regisss/math_qa huggingface dataset:
Problem: a can do a piece of work in 12 days and b alone can do it in 14 days . how much time will both take to finish the work ?
Options: a ) a ) 3.2222 , b ) b ) 5 , c ) c ) 6.46 , d ) d ) 8.3333 , e ) e ) 9
Rationale: this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 12 x 14 / ( 12 + 14 ) = 150 / 25 = 6.46 days answer : c
Answer: c
Problem: a jar full of whisky contains 40 % alcohol . a part of this whisky is replaced by another containg 19 % alcohol and now the percentage of alcohol was found to be 26 % . what quantity of whisky is replaced ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 4 / 5
Rationale: let us assume the total original amount of whiskey = 10 ml - - - > 4 ml alcohol and 6 ml non - alcohol . let x ml be the amount removed - - - > total alcohol left = 4 - 0.4 x new quantity of whiskey added = x ml out of which 0.19 is the alcohol . thus , the final quantity of alcohol = 4 - 0.4 x + 0.19 x - - - - > ( 4 - 0.21 x ) / 10 = 0.26 - - - > x = 20 / 3 ml . per the question , you need to find the x ml removed as a ratio of the initial volume - - - > ( 20 / 3 ) / 10 = 2 / 3 . hence , b is the correct answer .
Answer: b
Problem: two numbers are in the ratio 3 : 4 . if their l . c . m . is 96 . what is sum of the numbers ?
Options: a ) 48 , b ) 56 , c ) 76 , d ) 84 , e ) 85
Rationale: "explanation : let the numbers be 3 x and 4 x lcm of 3 x and 4 x = 12 x ( since lcm of 3 and 4 is 12 . hence lcm of 3 x and 4 x is 12 x ) given that lcm of 3 x and 4 x is 96 = > 12 x = 96 = > x = 96 / 12 = 8 sum of the numbers = 3 x + 4 x = 7 x = 7 x 8 = 56 answer : option b"
Answer: b
Problem: x ^ y + y ^ x = 2408 find the values of x ?
Options: a ) 2407 , b ) 2408 , c ) 2409 , d ) 2405 , e ) 32
Rationale: 2407 ^ 1 + 1 ^ 2407 = 2408 answer : a
Answer: a
Problem: the speed of a boat in still water in 20 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 12 minutes is :
Options: a ) 10.6 , b ) 5.2 , c ) 10.8 , d ) 5.4 , e ) 5.0
Rationale: "speed downstream = ( 20 + 6 ) = 26 kmph time = 24 minutes = 12 / 60 hour = 1 / 5 hour distance travelled = time × speed = 1 / 5 × 26 = 5.20 km answer is b ."
Answer: b
Problem: 15 litres of mixture contains 20 % alcohol and the rest water . if 5 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
Options: a ) 16.67 % , b ) 23 % , c ) 15 % , d ) 19.75 % , e ) 21.23 %
Rationale: "alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 5 = 20 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 20 = 15 % answer is c"
Answer: c
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1111 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 66 , c ) 77 , d ) 50 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1111 96 + 225 + 490 + 6 x = 1111 6 x = 300 = > x = 50 . answer : d"
Answer: d
Problem: the average of 3 numbers is 48 . the average of two of these numbers is 56 % . what is the third number ?
Options: a ) 64 , b ) 32 , c ) 46 , d ) 75 , e ) 47
Rationale: b 32 the total of three numbers must be 48 x 3 = 144 . the total of two numbers must be 56 x 2 = 112 . therefore , 144 - 112 = 32 .
Answer: b
Problem: by selling an article for $ 180 , a person gains $ 30 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 180 gain = $ 30 c . p . = 180 - 30 = 150 gain % = 30 / 150 * 100 = 20 % answer is d"
Answer: d
Problem: two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 2 litres from vessel p is mixed with 6 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
Options: a ) 13 : 1 , b ) 13 : 3 , c ) 13 : 8 , d ) 13 : 5 , e ) 13 : 2
Rationale: quantity of alcohol in vessel p = 62.5 / 100 * 2 = 5 / 4 litres quantity of alcohol in vessel q = 87.5 / 100 * 6 = 21 / 4 litres quantity of alcohol in the mixture formed = 5 / 4 + 21 / 4 = 13 / 2 = 6.5 litres as 8 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 6.5 : 1.5 = 13 : 3 . answer : b
Answer: b
Problem: what is 2 / 5 of 5 / 9 of 1 / 2 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 9 / 16 , d ) 5 / 8 , e ) 16 / 9
Rationale: "2 / 5 * 5 / 9 * 1 / 2 = 1 / 9 answer : b"
Answer: b
Problem: john completes a piece of work in 10 days , rose completes the same work in 40 days . if both of them work together , then the number of days required to complete the work is ?
Options: a ) 5 days , b ) 8 days , c ) 10 days , d ) 12 days , e ) 14 days
Rationale: "if a can complete a work in x days and b can complete the same work in y days , then , both of them together can complete the work in x y / x + y days . that is , the required no . of days = 10 × 40 / 50 = 8 days b )"
Answer: b
Problem: at a time a , do 20 % less work than b . if a do any work in 15 / 2 hour , then in how many hour b will finish work ?
