regisss/math_qa huggingface dataset:
Problem: a 30 kg metal bar made of alloy of tin and silver lost 3 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 3 kg when 30 kg alloy is immersed . this is a loss of ( 3 / 30 ) * 100 = 10 % . this is aavg the loss of tin is 1.375 kg for every 10 kg . this means it loses ( 1.375 / 10 ) * 100 = 13.75 % of its weight in water . this is a 1 . the loss of silver is . 375 kg for every 5 kg . this means it loses ( . 375 / 5 ) * 100 = 7.5 % of its weight in water . this is a 2 . weight of tin / weight of silver = ( silver ' s loss - avg loss ) / ( avg loss - tin ' s loss ) x / y = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2 / 3 e"
Answer: e
Problem: the diameter of a cylindrical tin is 14 cm and height is 2 cm . find the volume of the cylinder ?
Options: a ) 33 , b ) 45 , c ) 66 , d ) 77 , e ) 98
Rationale: "r = 7 h = 5 π * 7 * 7 * 5 = 98 π cc answer : e"
Answer: e
Problem: a shopkeeper sold an article for rs 2552.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: explanation : gain % = ( 152.36 * 100 / 2400 ) = 6.34 % = 6 % approx option c
Answer: c
Problem: the balance of a trader weighs 10 % less than it should . still the trader marks up his goods to get an overall profit of 30 % . what is the mark up on the cost price ?
Options: a ) 40 % , b ) 8 % , c ) 25 % , d ) 17 % , e ) 9 %
Rationale: "the most natural way to deal with ' weights ' questions is by assuming values . say the trader ' s balance shows 100 gms . it is actually 90 gms because it weighs 10 % less . say , the cost price is $ 90 ( $ 1 / gm ) . since he gets a profit of 30 % , the selling price must be 90 + ( 30 / 100 ) * 90 = $ 117 since the cost price is actually supposed to be $ 100 ( for 100 gms ) and the selling price is $ 117 , the mark up is simply 17 % . ans : d"
Answer: d
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of 3 hammers and 4 wrenches is one - third that of 10 hammers and 5 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 1 / 7
Rationale: "x be the weight of a hammer and y be the weight of a wrench . ( 3 x + 4 y ) = 1 / 3 * ( 10 x + 5 y ) 3 ( 3 x + 4 y ) = ( 10 x + 5 y ) 9 x + 12 y = 10 x + 5 y 7 y = x y = x / 7 ans - e"
Answer: e
Problem: if a is an integer greater than 2 but less than 7 and b is an integer greater than 4 but less than 13 , what is the range of a / b ?
Options: a ) 23 / 34 , b ) 57 / 60 , c ) 51 / 67 , d ) 19 / 71 , e ) 75 / 64
Rationale: "the way to approach this problem is 2 < a < 7 and 4 < b < 13 minimum possible value of a is 3 and maximum is 6 minimum possible value of b is 5 and maximum is 12 range = max a / min b - min a / max b ( highest - lowest ) 6 / 5 - 3 / 12 = 57 / 60 hence b"
Answer: b
Problem: all factors of a positive integer a are multiplied and the product obtained is a ^ 3 . if a is greater than 1 , how many factors does a have ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: answer = d = 6 number . . . . . . . . . . . . . . . . factors . . . . . . . . . . . . . . . . . . . . . . . . product 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 6 . . . . . . . . . . . . . . . . . . . . . . . . . 36 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 4 , 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 3 , 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 , 2 , 3 , 4 , 6 , 12 . . . . . . . . . . . . . . . . . 12 * 12 * 12 number which we are looking for = 12 answer = d
Answer: d
Problem: when 5 + 1 = 56 , 6 + 1 = 67 , 7 + 1 = 78 , then 8 + 1 = ?
Options: a ) 85 , b ) 98 , c ) 89 , d ) 105 , e ) 129
Rationale: "5 + 1 = > 5 x 1 = 5 & 5 + 1 = 6 = > 5 & 6 = > 56 6 + 1 = > 6 x 1 = 6 & 6 + 1 = 7 = > 6 & 7 = > 67 7 + 1 = > 7 x 1 = 7 & 7 + 1 = 8 = > 7 & 8 = > 78 then 8 + 1 = > 8 x 1 = 8 & 8 + 1 = 9 = > 8 & 9 = > 89 answer : c"
Answer: c
Problem: express 22 mps in kmph ?
Options: a ) 79.2 kmph , b ) 89.2 kmph , c ) 79.6 kmph , d ) 99.2 kmph , e ) 69.2 kmph
Rationale: "22 * 18 / 5 = 79.2 kmph answer : a"
Answer: a
Problem: for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 90 units raises the average to 58 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 4
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 50 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 50 n + 90 = 58 * ( n + 1 ) - - > n = 4 . or as 40 extra units increased the average for n + 1 days by 8 units per day then 40 / ( n + 1 ) = 8 - - > n = 4 . answer : e ."
Answer: e
Problem: the manager at a health foods store mixes a unique superfruit juice cocktail that costs $ 1399.45 per litre to make . the cocktail includes mixed fruit juice and a ç ai berry juice , which cost $ 262.85 per litre and $ 3104.35 per litre , respectively . the manager has already opened 32 litres of the mixed fruit juice . how many litres of the a ç ai berry juice does he need to add ?
