regisss/math_qa huggingface dataset:
Problem: abi decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month . if abi ' s savings by the end of the year from these monthly savings were 6 times the amount she spent per month , what should be the fraction of her salary that she spent each month ?
Options: a ) 6 / 9 , b ) 5 / 3 , c ) 2 / 3 , d ) 4 / 3 , e ) 5 / 3
Rationale: let abi ' s monthly savings = s abi ' s monthly pay = p abi ' s monthly expenditure = p - s abi ' s savings by the end of the year from these monthly savings were six times the amount she spent per month 12 s = 6 * ( p - s ) = > 2 s = p - s = > p = 3 s abi ' s monthly expenditure = p - s = 3 s - s = 2 s fraction of her salary that abi spent each month = 2 s / 3 s = p - s / p = 2 / 3 . answer is c
Answer: c
Problem: 3 people who work full - time are to work together on a project , but their total time on the project is to be equivalent to that of only one person working full - time . if one of the people is budgeted for 1 / 2 of his time to the project and a second person for 1 / 3 of her time , what part of the third worker ' s time should be budgeted to this project ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 6 , d ) 1 / 8 , e ) 1 / 9
Rationale: explanation : one - half ( 1 / 2 ) plus one - third ( 1 / 3 ) equals five - sixths ( 5 / 6 ) , so one - sixth ( 1 / 6 ) of the third worker ' s time should be budgeted to the project in order for the total time to be equivalent to that of one person working full - time . if x 2 - x - 6 = 0 , then ( x + 2 ) ( x - 3 ) = 0 , so x = - 2 or x = 3 . correct answer : a
Answer: a
Problem: the compound ratio of 1 : 2 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 3 : 5 , e ) 1 : 4
Rationale: "1 / 2 * 3 / 2 * 4 / 5 = 3 / 5 = 3 : 5 answer : d"
Answer: d
Problem: in an examination , a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 120 questions and secures 180 marks , the number of questions he attempts correctly , is :
Options: a ) 45 , b ) 90 , c ) 80 , d ) 75 , e ) 70
Rationale: "let the number of correct answers be x . number of incorrect answers = ( 120 â € “ x ) . 3 x â € “ ( 120 â € “ x ) = 180 or 4 x = 300 or x = 75 answer : d"
Answer: d
Problem: a train 240 m long , running with a speed of 108 km / hr will pass a tree in ?
Options: a ) 8 sec , b ) 16 sec , c ) 18 sec , d ) 14 sec , e ) 12 sec
Rationale: "speed = 108 * 5 / 18 = 30 m / sec time taken = 240 * 1 / 30 = 8 sec answer : a"
Answer: a
Problem: salad dressing p is made up of 30 % vinegar and 70 % oil , and salad dressing q contains 10 % vinegar and 90 % oil . if the two dressings are combined to produce a salad dressing that is 22 % vinegar , dressing p comprises what percentage of the new dressing ?
Options: a ) 35 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let x be the percentage of dressing p in the new dressing . 0.3 x + 0.1 ( 1 - x ) = 0.22 0.2 x = 0.12 x = 0.6 = 60 % the answer is d ."
Answer: d
Problem: we had $ 350 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 440 , b ) $ 460 , c ) $ 480 , d ) $ 500 , e ) $ 520
Rationale: "let x be the amount of money we started with . 0.7 x = 350 x = 500 the answer is d ."
Answer: d
Problem: a baseball card decreased in value 30 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 37 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "consider the initial value of the baseball card as $ 100 after first year price = 100 * 0.7 = 70 after second year price = 70 * 0.9 = 63 final decrease = [ ( 100 - 63 ) / 100 ] * 100 = 37 % correct answer - b"
Answer: b
Problem: when the oil from a circular cylinder leaked , the formula for the speed of the leak is v = kh ^ 2 , where h was the height of the remaining oil and k was constant . if the height of the cylinder is 4 , the speed of the leak is v â € ™ , when the height of the oil remaining is 12 , what was the speed of the leak , in terms of v â € ™ ?
Options: a ) 9 v â € ™
b ) 4 v â € ™
c ) v â € ™ / 2
d ) v â € ™ / 4
e ) v â € ™
Rationale: when h = 4 v = v ' so v ' = k . 16 hence k = v ' / 16 now when h = 12 v = ( v ' / 16 ) . 12 ^ 2 v = v ' . 144 / 16 v = 9 v ' ans : a
Answer: a
Problem: the population of bacteria culture doubles every 2 minutes . approximately how many minutes will it take for the population to grow from 1000 to 500000 bacteria ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 18 , e ) 20
Rationale: 2000 ^ 12000 ^ 22000 ^ 32000 ^ 4 . . . . . . . 2000 ^ 9 population increases in this sequence taking 9 * 2 = 18 answer : d
Answer: d
Problem: what is 15 % of 2 / 3 of 0.8 ?
Options: a ) 0.08 , b ) 0.8 , c ) 9 , d ) 90 , e ) none of the above
Rationale: "the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 8 / 10 ) = 240 / 3000 = 0.08 option a"
Answer: a
Problem: length of a rectangular plot is 40 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 60 m , c ) 58 m , d ) 70 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 40 ) metres . perimeter = 5300 / 26.5 m = 200 m . 2 [ ( x + 40 ) + x ] = 200 2 x + 40 = 100 2 x = 60 x = 30 . hence , length = x + 40 = 70 m d"
Answer: d
Problem: a envelop weight 8.5 gm , if 880 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 6.8 kg , c ) 7.48 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "880 * 8.5 7480.0 gm 7.48 kg answer : c"
Answer: c
Problem: there are 624 students in a school . the ratio of boys and girls in this school is 3 : 5 . find the total of girls & boys are there in this school ?