Options: a ) 5 hour , b ) 11 / 2 hour , c ) 6 hour , d ) 13 / 2 hour , e ) 8 hour
Rationale: let b will finish a work in x hour . then , in x hour a , 80 / 100 = 4 / 5 work do ratio of work done by a and b = inverse ratio of time taken 4 / 5 : 1 = 2 / 15 : 1 / x 4 / 5 * 1 / x = 1 * 2 / 15 = 4 / 5 x = 2 / 15 ; x = 6 . time = 6 hour answer c
Answer: c
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do the same job . how long it take both a & b , working together but independently , to do the same job ?
Options: a ) 20 / 9 , b ) 40 / 9 , c ) 50 / 9 , d ) 60 / 9 , e ) 80 / 9
Rationale: "one day work of a = 1 / 8 one day work of b = 1 / 10 so one day work of a and b together = 1 / 8 + 1 / 10 = 9 / 40 so total days required = 40 / 9 answer : b"
Answer: b
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units z digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : z . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Problem: 106 ã — 106 + 94 ã — 94 = ?
Options: a ) 20072 , b ) 20062 , c ) 10072 , d ) 20172 , e ) 10272
Rationale: "explanation : ( a + b ) 2 + ( a â ˆ ’ b ) 2 = 2 ( a 2 + b 2 ) ( reference : basic algebraic formulas ) 1062 + 942 = ( 100 + 6 ) 2 + ( 100 â ˆ ’ 6 ) 2 = 2 ( 1002 + 62 ) = 2 ( 10000 + 36 ) = 20072 . answer : option a"
Answer: a
Problem: in an office , totally there are 6400 employees and 65 % of the total employees are males . 25 % of the males in the office are at - least 50 years old . find the number of males aged below 50 years ?
Options: a ) 1040 , b ) 2080 , c ) 3120 , d ) 4160 , e ) none of these
Rationale: "number of male employees = 6400 * 65 / 100 = 4160 required number of male employees who are less than 50 years old = 4160 * ( 100 - 25 ) % = 4160 * 75 / 100 = 3120 . answer : c"
Answer: c
Problem: the ratio of a to b is 4 to 5 , where a and b are positive . if x equals a increased by 75 percent of a , and m equals b decreased by 80 percent of b , what is the value of m / x ?
Options: a ) 1 / 7 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 3 / 2
Rationale: "a / b = 4 / 5 m / x = ( 1 / 5 ) * 5 / ( 7 / 4 ) * 4 = 1 / 7 the answer is a ."
Answer: a
Problem: 9 . the least number which should be added to 28523 so that the sum is exactly divisible by 3 , 5 , 7 and 8 is
Options: a ) 41 , b ) 42 , c ) 32 , d ) 37 , e ) 39
Rationale: lcm of 3 , 5 , 7 and 8 = 840 28523 ÷ 840 = 33 remainder = 803 hence the least number which should be added = 840 - 803 = 37 answer : option d
Answer: d
Problem: find the value of ( 75983 * 75983 - 45983 * 45983 / 30000 )
Options: a ) 129166 , b ) 121696 , c ) 126196 , d ) 121966 , e ) none of them
Rationale: "given expression = ( 75983 ) 2 - ( 45983 ) 2 / ( 75983 - 45983 ) = ( a - b ) 2 / ( a - b ) = ( a + b ) ( a - b ) / ( a - b ) = ( a + b ) = 75983 + 45983 = 121966 answer is d ."
Answer: d
Problem: what is the value of 10 ^ 6 - 6 ^ 4 ?
Options: a ) 9 , 97,111 , b ) 9 , 97,322 , c ) 9 , 98,704 , d ) 9 , 98,851 , e ) 9 , 98,900
Rationale: "as 10 ^ n will always have last digit as 0 and 6 ^ n will always as last digit 6 . . hence difference of such sum should always be ending with 4 and there is only on option . . answer c"
Answer: c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 1250 resolutions ?
Options: a ) 1277 m , b ) 1760 m , c ) 1278 m , d ) 1288 m , e ) 1378 v
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 1250 resolutions . = 1250 * 2 * 22 / 7 * 22.4 = 176000 cm = 1760 m answer : b"
Answer: b
Problem: a man gains 20 % by selling an article for a certain price . if the sells it at double the price , the percentage of profit will be
Options: a ) 740 % , b ) 540 % , c ) 640 % , d ) 140 % , e ) 240 %
Rationale: "explanation : let c . p . = rs . x . then , s . p . = rs . ( 12 % of x ) = rs . 6 x / 5 new s . p . = 2 * 6 x / 5 = rs . 12 x / 5 profit = 12 x / 5 - x = rs . 7 x / 5 profit = 7 x / 5 * 1 / x * 100 = 140 % . answer : d"
Answer: d
Problem: the salary of a worker is first increased by 10 % and afterwards reduced by 10 % . what is the net change in the worker ' s salary ?
