regisss/math_qa huggingface dataset:
Problem: if x is 12 percent greater than 80 , then x =
Options: a ) 89.6 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a ."
Answer: a
Problem: a and b complete a work in 6 days . a alone can do it in 8 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.43 days , c ) 2.99 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 6 + 1 / 8 = 7 / 24 24 / 7 = 3.43 days answer : b"
Answer: b
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 8 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 8 = 76 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 â € “ 316 = 4 a = e + 4 = 76 + 4 = 80 d"
Answer: d
Problem: 130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?
Options: a ) 140.6 kg , b ) 145.3 kg , c ) 146.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c"
Answer: c
Problem: if each side of a square is increased by 325 % in length , find the percentage change in its area ?
Options: a ) 54 % , b ) 957 % , c ) 956.25 % , d ) 958.25 % , e ) 959.50 %
Rationale: "let each side of the square be a , then area = a x a new side = 325 a / 100 = 13 a / 4 new area = ( 13 a x 13 a ) / ( 4 x 4 ) = ( 25 a ² / 16 ) increased area = = ( 169 a ² / 16 ) - a ² increase % = [ ( 153 a ² / 16 ) x ( 1 / a ² ) x 100 ] % = 956.25 % answer : c"
Answer: c
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.80 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18.8 0.4 x = 2.8 = > x = 7 discounted tickets = 10 - x = 3 ans : a"
Answer: a
Problem: a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 5 days and b leaves after 3 days from the beginning . how long will work lost ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 10 + 3 / 15 + x / 20 = 1 x = 18 / 3 = 6 answer : d"
Answer: d
Problem: at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 120 , b ) 300 , c ) 401.36 , d ) 350.15 , e ) 342.86
Rationale: "system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86"
Answer: e
Problem: two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 3 . the first number is :
Options: a ) a ) 27 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 3 x = 9 = > 3 x = 27 answer : a"
Answer: a
Problem: the length of the bridge , which a train 130 metres long and travelling at 54 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 320 m , d ) 250 m , e ) 240 m
Rationale: "speed = [ 54 x 5 / 18 ] m / sec = [ 15 / 1 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) = 450 = > x = 450 - 130 = 320 m answer : c"
Answer: c
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 40 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 40 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Problem: what is 3 2 / 3 - 2 1 / 4 divided by 6 / 7 - 2 / 5 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 64 , d ) 15 / 4 , e ) 14 / 4
Rationale: "3 2 / 3 - 2 1 / 4 = 11 / 3 - 9 / 4 = ( 44 - 27 ) / 12 = 17 / 12 6 / 7 - 2 / 5 = ( 30 - 14 ) / 35 = 16 / 35 so 17 / 12 / 16 / 3 = 17 / 12 * 3 / 16 = 17 / 64 answer - c"
Answer: c
Problem: the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the youngest child ?
Options: a ) 4 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇔ 5 x = 20 ⇔ x = 4 . ∴ age of the youngest child = x = 4 years . answer a"
Answer: a
Problem: sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 30 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 18 , c ) 10 , d ) 12 , e ) 11
Rationale: "if there were all the expensive ones 2.5 . . . . there would be 30 / 2.5 or 12 of them but since 1.5 $ ones are also there , answer has to be > 12 . . . . if all were 1.5 $ ones , there will be 30 / 1.5 or 20 . . . so only 18 is left ans b . ."
Answer: b
Problem: the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 16 years , e ) 55 years
Rationale: "given that a + b = 16 + b + c = > a â € “ c = 16 + b â € “ b = 16 = > c is younger than a by 16 years answer : d"
Answer: d
Problem: the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 ° is ?
Options: a ) 35 m 2
b ) 36 m 2
c ) 37 m 2
d ) 38 m 2
e ) 40 m 2
Rationale: 30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c
Answer: c
Problem: find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1254 , b ) 1376 , c ) 1456 , d ) 1555 , e ) 1629
Rationale: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e"
Answer: e
Problem: solve the equation 2 – x = 2 b – 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 ≠ 0 , i . e . a ≠ 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b ≠ 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) ≠ 0 in this case the equation has no solution . if b = 7 and a ≠ 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b
Answer: b
Problem: in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .
Options: a ) 25 , b ) 20 , c ) 15 , d ) 13 , e ) 14
Rationale: let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c .
Answer: c
Problem: a motorcyclist goes from bombay to pune , a distance of 160 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 1 : 4 , d ) 1 : 1 , e ) 1 : 6
Rationale: "t = 160 / 32 = 5 h t = 5 - 3 = 2 time ratio = 5 : 2 = 5 : 2 speed ratio = 2 : 5 answer : b"
Answer: b
Problem: what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?