Options: a ) 320 , b ) 345 , c ) 375 , d ) 390 , e ) 400
Rationale: "in order to obtain a ratio of boys to girls equal to 3 : 5 , the number of boys has to be written as 3 x and the number of girls as 5 x where x is a common factor to the number of girls and the number of boys . the total number of boys and girls is 624 . hence 3 x + 5 x = 624 solve for x 8 x = 624 x = 78 number of boys 3 x = 3 × 78 = 234 number of girls 5 x = 5 × 78 = 390 d"
Answer: d
Problem: at a loading dock , each worker on the night crew loaded 1 / 2 as many boxes as each worker on the day crew . if the night crew has 4 / 5 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 7
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 1 / 2 * 4 / 5 x = 2 / 5 x % loaded by day crew = x / ( x + 2 / 5 x ) = 5 / 7 answer e"
Answer: e
Problem: company z has 53 employees . if the number of employees having birthdays on wednesday is more than the number of employees having birthdays on any other day of the week , each of which have same number of birth - days , what is the minimum number of employees having birthdays on wednesday .
Options: a ) 6 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 53 . now , plug options for x . d x > y as needed . answer : d ."
Answer: d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 50 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 50 = 21 ( x – 5 ) x = 55 answer : a"
Answer: a
Problem: if 2 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 7 , b ) - 4 , c ) - 5 , d ) 1 , e ) 6
Rationale: "the phrase “ 2 is one solution of the equation ” means that one value of x is 2 . thus , we first must plug 2 for x into the given equation to determine the value of k . so we have 2 ^ 2 + ( 3 ) ( 2 ) + k = 10 4 + 6 + k = 10 10 + k = 10 k = 0 next we plug 0 into the given equation for k and then solve for x . x ^ 2 + 3 x = 10 x ^ 2 + 3 x – 10 = 0 ( x + 5 ) ( x - 2 ) = 0 x = - 5 or x = 2 thus , - 5 is the other solution . answer c ."
Answer: c
Problem: what is the least value of x , so that 2 x 5452 is divisible by 9
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 0
Rationale: "explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 5 + 4 + 5 + 2 = 18 + x least value of x may be ' 0 ' , so that the total 18 + 0 = 18 is divisible by 9 . answer : option e"
Answer: e
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 1 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 344 , b ) 218 , c ) 200 , d ) 388 , e ) 211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 1 = > x = 200 answer : c ) rs 200"
Answer: c
Problem: the length of a rectangle is twice the breadth . if the area is 128 cm 2 , determine the length and the breadth .
Options: a ) b = 2 , l = 9
b ) b = 8 , l = 16
c ) b = 9 , l = 9
d ) b = 4 , l = 14
e ) b = 3 , l = 9
Rationale: we are given length l = 2 b and l × b = 128 ∴ 2 b × b = 128 2 b ^ 2 = 128 b ^ 2 = 64 b = ± 8 but breadth must be positive , therefore b = 8 cm , and l = 2 b = 16 cm . answer is b .
Answer: b
Problem: in a school with 5 classes , each class has 2 students less than the previous class . how many students are there in the largest class if the total number of students at school is 120 ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let x be the number of students in the largest class . then x + ( x - 2 ) + ( x - 4 ) + ( x - 6 ) + ( x - 8 ) = 120 5 x - 20 = 120 5 x = 140 x = 28 the answer is d ."
Answer: d
Problem: rs . 800 amounts to rs . 920 in 3 years at simple interest . if the interest is increased by 3 % , it would amount to how much ?
Options: a ) 288 , b ) 277 , c ) 209 , d ) 992 , e ) 612
Rationale: "( 800 * 3 * 3 ) / 100 = 72 920 + 72 = 992 answer : d"
Answer: d
Problem: when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 15 and the remainder is 1 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 691 , e ) 871
Rationale: "use the rule dividend = ( integer quotient ) * ( divisor ) + remainder to translate each sentence . the first sentence becomes n = 18 p + 7 . the second equation becomes n = ( p + 2 ) * 15 + 1 , which simplifies to n = 15 p + 31 . these are ordinary simultaneous equations since they both equal n already , let ’ s set them equal and solve for p . 18 p + 7 = 15 p + 31 3 p + 7 = 31 3 p = 24 p = 8 now that we know p = 8 , we can just plug in . the product 15 * 8 is particularly easy to do , without a calculator , by using the “ doubling and halving ” trick . double 15 to get 30 , and take half of 8 to get 4 — - 15 * 8 = 30 * 4 = 120 . so n = 15 ( 8 ) + 31 = 120 + 31 = 151 n = 151 , answer = a ."
Answer: a
Problem: car a runs at the speed of 35 km / hr & reaches its destination in 10 hr . car b runs at the speed of 25 km / h & reaches its destination in 6 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 7 : 3 , b ) 5 : 7 , c ) 9 : 7 , d ) 3 : 5 , e ) 11 : 6
Rationale: "sol . distance travelled by car a = 36 × 10 = 350 km distance travelled by car b = 25 × 6 = 150 km ratio = 350 / 150 = 7 : 3 a"
Answer: a
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . how many workers are there in the workshop ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "explanation : let the number of workers = x given that average salary of all the workers = rs . 8000 then , total salary of all workers = 8000 x given that average salary of 7 technicians is rs . 12000 = > total salary of 7 technicians = 7 × 12000 = 84000 count of the rest of the employees = ( x - 7 ) average salary of the rest of the employees = rs . 6000 total salary of the rest of the employees = ( x - 7 ) ( 6000 ) 8000 x = 84000 + ( x - 7 ) ( 6000 ) = > 8 x = 84 + ( x - 7 ) ( 6 ) = > 8 x = 84 + 6 x - 42 = > 2 x = 42 = > x = 42 / 2 = 21 answer : option a"
Answer: a
Problem: a 180 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other train ?