Options: a ) 1 % increase , b ) 1 % decrease , c ) 2 % increase , d ) 2 % decrease , e ) no change
Rationale: "let x be the original salary . the final salary is 0.9 ( 1.1 x ) = 0.99 x the answer is b ."
Answer: b
Problem: alok ordered 16 chapatis , 5 plates of rice , 7 plates of mixed vegetable and 6 ice - cream cups . the cost of each chapati is rs . 6 , that of each plate of rice is rs . 45 and that of mixed vegetable is rs . 70 . the amount that alok paid the cashier was rs . 1051 . find the cost of each ice - cream cup ?
Options: a ) 25 , b ) 40 , c ) 77 , d ) 99 , e ) 91
Rationale: "let the cost of each ice - cream cup be rs . x 16 ( 6 ) + 5 ( 45 ) + 7 ( 70 ) + 6 ( x ) = 1051 96 + 225 + 490 + 6 x = 1051 6 x = 240 = > x = 40 . answer : b"
Answer: b
Problem: the cost of painting the 4 walls of a room is rs . 350 . the cost of painting a room 3 times in length , breadth and height will be :
Options: a ) rs . 1050 , b ) rs . 1400 , c ) rs . 3150 , d ) rs . 4200 , e ) none
Rationale: explanation : area of 4 walls of the room = [ 2 ( l + b ) × h ] m 2 area of 4 walls of new room = [ 2 ( 3 l + 3 b ) × 3 h ] m 2 = 9 [ 2 ( l + b ) × h ] m 2 cost of painting the 4 walls of new room = rs . ( 9 × 350 ) = rs . 3150 correct option : c
Answer: c
Problem: a number is doubled and 5 is added . if the resultant is trebled , it becomes 123 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 18 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 123 6 x + 15 = 123 6 x = 108 x = 18 answer : d"
Answer: d
Problem: a certain number when divided by 899 leaves the remainder 63 . find the remainder when the same number is divided by 29 .
Options: a ) 5 , b ) 4 , c ) 1 , d ) 0 , e ) can not be determined
Rationale: "sol . ( a ) number = 899 q + 63 , where q is quotient = 31 × 29 q + ( 58 + 5 ) = 29 [ 31 q + 2 ] + 5 ∴ remainder = 5 answer a"
Answer: a
Problem: kelsey travelled for 10 hours . he covered the first half of the distance at 25 kmph and remaining half of the distance at 40 kmph . find the distance travelled by kelsey ?
Options: a ) 583 km , b ) 400 km , c ) 670 km , d ) 360 km , e ) 234 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 25 + ( x / 2 ) / 40 = 10 = > x / 50 + x / 80 = 10 = > ( 8 x + 5 x ) / 400 = 10 = > x = 400 km answer : b
Answer: b
Problem: a gambler has won 40 % of his 30 poker games for the week so far . if , all of a sudden , his luck changes and he begins winning 80 % of the time , how many more games must he play to end up winning 60 % of all his games for the week ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the number of additional games the gambler needs to play . 0.4 ( 30 ) + 0.8 x = 0.6 ( x + 30 ) 0.2 x = 6 x = 30 the answer is c ."
Answer: c
Problem: lola has $ 240.00 in her checking account . she spent $ 180.00 . what percentage does she have left in her account ?
Options: a ) 75 % , b ) 50 % , c ) 40 % , d ) 55 % , e ) none of these
Rationale: explanation : amount left : 240 - 180 = 60 amount left percentage = ( 60 / 240 x 100 ) % = 25 % answer : e
Answer: e
Problem: the length of the rectangular field is double its width . inside the field there is square shaped pond 5 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 ) 32
c ) 75
d ) 20
e ) 11
Rationale: a / 8 = 5 * 5 = > a = 5 * 5 * 8 x * 2 x = 5 * 5 * 8 x = 10 = > 2 x = 20 answer : d
Answer: d
Problem: if the length of a rectangle is halved and its breadth is tripled , what is the percentage change in its area ?
Options: a ) 30
b ) 40
c ) 50
d ) 60
e ) 70
Rationale: length is halved . i . e . , length is decreased by 50 % breadth is tripled i . e . , breadth is increased by 200 % formula for change in area is : = ( - x + y - xy / 100 ) % = ( − 50 + 200 − 50 × 200 / 100 ) % = 50 % i . e . , area is increased by 50 % answer is c .
Answer: c
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8587 for a computer table , then what was the cost price of the computer table ?