Options: a ) 17 litres , b ) 21.3 litres , c ) 11 litres , d ) 07 litres , e ) 38 litres
Rationale: "262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) solve the equation . 262.85 ( 32 ) + 3 , 104.35 x = 1 , 399.45 ( 32 + x ) 8 , 411.2 + 3 , 104.35 x = 44 , 782.4 + 1 , 399.45 x 8 , 411.2 + 1 , 704.9 x = 44 , 782.4 1 , 704.9 x = 36 , 371.2 x ≈ 21.3 answer is b ."
Answer: b
Problem: the sum of the squares of 3 numbers is 241 , while the sum of their products taken two at a time is 100 . their sum is :
Options: a ) 20 , b ) 11 , c ) 21 , d ) 41 , e ) none of these
Rationale: x ^ + y ^ 2 + z ^ 2 = 241 xy + yz + zx = 100 as we know . . ( x + y + z ) ^ 2 = x ^ 2 + y ^ 2 + z ^ 2 + 2 ( xy + yz + zx ) so ( x + y + z ) ^ 2 = 241 + ( 2 * 100 ) ( x + y + z ) ^ 2 = 441 so x + y + z = 21 answer : c
Answer: c
Problem: two goods trains each 720 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 22 sec , b ) 88 sec , c ) 48 sec , d ) 18 sec , e ) 72 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 750 + 750 = 1500 m . required time = 1500 * 6 / 125 = 72 sec . answer : e"
Answer: e
Problem: if w / x = 1 / 6 and w / y = 1 / 5 , then ( x + y ) / y =
Options: a ) 4 / 5 , b ) 6 / 5 , c ) 7 / 5 , d ) 11 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 6 = > x = 6 w and w / y = 1 / 5 = > y = 5 w ( x + y ) / y = ( 6 w + 5 w ) / 5 w = 11 w / 5 w = 11 / 5 correct option : d"
Answer: d
Problem: 35 liters of a mixture is created by mixing liquid p and liquid q in the ratio 4 : 3 . how many liters of liquid q must be added to make the ratio 5 : 7 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: let x be the amount of liquid q to be added . ( 3 / 7 ) * 35 + x = ( 7 / 12 ) * ( 35 + x ) 1260 + 84 x = 1715 + 49 x 35 x = 455 x = 13 the answer is d .
Answer: d
Problem: a jar contains a mixture of ab in the ratio 4 : 1 . when 20 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 12 , b ) 15 , c ) 32 , d ) 20 , e ) 25
Rationale: "20 litres of mixture that is replaced will contain 16 litres of a and 4 litres of b ( as a : b = 4 : 1 ) let the initial volume of the mixture be 4 k + 1 k = 5 k so by condition , [ 4 k - 16 ] / [ k - 4 + 20 ] = 2 / 3 = > 12 k - 48 = 2 k - 8 + 40 = > 10 k = 80 solve for k which is k = 8 so initial volume of liquid a = 4 k = 32 litres answer : c"
Answer: c
Problem: two trains 140 m and 160 m long run at the speed of 60 kmph and 40 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 40 = 100 kmph * 5 / 18 = 250 / 9 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec answer is c"
Answer: c
Problem: for a certain exam , a score of 60 was 2 standard deviations below mean and a score of 100 was 3 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "mean - 2 sd = 60 mean + 3 sd = 100 by solving above we get , sd ( absolute value ) = 8 mean = 76 ans . b"
Answer: b
Problem: the sum of the present age of henry and jill is 48 . what is their present ages if 9 years ago henry was twice the age of jill ?
Options: a ) and 27 , b ) and 24 , c ) and 22 , d ) and 29 , e ) of these
Rationale: "let the age of jill 9 years ago be x , age of henry be 2 x x + 9 + 2 x + 9 = 48 x = 10 present ages will be 19 and 29 answer : d"
Answer: d
Problem: the average of 15 numbers is calculated as 20 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) 30 , b ) 26 , c ) 16 , d ) 97 , e ) 12
Rationale: "15 * 20 + 36 – 26 = 300 / 10 = 30 answer : a"
Answer: a
Problem: what is the area of a square field whose diagonal of length 16 m ?
Options: a ) 128 , b ) 289 , c ) 200 , d ) 112 , e ) 178
Rationale: "d 2 / 2 = ( 16 * 16 ) / 2 = 128 answer : a"
Answer: a
Problem: the avg age of an adult class is 40 years . 12 new students with an avg age of 32 years join the class . therefore decreasingthe avg by 4 year . find what was the original strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 16 , e ) 19
Rationale: let original strength = y then , 40 y + 12 x 32 = ( y + 12 ) x 36 ⇒ 40 y + 384 = 36 y + 432 ⇒ 4 y = 48 ∴ y = 12 b
Answer: b
Problem: what distance will be covered by a bus moving at 108 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 276 , e ) 900
Rationale: "108 kmph = 108 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : e"
Answer: e
Problem: vijay sells a cupboard at 12 % below cost price . had he got rs . 1500 more , he would have made a profit of 12 % . what is the cost price of the cupboard ?