Options: a ) 320 meter , b ) 225 meter , c ) 230 meter , d ) 235 meter , e ) none of these
Rationale: "explanation : as trains are running in opposite directions so their relative speed will get added so , relative speed = 120 + 80 = 200 kmph = 200 * ( 5 / 18 ) = 500 / 9 m / sec let the length of other train is x meter then x + 180 / 9 = 500 / 9 = > x + 180 = 500 = > x = 320 so the length of the train is 320 meters option a"
Answer: a
Problem: 40 liters of a mixture is created by mixing liquid p and liquid q in the ratio 5 : 3 . how many liters of liquid q must be added to make the ratio 5 : 6 ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
Rationale: "let x be the amount of liquid q to be added . ( 3 / 8 ) * 40 + x = ( 6 / 11 ) * ( 40 + x ) 1320 + 88 x = 1920 + 48 x 40 x = 600 x = 15 the answer is e ."
Answer: e
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 100 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 11 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 86 95 11 ways . . 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 $ 500 more than d , what is d ' s share ?
Options: a ) $ 1000 , b ) $ 1200 , c ) $ 1500 , d ) $ 1800 , e ) $ 2000
Rationale: let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x respectively . then , 4 x - 3 x = 500 x = $ 500 d ' s share = 3 x = 3 * $ 500 = $ 1500 the answer is c .
Answer: c
Problem: what is 2 2 / 3 - 1 1 / 4 divided by 1 / 2 - 1 / 5 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 6 , d ) 17 / 4 , e ) 85 / 18
Rationale: 2 2 / 3 - 1 1 / 4 = 8 / 3 - 5 / 4 = ( 32 - 15 ) / 12 = 17 / 12 1 / 2 - 1 / 5 = ( 5 - 2 ) / 10 = 3 / 10 so 17 / 12 / 3 / 10 = 17 / 12 * 10 / 3 = 85 / 18 answer - e
Answer: e
Problem: mohit sold an article for $ 24000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 20000 , c ) 15000 , d ) 18000 , e ) 17000
Rationale: let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 20000 - 10 / 100 ( 20000 ) = 20000 - 2000 = $ 21600 = > 1.08 x = 21600 = > x = 20000 b
Answer: b
Problem: what is the greatest positive integer x such that 4 ^ x is a factor of 64 ^ 10 ?
Options: a ) 5 , b ) 9 , c ) 10 , d ) 20 , e ) 30
Rationale: "64 ^ 10 = ( 4 ^ 3 ) ^ 10 = 4 ^ 30 answer : e"
Answer: e
Problem: 9.009 / 2.002 =
Options: a ) 4.05 , b ) 4.50045 , c ) 4.501 , d ) 4.5045 , e ) 4.5
Rationale: "9.009 / 2.002 = 9009 / 2002 = 9 ( 1001 ) / 2 ( 1001 ) = 9 / 2 = 4.5 the answer is e ."
Answer: e
Problem: if 45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 , then * is equal to :
Options: a ) - 29 , b ) - 19 , c ) 20 , d ) 29 , e ) 39
Rationale: "45 - [ 28 - { 37 - ( 15 - * ) } ] = 59 = > 45 - [ 28 - { 37 - 15 + * } ] = 59 45 - [ 28 - 37 + 15 - * ] = 59 = > 45 [ 43 - 37 - * ] = 59 45 - [ 6 - * ] = 59 = > 45 - 6 + * = 59 39 + * = 59 = > * = 59 - 39 = 20 answer : c"
Answer: c
Problem: a marketing firm determined that , of 200 households surveyed , 80 used neither brand w nor brand b soap , 60 used only brand w soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap w and soap b ( d ) 40
Answer: d
Problem: if the wheel is 42 cm then the number of revolutions to cover a distance of 1056 cm is ?
Options: a ) 18 , b ) 4 , c ) 6 , d ) 8 , e ) 19
Rationale: "2 * 22 / 7 * 42 * x = 1056 = > x = 4 answer : b"
Answer: b
Problem: find the total number of prime factors in the expression ( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 .
Options: a ) 22 , b ) 29 , c ) 19 , d ) 5 , e ) 2
Rationale: "( 4 ) 11 x ( 7 ) 5 x ( 11 ) 2 = ( 2 x 2 ) 11 x ( 7 ) 5 x ( 11 ) 2 = 211 x 211 x 75 x 112 = 222 x 75 x 112 total number of prime factors = ( 22 + 5 + 2 ) = 29 . answer b 29"
Answer: b
Problem: the average salary of workers in an industry is rs . 300 the average salary of technicians being rs . 400 and that of non - technicians being rs . 125 . what is the total number of workers ?
Options: a ) 230 , b ) 234 , c ) 250 , d ) 547 , e ) 484
Rationale: 400 125 \ / 300 / \ 175 100 7 : 4 7 - > 150 11 - > ? = > 234 answer : b
Answer: b
Problem: if n is a natural number , t hen 6 n ^ 2 + 6 n is always divisible by ?