Options: a ) 6925 , b ) 6887 , c ) 6728 , d ) 6725 , e ) 2871
Rationale: ": cp = sp * ( 100 / ( 100 + profit % ) ) = 8587 ( 100 / 124 ) = rs . 6925 . answer : a"
Answer: a
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 25 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 20 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 25 = 75 km / hr time taken = 100 / 75 = 1 hr 20 min answer is b"
Answer: b
Problem: how many positive integers less than 600 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 5 5 5 number of possibilities = 5 * 4 * 4 = 80 . then , just add up the number of 1 digits numbers = 4 , so total is 80 + 4 = 84 . answer : e"
Answer: e
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 90 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 20 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 90 % of republicans ( which is ( 60 * 0.9 ) = 54 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 60 ( 54 + 6 ) voters voted for candidate x and 40 voted for candidate y . thus we can infer that candidate x is expected to win the election by 20 ( 60 - 40 ) votes . therefore candidate x is expected to win the election by ( 20 / 100 ) votes which is equivalent to 20 % . i think the answer is e ."
Answer: e
Problem: a man can row downstream at 22 kmph and upstream at 10 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 16 , 2 , b ) 16 , 4 , c ) 16 , 8 , d ) 16 , 6 , e ) 16 , 7
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 22 - - - ( 1 ) and x - y = 10 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 32 = > x = 16 , y = 6 . answer : d"
Answer: d
Problem: if | 7 x + 2 | = 16 , then find the product of the values of x ?
Options: a ) - 5.14 , b ) 6.19 , c ) - 7.18 , d ) - 8.62 , e ) 5.69
Rationale: "| 7 x + 2 | = 16 7 x + 2 = 16 or 7 x + 2 = - 16 7 x = 14 or 7 x = - 18 x = 2 or x = - 2.57 product = - 2.57 * 2 = - 5.14 answer is a"
Answer: a
Problem: the cost of an article is decreased by 15 % . if the original cost is $ 80 , find the decrease cost .
Options: a ) 33 , b ) 11 , c ) 68 , d ) 36 , e ) 91
Rationale: "original cost = $ 80 decrease in it = 15 % of $ 80 = 15 / 100 × 80 = 1200 / 100 = $ 12 therefore , decrease cost = $ 80 - $ 12 = $ 68 answer : c"
Answer: c
Problem: sandy bought 65 books for $ 1280 from one shop and 55 books for $ 880 from another shop . what is the average price that sandy paid per book ?
Options: a ) $ 12 , b ) $ 14 , c ) $ 16 , d ) $ 18 , e ) $ 20
Rationale: "average price per book = ( 1280 + 880 ) / ( 65 + 55 ) = 2160 / 120 = $ 18 the answer is d ."
Answer: d
Problem: a fruit seller had some apples . he sells 35 % and still has 6500 apples . originally , he had ?
Options: a ) 650 apples , b ) 600 apples , c ) 772 apples , d ) 700 apples , e ) none
Rationale: "answer â ˆ µ 65 % of n = 800 â ˆ ´ n = ( 650 x 100 ) / 65 = 1000 correct option : e"
Answer: e
Problem: each of the integers from 0 to 8 , inclusive , is written on a separate slip of blank paper and the 10 slips are dropped into hat . if the slips are then drawn one at a time without replacement , how many must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: you should consider the worst case scenario : if you pick numbers 0 , 1 , 2 , 3 , 4 and 5 then no two numbers out of these 6 add up to 10 . now , the next , 7 th number whatever it ' ll be ( 6,7 , or 8 ) will guarantee that two number will add up to 10 . so , 7 slips must be drawn to ensure that the numbers on two of the slips drawn will have a sum of 10 answer : c
Answer: c
Problem: at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 7 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 25 c"
Answer: c
Problem: an ore contains 25 % of an alloy that has 90 % iron . other than this , in the remaining 75 % of the ore , there is no iron . how many kilograms of the ore are needed to obtain 60 kg of pure iron ?
Options: a ) 250 kg , b ) 275 kg , c ) 300 kg , d ) 266.66 kg , e ) none
Rationale: solution : let there is 100 kg of ore . 25 % ore contains 90 % off iron that means 25 kg contains ; 25 * 90 / 100 = 22.5 kg iron . 22.5 kg iron contains 100 kg of ore . then , 1 kg of iron contains = 25 / 100 kg ore ; hence , 60 kg iron contains = 100 * 60 / 22.5 = 266.66 kg ore . answer : option d
Answer: d
Problem: how many integers are between 5 and 74 / 5 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 10
Rationale: "74 / 5 = 14 . xx we are not concerned about the exact value of 74 / 5 as we just need the integers . the different integers between 5 and 74 / 5 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13,14 . total number of integers = 10 option e"
Answer: e
Problem: find large number from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 8 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1557.9 , c ) 1378 , d ) 1635 , e ) 1489
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 8 x + 15 7 x = 1350 x = 192.9 large number = 192.9 + 1365 = 1557.9 b"
Answer: b
Problem: a is the average ( arithmetic mean ) of the first 7 positive multiples of 6 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 16 , e ) 24
Rationale: if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 24 , which also equals b . b is the second positive multiple of n , thus n = 24 / 2 = 12 . the answer is c .
Answer: c
Problem: cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 3 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 3 : 7 , c ) 2 : 5 , d ) 1 : 8 , e ) 1 : 5
Rationale: "2 % is 1 % - points below 3 % and 11 % is 8 % - points above 3 % . the ratio of a : b should be 1 : 8 . the answer is d ."
