: how many different values of positive integer x , for which | x + 5 | < x , are there ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
Rationale: "answer e i opted to put the random value option . i used 0 , 5 , - 5 and the the extreme of 40 and - 40 . . i was able to solve it in 1 : 09 e"
Answer: e
Problem: if a speaks the truth 80 % of the times , b speaks the truth 60 % of the times . what is the probability that they tell the truth at the same time
Options: a ) 0.49 , b ) 0.48 , c ) 0.41 , d ) 0.482 , e ) 0.411
Rationale: explanation : probability that a speaks truth is 80 / 100 = 0.8 probability that b speaks truth is 60 / 100 = 0.6 since both a and b are independent of each other so probability of a intersection b is p ( a ) × p ( b ) = 0.8 × 0.6 = 0.48 answer : b
Answer: b
Problem: tickets numbered from 1 to 27 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 , 27 ] p ( e ) = n ( e ) / n ( s ) = 9 / 27 = 1 / 3 the answer is a ."
Answer: a
Problem: a man can row downstream at the rate of 12 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 6,3 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 12 + 6 ) = 9 km / hr rate of current = 1 / 2 ( 12 - 6 ) = 3 km / hr answer : option c"
Answer: c
Problem: if a is an integer greater than 7 but less than 25 and b is an integer greater than 34 but less than 44 , what is the range of a / b ?
Options: a ) 21 / 34 , b ) 1 / 12 , c ) 15 / 64 , d ) 17 / 35 , e ) 7 / 6
Rationale: "the way to approach this problem is 7 < a < 25 and 34 < b < 41 minimum possible value of a is 8 and maximum is 24 minimum possible value of b is 35 and maximum is 40 range = max a / min b - min a / max b ( highest - lowest ) 24 / 35 - 8 / 40 = 17 / 35 hence d"
Answer: d
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 55 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 56.37 , b ) s . 53.22 , c ) s . 56.219 , d ) s . 51.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 55 * 100 ) / ( 2 * 5 ) = rs . 550 amount = [ 550 * ( 1 + 5 / 100 ) 2 ] = rs . 606.375 c . i . = ( 606.375 - 550 ) = rs . 56.37 answer : a"
Answer: a
Problem: if 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) , what is the value of w ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: 2 ^ ( 2 w ) = 8 ^ ( w − 4 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 4 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 12 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 12 w = 12 the answer is d .
Answer: d
Problem: a is twice as good as b . and together they finish a piece of work in 18 days . in how many days will a alone finish the work
Options: a ) 25 , b ) 27 , c ) 15 , d ) 18 , e ) 21
Rationale: ( a ' s 1 day work ) : ( b ' s 1 day work ) = 2 : 1 a + b 1 day work = 1 / 18 a ' s 1 day work = ( 1 / 18 ) * ( 2 / 3 ) = 1 / 27 a alone can finish the work in 27 days answer is b
Answer: b
Problem: what is the local value of 7 in the difference of 100889 and local value of 3 in 28943712 ?
Options: a ) 7000 , b ) 700 , c ) 70000 , d ) 70 , e ) 7
Rationale: "100889 - ( local value of 3 ) = 100889 - 3000 = 97889 local value of 7 in 97889 = 7000 a"
Answer: a
Problem: everyone shakes hands with everyone else in a room . total number of handshakes is 55 . number of persons = ?
Options: a ) 14 , b ) 12 , c ) 11 , d ) 15 , e ) 16
Rationale: "in a room of n people , the number of possible handshakes is c ( n , 2 ) or n ( n - 1 ) / 2 so n ( n - 1 ) / 2 = 55 or n ( n - 1 ) = 110 or n = 11 answer is ( c )"
Answer: c
Problem: what will be the fraction of 4 %
Options: a ) 1 / 20 , b ) 1 / 50 , c ) 1 / 75 , d ) 1 / 25 , e ) none of these
Rationale: "explanation : 4 * 1 / 100 = 1 / 25 . friends i know it is quite simple , but trust me while solving percentage questions in hurry we use to do these types of mistake only . so i recommend you to have a bit practise of this option d"
Answer: d
Problem: the least number which must be subtracted from 670 to make it exactly divisible by 9 is :
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 6
Rationale: "on dividing 670 by 9 , we get remainder = 4 therefore , required number to be subtracted = 4 answer : c"
Answer: c
Problem: three unbiased coins are tossed . what is the probability of getting 2 heads and 2 tail ?