Options: a ) 7450 , b ) 14900 , c ) 6250 , d ) 6000 , e ) none of these
Rationale: "explanation : cost price = 1500 / ( 0.12 + 0.12 ) = 1500 / 0.24 = rs . 6250 answer c"
Answer: c
Problem: if 20 men can build a wall 112 metres long in 6 days , what length of a similar wall can be built by 30 men in 3 days ?
Options: a ) 65 mtr . , b ) 84 mtr , c ) 70 mtr . , d ) 78 mtr . , e ) 17 mtr .
Rationale: 20 men is 6 days can build 112 metres 30 men in 3 days can build = 112 * ( 30 / 20 ) x ( 3 / 6 ) = 84 meters answer : b .
Answer: b
Problem: if the speed of a man is 57 km per hour , then what is the distance traveled by him in 30 seconds ?
Options: a ) 275 m , b ) 360 m , c ) 475 m , d ) 420 m , e ) 440 m
Rationale: "the distance traveled in 30 sec = 57 * ( 5 / 18 ) * 30 = 475 m answer : c"
Answer: c
Problem: victor gets 90 % marks in examinations . if these are 405 marks , find the maximum marks .
Options: a ) 334 , b ) 500 , c ) 376 , d ) 450 , e ) 271
Rationale: "let the maximum marks be m then 90 % of m = 405 ⇒ 90 / 100 × m = 405 ⇒ m = ( 405 × 100 ) / 90 ⇒ m = 40500 / 90 ⇒ m = 450 therefore , maximum marks in the examinations are 450 answer : d"
Answer: d
Problem: there are 3 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 45 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 3 c 2 number of ways of selecting 2 non fiction books = 6 c 2 3 c 2 * 6 c 2 = 3 * 15 = 45 answer : c"
Answer: c
Problem: when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 134.08 here 134 is the quotient . given that remainder = 16 so , 134.08 = 134 + 16 / j so , j = 200 ans e"
Answer: e
Problem: find the circumference and area of radius 13 cm .
Options: a ) 124 cm ² , b ) 531 cm ² , c ) 354 cm ² , d ) 584 cm ² , e ) 594 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 13 × 13 cm ² = 531 cm ² answer : b"
Answer: b
Problem: ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) =
Options: a ) 8.4 , b ) 840 , c ) 84.0 , d ) 0.84 , e ) 0.084
Rationale: ( 0.0048 ) ( 3.5 ) / ( 0.05 ) ( 0.1 ) ( 0.004 ) = 0.0048 * 350 / 5 ( 0.1 ) ( 0.004 ) = 0.048 * 70 / 1 ( 0.004 ) = 48 * 70 / 4 = 12 * 70 = 840 answer : b
Answer: b
Problem: a batsman in his 17 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 17 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: average score before 17 th innings = 85 - 3 × 17 = 34 average score after 17 th innings = > 34 + 3 = 37 answer : b
Answer: b
Problem: a snooker tournament charges $ 40.00 for vip seats and $ 15.00 for general admission ( “ regular ” seats ) . on a certain night , a total of 300 tickets were sold , for a total cost of $ 7,500 . how many fewer tickets were sold that night for vip seats than for general admission seats ?
Options: a ) 190 , b ) 180 , c ) 150 , d ) 200 , e ) 300
Rationale: "let no of sits in vip enclosure is x then x * 40 + 15 ( 300 - x ) = 7500 or 25 x = 7500 - 4500 , x = 3000 / 25 = 120 vip = 120 general 200 d"
Answer: d
Problem: a hiker walked for 3 days . she walked 18 miles on the first day , walking 3 miles per hour . on the second day she walked for one less hour but she walked one mile per hour , faster than on the first day . on the third day she walked the same number of hours as on the first day , but at the same speed as on the second day . how many miles in total did she walk ?
Options: a ) 24 , b ) 44 , c ) 58 , d ) 60 , e ) 62
Rationale: first day - 18 miles with 3 miles per hours then total - 6 hours for that day second day - 4 miles per hour and 5 hours - 20 miles third day - 4 miles per hour and 6 hours - 24 miles total 18 + 20 + 24 - 62 answer : option e .
Answer: e
Problem: sum of two numbers is 30 . two times of the first exceeds by 10 from the three times of the other . then the numbers will be ?
Options: a ) 14 , 16 , b ) 16 , 14 , c ) 18 , 12 , d ) 12 , 18 , e ) 17 , 13
Rationale: "explanation : x + y = 30 2 x ã ¢ â ‚ ¬ â € œ 3 y = 10 x = 16 y = 14 answer : b"
Answer: b
Problem: a runner runs the 40 miles from marathon to athens at a constant speed . halfway through the run she injures her foot , and continues to run at half her previous speed . if the second half takes her 4 hours longer than the first half , how many hours did it take the runner to run the second half ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "the runner runs the first 20 miles at speed v and the second 20 miles at speed v / 2 . the time t 2 to run the second half must be twice the time t 1 to run the first half . t 2 = 2 * t 1 = t 1 + 4 t 1 = 4 and so t 2 = 8 . the answer is c ."