Answer: d
Problem: in a class of 20 students , 2 students did not borrow any books from the library , 10 students each borrowed 1 book , 5 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the total number of books the students borrowed is 20 * 2 = 40 . the students who borrowed zero , one , or two books borrowed 10 * 1 + 5 * 2 = 20 books . the 3 students who borrowed at least three books borrowed 40 - 20 = 20 books . if 2 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 20 - 6 = 14 books . the answer is c ."
Answer: c
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations g are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) g = 8
Rationale: "the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10 , 24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . . e"
Answer: e
Problem: the reciprocal of the hcf and lcm of two are 1 / 15 and 1 / 312 . if one of the number is 24 then other no . is
Options: a ) 126 , b ) 136 , c ) 146 , d ) 156 , e ) 195
Rationale: "reciprocal of the hcf and lcm of two are 1 / 15 and 1 / 312 so , hcf = 15 , lcm = 312 lcm * hcf = product of two numbers = a * b = > b = lcm * hcf / a so , other = 15 * 312 / 24 = 195 answer : e"
Answer: e
Problem: x and y start a business with rs . 3000 and rs . 6000 respectively . hoe should they share their profits at the end of one year ?
Options: a ) 3 : 1 , b ) 2 : 1 , c ) 1 : 2 , d ) 1 : 3 , e ) 1 : 4
Rationale: explanation : they should share the profits in the ratio of their investments . the ratio of the investments made by x and y = 3000 : 6000 = > 1 : 2 answer : c
Answer: c
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 60 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320 $ , b ) 389 $ , c ) 420 $ , d ) 450 $ , e ) 489 $
Rationale: total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 60 ) = 489 hence answer will be ( e )
Answer: e
Problem: set x consists of 10 integers and has median of 10 and a range of 10 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 20 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 this is possible . hence it is the greatest such number . answer ( d )"
Answer: d
Problem: a boy is traveling from his house to school at 3 km / hr and reached school 9 minutes late . next day he traveled 4 km / hr and reached 6 minutes early . then find the distance between house and school ?
Options: a ) 3 km , b ) 4.5 km , c ) 5 km , d ) 2.5 km , e ) 6 km
Rationale: "let distance be x s 1 = 3 km / hr s 2 = 4 km / hr t 1 = x / 3 hr t 2 = x / 4 hr difference in time = 9 + 6 = 15 m = 1 / 4 hr ( x / 3 ) - ( x / 4 ) = 1 / 4 x = 3 km answer is a"
Answer: a
Problem: a student chose a number , multiplied it by 2 , then subtracted 140 from the result and got 102 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 121
Rationale: "solution : let x be the number he chose , then 2 * x * 140 = 102 2 x = 242 x = 121 correct answer e"
Answer: e
Problem: a can do a work in 15 days and b in 20 days . if they work on it together for 6 days , then the fraction of the work that is left is
Options: a ) 8 / 17 , b ) 7 / 15 , c ) 3 / 10 , d ) 8 / 15 , e ) 1 / 4
Rationale: "person ( a ) ( b ) ( a + b ) time - ( 15 ) ( 20 ) ( - ) rate - ( 20 ) ( 15 ) ( 35 ) work - ( 300 ) ( 300 ) ( 300 ) therefore a + b requires ( 300 / 35 ) days to complete entire work for 1 st 4 days they work 35 * 6 = 210 remaining work is 300 - 210 = 90 remaining fraction of work is = 90 / 300 = 3 / 10 answer c"
Answer: c
Problem: a certain quantity is measured on two different scales , the p - scale and the s - scale , that are related linearly . measurements on the p - scale of 6 and 24 correspond to measurements on the s - scale of 30 and 60 , respectively . what measurement on the p - scale corresponds to a measurement of 100 on the s - scale ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 60 , e ) 84
Rationale: first , we have to understand what linearly means . it ' s not a straight ratio ( since 6 : 30 does not equal 24 : 60 ) . we need to look at the increases in each measurement to see what the scalar actually is . from 6 to 24 we have an increase of 18 . from 30 to 60 we have an increase of 30 . therefore , the increase ratio is 18 : 30 or 3 : 5 . in other words , for every 3 that p increases , s increases by 5 . we know that s is 100 . to get from 60 to 100 , we went up by 40 , or 8 jumps of 5 ; therefore , p will go up by 8 jumps of 3 . 24 + 8 ( 3 ) = 24 + 24 = 48 = c
Answer: c
Problem: set a contains all the even numbers between 2 and 50 inclusive . set b contains all the even numbers between 102 and 150 inclusive . what is the difference between the sum of elements of set b and the sum of the elements of set a ?
Options: a ) 2500 , b ) 2550 , c ) 5050 , d ) 6275 , e ) 11325
Rationale: "set a contains 2,4 , 6 . . . 50 set b contains 102 , 104 , 106 . . . 150 number of terms in each set = 25 difference between corresponding terms in set a and b = 100 difference between sum of set b and set a = 100 * 25 = 2500 answer a"
Answer: a
Problem: a whale goes on a feeding frenzy that lasts for 12 hours . for the first hour he catches and eats 30 kilos of plankton . in every hour after the first , it consumes 2 kilos of plankton more than it consumed in the previous hour . if by the end of the frenzy the whale will have consumed a whopping accumulated total 600 kilos of plankton , how many kilos did he consume on the 10 th hour ?
