regisss/math_qa huggingface dataset:
Problem: a hostel had provisions for 250 men for 36 days . if 50 men left the hostel , how long will the food last at the same rate ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 60 , e ) 65
Rationale: "a hostel had provisions for 250 men for 36 days if 50 men leaves the hostel , remaining men = 250 - 50 = 200 we need to find out how long the food will last for these 200 men . let the required number of days = x days more men , less days ( indirect proportion ) ( men ) 250 : 200 : : x : 36 250 × 36 = 200 x 5 × 36 = 4 x x = 5 × 9 = 45 answer b"
Answer: b
Problem: 3 , 4 , 6 , 10 , 18 , ( . . . )
Options: a ) 22 , b ) 34 , c ) 27 , d ) 32 , e ) 25
Rationale: "explanation : 3 3 × 2 - 2 = 4 4 × 2 - 2 = 6 6 × 2 - 2 = 10 10 × 2 - 2 = 18 18 × 2 - 2 = 34 answer : option b"
Answer: b
Problem: the average of runs of a cricket player of 10 innings was 15 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 87 , b ) 16 , c ) 10 , d ) 76 , e ) 59
Rationale: average after 11 innings = 19 required number of runs = ( 19 * 11 ) - ( 15 * 10 ) = 209 - 150 = 59 . answer : e
Answer: e
Problem: 16 men can complete a piece of work in 25 days . in how many days can 15 men complete that piece of work ?
Options: a ) 26.7 days , b ) 77 days , c ) 20 days , d ) 88 days , e ) 44 days
Rationale: "16 * 25 = 15 * x = > x = 26.7 days answer : a"
Answer: a
Problem: a bus trip of 280 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "the time is the distance / speed . the time difference is 1 hour . 280 / v - 280 / ( v + 5 ) = 1 280 ( v + 5 ) - 280 v = ( v ) ( v + 5 ) 1400 = ( v ) ( v + 5 ) 35 * 40 = ( v ) ( v + 5 ) v = 35 mph the answer is a ."
Answer: a
Problem: the total age of a and b is 15 years more than the total age of b and c . c is how many years younger than a ?
Options: a ) 12 , b ) 15 , c ) c is elder than a , d ) data inadequate , e ) none
Rationale: "solution [ ( a + b ) - ( b + c ) ] = 15 â € ¹ = â € º a - c = 15 . answer b"
Answer: b
Problem: if the diagonal of a rectangle is 17 cm long and its perimeter is 46 cm , find the area of the rectangle .
Options: a ) 127 cm ^ 2
b ) 125 cm ^ 2
c ) 120 cm ^ 2
d ) 102 cm ^ 2
e ) none of them
Rationale: let length = x and breadth = y . then , 2 ( x + y ) = 46 or x + y = 23 and x ^ 2 + y ^ 2 = ( 17 ) ^ 2 = 289 . now , ( x + y ) ^ 2 = ( 23 ) ^ 2 < = > ( x ^ 2 + y ^ 2 ) + 2 xy = 529 < = > 289 + 2 xy = 529 = xy = 120 area = xy = 120 cm ^ 2 answer is c .
Answer: c
Problem: the toll for crossing a certain bridge is $ 0.75 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 11.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : e
Answer: e
Problem: mother , her daughter and her grand child weighs 160 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 40
Rationale: "mother + daughter + child = 160 kg daughter + child = 60 kg mother = 160 - 60 = 100 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 100 = 20 kg so now daughter = 120 - ( mother + child ) = 160 - ( 100 + 20 ) = 40 kg answer : e"
Answer: e
Problem: a batsman makes a score of 100 runs in the 17 th inning and thus increases his averages by 5 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 20 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 100 then average run after 17 th inning = ( 16 x + 100 ) / 17 ( 16 x + 100 ) / 17 = x + 5 = > 16 x + 100 = 17 x + 85 = > x = 15 x = 15 ; average after 17 th inning = 15 + 5 = 20 answer : c"
Answer: c
Problem: a fair coin is tossed 5 times . what is the probability of getting more heads than tails in 5 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Problem: the difference between the squares of two consecutive numbers is 35 . the numbers are
Options: a ) 14,15 , b ) 15,16 , c ) 17,18 , d ) 18,19 , e ) none
Rationale: "explanation : let the numbers be a and ( a + 1 ) ( a + 1 ) 2 − a 2 = 35 ⇒ a 2 + 2 a + 1 − a 2 = 35 ⇒ 2 a = 34 ⇒ 2 a = 34 or a = 17 the numbers are 17 & 18 . correct option : c"
Answer: c
Problem: john want to buy a $ 100 trouser at the store , but he think it ’ s too expensive . finally , it goes on sale for $ 60 . what is the percent decrease ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 70 % , e ) 80 %
Rationale: the is always the difference between our starting and ending points . in this case , it ’ s 100 – 60 = 40 . the “ original ” is our starting point ; in this case , it ’ s 100 . ( 40 / 100 ) * 100 = ( 0.4 ) * 100 = 40 % . c
Answer: c
Problem: if rs . 561 be divided among a , b , c in such a way that a gets 2 / 3 of what b gets and b gets 1 / 4 of what c gets , then their shares are respectively ?