Options: a ) 6 only , b ) 6 and 12 , c ) 12 only , d ) 18 only , e ) 20 only
Rationale: "6 n ^ 2 + 6 n = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer is b"
Answer: b
Problem: a man buys 10 lts of liquid which contains 20 % of the liquid and the rest is water . he then mixes it with 15 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 74 , b ) 84 , c ) 94 , d ) 49 , e ) 47
Rationale: "20 % in 10 lts is 2 . so water = 10 - 2 = 8 lts . 30 % of 15 lts = 4.5 . so water in 2 nd mixture = 15 - 4.5 = 10.5 lts . now total quantity = 10 + 15 = 25 lts . total water in it will be 8 + 10.5 = 18.5 lts . % of water = ( 100 * 18.5 ) / 25 = 74 answer : a"
Answer: a
Problem: a man can buy a new house in 4 years with all of his earnings . but he spend the same amount in household expenses in 8 years and for savings in 12 years . how many time needed for buying the house ?
Options: a ) 12 , b ) 20 , c ) 30 , d ) 15 , e ) 24
Rationale: his savings in 1 year = 1 / 4 - ( 1 / 8 + 1 / 12 ) = 1 / 24 he can buy a new house in 24 years answer : e
Answer: e
Problem: a man can do a piece of work in 6 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 5 1 / 2 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 6 = 1 / 6 son alone can do the work in 6 days = 6 days answer is d"
Answer: d
Problem: what is the least whole number that should be added to 784839 if it is to be divisible by 10 ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 6
Rationale: "a number is divisible by 10 if the last digit is 0 . here , 784839 = 9 , ( last digit is not 0 . 1 must be added to 784839 to make it divisible by 10 c"
Answer: c
Problem: there are 12 slate rocks , 16 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 3 / 32 , b ) 7 / 64 , c ) 11 / 105 , d ) 15 / 127 , e ) 19 / 134
Rationale: 12 / 36 * 11 / 35 = 11 / 105 the answer is c .
Answer: c
Problem: two train 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 80 sec , b ) 252 sec , c ) 320 sec , d ) 330 sec , e ) none
Rationale: sol . relative speed = ( 45 - 40 ) kmph = 5 kmph = [ 5 * 5 / 18 ] m / sec = 25 / 18 m / sec . total distance covered = sum of lengths of trains = 350 m . ∴ time taken = [ 350 * 18 / 25 ] sec = 252 sec . answer b
Answer: b
Problem: a can do a work in 4 days . b can do the same work in 12 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 6
Rationale: a rate = 1 / 4 b rate = 1 / 16 ( a + b ) rate = ( 1 / 4 ) + ( 1 / 12 ) = 1 / 3 a & b finish the work in 3 days correct option is a
Answer: a
Problem: how many positive integers less than 254 are multiple of 4 but not multiples of 6 ?
Options: a ) 20 , b ) 31 , c ) 42 , d ) 43 , e ) 64
Rationale: "252 / 4 = 63 multiples of 4 which are a multiple of 6 will be of the form 2 * 2 * 3 = 12 n where n > 0 240 / 12 = 20 63 - 20 = 43 answer : d"
Answer: d
Problem: how many 4 - digit numerals begin with a digit that represents a prime and end with a digit that represents a prime number ?
Options: a ) 1600 , b ) 80 , c ) 160 , d ) 180 , e ) 240
Rationale: "prime digits 2 , 3,5 and 7 . three digit numbers _ _ _ 1 st place can be filled in 4 ways 2 nd place can be filled in 10 ways 3 rd place can be filled in 10 ways 3 rd place can be filled in 4 ways total = 4 * 10 * 10 * 4 = 1600 ans : a"
Answer: a
Problem: a courtyard is 28 meter long and 13 meter board is to be paved with bricks of dimensions 22 cm by 12 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 14567 , c ) 13787 , d ) 13456 , e ) none of these
Rationale: explanation : number of bricks = courtyard area / 1 brick area = ( 2800 ã — 1300 / 22 ã — 12 ) = 13787 option c
Answer: c
Problem: andy solves problems 80 to 125 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 52 , c ) 51 , d ) 46 , e ) 49
Rationale: "125 - 80 + 1 = 52 ' d ' is the answer"
Answer: d
Problem: set a of 8 positive integers may have the same element and have 39 . and set b of 8 positive integers must have different elements and have 39 . when m and n are the greatest possible differences between 39 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 23 , c ) 21 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 39 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 32 and 39 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 11 . so , 32 - 11 = 21 . the correct answer is c .
Answer: c
Problem: find the value of 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 900 , d ) 1200 , e ) none
Rationale: "answer 1.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 1.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 1.5 x 4 x 4 x 50 = 1200 correct option : d"
Answer: d
Problem: the length of one pair of opposite sides of a square is increased by 5 cm on each side the ratio of the length and the breadth of the newly formed rectangle becomes 3 : 2 . what is the area of the original square ?
Options: a ) 25 sq . cm
b ) 81 sq . cm
c ) 120 sq . cm
d ) 225 sq . cm
e ) none of these
Rationale: let original length of each side = x cm . then , its area = ( x 2 ) cm 2 . length of rectangle formed = ( x + 5 ) cm and its breadth = x cm . ∴ x + 5 / x = 3 / 2 ⇔ 2 x + 10 = 3 x ⇔ x = 10 ∴ original length of each side = 10 cm and its area = 100 cm 2 answer e
Answer: e
Problem: a shopkeeper sold an article at $ 100 with 20 % profit . then find its cost price ?