Options: a ) 36 , b ) 45 , c ) 28 , d ) 48 , e ) 52
Rationale: therefor in 10 th hour he consume x + 2 * 9 = 30 + 18 = 48 correct option is d
Answer: d
Problem: the average age of 19 students in a group is 17 years . when teacher ’ s age is included to it , the average increases by one . what is the teacher ’ s age in years ?
Options: a ) 36 , b ) 37 , c ) 38 , d ) can not be determined , e ) none of these
Rationale: "age of the teacher = ( 20 × 18 – 19 × 17 ) years = 37 years . answer b"
Answer: b
Problem: machine x takes 10 hours longer than machine y to produce 1080 widgets . machine y produces 20 percent more widgets in an hour than machine x does in an hour . how many widgets per hour does machine x produce
Options: a ) 100 , b ) 65 , c ) 25 , d ) 11 , e ) 18
Rationale: "machine y produces 20 percent more widgets in an hour than machine x does in an hour . so if machine x produces 100 widgets , then machine y produces 120 widgets . ratio of 120 / 100 = 6 / 5 . this is their speed of work ( y : x ) . i . e . speed of their work ( x : y ) = 5 / 6 now , time is inversely proportional to speed . hence the ratio of the time spent ( x : y ) = 6 / 5 let us assume that they spend 6 x and 5 x hours . given that 6 x - 5 x = 10 so , x = 10 . hence 6 x = 6 * 10 = 60 hours . hence x takes 120 hours to produce 1080 widgets . so , in 1 hour , it can produce ( 1 * 1080 ) / 60 = 18 hence option ( e ) ."
Answer: e
Problem: a train is running at a speed of 40 km / hr and it crosses a post in 16.2 seconds . what is the length of the train ?
Options: a ) 190 metres , b ) 160 metres , c ) 200 metres , d ) 120 metres , e ) 250 metres
Rationale: "speed of the train , v = 40 km / hr = 40000 / 3600 m / s = 400 / 36 m / s time taken to cross , t = 16.2 s distance covered , d = vt = ( 400 / 36 ) ã — 16.2 = 160 m distance covered is equal to the length of the train = 160 m correct answer is 160 metres b"
Answer: b
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 30 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 82 % , e ) 95 %
Rationale: find the product of the two increases : ( 14 / 10 ) * ( 13 / 10 ) which is 1.82 and a 82 % increase . d
Answer: d
Problem: if 4 % more is gained by selling an article for rs . 350 than by selling it for rs . 340 , the cost of the article is
Options: a ) 250 , b ) 231 , c ) 200 , d ) 288 , e ) 111
Rationale: "explanation : let c . p . be rs . x . then , 4 % of x = 350 - 340 = 10 x / 25 = 10 = > x = 250 answer : a"
Answer: a
Problem: on increasing the price of t . v . sets by 50 % , their sale decreases by 20 % . what is the effect on the revenue receipts of the shop ?
Options: a ) 4 , b ) 5 , c ) 56 , d ) 20 , e ) 7
Rationale: "explanation : let the price be = rs . 100 , and number of units sold = 100 then , sale value = rs . ( 100 × 100 ) = rs . 10000 new sale value = rs . ( 150 × 80 ) = rs . 12000 increase % = 2000 / 10000 × 100 = 20 % answer : d"
Answer: d
Problem: p software has coding line 5 % more than n , n software has coding line 4 / 13 more than m . m software has 78 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "m s / w has 78 line of code n s / w has = 78 + 78 * 4 / 13 = 102 line of code p s / w 5 % more n ' code 102 + 5.1 = 107.1 or 107 line of code answer : b"
Answer: b
Problem: a , b and c started a business with capitals of rs . 8000 , rs . 10000 and rs . 12000 respectively . at the end of the year , the profit share of b is rs . 1600 . the difference between the profit shares of a and c is ?
Options: a ) 288 , b ) 266 , c ) 155 , d ) 600 , e ) 640
Rationale: ratio of investments of a , b and c is 8000 : 10000 : 12000 = 4 : 5 : 6 and also given that , profit share of b is rs . 1600 = > 5 parts out of 15 parts is rs . 1600 now , required difference is 6 - 4 = 2 parts required difference = 2 / 5 ( 1600 ) = rs . 640 answer : e
Answer: e
Problem: machine a can finish a job in 4 hours , machine в can finish the job in 12 hours , and machine с can finish the job in 6 hours . how many hours will it take for a , b , and с together to finish the job ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the combined rate is 1 / 4 + 1 / 12 + 1 / 6 = 1 / 2 of the job per hour . the time to complete the job is 2 / 1 = 2 hours . the answer is b ."