Options: a ) s . 300 , b ) s . 360 , c ) s . 396 , d ) s . 368 , e ) s . 323
Rationale: "( a = 2 / 3 b and b = 1 / 4 c ) = a / b = 2 / 3 and b / c = 1 / 4 a : b = 2 : 3 and b : c = 1 : 4 = 3 : 12 a : b : c = 2 : 3 : 12 a ; s share = 561 * 2 / 17 = rs . 66 b ' s share = 561 * 3 / 17 = rs . 99 c ' s share = 561 * 12 / 17 = rs . 396 . answer : c"
Answer: c
Problem: a certain car can travel 56 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 78 , d ) 91 , e ) 104
Rationale: fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 56 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 56 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : d ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 56 x 3.9 x 3.8 / 5.7 x 1.6 = 91 d
Answer: d
Problem: if the length of the longest chord of a certain circle is 14 , what is the radius of that certain circle ?
Options: a ) 2.5 , b ) 5 , c ) 10 , d ) 7 , e ) 9
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 14 = 2 * 7 so radius of the circle = 7 correct answer - d"
Answer: d
Problem: at a certain organisation , the number of male members went up by 13 % in the year 2001 from year 2000 , and the number of females members went down by 6 % in the same time period . if the total membership at the organisation went up by 1.2 % from the year 2000 to 2001 , what was the ratio of male members to female members in the year 2000 ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 2 : 3 , d ) 3 : 5 , e ) 2 : 1
Rationale: men increase by 13 % = = > 1.13 m = males in 2001 women decrease by 6 % = = > 0.94 f = women in 2001 total employees increase by 1.2 % = = > 1.012 * ( m + f ) = total number of employees in 2001 obviously ( males in 2001 ) + ( females in 2001 ) = total number of employees in 2001 1.13 m + 0.94 f = 1.012 * ( m + f ) 1.13 m + 0.94 f = 1.012 m + 1.012 f 1.13 m - 1.012 m = 1.012 f - 0.94 f 0.108 m = 0.072 f m / f = ( 0.072 ) / ( 0.118 ) = 72 / 118 = 3 / 5 answer = ( d )
Answer: d
Problem: in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 50 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 1,000
Rationale: "this is a rather straight forward ratio problem . 1 . 40 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 40 / x thus , x = 1000 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . e"
Answer: e
Problem: set a of 8 positive integers may have the same element and have 35 . and set b of 8 positive integers must have different elements and have 35 . when m and n are the greatest possible differences between 35 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 26 , c ) 23 , d ) 25 , e ) 21
Rationale: this is maximum - minimum . hence , 35 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 28 and 35 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 7 . so , 28 - 7 = 21 . the correct answer is e .
Answer: e
Problem: a vessel of capacity 50 litres is fully filled with pure milk . nine litres of milk is removed from the vessel and replaced with water . nine litres of the solution thus formed is removed and replaced with water . find the quantity of pure milk in the final milk solution ?
Options: a ) 23.89 , b ) 72.9 , c ) 33.62 , d ) 78.3 , e ) 79.3
Rationale: "explanation : let the initial quantity of milk in vessel be t litres . let us say y litres of the mixture is taken out and replaced by water for n times , alternatively . quantity of milk finally in the vessel is then given by [ ( t - y ) / t ] ^ n * t for the given problem , t = 50 , y = 9 and n = 2 . hence , quantity of milk finally in the vessel = [ ( 50 - 9 ) / 50 ] ^ 2 ( 50 ) = 33.62 litres . answer : option c"
Answer: c
Problem: on a saturday night , each of the rooms at a certain motel was rented for either $ 40 or $ 60 . if 10 of the rooms that were rented for $ 60 had instead been rented for $ 40 , then the total rent the motel charged for that night would have been reduced by 20 percent . what was the total rent the motel actually charged for that night ?
Options: a ) $ 600 , b ) $ 800 , c ) $ 1,000 , d ) $ 1,600 , e ) $ 2,400
Rationale: "let total rent the motel charge for all rooms = x if 10 rooms that were rented for 60 $ had instead been rented for 40 $ , then total difference in prices = 20 $ * 10 = 200 $ total rent the motel charged would have been reduced by 20 % . 2 x = 200 = > x = 1000 answer c"
Answer: c
Problem: total of the ages of a , b ahd c at present is 90 years . 10 years ago , the ratio of their ages was 1 : 2 : 3 . what is the age of b at present
Options: a ) 25 , b ) 30 , c ) 45 , d ) 60 , e ) 65
Rationale: explanation : let their ages 10 years ago is x , 2 x and 3 x years . 10 + 2 x + 10 + 3 x + 10 = 90 hence x = 10 b � s present age = ( 2 x + 10 ) = 30 years answer : option b
Answer: b
Problem: ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 8.0 = ?