Options: a ) 5 / 8 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) 1 / 8
Rationale: "let , h - - > head , t - - > tail here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting 3 heads then e = { thh , hth , hht , tht , tth } p ( e ) = n ( e ) / n ( s ) = 5 / 8 answer is a"
Answer: a
Problem: in an election a candidate who gets 84 % of the votes is elected by a majority of 476 votes . what is the total number of votes polled ?
Options: a ) 630 , b ) 700 , c ) 535 , d ) 450 , e ) 815
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 84 ) % of x = 16 % of x 84 % of x - 16 % of x = 476 68 x / 100 = 476 x = 476 * 100 / 68 = 700 answer is b"
Answer: b
Problem: 3 numbers are in the ratio 5 : 6 : 8 . the sum of its longest and smallest numbers equals the sum of the third number and 49 . find the third number ?
Options: a ) a ) 54 , b ) b ) 75 , c ) c ) 48 , d ) d ) 42 , e ) e ) 63
Rationale: let the numbers be 5 x , 6 x , 8 x . largest number = 8 x . smallest number = 5 x . third number = 6 x . 8 x + 5 x = 6 x + 49 7 x = 49 = > x = 7 6 x = 42 = > third number is 42 . answer : d
Answer: d
Problem: the price of an item changed from $ 120 to $ 100 . then later the price decreased again from $ 100 to $ 80 . which of the two decreases was larger in percentage term ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: first decrease in percent part / whole = ( 120 - 100 ) / 120 = 0.17 = 17 % second decrease in percent part / whole = ( 100 - 80 ) / 100 = 0.20 = 20 % the second decrease was larger in percent term . the part were the same in both cases but the whole was smaller in the second decrease . answer b
Answer: b
Problem: what is the next number : 3 , 11 , 83 , __
Options: a ) 631 , b ) 731 , c ) 831 , d ) 849 , e ) 901
Rationale: "3 ^ 0 + 2 = 3 3 ^ 2 + 2 = 11 3 ^ 4 + 2 = 83 3 ^ 6 + 2 = 731 the answer is b ."
Answer: b
Problem: a man sells a car to his friend at 14 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22325.58 , b ) rs . 32325.58 , c ) rs . 52325.58 , d ) rs . 62325.58 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 14 % . now s . p = rs . 45000 and loss = 14 % c . p . rs . [ 100 / 86 ã — 45000 ] = rs . 52325.58 . correct option : c"
Answer: c
Problem: a dishonest shopkeeper professes to sell pulses at the cost price , but he uses a false weight of 960 gm . for a kg . his gain is … % .
Options: a ) 4.16 % , b ) 5.36 % , c ) 4.26 % , d ) 6.26 % , e ) 7.26 %
Rationale: "his percentage gain is 100 * 40 / 960 as he is gaining 40 units for his purchase of 960 units . so 4.16 % . answer : a"
Answer: a
Problem: if two sides of a triangle have lengths 3 and 8 , which of the following could be the perimeter of the triangle ? i . 9 ii . 15 iii . 19
Options: a ) none
b ) i only
c ) ii only
d ) iii only
e ) i , ii , and iii
Rationale: the length of any side of a triangle must be larger than the positive difference of the other two sides , but smaller than the sum of the other two sides . therefore : ( 8 - 3 ) < { third side } < ( 8 + 3 ) . 5 < { third side } < 11 . perimeter = { third side } + 8 + 3 = { third side } + 11 . 16 < { perimeter } < 22 . answer d
Answer: d
Problem: increasing the original price of an article by 10 percent and then increasing the new price by 10 percent is equivalent to increasing the original price by
Options: a ) 20 % , b ) 20.5 % , c ) 20.8 % , d ) 21 % , e ) 21.8 %
Rationale: "1.1 * 1.1 * x = 1.21 * x the answer is d ."
Answer: d
Problem: a can run 1.5 km distance in 2 min 20 seconds , while b can run this distance in 2 min 30 sec . by how much distance can a beat b ?