Options: a ) 95 % , b ) 90 % , c ) 85 % , d ) 96 % , e ) 25 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d"
Answer: d
Problem: how many shots of 1 cm radius can be prepared from a sphere of 5 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 125 , e ) 199
Rationale: 4 / 3 ï € * 5 * 5 * 5 = 4 / 3 ï € * 1 * 1 * 1 * x x = 125 answer : d
Answer: d
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b
Answer: b
Problem: a train 124 m long running at 68 kmph crosses a platform in 19 sec . what is the length of the platform ?
Options: a ) 338 , b ) 234 , c ) 240 , d ) 881 , e ) 271
Rationale: "d = 68 * 5 / 18 = 19 = 358 – 124 = 234 answer : b"
Answer: b
Problem: the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d"
Answer: d
Problem: given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 8 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = d = 7 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 8 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 8 = 3 ( 3 x - 6 ) - 5 6 x - 2 = 9 x - 23 x = 7"
Answer: d
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 468 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 13
Rationale: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 468 . hourly wage = 468 / 36 = 13 answer : e"
Answer: e
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 72 % , c ) 20 % , d ) 82 % , e ) 16 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 150 / 100 ) = 120 100 - 120 = 20 % answer : c"
Answer: c
Problem: we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1 , 052.50 . how much money did we invest at 3 % ?
Options: a ) $ 160 , b ) $ 190 , c ) $ 220 , d ) $ 250 , e ) $ 280
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.06 ( 1000 - x ) = 1052.50 . 0.03 x = 1060 - 1052.50 . 0.03 x = 7.50 . 3 x = 750 . x = 250 . the answer is d ."
Answer: d
Problem: | x + 3 | – | 4 - x | = | 9 + x | how many solutions will this equation have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "you have | x + 3 | - | 4 - x | = | 8 + x | first , look at the three values independently of their absolute value sign , in other words : | x + 3 | - | 4 - x | = | 8 + x | ( x + 3 ) - ( 4 - x ) = ( 8 + x ) now , you ' re looking at x < - 8 , so x is a number less than - 8 . let ' s pretend x = - 10 here to make things a bit easier to understand . when x = - 10 i . ) ( x + 3 ) ( - 10 + 3 ) ( - 7 ) ii . ) ( 4 - x ) ( 4 - [ - 10 ] ) ( double negative , so it becomes positive ) ( 4 + 10 ) ( 14 ) iii . ) ( 8 + x ) ( 8 + - 10 ) ( - 2 ) in other words , when x < - 8 , ( x + 3 ) and ( 8 + x ) are negative . to solve problems like this , we need to check for the sign change . here is how i do it step by step . i . ) | x + 3 | - | 4 - x | = | 8 + x | ii . ) ignore absolute value signs ( for now ) and find the values of x which make ( x + 3 ) , ( 4 - x ) and ( 8 + x ) = to zero as follows : ( x + 3 ) x = - 3 ( - 3 + 3 ) = 0 ( 4 - x ) x = 4 ( 4 - 4 ) = 0 ( 8 + x ) x = - 8 ( 8 + - 8 ) = 1 b"
Answer: b
Problem: the area of a rectangular plot is 460460 square metres . if the length is 15 % 15 % more than the breadth , what is the breadth of the plot ?
Options: a ) 14 metres , b ) 20 metres , c ) 18 metres , d ) 12 metres , e ) 16 metres
Rationale: "explanation : length 115 % of breadth . length × breadth = 460 m 2 ⇒ 115 % of breadth × breadth = 460 m 2 ⇒ 115 / 100 × breadth × breadth = 460 m 2 ⇒ breadth × breadth = 400 m 2 ⇒ breadth = 20 m answer : option b"
Answer: b
Problem: two pipes a and b can separately fill a tank in 16 and 18 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 18 minutes . what is the capacity of the tank ?
Options: a ) 590 liters , b ) 720 liters , c ) 740 liters , d ) 860 liters , e ) 620 liters
Rationale: "1 / 16 + 1 / 18 - 1 / x = 1 / 18 x = 16 16 * 45 = 720 answer : b"
Answer: b
Problem: 17 balls are numbered 1 to 17 . a ball is drawn and then another ball is drawn without replacement . what is the probability that both balls have even numbers ?
Options: a ) 1 / 7 , b ) 3 / 14 , c ) 5 / 23 , d ) 7 / 34 , e ) 9 / 41
Rationale: p ( 1 st ball is even ) = 8 / 17 p ( 2 nd ball is also even ) = 7 / 16 p ( both balls are even ) = 8 / 17 * 7 / 16 = 7 / 34 the answer is d .