Options: a ) $ 120 , b ) $ 100 , c ) $ 91 , d ) $ 83 , e ) $ 69
Rationale: "cost price = selling price * 100 / ( 100 + profit ) c . p . = 100 * 100 / 120 = $ 83 ( approximately ) answer is d"
Answer: d
Problem: the compound ratio of 1 : 3 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 9 , b ) 1 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 1 : 4
Rationale: "1 / 3 * 3 / 2 * 4 / 5 = 2 / 5 = 2 : 5 answer : d"
Answer: d
Problem: a number increased by 10 % gives 550 . the number is
Options: a ) 250 , b ) 500 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 10 % = 110 % 110 % - - - - - - - > 550 ( 110 × 5 = 550 ) 100 % - - - - - - - > 500 ( 100 × 5 = 500 ) b )"
Answer: b
Problem: by how much does the larger root of the equation 2 z ^ 2 + 5 z = 12 exceed the smaller root ?
Options: a ) 5 / 2 , b ) 10 / 3 , c ) 7 / 2 , d ) 14 / 3 , e ) 11 / 2
Rationale: "for 2 z ^ 2 + 5 z = 12 roots are [ - 5 + sqrt ( 25 + 96 ) ] / 4 or [ - 5 - sqrt ( 25 + 96 ) ] / 4 = 1.5 or - 4 hence larger root 1.5 is 1.5 - ( - 4 ) = 5.5 = 11 / 2 greater than smaller root ( - 4 ) . hence option ( e ) ."
Answer: e
Problem: . star question : if f ( 1 ) = 4 and f ( x + y ) = f ( x ) + f ( y ) + 7 xy + 4 , then f ( 2 ) + f ( 5 ) = ?
Options: a ) 125 , b ) 977 , c ) 289 , d ) 1077 , e ) 111
Rationale: let x = 1 and y = 1 f ( 1 + 1 ) = f ( 1 ) + f ( 1 ) + 7 x 1 x 1 + 4 ⇒ ⇒ f ( 2 ) = 19 let x = 2 and y = 2 f ( 2 + 2 ) = 19 + 19 + 7 x 2 x 2 + 4 ⇒ ⇒ f ( 4 ) = 70 let x = 1 and y = 4 f ( 1 + 4 ) = 4 + 70 + 28 + 4 = 106 f ( 2 ) + f ( 5 ) = 125 answer : a
Answer: a
Problem: a man saves 30 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 30 % , he is only able to save rs . 300 per month . what is his monthly salary ?
Options: a ) rs . 4000 , b ) rs . 3750 , c ) rs . 5000 , d ) rs . 5500 , e ) rs . 6500
Rationale: "income = rs . 100 expenditure = rs . 70 savings = rs . 30 present expenditure 70 + 70 * ( 30 / 100 ) = rs . 91 present savings = 100 – 91 = rs . 8 if savings is rs . 8 , salary = rs . 100 if savings is rs . 300 , salary = 100 / 8 * 300 = 3750 answer : b"
Answer: b
Problem: the probability that a man will be alive for 10 more yrs is 1 / 3 & the probability that his wife will alive for 10 more yrs is 5 / 8 . the probability that none of them will be alive for 10 more yrs , is
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 3 , d ) 3 / 4 , e ) 2
Rationale: "sol . required probability = pg . ) x p ( b ) = ( 1 — d x ( 1 — i ) = : x 1 = 1 / 4 ans . ( b )"
Answer: b
Problem: the average ( arithmetic mean ) of 20 , 40 , and 60 is 8 more than the average of 10 , 70 , and what number ?
Options: a ) 16 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 8 = 32 sum of second list = 32 * 3 = 96 therefore the number = 96 - 80 = 16 answer : a"
Answer: a
Problem: for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 1 * / 4 * ?
Options: a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
Rationale: "when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . based on this definition . . . . if . . . . k = 2 k * = ( 1 / 1 ) ( 1 / 2 ) = 1 / 2 if . . . . k = 3 k * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) = 1 / 6 we ' re asked to find the value of 5 * / 4 * now that we know how the symbol ' works ' , solving this problem should n ' t be too difficult . you can actually choose to do the math in a couple of different ways . . . . 5 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) do n ' t calculate this just yet though . . . . since we ' re dividing by 4 * , many of those fractions will ' cancel out . ' 4 * = ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) we ' re looking for the value of : ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) ( 1 / 5 ) / ( 1 / 1 ) ( 1 / 2 ) ( 1 / 3 ) ( 1 / 4 ) since the first four fraction in the numerator and denominator cancel out , we ' re left with just one fraction : 4 / 5 a"
Answer: a
Problem: working at constant rate , pump x pumped out half of the water in a flooded basement in 2 hours . the pump y was started and the two pumps , working independently at their respective constant rates , pumped out rest of the water in 3 hours . how many hours would it have taken pump y , operating alone at its own constant rate , to pump out all of the water that was pumped out of the basement ?
Options: a ) a . 10 , b ) b . 12 , c ) c . 14 , d ) d . 18 , e ) e . 24
Rationale: rate of x = 1 / 8 rate of x + y = 1 / 6 rate of y = 1 / 6 - 1 / 8 = 1 / 24 18 hours d
Answer: d
Problem: a cement mixture is composed of 3 elements . by weight , 1 / 5 of the mixture is sand , 3 / 4 of the mixture is water , and the remaining 6 pounds of the mixture is gravel . what is the weight of the entire mixture in pounds ?
Options: a ) 100 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "let the total weight be x . sand content = ( 1 / 5 ) x water content = ( 3 / 4 ) x gravel = x - ( 1 / 5 ) x - ( 3 / 4 ) x = ( 1 / 20 ) x = 6 x = 120 then answer will be b = 120"
Answer: b
Problem: for each month of a given year except december , a worker earned the same monthly salary and donated one - tenth of that salary to charity . in december , the worker earned n times his usual monthly salary and donated one - fifth of his earnings to charity . if the worker ' s charitable contributions totaled one - nineth of his earnings for the entire year , what is the value of n ?