Answer: b
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 720 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 92 , c ) 68 , d ) 88 , e ) none
Rationale: "explanation we have : l = 20 ft and lb = 720 sq . ft . so , b = 36 ft . length of fencing = ( l + 2 b ) = ( 20 + 72 ) ft = 92 ft . answer b"
Answer: b
Problem: positive integer y is 50 percent of 50 percent of positive integer x , and y percent of x equals 4 . what is the value of x ?
Options: a ) 40 , b ) 100 , c ) 200 , d ) 400 , e ) 600
Rationale: "y = 0.5 * 0.5 * x = x / 4 y % * x = 4 ( y / 100 ) * x = 4 ( x / 400 ) * x = 4 x ^ 2 = 4 * 400 x = 40 the answer is a ."
Answer: a
Problem: walking with 3 / 5 of my usual speed , i miss the bus by 5 minutes . what is my usual time ?
Options: a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 15 min
Rationale: "speed ratio = 1 : 3 / 5 = 5 : 3 time ratio = 3 : 5 1 - - - - - - - - 5 3 - - - - - - - - - ? è 15 answer : e"
Answer: e
Problem: [ ( 3.241 x 14 ) / 100 ] = ?
Options: a ) 0.045374 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) none of these
Rationale: "answer multiplying 3.241 x 14 = 4.5374 now divide 4.5374 by 100 so , 4.5374 ÷ 100 = 0.045374 ∴ shift the decimal two places to the left as 100 correct option : a"
Answer: a
Problem: a person borrows rs . 4000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 80 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 4000 * 6 * 2 ) / 100 ] - [ ( 4000 * 4 * 2 ) / 100 ] 480 - 320 = 160 gain in 1 year = ( 160 / 2 ) = 80 rs answer : b"
Answer: b
Problem: 365 : 90 : : 623 : ?
Options: a ) 36 , b ) 45 , c ) 123 , d ) 63 , e ) none of these
Rationale: "365 - - - 3 * 6 * 5 . . . . 90 623 - - - 6 * 2 * 3 . . . . 36 answer a"
Answer: a
Problem: the volumes of two cones are in the ratio 1 : 20 and the radii of the cones are in the ratio of 1 : 2 . what is the length of the wire ?
Options: a ) 4 : 5 , b ) 4 : 9 , c ) 4 : 2 , d ) 5 : 2 , e ) 2 : 8
Rationale: "the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 1 ^ 2 . h 1 / r 2 ^ 2 . h 2 = > 1 / 20 = ( 1 ) ^ 2 h 1 / ( 2 ) ^ 2 h 2 = > h 1 / h 2 = 4 / 5 i . e . h 1 : h 2 = 4 : 5 answer : a"
Answer: a
Problem: let p and q be the root of the quadratic equation x 2 - ( ∝ - 2 ) x - ∝ - 1 = 0 . what is the minimum possible value of p 2 + q 2 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: explanation : p + q = α – 2 and pq = – α – 1 ( p + q ) 2 = p 2 + q 2 + 2 pq , thus ( α – 2 ) 2 = p 2 + q 2 + 2 ( – α – 1 ) p 2 + q 2 = α 2 – 4 α + 4 + 2 α + 2 p 2 + q 2 = α 2 – 2 α + 6 p 2 + q 2 = α 2 – 2 α + 1 + 5 p 2 + q 2 = ( α – 1 ) 2 + 5 thus , minimum value of p 2 + q 2 is 5 . answer : d
Answer: d
Problem: in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 3.5 ) , ( 9 , 0 ) , ( 0 , - 3.5 ) , ( - 9 , 0 ) ?
Options: a ) 63 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 9 + 9 = 18 length of 2 nd diagonal = 3.5 + 3.5 = 7 area = 1 / 2 * 18 * 7 = 63 a is the answer"
Answer: a
Problem: each of the 35 points is placed either inside or on the surface of a perfect sphere . if 88 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7 , b ) 11 , c ) 13 , d ) 14 , e ) 15
Rationale: "maximum number of points on the surface is 88 % * 35 = 30.8 . . . or 30 since it has to be an integer now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 30 points , so at best we can form 15 pairs ( 30 ) . so , answer is ( e )"
Answer: e
Problem: 6 years ago , p was half of q in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) a ) 21 , b ) b ) 34 , c ) c ) 45 , d ) d ) 25 , e ) e ) 26
Rationale: explanation : let the present age of p and q be 3 x and 4 x respectively . six years ago , p was half of q in age = > 2 ( 3 x – 6 ) = ( 4 x – 6 ) = > 6 x – 12 = 4 x – 6 = > 2 x = 6 = > x = 3 7 x = 7 * 3 = 21 answer : option a
Answer: a
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 266 , d ) 288 , e ) 261
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 . answer : a"
Answer: a
Problem: if 2 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 4 , e ) 8
Rationale: "2 ( log 2 ^ 2 * 5 ^ 2 ) = x 2 log ( 5 * 2 ) ^ 2 = x 2 * 2 log ( 5 * 2 ) = x 4 log 10 = x log 10 base 10 = 1 so 4 * 1 = x x = 4 answer : d"
Answer: d
Problem: a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 3 / 4 of the current inventory is speedsters , of which 3 / 5 are convertibles . if there are 30 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 54 , c ) 60 , d ) 70 , e ) 90
Rationale: "total vehicle = 3 / 4 of speedster + 1 / 4 of others . speedster convertibles = 3 / 4 total vehicle * 3 / 5 given : 1 / 4 constitutes 30 vehicles . hence 3 / 4 constitutes 90 speedster convertibls = 90 * 3 / 5 = 54 b"
Answer: b
Problem: a rower can row 6 km / h in still water . when the river is running at 1 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.66 , b ) 2.78 , c ) 2.8 , d ) 2.87 , e ) 2.92
Rationale: "let x be the distance to big rock . time = x / 5 + x / 7 = 1 x = 35 / 12 = 2.92 the answer is e ."