Answer: d
Problem: aarti can do a piece of work in 9 days . in how many days will she complete three time of work of same type ?
Options: a ) 6 days , b ) 18 days , c ) 21 days , d ) 27 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 9 days . three times of work of same type can be done in 9 x 3 = 27 days answer d"
Answer: d
Problem: what is the value of n if the sum of the consecutive odd intergers r from 1 to n equals 169 ?
Options: a ) 47 , b ) 25 , c ) 37 , d ) 33 , e ) 29
Rationale: "before you tackle this question you must first understand that the question is comprised of two key parts , 1 st is finding out how manytermsis in that sequence and 2 nd whatactual number valuethat term is . in an arithmetic progression , in this case consecutive odd integers 1 , 3 , 5 , . . . . , there are two set of rules . rule # 1 ( arithmetic sequence ) : xn = a + d ( n - 1 ) identifies what the actual # in the sequence would be . each number in the sequence has a term such as 1 ( is the first term ) , 3 ( is the second term ) and so on . so if i were to ask you to find out what the 10 th term is of that sequence you would use that formula to find that value . a = 1 ( first term ) d = 2 ( the common difference ) remember in the sequence 1 , 3 , 5 , 7 the common difference is always 2 * on a side note we use n - 1 because we do n ' t have d in the first term , therefore if we were solving for the first term we would get 0 as n - 1 and 0 times d would give us 0 , leaving only the first term . this works regardless what your first term is in any sequence . but remember the question askswhat is thevalueof n if the sum of the consecutive odd integers from 1 to n equals 169 ? which means we first need a consecutive sequence that sums up to 169 and than find what the value of the n is , in this case it would be the last number in that sequence . in order to find that we first need to knowhow many terms ( how many of the n there is ) in order to be able to plug n in this formula given we know what the sum is . for that to happen we need to use rule # 2 . rule # 2 ( summing an arithmetic series ) : 169 = n / 2 ( 2 a + ( n - 1 ) d ) . given the question gives us what the sum is ( 169 in this case ) we would simply use this formula to solve for n . once we solve for n ( 13 in this case ) we can simply plug n into the first formula ( rule 1 ) and find the value . it feels very confusing and difficult at first , but once you identify the steps all you need to do is plug and play . we have the sum ( 169 ) of a sequence , the number of terms in that sequence is ( unknown ) . rule # 2 tells us how many numbers there are in that sequence and rule # 1 gives us what that last term is ."
Answer: b
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 7 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 10
Rationale: "let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 7 = > m = 21 answer d"
Answer: d
Problem: there are 7 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair . what is the number of pair that can be formed .
Options: a ) 40 , b ) 49 , c ) 41 , d ) 56 , e ) 42
Rationale: "first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 7 and for second = 6 so total methods = 7 * 6 = 42 answer : e"
Answer: e
Problem: what is the lowest positive integer that is divisible by 4 through 6 , inclusive ?
Options: a ) 120 , b ) 48 , c ) 82 , d ) 76 , e ) 160
Rationale: "the integer should be divisible by : 4 , 5 , and 6 . the least common multiple of these integers is lcm = 4 * 5 * 6 = 7920 answer : a"
Answer: a
Problem: when a stone is dropped from a building 200 m high , its speed is proportional to the time elapsed after dropping . the distance traveled is proportional to the square of the time elapsed . after 1 second the speed of the train was 10 m / sec and it was 190 m above the ground . when its speed is 25 m / sec , what would be its distance from the ground ?
Options: a ) 140 m , b ) 137.5 m , c ) 125.75 m , d ) 142.5 m , e ) 152.5 m
Rationale: v = x * t and s = y * t ^ 2 10 = x * 1 , hence x = 10 units ( 200 - 190 ) = y * 1 * 1 y = 10 when speed = 25 m / sec , time elapsed = 25 / 10 = 2.5 sec distance travelled by stone = 10 * ( 2.5 ) ^ 2 = 62.5 mts so distance of stone above ground = 200 - 62.5 = 137.5 mtrs answer : b
Answer: b
Problem: if 2 x = 3 y = 10 , then 15 xy = ?
Options: a ) 1,200 , b ) 200 , c ) 120 , d ) 40 , e ) 250
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 15 xy = 15 * 5 * 10 / 3 = 250 answer : e ."
Answer: e
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 30 km / hr and 90 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 90 + 30 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b"
Answer: b
Problem: the ratio of three numbers is 5 : 1 : 4 and their sum is 1000 . the last number of the three numbers is ?