Options: a ) 8 / 5 , b ) 5 / 2 , c ) 3 , d ) 11 / 3 , e ) 22
Rationale: let monthly salary for each of the 11 months except december was x , then 11 x * 1 / 10 + nx * 1 / 5 = 1 / 9 ( 11 x + nx ) ; 11 / 10 + n / 5 = 1 / 9 ( 11 + n ) = > 11 + 2 n / 10 = 11 + n / 9 = > 66 + 12 n = 110 + 10 n = > 2 n = 44 n = 22 answer : e
Answer: e
Problem: ajay can walk 3 km in 1 hour . in how many hours he can walk 50 km ?
Options: a ) 5 hrs , b ) 16.6 hrs , c ) 15.6 hrs , d ) 20.4 hrs , e ) 30 hrs
Rationale: "1 hour he walk 3 km he walk 50 km in = 50 / 3 * 1 = 16.6 hours answer is b"
Answer: b
Problem: the income of a broker remains unchanged though the rate of commission is increased from 4 % to 5 % . the percentage of slump in business is ?
Options: a ) 8 % , b ) 1 % , c ) 20 % , d ) 80 % , e ) none
Rationale: answer let the business value change from a to b . then , 4 % of a = 5 % of b ⇒ 4 a / 100 = 5 b / 100 ⇒ b = 4 a / 5 ∴ change in business = ( a - 4 a / 5 ) = a / 5 percentage slump in business = { ( a / 5 ) / a } x 100 % = 20 % correct option : c
Answer: c
Problem: find 44 % of 240
Options: a ) 96 , b ) 105.6 , c ) 86 , d ) 74 , e ) 110
Rationale: "we know that r % of m is equal to r / 100 × m . so , we have 44 % of 240 44 / 100 × 240 = 105.6 answer : b"
Answer: b
Problem: there were two candidates in an election . winner candidate received 62 % of votes and won the election by 324 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 837 , c ) 912 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 324 62 % - - - - - - - - ? = > 837 answer : b"
Answer: b
Problem: r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ?
Options: a ) none , b ) three , c ) four , d ) five , e ) seven
Rationale: "r is the set of positive even integers less than 51 , and s is the set of the squares of the integers in r . how many elements does the intersection of r and s contain ? r = 2,4 , 6,8 , 10,12 . . . s = 4,16 , 36,64 . . . numbers : 4 , 16 , and 36 are even integers ( less than 51 ) that are in both sets . solution : three answer : b"
Answer: b
Problem: a die is rolled twice . what is the probability of getting a sum equal to 9 ?
Options: a ) 2 / 9 , b ) 5 / 7 , c ) 1 / 7 , d ) 1 / 9 , e ) 3 / 7
Rationale: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible when a die is rolled twice , n ( s ) = 6 × 6 = 36 e = getting a sum of 9 when the two dice fall = { ( 3 , 6 ) , { 4 , 5 } , { 5 , 4 } , ( 6 , 3 ) } hence , n ( e ) = 4 p ( e ) = n ( e ) / n ( s ) = 4 / 36 = 1 / 9 answer : option d
Answer: d
Problem: if xy > 0 , 1 / x + 1 / y = 2 , and 1 / xy = 8 , then ( x + y ) / 4 = ?
Options: a ) 1 / 16 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 2 canbe solved as { ( x + y ) / xy } = 8 . substituting for 1 / xy = 8 , we get x + y = 2 / 8 = = > ( x + y ) / 4 = 2 / ( 8 * 4 ) = 1 / 16 . a"
Answer: a
Problem: the difference in compound interest earned on a deposit ( compounded annually ) in year 1 and year 2 is $ 40 . had the interest rate been 3 times its present value , the difference a would have been how much ?
Options: a ) 40 / 3 , b ) 40 , c ) 120 , d ) 360 , e ) 420
Rationale: case 1 : deposit = $ x ; rate of increase = r . interest yearned in 1 year = xr . deposit in 1 year = x + xr . interest yearned in 2 year = ( x + xr ) r . the difference a = ( x + xr ) r - xr = xr ^ 2 = 40 . case 2 : deposit = $ x ; rate of increase = 3 r . interest yearned in 1 year = x ( 3 r ) . deposit in 1 year = x + 3 xr . interest yearned in 2 year = ( x + 3 xr ) 3 r . the difference = ( x + 3 xr ) 3 r - 3 xr = 9 xr ^ 2 . since from case 1 we know that xr ^ 2 = 40 , then 9 xr ^ 2 = 9 * 40 = 360 . answer : d .
Answer: d
Problem: an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?
Options: a ) 1320 , b ) 1196 , c ) 1210 , d ) 1440 , e ) 1050
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 3120 = rs . 1440 answer : d"
Answer: d
Problem: a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number k is
Options: a ) 74 , b ) k = 75 , c ) k = 175 , d ) k = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Problem: a circular road runs round a circular ground . if the difference between the circumferences of the outer circle and inner circle is 66 metres , the width of the road is :
Options: a ) 5.25 m
b ) 7 m
c ) 10.5 m
d ) 21 m
e ) 22 m
Rationale: 2 π ( r - r ) = 60 = > 2 * 22 / 7 * ( r - r ) = 60 . therefore , ( r - r ) = ( 66 * 7 / 44 ) = 10.5 m answer : c
Answer: c
Problem: find 12 × × 19
Options: a ) 238 , b ) 228 , c ) 208 , d ) 277 , e ) 101
Rationale: "mentally imagine this number as ( 10 + 2 ) × × 19 = 190 + 38 = 228 . answer : b"
Answer: b
Problem: how many integers between 334,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,239
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 334,700 and 458,600 is 458,600 - 334,700 = 123,900 - one number per each hundred gives 123,900 / 100 = 1,239 numbers . answer : e ."