Answer: e
Problem: in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ?
Options: a ) 3 % , b ) 5 % , c ) 2.5 % , d ) 4 % , e ) 3.6 %
Rationale: explanation : let there be 100 products in the stockpile . 40 % and 30 % were manufactured by m 1 and m 2 respectively . so , 30 % are manufactured by m 3 . products from m 1 = 40 , from m 2 = 30 and from m 3 = 30 . number of defective products from m 1 = 0.03 x 40 = 1.2 , from m 2 = 0.01 x 30 = 0.3 and from m 3 = 0.07 x 30 = 2.1 therefore , total number of defective products = 3.6 answer : e
Answer: e
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 44.0 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 14 ) = 22 / 7 * 14 = 44 cm answer : a"
Answer: a
Problem: the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ?
Options: a ) 22 , b ) 0 , c ) 49 , d ) 58 , e ) 66
Rationale: it is clear that 22 x 48 = 10 x 55 + k + 11 x 40 ⇒ ⇒ k = 66 answer : e
Answer: e
Problem: ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the minimum and maximum possible values of ' a + b ' ?
Options: a ) 0 , b ) - 24 , c ) - 32 , d ) - 20 , e ) - 12
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 9 - 21 = - 12 . ans e ."
Answer: e
Problem: a certain company reported that the revenue on sales increased 50 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 20 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 150 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 150 ) / 150 = 30 / 150 = ~ 20 % . answer : a"
Answer: a
Problem: if 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 21 lines is 21 c 2 = 210 the answer is d ."
Answer: d
Problem: three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 22 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters
b ) 20 square meters
c ) 24 square meters
d ) 19 square meters
e ) 30 square meters
Rationale: total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 200 - 22 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : d .
Answer: d
Problem: find the simple interest on $ 3200 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 960
Rationale: "si = ptr / 100 = 3200 * 3 * 10 / 100 = $ 960 answer is e"
Answer: e
Problem: if a person walks at 12 km / hr instead of 8 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 58 km , c ) 60 km , d ) 40 km , e ) 65 km
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 12 3 x - 2 x = 40 = > x = 40 km . answer : d"
Answer: d
Problem: two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer e between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) e = 18 , e ) 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Problem: a merchant purchased a jacket for $ 60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "markup = x x = 0.25 ( 60 + x ) = > 3 x / 4 = 15 = > x = 20 so sp = 80 but actual sp = 0.8 * 80 = 64 so profit = $ 4 answer - c"
Answer: c
Problem: a car travels at a speed of 65 miles per hour . how far will it travel in 7 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 455 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 7 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 = 7 × 65 = 455 miles correct answer is c ) 455 miles"
Answer: c
Problem: the percentage profit earned by selling an article for rs . 1720 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 1875 , d ) 5600 , e ) 3400
Rationale: "then , ( 1720 - x ) / x * 100 = ( x - 1280 ) / x * 100 1720 - x = x - 1280 2 x = 3000 = > x = 1500 required s . p . = 125 % of rs . 1500 = 125 / 100 * 1500 = rs . 1875 . answer c"
Answer: c
Problem: find the surface area of a 10 cm x 4 cm x 2 cm brick .
Options: a ) 136 cu cm , b ) 124 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none
Rationale: "sol . surface area = [ 2 ( 10 x 4 + 4 x 2 + 10 x 2 ) ] = ( 2 x 68 ) = 136 cu cm answer a"
Answer: a
Problem: a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 10 : 40
Rationale: "explanation : t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2 answer is a"
Answer: a
Problem: a certain country is divided into 4 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 4 p / 12 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Problem: 12.5 * 3.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 646 , e ) 742
Rationale: "a 352 ? = 12.5 * 3.2 * 8.8 = 352"
Answer: a
Problem: vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6069 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2100 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6069 = x = 6069 / 2.89 = 2100 therefore , amount invested by raghu is rs . 2100 . answer : c"
Answer: c
Problem: a train 125 m long passes a man , running at 7 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 50 , c ) 52 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 7 ) km / hr . x - 7 = 45 = = > x = 52 km / hr . answer : c"
Answer: c