Answer: c
Problem: a man can do a job in 15 days . his father takes 20 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.4 days , b ) 4.4 days , c ) 5.4 days , d ) 8.4 days , e ) 2.4 days
Rationale: a 6.4 days 1 day work of the three persons = ( 1 / 15 + 1 / 20 + 1 / 25 ) = 47 / 300 so , all three together will complete the work in 300 / 47 = 6.4 days . -
Answer: a
Problem: cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 272 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 7.5 , e ) 8
Rationale: required run rate = 272 - ( 3.2 x 10 ) = 240 = 6 40 40 a
Answer: a
Problem: two numbers are less than third number by 34 % and 37 % respectively . how much percent is the second number less than by the first
Options: a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 22 %
Rationale: "let the third number is x . then first number = ( 100 - 34 ) % of x = 66 % of x = 66 x / 100 second number is ( 63 x / 100 ) difference = 66 x / 100 - 63 x / 100 = 3 x / 100 so required percentage is , difference is what percent of first number ( 3 x / 100 * 100 / 63 x * 100 ) % = 22 % answer : e"
Answer: e
Problem: how many liters of a 40 % iodine solution need to be mixed with 35 liters of a 20 % iodine solution to create a 30 % iodine solution ?
Options: a ) 30.5 , b ) 49 , c ) 100 , d ) 105 , e ) 140
Rationale: "solution 1 : assume the iodine solution to be mixed = x lts . iodine = 0.4 x lts , water = 0.6 x lts . solution 2 : 35 liters of a 20 % iodine solution iodine = 7 lts , water = 28 lts . total iodine = 0.4 x + 7 total water = 0.6 x + 28 the resultant is a 35 % idoine solution . hence ( 0.4 x + 7 ) / ( x + 35 ) = 30 / 100 40 x + 700 = 30 x + 1050 10 x = 305 x = 30.5 lts correct option : a"
Answer: a
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 5.5 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.5 tax on others = 3 percentage = 5.5 / 100 = 5.5 % answer : a"
Answer: a
Problem: in a certain warehouse , 70 percent of the packages weigh less than 75 pounds , and a total of 48 packages weigh less than 25 pounds . if 80 percent of the packages weigh at least 25 pounds , how many of the packages weigh at least 25 pounds but less than 75 pounds ?
Options: a ) 8 , b ) 64 , c ) 120 , d ) 102 , e ) 144
Rationale: if 80 % of the packages weigh at least 25 pounds this means that 20 % of the packages weigh less than 25 pounds let t = total number of packages so , 20 % of t = # of packages that weigh less than 25 pounds 48 packages weigh less than 25 pounds great . so , 20 % of t = 48 rewrite to get : 0.2 t = 48 solve : t = 240 70 % of the packages weigh less than 75 pounds so , 70 % oft = number of packages that weigh less than 75 pounds 70 % of 240 = 168 , so 168 packages weigh less than 75 pounds of those 168 packages that weigh less than 75 pounds , 48 packages weigh less than 25 pounds . so , the number of packages that weight between 25 and 75 pounds = 168 - 48 = 120 = c
Answer: c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the sport formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the sport formulation contains 2 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 15 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: standard : fl : corn s : water = 1 : 12 : 30 sport : fl : corn s : water = 3 : 12 : 180 this simplifies to 1 : 4 : 60 if the large bottle has a capacity of x ounces , then 4 x / 65 = 2 . so , x = 32.5 ounces . water = ( 60 / 65 ) * ( 65 / 2 ) = = 30 ounces . ans b
Answer: b
Problem: a machine , working at a constant rate , manufactures 18 pens in 30 minutes . how many pens does it make in 1 hr 45 min ?
Options: a ) 63 , b ) 65 , c ) 62 , d ) 60 , e ) 45
Rationale: change 1 hr 45 min to 105 min . for this , we need to set up a simple proportion of pens per time 18 / 30 = s / 105 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can see this post . we can cancel 18 / 30 as 6 / 10 6 / 10 = s / 105 we can cross - multiply . 10 * s = 6 * 105 = 630 if we divide both sides by 10 , s = 63 the machine would be 63 pens in 1 hr 45 min . answer : a
Answer: a
Problem: a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 225 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 220 , b ) 200 , c ) 210 , d ) 225 , e ) 230
Rationale: "b 225 * t = 1 km = > t = 1 / 225 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 225 + 2 / 3600 ) = 1 = > v = 200 km / h"
Answer: b
Problem: if ( - 7 ) ^ ( 8 x ) = 7 ^ ( 12 - 5 x ) and x is an integer , what is the value of x ?