Options: a ) 24 , b ) 26 , c ) 27 , d ) 400 , e ) 30
Rationale: "5 : 1 : 4 total parts = 10 10 parts - - > 1000 1 part - - - - > 100 the last number of the three numbers is = 4 * 100 = 400 answer : d"
Answer: d
Problem: in a bag of small balls 1 / 4 are green , 1 / 8 are blue , 1 / 12 are yellow and the remaining 26 white . how many balls are blue ?
Options: a ) 6 , b ) 5 , c ) 4 , d ) 3 , e ) 8
Rationale: let us first find the fraction of green , blue and yellow balls 1 / 4 + 1 / 8 + 1 / 12 = 6 / 24 + 3 / 24 + 2 / 24 , common denominator = 11 / 24 , add numerators the fraction of white balls is given by 24 / 24 - 11 / 24 = 13 / 24 so the fraction 13 / 24 corresponds to 26 balls . if x is the total number of balls then ( 13 / 24 ) of x = 26 balls or ( 13 / 24 ) ? x = 26 x = 26 ? ( 24 / 13 ) = 48 , total number of balls the fraction of blue balls is 1 / 8 of x . the number of blue balls is given by ( 1 / 8 ) of 48 = 6 balls . correct answer a
Answer: a
Problem: a crow leaves its nest , and flies back and forth from its nest to a nearby ditch to gather worms . the distance between the nest and the ditch is 250 meters . in one and a half hours , the crow manages to bring worms to its nest 15 times . what is the speed of the crow in kilometers per hour ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "the distance between the nest and the ditch is 250 meters . 15 times mean = a crow leaves its nest , and flies back ( going and coming back ) i . e . 2 times we get total 30 rounds . so the distance is 30 * 250 = 7500 . d = st 7500 / 1.5 = t , i think we can take 7500 meters as 7.5 km , then only we get t = 5 . ( 1000 meters = 1 km ) d )"
Answer: d
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 300 milliliters of solution x to create a solution that is 15 percent alcohol by volume ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: "15 % is 5 % - points higher than 10 % but 15 % - points lower than 30 % . thus there should be 3 parts of solution x for 1 part of solution y . we should add 100 ml of solution y . the answer is b ."
Answer: b
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 40 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 500 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 40 % . 4 x = 200 = > x = 500 answer a"
Answer: a
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 9 m long . if the area of the pond is 1 / 8 of the area of the field . what is the length of the field ?
Options: a ) 54 , b ) 36 , c ) 75 , d ) 28 , e ) 11
Rationale: "a / 8 = 9 * 9 = > a = 9 * 9 * 8 x * 2 x = 9 * 9 * 8 x = 18 = > 2 x = 36 answer : b"
Answer: b
Problem: how much time will a train of length 380 m moving at a speed of 72 kmph take to cross another train of length 540 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 92 , e ) 12
Rationale: "the distance to be covered = sum of their lengths = 380 + 540 = 920 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 920 / 10 = 92 sec . answer : d"
Answer: d
Problem: the area of a circle is increased by 800 % . by what percent has the radius of the circle increased ?
Options: a ) 100 % , b ) 400 % , c ) 300 % , d ) 600 % , e ) 200 %
Rationale: "the area of the circle is increased by 800 % , thus the area is increased 9 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 3 times ( diameter increase 3 times = area increase 9 times ) , which is increase by 200 % . answer : e ."
Answer: e
Problem: adam borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years , and at the rate of 14 % p . a . for the period beyond 5 years . 1 £ he pays a total interest of rs . 11400 at the end of 9 years how much money did he borrow ?
Options: a ) rs . 8000 , b ) rs . 09000 , c ) rs . 11000 , d ) rs . 10000 , e ) rs . 12000
Rationale: let the sum borrowed be x . then , ( x * 2 * 6 ) / 100 + ( x * 9 * 3 ) / 100 + ( x * 14 * 4 ) / 100 = 11400 ( 3 x / 25 + 27 x / 100 + 14 x / 25 ) = 11400 95 x / 100 = 11400 x = ( 11400 * 100 ) / 95 = 12000 . hence , sum borrowed = rs . 12000 answer is e .
Answer: e
Problem: which number need to add to 859622 to get a number divisible by 456 ?
Options: a ) 565771 , b ) 456578 , c ) 676885 , d ) 788090 , e ) 859622
Rationale: "dividend = quotient * divisor + reminder 859622 / 456 gives quotient = 1885 and reminder = 62 . so , the next number divisible by 456 is 456 places infront of 456 * 1885 which means 456 – 62 = 394 should be added to 859622 . e"
Answer: e
Problem: if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 50 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 50 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 100 ans a"
Answer: a
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 8,4 ) , and ( 8,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 2 / 5
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 32 . p ( x + y < 4 ) = 8 / 32 = 1 / 4 the answer is d ."