Answer: e
Problem: if number divisible by both 3 and 2 , then the same number divisible by which number ?
Options: a ) 4 , b ) 5 , c ) 8 , d ) 6 , e ) 9
Rationale: obviously , the answer is 6 option d
Answer: d
Problem: the radii of two cones are in ratio 2 : 1 , their volumes are equal . find the ratio of their heights .
Options: a ) 1 : 4
b ) 1 : 3
c ) 1 : 2
d ) 1 : 5
e ) none of these
Rationale: explanation : let their radii be 2 x , x and their heights be h and h resp . then , volume of cone = 1 / 3 π r 2 h 1 / 3 ∗ π ∗ ( 2 x ) 2 ∗ h / 1 / 3 ∗ π ∗ x 2 ∗ h = > hh = 14 = > h : h = 1 : 4 option a
Answer: a
Problem: the average of first 50 non - zero positive integers is
Options: a ) 11.5 , b ) 25.5 , c ) 22 , d ) 25 , e ) 27
Rationale: "explanation : sum of first n non - zero positive integers n ( n + 1 ) / 2 so , average of first n non - zero positive integers n ( n + 1 ) / 2 n = ( n + 1 ) / 2 = > ( 50 + 1 ) / 2 = 25.5 answer : b"
Answer: b
Problem: excluding stoppages , the speed of the bus is 54 kms / hr and with stoppages , it is 45 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 20
Rationale: by including stoppages , bus will cover 9 km less . . ( 54 km - 45 km = 9 km ) excluding stoppages , x = 54 kmph including stoppages , y = 45 kmph difference , z = 9 km time taken to cover that 9 km ( bus stops per hour ( 60 minutes ) ) = z / x ( 60 minutes ) = 9 / 54 ( 60 ) = 1 / 6 ( 60 ) = 10 minutes . answer : b
Answer: b
Problem: sanoop bought 8 t - shirts at an average price ( arithmetic mean ) of rs . 526 . if sanoop returned 1 t - shirts to the retailer , and the average price of the remaining t - shirts was rs . 505 , then what is the average price , of the 3 returned t - shirts ?
Options: a ) 560 , b ) 561 , c ) 562 , d ) 563 , e ) 673
Rationale: total price of 8 t - shirts = 8 * 526 = 4208 total price of 7 t - shirts = 7 * 505 = 3535 total price of 1 t - shirts = 4208 - 3535 = 673 average price of 3 t - shirts = 673 correct option answer : e
Answer: e
Problem: in how many q ways can 5 people from a group of 6 people be seated around a circular table
Options: a ) 56
b ) 80
c ) 100
d ) 120
e ) 144
Rationale: q = 6 c 5 * ( 5 - 1 ) ! ( select 5 out of 6 and arrange them in circular manner ) = 6 * 4 ! = 6 * 24 = 144 answer - e
Answer: e
Problem: a number is doubled and 6 is added . if resultant is trebled , it becomes 72 . what is that number
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 6 ) = 72 = > 2 x + 6 = 24 = > x = 9 option c"
Answer: c
Problem: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 5.3 ) + e ( – 6.7 ) + o ( – 3.3 ) + e ( 4.7 ) is :
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) 1 , e ) 3
Rationale: "o ( 5.3 ) + e ( – 6.7 ) + o ( – 3.3 ) + e ( 4.7 ) = 7 + ( - 6 ) + ( - 5 ) + 4 = 0 the answer is c ."
Answer: c
Problem: i gain 70 paise on rs . 70 . my gain percent is :
Options: a ) 0.1 % , b ) 1 % , c ) 7 % , d ) 10 % , e ) noneof these
Rationale: solution 11.1 gain % = ( 0.70 / 70 x 100 ) % = 1 % . answer b
Answer: b
Problem: a fruit seller had some oranges . he sells 20 % oranges and still has 400 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 500 , e ) none of these
Rationale: "explanation : he sells 20 % of oranges and still there are 400 oranges remaining = > 80 % of oranges = 400 ⇒ ( 80 × total oranges ) / 100 = 400 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d"
Answer: d
Problem: in a group of 800 people , 3 / 5 play at least one instrument , 96 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 12 / 25 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 5
Rationale: p ( playing 2 or more instruments ) = 96 / 800 = 3 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 3 / 5 - 3 / 25 = 12 / 25 . answer b .
Answer: b
Problem: the ratio of the volumes of two cubes is 1728 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 12 : 18 , b ) 144 : 169 , c ) 44 : 22 , d ) 28 : 144 , e ) 96 : 12
Rationale: "ratio of the sides = â ³ â ˆ š 1728 : â ³ â ˆ š 2197 = 12 : 13 ratio of surface areas = 144 : 169 answer : b"
Answer: b
Problem: in an election between two candidates , the first candidate got 60 % of the votes and the second candidate got 240 votes . what was the total number of votes ?
Options: a ) 400 , b ) 600 , c ) 800 , d ) 1000 , e ) 1200
Rationale: let v be the total number of votes . 0.4 v = 240 v = 600 the answer is b .
Answer: b
Problem: a man sitting in a train which is travelling at 50 kmph observes that a goods train travelling in a opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed .
Options: a ) 58 , b ) 62 , c ) 74 , d ) 81 , e ) 65
Rationale: "relative speed = ( 280 / 9 ) m / s = ( 280 / 9 ) * ( 18 / 5 ) = 112 kmph speed of goods train = 112 - 50 = 62 kmph answer is b"
Answer: b
Problem: what is the smallest 6 digit number exactly divisible by 111 ?
Options: a ) 100010 , b ) 100012 , c ) 100011 , d ) 100013 , e ) 120012
Rationale: "smallest 6 digit number = 100000 100000 / 111 = 900 , remainder = 100 . hence 11 more should be added to 100000 to get the smallest 6 digit number exactly divisible by 111 = > smallest 6 digit number exactly divisible by 111 = 100000 + 11 = 100011 answer is c"
Answer: c
Problem: a bag contains 4 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 17 / 33
Rationale: "drawing two balls of same color from four green balls can be done in 4 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 4 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 17 / 33 answer : e"
Answer: e
Problem: jar x is 1 / 2 full of water . jar y , which has half the capacity of jar x , is 1 / 2 full of water . if the water in jar y is poured into jar x , then jar x will be filled to what fraction of its capacity ?
Options: a ) 3 / 4 , b ) 5 / 6 , c ) 7 / 8 , d ) 5 / 8 , e ) 7 / 12
Rationale: let p be the capacity of jar x . the amount of water in jar y is 1 / 2 * p / 2 = p / 4 then the total amount in jar x is p / 2 + p / 4 = 3 p / 4 the answer is a .
Answer: a
Problem: if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 6 strokes ?
Options: a ) 63 / 64 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 left after 4 th stroke = 1 / 2 * 1 / 8 = 1 / 16 left after 5 th stroke = 1 / 2 * 1 / 16 = 1 / 32 left after 6 th stroke = 1 / 2 * 1 / 32 = 1 / 64 so removed = 1 - 1 / 64 = 63 / 64"
Answer: a
Problem: a certain ball team has an equal number of right - and left - handed players . on a certain day , one - third of the players were absent from practice . of the players at practice that day , one - third were left handed . what is the ratio of the number of right - handed players who were not at practice that day to the number of lefthanded players who were not at practice ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 5 / 7 , d ) 7 / 5 , e ) 3 / 2
Rationale: say the total number of players is 18 , 9 right - handed and 9 left - handed . on a certain day , two - thirds of the players were absent from practice - - > 6 absent and 12 present . of the players at practice that day , one - third were left - handed - - > 12 * 1 / 3 = 4 were left - handed and 8 right - handed . the number of right - handed players who were not at practice that day is 9 - 8 = 1 . the number of left - handed players who were not at practice that days is 9 - 4 = 5 . the ratio = 1 / 5 . answer : a .
Answer: a
Problem: a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 4 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 12 , e ) 16
Rationale: "d = s * t given condition is for up the mountain hikers takes 4 miles per day and total 2 days . . . miles = 8 miles . . . for down speed they take = 3 / 2 ( 4 ) = 6 miles per day and for the same 2 days . . . miles = 12 miles . . answer : option d is correct answer"
Answer: d
Problem: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 3 per page each time a page is revised . if a certain manuscript has 200 pages , of which 80 were revised only once , 20 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1360 , b ) $ 1620 , c ) $ 1650 , d ) $ 680 , e ) $ 770
Rationale: "for 200 - 80 - 20 = 100 pages only cost is 5 $ per page for the first time page is typed - 100 * 5 = 500 $ ; for 80 pages the cost is : first time 5 $ + 3 $ of the first revision - 80 * ( 5 + 3 ) = 640 $ ; for 20 pages the cost is : first time 5 $ + 3 $ of the first revision + 3 $ of the second revision - 20 ( 5 + 3 + 3 ) = 220 $ ; total : 500 + 640 + 220 = 1360 $ . answer : a ."
Answer: a
Problem: the line y = 5 x / 3 + b goes through the point ( 7 , – 1 ) . what is the value of b ?
Options: a ) 3 , b ) – 5 / 3 , c ) – 7 / 5 , d ) 16 / 3 , e ) – 38 / 3
Rationale: “ finding the equation ” procedure . plug ( x , y ) = ( 7 , – 1 ) into this equation : { - 1 } = { { 5 ( 7 ) } / 3 } + b = { 35 / 3 } + b b = { - 35 / 3 } - 1 = { - 35 / 3 } - { 3 / 3 } = - { 38 / 3 } answer = e
Answer: e
Problem: the average monthly salary of 20 employees in an organisation is rs . 1700 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 3800 , c ) rs . 1288 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1800 * 21 - 1700 * 20 ) = rs . 3800 . answer : b"
Answer: b
Problem: on dividing 17698 by a certain number , we get 89 as quotient and 14 as remainder . what is the divisor ?
Options: a ) 199 , b ) 154 , c ) 852 , d ) 741 , e ) 785
Rationale: "divisor * quotient + remainder = dividend divisor = ( dividend ) - ( remainder ) / quotient ( 17698 - 14 ) / 89 = 199 answer ( a )"
Answer: a
Problem: two trains start from same place at same time at right angles to each other . their speeds are 36 km / hr and 48 km / hr respectively . after 30 seconds the distance between them will be ?
Options: a ) 270 mts , b ) 190 mts , c ) 100 mts , d ) 500 mts , e ) 110 mts
Rationale: explanation : using pythagarous theorem , distance travelled by first train = 36 x 5 / 18 x 30 = 300 m distance travelled by second train = 48 x 5 / 18 x 30 = 400 m so distance between them = â ˆ š ( 90000 + 160000 ) = â ˆ š 250000 = 500 mts . answer : d
Answer: d