Options: a ) 5 , b ) - 4 , c ) 1 , d ) 2 , e ) 3
Rationale: "since x is an integer , ( - 7 ) ^ ( 8 x ) is always positive . so , 7 ^ 8 x = 7 ^ ( 13 - 5 x ) 8 x = 12 - 5 x 12 x = 12 x = 1 answer : c"
Answer: c
Problem: a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 4 of the volumes were transferred to another location and 1 / 3 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 17.67 % , c ) 28.8 % , d ) 45.2 % , e ) 73.6 %
Rationale: "fiction novels = 5,508 transferred to another location = 4590 transferred fiction novels = 1530 non transferred fiction novels = 3,978 percent of the remaining collection was fiction novels = 3978 / ( 18360 - 4590 ) * 100 = > 28.888 . . . % hence answer will be ( c )"
Answer: c
Problem: ( 51 + 52 + 53 + … … … + 100 ) is equal to :
Options: a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 3885
Rationale: "( 51 + 52 + 53 + … … … + 100 ) = ( 1 + 2 + 3 + … … . + 100 ) - ( 1 + 2 + 3 + 4 + … … + 50 ) = ( 100 * 101 ) / 2 - ( 50 * 51 ) / 2 = ( 5050 - 1275 ) = 3775 . answer : d"
Answer: d
Problem: the mean of 50 observations was 30 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 30.5 , d ) 39.1 , e ) none
Rationale: "sol . therefore correct sum = ( 30 × 50 + 48 – 23 ) = 1525 . therefore correct mean = 1525 / 50 = 30.5 . answer c"
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 42 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 700 metres , c ) 324 metres , d ) 828 metres , e ) 600 metres
Rationale: "speed = 60 x 5 / 18 m / sec = 50 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 50 / 3 x 42 m = 150 m . option b"
Answer: b
Problem: the average weight of 6 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 47 kg . what might be the weight of the new person ?
Options: a ) 60 kg , b ) 75 kg , c ) 68 kg , d ) 85 kg , e ) 90 kg
Rationale: "total weight increased = ( 6 x 3.5 ) kg = 21 kg . weight of new person = ( 47 + 21 ) kg = 68 kg option c"
Answer: c
Problem: ajay can walk 6 km in 1 hour . in how many hours he can walk 70 km ?
Options: a ) 5 hrs , b ) 11.6 hrs , c ) 15.6 hrs , d ) 20.1 hrs , e ) 30 hrs
Rationale: "1 hour he walk 6 km he walk 70 km in = 70 / 6 * 1 = 11.6 hours answer is b"
Answer: b
Problem: the speed of a boat in still water in 18 km / hr and the rate of current is 6 km / hr . the distance travelled downstream in 14 minutes is :
Options: a ) 11.4 km , b ) 10.9 km , c ) 10.4 km , d ) 6.06 km , e ) 12.56 km
Rationale: "explanation : speed downstream = ( 18 + 6 ) = 24 kmph time = 14 minutes = 14 / 60 hour = 7 / 30 hour distance travelled = time × speed = ( 7 / 30 ) × 26 = 6.06 km answer : option d"
Answer: d
Problem: tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 133 per kg , the price of the third variety per kg will be
Options: a ) rs . 169.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 155.50 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 133 / 22.50 = 1 = â € º x - 133 = 22.50 = â € º x = 155.50 . hence , price of the third variety = rs . 155.50 per kg . answer d"
Answer: d
Problem: find the simple interest on rs . 71,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 8875 , d ) 9500 , e ) none of them
Rationale: "p = rs . 71000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 71,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8875 answer is c ."
Answer: c
Problem: john makes $ 65 a week from his job . he earns a raise andnow makes $ 72 a week . what is the % increase ?
Options: a ) 16 % , b ) 10.76 % , c ) 10.69 % , d ) 10.98 % , e ) 10 %
Rationale: "increase = ( 7 / 65 ) * 100 = ( 7 / 65 ) * 100 = 10.76 % . b"
Answer: b
Problem: if 20 men take 15 days to to complete a job , in how many days can 20 men finish that work ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: ans . 15 days
Answer: a
Problem: a can do a piece of work 40 days . b can do work in 60 days . in how many days they will complete the work together ?
Options: a ) 15 days , b ) 16 days , c ) 19 days , d ) 17 days , e ) 24 days
Rationale: "lcm = 120 , ratio = 40 : 60 = 2 : 3 no of days = 120 / ( 2 + 3 ) = 90 / 5 = 24 days answer : e"
Answer: e
Problem: a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 . what is the difference between their profit shares ?
Options: a ) s . 260 , b ) s . 160 , c ) s . 360 , d ) s . 50 , e ) s . 90
Rationale: "a profit of rs . 800 is divided between x and y in the ratio of 1 / 2 : 1 / 3 or 3 : 2 . so profits are 480 and 320 . difference in profit share = 480 - 320 = 160 answer : b"
Answer: b
Problem: two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.50 km and 1.0 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 48 , b ) 9 , c ) 7 , d ) 60 , e ) 15
Rationale: ": relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.50 + 1.0 = 2.5 km = 2500 m . required time = 2500 * 3 / 125 = 60 sec . answer : d"
Answer: d
Problem: what is the smallest integer that is multiple of 3 , 5,9
Options: a ) a ) 70 , b ) b ) 45 , c ) c ) 200 , d ) d ) 280 , e ) e ) 140
Rationale: "it is the lcm of 3 , 5 and 9 which is 45 . the answer is b ."
Answer: b
Problem: a book is bought for $ 60 and sold for $ 78 . what is the profit in percentage ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "78 / 60 = 1.3 the answer is c ."