Answer: d
Problem: harold and millicent are getting married and need to combine their already - full libraries . if harold , who has 1 / 2 as many books as millicent , brings 1 / 3 of his books to their new home , then millicent will have enough room to bring 1 / 5 of her books to their new home . what fraction of millicent ' s old library capacity is the new home ' s library capacity ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 11 / 30 , e ) 5 / 6
Rationale: "because we see h willbring 1 / 3 of his booksto the new home - - > try to pick a number that isdivisible by 3 . before : assume h = 30 books h = 1 / 2 m - - > m = 60 books after : h ' = 1 / 3 h = 10 books m ' = 1 / 5 m = 12 books total = 22 books m ' = 22 = 11 / 30 * 60 ratio : 11 / 30 ans : d"
Answer: d
Problem: let the number which when multiplied by 16 is increased by 375 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 25 , e ) 30
Rationale: "solution let the number be x . then , 16 x - x = 375 ‹ = › 15 x = 375 x ‹ = › 25 . answer d"
Answer: d
Problem: a can finish a work in 60 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 25 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 60 work is done by a in 1 day 5 / 12 work is done by a in 60 * 5 / 12 = 25 days answer is b"
Answer: b
Problem: jill has 14 gallons of water stored in quart , half - gallon , and one gallon jars . she has equal numbers of each size jar holding the liquid . what is the total number of water filled jars ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 24
Rationale: let the number of each size of jar = wthen 1 / 4 w + 1 / 2 w + w = 14 1 3 / 4 w = 14 w = 8 the total number of jars = 3 w = 24 answer : e
Answer: e
Problem: a cricket player whose bowling average was 21.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 111 , d ) 721 , e ) 108
Rationale: "average = total runs / total wickets total runs after last match = 21.5 w + 52 total wickets after last match = w + 5 ( 21.5 w + 52 ) / ( w + 5 ) = 21.5 - 0.5 = 21 w = 106 so total wickets aftr last match = w + 5 = 111 answer : c"
Answer: c
Problem: 8 men , working 8 hours a day can complete a work in 18 days . how many hours a day must 12 men work to complete the same work in 12 days ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the number of hours required to complete the work is 8 * 8 * 18 = 1152 12 × 12 × ( x ) = 1152 x = 8 the answer is c ."
Answer: c
Problem: 1 , 8 , 27 , 64 , 125 , 216 , ( . . . . )
Options: a ) 354 , b ) 343 , c ) 245 , d ) 392 , e ) 400
Rationale: "the pattern is 1 ^ 3 , 2 ^ 3 , 3 ^ 3 , 4 ^ 3 , 5 ^ 3 , 6 ^ 3 , etc hence , next number is 7 ^ 3 = 343 answer is b"
Answer: b
Problem: if 3 men or 4 women can do a piece of work in 16 days , in how many days can 12 men and 8 women do the same piece of work ?
Options: a ) 8 / 3 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "3 men can finish a work in 16 days , so in 1 day 3 men finish 1 / 16 th of work and in 1 day 1 men can finish , 1 / 48 th of work . similarly , in 1 day 1 women can finish 1 / 64 th of work . 12 men in 1 day can finish , 12 / 48 = 1 / 4 , 8 women in 1 day can finish = 8 / 64 = 1 / 8 1 / 4 + 1 / 8 = 3 / 8 . hence number of days to complete is 8 / 3 days . answer : a"
Answer: a
Problem: two trains are running in opposite directions in the same speed . the length of each train is 120 meter . if they cross each other in 24 seconds , the speed of each train ( in km / hr ) is
Options: a ) 18 , b ) 36 , c ) 28 , d ) 20 , e ) 24
Rationale: "explanation : distance covered = 120 + 120 = 240 m time = 24 s let the speed of each train = v . then relative speed = v + v = 2 v 2 v = distance / time = 240 / 24 = 10 m / s speed of each train = v = 10 / 2 = 5 m / s = 5 × 36 / 10 km / hr = 18 km / hr answer : option a"
Answer: a
Problem: john has $ 1,600 at the beginning of his trip , after spending money , he still has exactly $ 600 less than he spent on the trip . how much money does john still have ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 500
Rationale: suppose total money spent = x not spend ( money he still has ) = x - 600 x + x - 600 = 1600 x = 1100 money not spend = 1100 - 600 = 500 answer : e
Answer: e
Problem: a , b and c started a business by investing rs . 800 / - , rs . 1000 / - and rs . 1200 / - respectively for two years . total profit is rs . 1000 / - . find the c ' s share ?