Options: a ) 90 m , b ) 100 m , c ) 120 m , d ) 180 m , e ) 190 m
Rationale: "a takes time 2.20 minutes = 140 sec b takes time 2.30 minutes = 150 sec diffrence = 150 - 140 = 10 sec now we are to find distance covered in 10 sec by b 150 sec = 1500 m 1 sec = 10 m 10 sec = 10 x 10 = 100 m answer : b"
Answer: b
Problem: a 6 % stock yields 8 % . the market value of the stock is ?
Options: a ) rs . 11 , b ) rs . 75 , c ) rs . 17 , d ) rs . 16 , e ) rs . 22
Rationale: "for an income of rs . 8 , investment = rs . 100 . for an income of rs 6 , investment = rs . \ inline \ left ( \ frac { 100 } { 8 } \ times 6 \ right ) = rs . 75 market value of rs . 100 stock = rs . 75 . answer : b"
Answer: b
Problem: if y is the smallest positive integer such that 6300 multiplied by y is the square of an integer , then y must be
Options: a ) 5 , b ) 7 , c ) 15 , d ) 35 , e ) 45
Rationale: "6300 = 2 ^ 2 * 3 ^ 2 * 5 ^ 2 * 7 to be perfect square , we need to multiply by at least 7 . the answer is b ."
Answer: b
Problem: if the farmer sells 75 of his chickens , his stock of feed will last for 20 more days than planned , but if he buys 100 more chickens , he will run out of feed 15 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 275 , e ) 300
Rationale: let v denote the volume of feed one chicken consumes per day . then the total volume of feed in stock will be v ∗ d ∗ c where d is the number of days the feed will last if the number of chickens does not change and cc is the current number of chickens . from the question it follows that v ( d + 20 ) ( c − 75 ) = vdc v ( d − 15 ) ( c + 100 ) = vdc the first equation simplifies to 20 c − 75 d = 1500 . the second equation simplifies to ( − 15 ) c + 100 d = 1500 after dividing everything by 5 we get the linear system : 4 c − 15 d = 300 ( − 3 ) c + 20 d = 300 solving it we get c = 300 d = 60 answer : e
Answer: e
Problem: if the average of t , b , c , 14 and 15 is 12 . what is the average value of t , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: t + b + c + 14 + 15 = 12 * 5 = 60 = > t + b + c = 60 - 29 = 31 t + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Problem: a square of 2 unit is given and four circles are made on its corners having equal radius of each . and another circle of equal radius is made on the center of the square . find out the area of square which is not covered by circles ?
Options: a ) 0.76
b ) 0.86
c ) 0.96
d ) 1.16
e ) 1.26
Rationale: let the radius of circle is ' r ' area of the circle which is at corner = ( 22 / 7 * r ^ 2 ) / 4 hence the area of all four circles are = 22 / 7 * r ^ 2 areaof circle which is made on center of suare is = 22 / 7 * r ^ 2 total area of all circles are = 2 * 22 / 7 * r ^ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) if we construct the diagram we get the relation 4 r = 2 sqrt 2 r = 1 / sqrt 2 put the value of r in eqn 1 and we get 2 * 22 / 7 * 1 / 2 = 22 / 7 = 3.14 area of suare = 2 ^ 2 = 4 area of remaining part = 4 - 3.14 = 0.86 answer : b
Answer: b
Problem: sachin is younger than rahul by 6 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 14 , c ) 15 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 6 , so ( x - 6 ) / x = 7 / 9 = > 9 x - 42 = 7 x = > 2 x = 42 = > x = 21 so sachin age is 21 - 6 = 15 answer : c"
Answer: c
Problem: 31 of the scientists that attended a certain workshop were wolf prize laureates , and 13 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 51 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 25 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 52 . . not w = 52 - 31 = 21 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 21 or x = 9 . . so who won nobel but not wolf = x + 3 = 12 . . but people who won both w and n = 13 . . so total who won n = 12 + 13 = 25 . . d"
Answer: d
Problem: a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area covered by the two roads ?
Options: a ) 400
b ) 1550
c ) 1575
d ) 1600
e ) 1625
Rationale: area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads = 1000 + 600 - 25 = 1575 answer : option c
Answer: c
Problem: if p # q denotes the least common multiple of p and q , then q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Problem: the difference between a two - digit number and the number obtained by interchanging the digits is 9 . what is the difference between the two digits of the number ?