Answer: c
Problem: a is a positive integer and multiple of 2 ; p = 4 ^ a , what is the remainder when p is divided by 10 ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined
Rationale: it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the a is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , a must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since a must be an even integer , the units digit of p = 4 ^ a will always be 6 . consequently , the remainder when p = 4 ^ a is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : a = 2 - - > p = 4 ^ a = 16 - - > p / 10 = 1 with a remainder of 6 a = 4 - - > p = 4 ^ a = 256 - - > p / 10 = 25 with a remainder of 6 a = 6 - - > p = 4 ^ a = 4096 - - > p / 10 = 409 with a remainder of 6 a = 8 - - > p = 4 ^ a = 65536 - - > p / 10 = 6553 with a remainder of 6 answer : b .
Answer: b
Problem: product of two natural numbers is 7 . then , the sum of reciprocals of their squares is
Options: a ) 50 / 49 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 7 , as 17 is a prime number , so a = 1 , b = 7 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 7 ( 2 ) = 50 / 49 option a"
Answer: a
Problem: in a fuel station the service costs $ 1.15 per car , every liter of fuel costs 0.4 $ . assuming that you own 2 sports cars and 2 executive cars and all fuel tanks are empty . how much will it cost to fuel all cars together if a sports car tank is 32 liters and an executive car tank is 75 % bigger ?
Options: a ) 37.5 $ , b ) 75 $ , c ) 87.5 $ , d ) 94.5 $ , e ) 98.4 $
Rationale: "total cars = 4 1.15 * 4 = 4.6 - > service cost fuel cost in sports car = 2 * 32 * 0.4 = 25.6 fuel cost in executive car = 25.6 * 7 / 4 = 44.8 total fuel cost = 25.6 + 44.8 = 70.4 cost to fuel car = 70.4 + 4.6 = 75 answer : b"
Answer: b
Problem: a , band c can do a piece of work in 11 days , 20 days and 67 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7.1 days , b ) 8.1 days , c ) 9.1 days , d ) 10 days , e ) 11 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 11 + 1 / 20 = 31 / 220 ( a + c ) ' s 1 day ' s work = 1 / 11 + 1 / 67 = 78 / 737 work done in 2 day ' s = 31 / 220 + 78 / 737 = 19 / 77 19 / 77 th work done in 2 days work done = 77 / 19 * 2 = 8.1 days answer : b"
Answer: b
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 6 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 22 , c ) 26 , d ) 24 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 and will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : c"
Answer: c
Problem: in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 3,5 ) , ( 9,5 ) , ( 2,7 ) , ( 8,7 ) ?
Options: a ) 21 . , b ) 28 . , c ) 35 . , d ) 12 . , e ) 52 .
Rationale: "delta x will give us the dimension of one side of the parallelogram = 9 - 3 = 6 unit delta y will give us the dimension of the other side of parallelogram = 7 - 5 = 2 unit area of parallelogram = 6 * 2 = 12 answer is d"
Answer: d
Problem: find the c . i . on a sum of rs . 10000 for 6 months at 25 % per annum , interest being compounded quarterly ?
Options: a ) 10290 , b ) 5290 , c ) 1289 , d ) 1290 , e ) 2290
Rationale: c . i . = 2000 ( 21 / 20 ) ^ 2 - 1800 = 1289 answer : c
Answer: c
Problem: you collect pens . suppose you start out with 5 . mike gives you another 20 pens . since her father makes pens , cindy decides to double your pens . since you ' re nice , you give sharon 10 pens . how many pens do you have at the end ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "solution start with 5 pens . mike gives you 20 pens : 5 + 20 = 25 pens . cindy doubles the number of pens you have : 25 ã — 2 = 50 pens . sharon takes 10 pens from you : 50 - 10 = 40 pens . so you have 40 at the end . correct answer : b"
Answer: b
Problem: a sum of money at simple interest amounts to rs . 1560 in 4 years and to rs . 1590 in 6 years . the sum is :
Options: a ) rs . 1400 , b ) rs . 1450 , c ) rs . 1500 , d ) rs . 1550 , e ) rs . 1525
Rationale: "s . i . for 2 years = rs . ( 1590 - 1560 ) = rs . 30 . s . i . for 4 years = rs . ( 30 x 2 ) = rs . 60 . principal = rs . ( 1560 - 60 ) = rs . 1500 . answer : option c"
Answer: c
Problem: a lady has fine gloves and hats in her closet - 18 blue , 32 red , and 25 yellow . the lights are out and it is totally dark . in spite of darkness , she can make out the difference between a hat and a glove . she takes out an item out of the closet only if she is sure that it is a glove . how many gloves must she take out to make sure she has a pair of each color ?
Options: a ) 60 , b ) 65 , c ) 70 , d ) 75 , e ) 80
Rationale: "32 r + 24 y + 1 y + 1 b + 2 b = 60 answer : a"
Answer: a
Problem: of the total amount that jill spent on a shopping trip , excluding taxes , she spent 40 percent on clothing , 30 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 3.6 % , c ) 4 % , d ) 5.2 % , e ) 6.0 %
Rationale: "let amount spent by jill = 100 clothing = 40 , food = 30 , others = 30 tax on clothing = 1.6 tax on others = 2.4 percentage = 4 / 100 = 4 % answer : c"
Answer: c
Problem: a student chose a number , multiplied it by 5 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 48 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "solution : let xx be the number he chose , then 5 ⋅ x − 138 = 102 5 x = 240 x = 48 answer a"
Answer: a
Problem: in a class , 30 students pass in english and 20 students in maths , while some students among these pass in both . how many students do only english as compared to those doing only maths ?