Options: a ) rs . 600 , b ) rs . 500 , c ) rs . 400 , d ) rs . 800 , e ) rs . 900
Rationale: solution : a : b : c = ( 800 * 2 ) : ( 1000 * 2 ) : ( 12000 * 2 ) = 4 : 5 : 6 . so c ' s share = rs . ( 1000 * 6 / 15 ) = rs . 400 . answer : option c
Answer: c
Problem: the speed of a car is 85 km in the first hour and 45 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 65 kmph , c ) 30 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: s = ( 85 + 45 ) / 2 = 65 kmph answer : b
Answer: b
Problem: find the number which multiplied by 15 is increased by 196 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 27
Rationale: "let the number be x . then , 15 x - x = 196 x = 14 answer : a"
Answer: a
Problem: the positive value of x that satisfies the equation ( 3 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is between bunuel , can you please explain this one ?
Options: a ) 0 and 0.5 , b ) 0.5 and 1 , c ) 1 and 1.5 , d ) 1.5 and 2 , e ) 2 and 2.5
Rationale: trial and error would probably be the easiest way to solve this problem . when x is large enough positive number , then because of the exponents ( 5 > 4 ) , lhs will be more than rhs ( as you increase the positive value of x the distance between the values of lhs and rhs will increase ) . try x = 1 - - > lhs = 3 ^ 5 = 81 * 3 = 243 and rhs = 4 ^ 4 = 64 * 4 = 256 , so ( 1 + 2 x ) ^ 5 < ( 1 + 3 x ) ^ 4 . as you can see lhs is still slightly less than than rhs . so , the value of x for which ( 1 + 2 x ) ^ 5 = ( 1 + 3 x ) ^ 4 is slightly more than 1 . answer : d .
Answer: d
Problem: the h . c . f . of two numbers is 20 and the other two factors of their l . c . m . are 11 and 15 . the larger of the two numbers is :
Options: a ) 276 , b ) 300 , c ) 299 , d ) 322 , e ) 345
Rationale: "the numbers are ( 20 x 11 ) and ( 20 x 15 ) . larger number = ( 20 x 15 ) = 300 . answer : b"
Answer: b
Problem: two numbers are in the ratio of 1 : 2 . if 6 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 6 ) / ( y + 6 ) = 3 / 5 = > x = 12 and y = 24 answer : b"
Answer: b
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 10 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.66 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 10 = 40 44 / 12 = 3.66 feet answer : b"
Answer: b
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction w of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives w = 1 / 9 . a"
Answer: a
Problem: the cash difference between the selling prices of an article at a profit of 4 % and 2 % is rs . 3 . the ratio of the two selling prices is ?
Options: a ) 52 : 51 , b ) 52 : 53 , c ) 52 : 50 , d ) 22 : 56 , e ) 52 : 51
Rationale: "let c . p . of the article be rs . x . then , required ratio = 104 % of x / 102 % of x = 104 / 102 = 52 / 51 = 52 : 51 answer : a"
Answer: a
Problem: two whole numbers whose sum is 100 can not be in the ratio
Options: a ) 2 : 23 , b ) 5 : 45 , c ) 10 : 10 , d ) 2 : 6 , e ) 2 : 3
Rationale: d ) 2 : 6
Answer: d
Problem: what least number must be added to 696 , so that the sum is completely divisible by 20 ?
Options: a ) 2 , b ) 4 , c ) 3 , d ) 5 , e ) 6
Rationale: "if we divide 696 by 20 remainder is 16 20 - 16 = 4 answer : b"
Answer: b
Problem: line q has the equation 5 y – 3 x = 30 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 22 , b ) 33 , c ) 36 , d ) 41 , e ) 58
Rationale: "5 y - 3 x = 30 and so y = 3 x / 5 + 6 when x = 0 , then y = 6 . when y = 0 , then x = - 10 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 10 , 0 ) , 0 = - 5 ( - 10 ) / 3 + c the y - intercept is c = - 50 / 3 < - 16 . thus the perpendicular line s can have y - intercepts from - 16 up to 5 . the number of possible lines is 16 + 5 + 1 = 22 the answer is a ."