Options: a ) 8 , b ) 2 , c ) 7 , d ) can not be determined , e ) none of these
Rationale: "suppose the two - digit number be 10 x + y . then we have been given l 0 x + y – ( 10 y + x ) = 9 ⇒ 9 x – 9 y = 9 ⇒ x – y = 1 hence , the required difference = 1 note that if the difference between a two - digit number and the number obtained by interchanging the digits is d , then the difference between the two digits of the number = d ⁄ 9 answer e"
Answer: e
Problem: 81 , 64 , 27 , 16 . . .
Options: a ) 12 , b ) 4 , c ) 9 , d ) 3 , e ) 1
Rationale: "81 / 3 = 27 64 / 4 = 16 27 / 3 = 9 answer : c"
Answer: c
Problem: set x consists of all two - digit primes and set y consists of all positive odd multiples of 7 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 7 , 21 , 35 , . . . . . . . . . . . . . . . , 77 , 91 , } combining two sets , say set z set z = { 7 , 11 , 13 , 17,21 , . . . . . . . . . . . . . . . . . . . , 77 , 83 , 89 , 91 , 97 } range = max value - min value range ( z ) = 97 - 7 = 90 oa c is the answer .
Answer: c
Problem: a shopkeeper sold an article offering a discount of 10 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 39 % , b ) 52 % , c ) 15 % , d ) 21 % , e ) 28 %
Rationale: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 90 / 100 * x = 125 x = 12500 / 90 = $ 139 now , s . p . = $ 139 , c . p . = rs . 100 profit % = 39 % . answer : a"
Answer: a
Problem: a certain high school has 500 students . of these students , 30 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 20 z = 10 so , we have 30 students taking music , 20 taking art and 10 taking both music and art . 20 student taking just music 10 student taking just art 10 student taking both music and art total = 40 students we ' re asked for the total number of students who are taking neither course . that is 500 - 40 = 460 . d"
Answer: d
Problem: a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 130 , b ) 141 , c ) 152 , d ) 163 , e ) 174
Rationale: "3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 3 = 83 . the minimum number of horses and ponies is 163 . the answer is d ."
Answer: d
Problem: two bullet trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "c 12 sec . speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 15 m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = 20 m / sec . required time = ( 120 + 120 ) / 20 sec = 12 sec ."
Answer: c
Problem: there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 8 days more ?
Options: a ) 1122 , b ) 1140 , c ) 1199 , d ) 1188 , e ) 1166
Rationale: 760 - - - - 22 760 - - - - 20 x - - - - - 8 x * 8 = 760 * 20 x = 1900 760 - - - - - - - 1140 answer : b
Answer: b
Problem: if the price of a tv is first decreased by 20 % and then increased by 55 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 24 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 155 % of ( 80 % of 100 ) = rs . 155 / 100 * 80 / 100 * 100 = rs . 124 . . ' . increase = 24 % answer : b"
Answer: b
Problem: what is the smallest integer c for which 27 ^ c > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ c > 3 ^ 24 converting into the same bases : 27 ^ c > 27 ^ 8 therefore for the equation to hold true , c > 8 or c = 9 option c"
Answer: c
Problem: in order to obtain an income of rs . 600 from 12 % stock at rs . 106 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 2368 , d ) 7632 , e ) 7732
Rationale: "to obtain rs . 10 , investment = rs . 106 . to obtain rs . 600 , investment = = rs . 7632 answer : d"
Answer: d
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7200 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7200 / 18 + 7200 / 14 = 400 + 514.2 = 914.2 hours answer : option a"
Answer: a
Problem: a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 7000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 800 , e ) s . 875
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 7000 ) = rs . 875 answer = e"
Answer: e
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 400 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 210
Rationale: "we ' re asked for the average of all of the multiples of 10 from 10 to 400 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 40 ( 10 ) = 400 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 400 = 410 20 + 390 = 410 30 + 380 = 410 etc . since there are 40 total terms , this pattern will create 20 ' pairs ' of 410 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 20 ) ( 410 ) / ( 40 ) = 410 / 2 = 205 final answer : d"
Answer: d
Problem: a train 130 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 10 , b ) 6.5 , c ) 7 , d ) 7.13 , e ) 10.2
Rationale: "speed of train relative to man = 60 + 4 = 64 km / hr . = 64 * 5 / 18 = 160 / 9 m / sec . time taken to pass the men = 130 * 9 / 160 = 7.13 sec . answer : option d"
Answer: d
Problem: after giving a discount of rs . 80 the shopkeeper still gets a profit of 10 % , if the cost price is rs . 200 . find the markup % ?