Options: a ) 10 , b ) 15 , c ) 4 , d ) 12 , e ) indeterminate
Rationale: "for doing union or intersection we would need three values . in this question the missing information in this question is total no . of students in the class . answer : e"
Answer: e
Problem: if 31 / 198 = 0.1565 , what is the 97 nd digit to the right of the decimal point of the fraction ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 7 , e ) 9
Rationale: "we are not concerned what 31 / 198 means . . we have to look at the decimal . . 0.1565 means 0.1565656 . . . . so leaving girst and second digit to the right of decimal , all odd numbered are 6 and all even numbered are 5 . . here 97 is odd , so ans is 6 c"
Answer: c
Problem: sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 24 , d ) 19 / 30 , e ) 11 / 15
Rationale: let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c
Answer: c
Problem: robert spent $ 100 in buying raw materials , $ 125 in buying machinery and 10 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 150 , b ) $ 210 , c ) $ 250 , d ) $ 160 , e ) $ 200
Rationale: let the total amount be x then , ( 100 - 10 ) % of x = 100 + 125 90 % of x = 225 90 x / 100 = 225 x = $ 250 answer is c
Answer: c
Problem: a 12 % stock yields 8 % . the market value of the stock is :
Options: a ) rs . 72 , b ) rs . 150 , c ) rs . 112.50 , d ) rs . 116.50 , e ) none of these
Rationale: "solution to obtain rs . 8 , investment = rs . 100 . to obtain rs . 12 , investment = rs . ( 100 / 8 x 12 ) = rs . 150 ∴ market value of rs . 100 stock = rs . 150 answer b"
Answer: b
Problem: there is a square with sides of 13 . what is the area of the biggest circle that can be cut out of this square ?
Options: a ) 132.73 , b ) 231.92 , c ) 530.93 , d ) 113.1 , e ) 204.33
Rationale: "area of a circle = a = ï € r ^ 2 square is 13 wide , so circle ' s diameter would be 13 , and radius would be 6.5 a = ï € 6.5 ^ 2 which is approximately 132.73 answer is a"
Answer: a
Problem: how long does a train 130 m long running at the speed of 98 km / hr takes to cross a bridge 160 m length ?
Options: a ) 13.9 sec , b ) 13.1 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 98 * 5 / 18 = 27 m / sec total distance covered = 130 + 160 = 290 m . required time = 290 / 22 = 13.1 sec . answer : b"
Answer: b
Problem: a , band c enter into partnership . a invests 3 times as much as b and b invests two - third of what c invests . at the end of the year , the profit earned is rs . 5500 . what is the share of b ?
Options: a ) 1000 , b ) 800 , c ) 1400 , d ) 1200 , e ) none of them
Rationale: "let c ' s capital = rs . x . then , b ' s capital = rs . ( 2 / 3 ) x a ’ s capital = rs . ( 3 x ( 2 / 3 ) . x ) = rs . 2 x . ratio of their capitals = 2 x : ( 2 / 3 ) x : x = 6 : 2 : 3 . hence , b ' s share = rs . ( 5500 x ( 2 / 11 ) ) = rs . 1000 . answer is a"
Answer: a
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 14 } + { 12 } ?
Options: a ) 23 , b ) 20 , c ) 15 , d ) 5 , e ) 2
Rationale: "soln : { 14 } + { 12 } = 14 * { 12 } + { 12 } = 15 * { 12 } answer : c"
Answer: c
Problem: if x + ( 1 / x ) = 5 , what is the value of w = x ^ 2 + ( 1 / x ) ^ 2 ?
Options: a ) w = 21 , b ) w = 22 , c ) w = 23 , d ) w = 24 , e ) 27
Rationale: "squaring on both sides , x ^ 2 + ( 1 / x ) ^ 2 + 2 ( x ) ( 1 / x ) = 5 ^ 2 x ^ 2 + ( 1 / x ) ^ 2 = 23 answer : c"
Answer: c
Problem: a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 7 m , the volume of the box ( in m 3 ) is :
Options: a ) 4830 , b ) 5236 , c ) 6420 , d ) 8960 , e ) 7960
Rationale: "clearly , l = ( 48 - 14 ) m = 34 m , b = ( 36 - 14 ) m = 22 m , h = 8 m . volume of the box = ( 34 x 22 x 7 ) m 3 = 5236 m 3 . answer : option b"
Answer: b
Problem: if the price of a certain computer increased 30 percent from d dollars to 351 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 700
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 351 ( given ) i . e . d = 351 / 1.3 = $ 270 i . e . 2 d = 2 * 270 = 540 answer : option a"
Answer: a
Problem: a certain number of men can do a work in 54 days . if there were 6 men more it could be finished in 6 days less . how many men were there in the beginning ?