Answer: a
Problem: in a certain warehouse , 30 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 24 , d ) 102 , e ) 144
Rationale: "if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 30 % of the packages weigh less than 75 pounds so , 30 % oft = number of packages that weigh less than 75 pounds 30 % of 240 = 72 , so 72 packages weigh less than 75 pounds of those 72 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 72 - 48 = 24 = c"
Answer: c
Problem: a student took 5 papers in an examination , where the full marks were the same for each paper . his marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10 . in all papers together , the candidate obtained 60 % of the total marks then , the number of papers in which he got more than 50 % marks is
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: solution : let the marks obtained in five subjects be 6 x , 7 x , 8 x , 9 x and 10 x . total marks obtained = 40 x max . marks of the five subjects = 40 x / 0.6 [ 40 x is 60 % of total marks ] max . marks in each subject = 40 x / 0.6 * 5 = 13.33 x hence , % of each subject = 6 x * 100 / 13.33 = 45.01 % or , 7 x * 100 / 13.33 = 52.51 in same way other percentage are 60.01 % , 67.52 % , 75.01 % . hence , number of subjects in which he gets more than 50 % marks = 4 . answer : option c
Answer: c
Problem: subtracting 5 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.95 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 5 % of a = ab . ⇒ ( 95 x a ) / 100 = ab ∴ b = 0.95 correct option : a"
Answer: a
Problem: a bag consists of 20 marbles , of which 5 are blue , 7 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 5 are blue , 7 are red remainder are white . so , white = 20 - 5 - 7 = 8 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 7 / 20 + 8 / 20 = 15 / 20 = 3 / 4 hence , answer will be a ."
Answer: a
Problem: a trader bought a car at 20 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 28 % , b ) 72 % , c ) 12 % , d ) 82 % , e ) 16 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 160 / 100 ) = 128 100 - 128 = 28 % answer : a"
Answer: a
Problem: an aeroplane covers a certain distance at a speed of 150 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 1300 kmph , b ) 160 kmph , c ) 180 kmph , d ) 1080 kmph , e ) none
Rationale: "explanation : distance = ( 150 x 2 ) = 300 km . speed = distance / time speed = 300 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 300 x 3 / 5 km / hr = 180 km / hr . answer : option c"
Answer: c
Problem: what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 67 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "to find : the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 let ' s reduce the clutter and simplify the product ( 7 ^ 83 ) ( 3 ^ 82 ) ( 1 ^ 87 ) 7 has a cyclicity of 4 : the last digit of any positive power of 7 repeats itself after every 4 th power so 7 ^ 5 has the same last digit as 7 ^ 1 , 7 ^ 9 , 7 ^ 13 thus , 7 ^ 83 has the same last digit as 7 ^ 3 , 7 ^ 7 , 7 ^ 11 i . e . 3 3 has a cyclicity of 4 : exactly the same routine as above thus , 3 ^ 82 has the same last digit as 3 ^ 2 , 3 ^ 6 , 3 ^ 10 i . e . 9 any power of 1 will result in 1 as the last digit so , product of our last digits = 3 x 9 x 1 = 27 . . . . last digit is 4 correct option : a"
Answer: a
Problem: how many seconds will a 550 m long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 12 sec , b ) 30 sec , c ) 33 sec , d ) 16 sec , e ) 18 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 550 * 3 / 50 = 33 sec . answer : c"
Answer: c
Problem: jansi went out for shopping . she had in her handbag approximately rs . 15 / - in one rupee notes and 20 p . coins . when she returned she had as many one rupee notes as she originally had and as many 20 p . coins as she originally had one rupee notes . she actually came back with about one - third of what she had started out with . how much did she spend and exactly how much did she have with her when she started out ?
Options: a ) 9.6 , b ) 10.6 , c ) 11.0 , d ) 9.4 , e ) 8.1
Rationale: a 9.60 let us assume that originally jansi had x rupees and y 20 paise coins . going shopping she had ( 100 x + 20 y ) paise . she returned with only ( 100 y + 20 x ) paise . this last sum , as we know , is one - third of the original and therefore 3 ( 100 y + 20 x ) = 100 x + 20 y simplifying we have x = 7 y if y is 1 thenx is 7 . assuming this so jansi had 7.20 rupees when she set out for shopping . this is wrong because jansi actually had about 15 rupees . let us see now what we get if y = 2 . then x = 14 . the original sum was 14.40 rupees which accords with the condition of the problem . if we assume that y = 3 then the sum will be too big — 21.60 rupees . therefore the only suitable answer is 14.40 rupees . after shopping jansi had 2 one rupee notes and 14 twenty paise coins . this is actually l / 3 rd of the original sum 1,440 : 3 = 480 . jansi ' s purchases , therefore , cost 14.40 — 4.80 = rs 9.60
Answer: a
Problem: at a certain organisation , the number of male members went up by 15 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 1
Rationale: "men increase by 15 % = = > 1.15 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.15 m + 0.94 f = 1.012 * ( m + f ) 1.15 m + 0.94 f = 1.012 m + 1.012 f 1.15 m - 1.012 m = 1.012 f - 0.94 f 0.138 m = 0.072 f m / f = ( 0.072 ) / ( 0.138 ) = 72 / 138 = 1 / 2 answer = ( a )"
Answer: a
Problem: in a party every person shakes hands with every other person . if there were a total of 120 handshakes in the party then what is the number of persons present in the party ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "explanation : let the number of persons be n ∴ total handshakes = nc 2 = 120 n ( n - 1 ) / 2 = 120 ∴ n = 16 answer : option b"
Answer: b
Problem: a square mirror has exactly half the area of the rectangular wall on which it is hung . if each side of the mirror is 21 inches and the width of the wall is 28 inches , what is the length of the wall , in inches ?