Options: a ) 31 % , b ) 33 % , c ) 28 % , d ) 30 % , e ) 32 %
Rationale: "cost price = 180 s . p = 200 * 110 / 100 = 220 disc = 80 so . . . mark price = 216 + 80 = 296 . . . . . . mark up % = 261 - 200 / 200 = 61 / 200 = 0.305 or 31 % answer : a"
Answer: a
Problem: if the digits 27 in the decimal 0.00027 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00027 ) ?
Options: a ) 0.27 , b ) 0.027 , c ) 27 , d ) 0.0027 , e ) 2.7 e - 06
Rationale: "99 * 0.27 = 26.73 approx . 27 answer : c"
Answer: c
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 200 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 80 2.5 h = 80 h = 80 . a is the answer ."
Answer: a
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 5 , 3 ) , what is the area of that square ?
Options: a ) 100 , b ) 169 , c ) 225 , d ) 324 , e ) 256
Rationale: "one point ( - 3 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 3 - 5 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 e"
Answer: e
Problem: in a school with 652 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 250 , d ) 163 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 652 - x ) . then , ( 11 3 / 4 × 652 ) ⇔ 11 x + 12 ( 652 - x ) ⇔ x = 7824 - 7661 ⇔ 163 . answer d"
Answer: d
Problem: ( 35423 + 7164 + 41720 ) - ( 317 x 89 ) = ?
Options: a ) 28213 , b ) 84307 , c ) 50694 , d ) 54094 , e ) none of them
Rationale: "= ( 84307 ) - 317 x 89 = 84307 - ( 317 x ( 90 - 1 ) ) = 84307 - ( 317 x 90 - 317 ) = 84307 - 28213 = 54094 answer is d"
Answer: d
Problem: in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 2 / 3 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 2 / 3 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 3 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 1 / 3 * 1 / 2 = 1 / 6 , or a ."
Answer: a
Problem: how many words , with or without meaning , can be formed using all letters of the word beautiful using each letter exactly once ?
Options: a ) 388,620 , b ) 388,260 , c ) 362,880 , d ) 352,880 , e ) 342,880
Rationale: "the word beautiful has exactly 9 letters which are all different . therefore the number of words that can be formed = number of permutations of 9 letters taken all at a time . = p ( 9 , 9 ) = 9 ! = 9 x 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 362,880 answer : c"
Answer: c
Problem: a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams . find the profit percent .
Options: a ) 7.38 , b ) 5.38 , c ) 4.38 , d ) 6.38 , e ) 3.38
Rationale: explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 940 100 + g / 100 + 0 = 1000 / 940 100 + g = 100 / 94 * 100 g = 6.38 answer : d
Answer: d
Problem: the average of first six multiples of 4 is :
Options: a ) 14 , b ) 9 , c ) 12 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 84 / 6 = 14 answer a"
Answer: a
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 20 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 96 km , d ) 12 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 20 2 x + 3 x = 480 x = 96 km answer is c"
Answer: c
Problem: during a sale , the price of a pair of shoes is marked down 20 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 25 %
Rationale: "assume the price = 100 price during sale = 80 price after sale = 100 percent increase = 20 / 80 * 100 = 25 % approx . correct option : e"
Answer: e
Problem: in what time will a train 320 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 8.0 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 320 / 40 = 8.0 sec . answer : b"
Answer: b
Problem: among 200 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 172 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 60 using your analysis : we see that the total number of students who study either maths or sociology = 88 + 112 - 60 = 140 so , in the image we know that the number of students in the zone with the black boundary = 140 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 200 , we can write : 140 + b + w = 200 or , b + w = 200 - 140 = 60 that is , b = 60 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 60 a"
Answer: a
Problem: a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Rationale: speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 5 2 x + 3 x = 120 x = 24 km answer is a
Answer: a
Problem: what is the cost of leveling the field in the form of parallelogram at the rate of rs . 70 / 10 sq . metre , whose base & perpendicular distance from the other side being 84 m & 24 m respectively ?