Options: a ) 50 , b ) 48 , c ) 70 , d ) 40 , e ) 50
Rationale: "explanation : m ( 54 ) = ( m + 6 ) ( 48 ) 9 m - 8 m = 48 m = 48 answer : option b"
Answer: b
Problem: in traveling from a dormitory to a certain city , a student went 1 / 2 of the way by foot , 3 / 5 of the way by bus , and the remaining 4 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 20 , b ) 15 , c ) 40 , d ) 10 , e ) 12
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 2 x + 3 / 5 x + 4 x - 1 / 2 x - 3 / 5 x = 4 x = 20 km option : a"
Answer: a
Problem: a small pool filled only with water will require an additional 500 gallons of water in order to be filled to 80 % of its capacity . if pumping in these additional 500 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1600 , e ) 1875
Rationale: "since pumping in additional 500 gallons of water will increase the amount of water in the pool by 30 % , then initially the pool is filled with 1,000 gallons of water . so , we have that 1,000 + 500 = 0.8 * { total } - - > { total } = 1,875 answer : e ."
Answer: e
Problem: a certain bag contains 60 balls — 22 white , 18 green , 17 yellow , 3 red , and 1 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.85 , e ) 0.95
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 17 ) / 60 = 57 / 60 = 0.95 . answer : e ."
Answer: e
Problem: if a speaks the truth 40 % of the times , b speaks the truth 20 % of the times . what is the probability that at least one will tell the truth
Options: a ) 1.8 , b ) 2.0 , c ) 1.52 , d ) 0.52 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 4 / 10 ; false = 6 / 10 probability of b speaks truth p ( b ) = 2 / 10 ; false = 8 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 6 / 10 ) * ( 8 / 10 ) ] = 1 - 48 / 100 = 1 - 0.48 = 0.52 answer : d"
Answer: d
Problem: find the number of zeroes in 58 ! ( 58 factorial )
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "no of zeroes is 58 / 5 = 11 11 / 5 = 2 11 + 2 = 13 answer : b"
Answer: b
Problem: find the cost of fencing around a circular field of diameter 36 m at the rate of rs . 3.50 a meter ?
Options: a ) 438 , b ) 395 , c ) 378 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 18 = 113 113 * 3 1 / 2 = rs . 395 answer : b"
Answer: b
Problem: a number when divided by 342 gives a remainder 47 . when the same number ift divided by 19 , what would be the remainder ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 21 , e ) 14
Rationale: "sol . on dividing the given number by 342 , let k be the quotient and 47 as remainder . then , number – 342 k + 47 = ( 19 x 18 k + 19 x 2 + 9 ) = 19 ( 18 k + 2 ) + 9 . the given number when divided by 19 , gives ( 18 k + 2 ) as quotient and 9 as remainder . option c"
Answer: c
Problem: which is the least number that must be subtracted from 1100 so that the remainder when divided by 7 , 12 , 16 is 4 ?
Options: a ) 58 , b ) 68 , c ) 78 , d ) 88 , e ) 90
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1100 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 88 d"
Answer: d
Problem: two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 1 . find the larger integer .
Options: a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54
Rationale: "one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 1 , then x + 12 = y . substituting y = 4 x into the second equation yields x + 12 = 4 x . so , x = 4 ( smaller integer ) and , y = 4 x = 16 ( larger integer ) so b is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 1 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . therefore ( b ) is correct . c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 1 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 1 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 no good . we want a resulting ratio of 1 to 1 eliminate d e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore b is the only correct choice ."
Answer: b
Problem: the salaries of a and b together amount to $ 4000 . a spends 95 % of his salary and b , 85 % of his . if now , their savings are the same , what is a ' s salary ?
Options: a ) $ 1000 , b ) $ 1250 , c ) $ 2500 , d ) $ 3000 , e ) $ 1200
Rationale: let a ' s salary is x b ' s salary = 4000 - x ( 100 - 95 ) % of x = ( 100 - 85 ) % of ( 4000 - x ) x = $ 3000 answer is d
Answer: d
Problem: 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 =
Options: a ) 29 / 16 , b ) 19 / 16 , c ) 15 / 16 , d ) 17 / 4 , e ) 0
Rationale: 1 / 2 + [ ( 2 / 3 * 3 / 8 ) + 4 ] - 8 / 16 = 1 / 2 + [ ( 1 / 4 ) + 4 ] - 8 / 16 = 1 / 2 + [ 17 / 4 ] - 9 / 16 = 8 / 16 + 68 / 16 - 8 / 16 = 68 / 16 = 17 / 4 d
Answer: d
Problem: michelle deposited a certain sum of money in a savings account on july 1 st , 2007 . she earns an 6 % interest compounded semiannually . the sum of money in the account on december 31 st , 2009 is approximately what percent of the initial deposit ?
Options: a ) 117 % , b ) 120 % , c ) 121 % , d ) 135 % , e ) 140 %
Rationale: "since michelle earns 6 % interest compounded semiannually , then she earns 3 % interest every 6 months . now , the simple interest earned in 5 periods ( 30 months = 5 * 6 months ) would be 3 % * 5 = 15 % . but , since the interest iscompoundedevery 6 months , then there would be interest earned on interest ( very small amount ) thus the actual interest earned would be a little bit more than 15 % , only answer choice a fits . answer : a"
Answer: a