Options: a ) 21.5 , b ) 31.5 , c ) 41.5 , d ) 61.5 , e ) 71.5
Rationale: "since the mirror is 42 inches in all sides , it must be a square . area of a square is a = a ^ 2 ; 21 ^ 2 = 441 . area of rectangle is double of that 2 * 441 = 882 . now a = lw and we need find w so a / l = w ; 882 / 28 = 31.5 answer ! answer is b"
Answer: b
Problem: when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 96.15 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 40 , d ) 25 , e ) 12
Rationale: "by the definition of a remainder , the remainder here is equal to 6 / y . the remainder in decimal form is given as . 15 therefore , 6 / y = . 15 solve for y and get 40 . c"
Answer: c
Problem: if the product of the integers w , x , y and z is 840 , and if 1 < w < x < y < z , what is the value of w + z ?
Options: a ) 10 , b ) 11 , c ) 16 , d ) 18 , e ) 21
Rationale: "840 = 4 * 5 * 6 * 7 so w = 4 , x = 5 , y = 6 , z = 7 w + z = 4 + 7 = 11 answer - b"
Answer: b
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets 1000 more than d , what is b ’ s share ?
Options: a ) 500 , b ) 1500 , c ) 2000 , d ) 1400 , e ) none of these
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x , 3 x respectively . then , 4 x – 3 x = 1000 ⇒ x = 1000 ∴ b ’ s share = 2 x = 2000 answer c"
Answer: c
Problem: in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let r be the average rental price for all apartments in the building . if r is $ 5,600 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 10,400 higher that r , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 26 % , b ) 35 % , c ) 39 % , d ) 42 % , e ) 52 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 5400 : 104000 - - - - - > 7 : 13 let total number of apartments be x no . of 2 bedroom apartment = ( 7 / 20 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 7 / 20 ) * 100 - - - > 35 % option b is correct"
Answer: b
Problem: if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 276 games will be played during the tournament . find the number of participants .
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "let p be the number of participants . pc 2 = 276 ( p ) ( p - 1 ) = 552 = 24 * 23 p = 24 the answer is c ."
Answer: c
Problem: x starts a business with rs . 45000 . y joins in the business after 3 months with rs . 30000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 1 : 2 , b ) 2 : 1 , c ) 1 : 3 , d ) 3 : 1 , e ) 1 : 1
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 45000 × 12 : 30000 × 9 = 45 × 12 : 30 × 9 = 3 × 12 : 2 × 9 = 2 : 1 answer : option b"
Answer: b
Problem: 3 friends had dinner at a restaurant . when the bill was received , akshitha paid 3 / 4 as much as veena paid and veena paid 1 / 2 as much as lasya paid . what fraction of the bill did veena pay ?
Options: a ) 4 / 15 , b ) 3 / 12 , c ) 3 / 11 , d ) 3 / 10 , e ) 3 / 14
Rationale: let veena paid x , so akshitha paid 3 x / 4 , and lasya paid 2 x , so total bill paid is given by x + ( 3 x / 4 ) + 2 x = 1 , we get i . e . x = 4 / 15 answer : a
Answer: a
Problem: a number x is 5 times another number y . the percentage that y is less than x is
Options: a ) 12.5 % , b ) 87.5 % , c ) 80 % , d ) 11 % , e ) 1 %
Rationale: "say y = 1 and x = 5 . then y = 1 is less than x = 5 by ( 5 - 1 ) / 5 * 100 = 4 / 5 * 100 = 80 % . answer : c ."
Answer: c
Problem: marketing executives for a certain chewing gum company projected a 40 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 30 % . what percent of the projected revenue was the actual revenue ?
Options: a ) 50 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %
Rationale: last year revenue = 100 ( assume ) ; this year revenue = 70 ; projected revenue = 140 . actual / projected * 100 = 70 / 140 * 100 = 50 % . answer : a .
Answer: a