Options: a ) s . 2400 , b ) s . 2016 , c ) s . 1400 , d ) s . 3480 , e ) s . 2000
Rationale: "area of the parallelogram = length of the base * perpendicular height = 84 * 24 = 2016 m . total cost of levelling = rs . 2016 b"
Answer: b
Problem: during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) a / 14 , b ) 5 a / 7 , c ) 7 a / 5 , d ) 14 a , e ) 35 a
Rationale: "total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 5 * action = 30 - - > action = a = 5 . comedies = 70 = 14 a . answer : d ."
Answer: d
Problem: country x taxes each of its citizens an amount equal to 11 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 58,000 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.11 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,400 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,600 - - > x = 58,000 . answer : d ."
Answer: d
Problem: list k consists of 14 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: answer = d = 8 if least = - 4 , then largest = 9 range = 9 - 1 = 8
Answer: d
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 40 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 2.55 km
Rationale: "e 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 40 / 60 47 x / 60 = 40 / 60 = > x = 0.85 . total distance = 3 * 0.85 = 2.55 km ."
Answer: e
Problem: the average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results ?
Options: a ) 30 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 85 result = sum of 20 result + sum of 65 result . = 20 x 65 + 65 x 20 = 2600 correct option : a"
Answer: a
Problem: by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at
Options: a ) 46 , b ) 96 , c ) 35 , d ) 87 , e ) 13
Rationale: "to earn rs . 135 , investment = rs . 1620 . to earn rs . 8 , investment = rs . 96 . market value of rs . 100 stock = rs . 96 . answer : b"
Answer: b
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 192 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 480 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 192 = > 4 x / 10 = 192 = > 4 x = 1920 = > x = 480 . answer : d"
Answer: d
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ?
Options: a ) 45 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 20 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 20 x = 30 since you need a 15 l solution , you must evaporate 45 of the original 50 l solution to get a 20 % solution . answer is a ."
Answer: a
Problem: a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Problem: find the average of all the numbers between 6 and 34 which is divisible by 5
Options: a ) 15 , b ) 18 , c ) 13 , d ) 19 , e ) 20
Rationale: "avg = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = > 20 answer e"
Answer: e
Problem: . 3 + 33 + 333 + 3.33 = ?
Options: a ) 369.63 , b ) 372.33 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: . 3 33 333 3.33 - - - - - - - - - - 369.63 - - - - - - - - - - answer is a
Answer: a
Problem: an woman swims downstream 45 km and upstream 25 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 2.1
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - - 5 us = 5 ? - - - - 1 s = ? s = ( 9 - 5 ) / 2 = 2 answer : a"
Answer: a
Problem: find a sum for first 6 prime number ' ss ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 41
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option e
Answer: e
Problem: a computer factory produces 8400 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 8400 / ( 28 * 24 * 2 ) = 6.25 answer e"
Answer: e
Problem: what least number should be subtracted from 3,381 so that the remainder when divided by 9 , 11 , and 17 will leave in each case the same remainder 8 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 15
Rationale: "the lcm of 9 , 11 and 17 is 1,683 . the next multiple is 2 * 1,683 = 3,366 . 3,366 + { remainder } = 3,366 + 8 = 3,374 , which is 7 less than 3,381 . answer : b ."
Answer: b
Problem: a trader marked the selling price of an article at 40 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 7.8 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: sol . let c . p . = rs . 100 . then , marked price = rs . 140 , s . p . = rs . 99 . ∴ discount % = [ 11 / 140 * 100 ] % = 7.8 % answer b
Answer: b
Problem: diana is painting statues . she has 7 / 16 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 7 / 16 ÷ 1 / 16 = 7 / 16 * 16 / 1 = 7 / 1 = 7 answer is a ."
Answer: a
Problem: in an election a candidate who gets 60 % of the votes is elected by a majority of 1300 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6500
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1300 20 x / 100 = 1300 x = 1300 * 100 / 20 = 6500 answer is e"
Answer: e
Problem: fresh grapes contain 60 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 30 kg of fresh grapes ?
Options: a ) 10 kg , b ) 15 kg , c ) 20 kg , d ) 25 kg , e ) 40 kg
Rationale: "from the question we know : 30 kg * 60 % = 18 kg of water in the fresh grapes 30 kg - 18 kg of water = 12 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 20 % of the weight of the dry graps is water and we know that 12 kg is non - water mass we can set up the following equation : x = 1 / 5 ( x ) + 12 kg 4 / 5 ( x ) = 12 kg x = 15 kg answer - b"
Answer: b