Options: a ) - 0.53 , b ) 1.0 , c ) 1.07 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 7.0 = - 0.53 answer a"
Answer: a
Problem: two pipes a and b can separately fill a tank in 12 and 20 minutes respectively . a third pipe c can drain off 45 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 542 , b ) 540 , c ) 675 , d ) 829 , e ) 279
Rationale: 1 / 12 + 1 / 20 - 1 / x = 1 / 15 x = 15 15 * 45 = 675 answer : c
Answer: c
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability e that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes e = 15 / 36 . answer : c ."
Answer: c
Problem: if 100 < x < 199 and 20 < y < 100 , then the product xy can not be equal to :
Options: a ) 1900 , b ) 19,303 , c ) 19 , 356.732 , d ) 19,502 , e ) 19,909
Rationale: "correct answer : ( a ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 20 . the largest value must be less than 199 * 100 . this means that 2000 < xy < 19,900 . ( a ) is outside of this range , so it is not a possible product of xy ."
Answer: a
Problem: if d | | d ' , d : 2 x - y = 1 and d ' : ( a - 1 ) x + 2 y = x - 2 , then find the value of a .
Options: a ) - 3 , b ) - 2 , c ) - 1 , d ) 0 , e ) 1
Rationale: d : 2 x − y = 1 , d ’ : ( a − 1 ) x + 2 y = x − 2 d : 2 x − y = 1 , d ′ : ( a − 1 ) x + 2 y = x − 2 d ∥ d ′ ⇒ md = m ′ dd ∥ d ′ ⇒ md = md ′ 2 x − y = 1 → y = 2 x − 1 → md = 22 x − y = 1 → y = 2 x − 1 → md = 2 ( a − 1 ) x + 2 y = x − 2 → 2 y = x ( 1 − a + 1 ) − 2 → 2 y = x ( 2 − a ) − 2 → ( a − 1 ) x + 2 y = x − 2 → 2 y = x ( 1 − a + 1 ) − 2 → 2 y = x ( 2 − a ) − 2 → y = x × ( 2 − a ) 2 − 1 → m ′ d = ( 2 − a ) 2 y = x × ( 2 − a ) 2 − 1 → md ′ = ( 2 − a ) 2 md = m ′ d → ( 2 − a ) 2 = 2 → 2 − a = 4 → a = − 2 answer : b - 2
Answer: b
Problem: money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 2500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 8,100 , d ) $ 15,000 , e ) $ 22,500
Rationale: solution : money compounded annually at x % triples in 112 / x years . we need to find the final amount of 2500 at the end of the 28 years . . compounded annually at 8 % by putting the value in formula it will give us = 2500 ( 1.08 ) ^ 28 there must be a relation between these two conditions ? x = 8 % so money will triple in 112 / 8 = 14 years so money will be 3 ^ 2 = 9 times in 28 years so 2500 * 9 = 22500 answer : e
Answer: e
Problem: let a be the event that a randomly selected two digit number is divisible by 3 and let b be the event that a randomly selected two digit number is divisible by 2 . what is p ( a and b ) ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 3 * 1 / 2 = 1 / 6 the answer is b ."
Answer: b
Problem: replace x with the appropriate number in 4 , 5 , 14 , 15 , 24 , 25 , x
Options: a ) 30 , b ) 29 , c ) 34 , d ) 21 , e ) 20
Rationale: c list of consecutive numbers that has an ' f ' in the spelling
Answer: c
Problem: the radius of a semi circle is 3.5 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 32.1 , d ) 18 , e ) 32.9
Rationale: "diameter = 7 cm 1 / 2 * 22 / 7 * 7 + 7 = 18 answer : d"
Answer: d
Problem: if bill can buy 3 pairs of jeans and 2 shirts for $ 69 or 2 pairs of jeans and 3 shirts for $ 71 , how much does one shirt cost ?
Options: a ) $ 10 , b ) $ 12 , c ) $ 13.20 , d ) $ 15 , e ) $ 16.80
Rationale: "3 j + 2 s = 69 2 j + 3 s = 71 - - - - - - - - - - - - - - - - 5 j + 5 s = 140 - - - - ( divide by 5 ) - - - > j + s = 28 3 j + 2 s = j + 2 ( j + s ) = j + 56 = 69 - - - > j = 13 3 * 13 + 2 s = 69 39 + 2 s = 69 2 s = 30 s = 15 answer : d"
Answer: d
Problem: 3 friends a , b , c went for week end party to mcdonald ’ s restaurant and there they measure there weights in some order in 7 rounds . a , b , c , ab , bc , ac , abc . final round measure is 165 kg then find the average weight of all the 7 rounds ?
Options: a ) 94.2 kgs , b ) 88.5 kgs , c ) 86.5 kgs , d ) 67.5 kgs , e ) 88.2 kgs
Rationale: "average weight = [ ( a + b + c + ( a + b ) + ( b + c ) + ( c + a ) + ( a + b + c ) ] / 7 = 4 ( a + b + c ) / 7 = 4 x 165 / 7 = 94.2 kgs answer : a"
Answer: a
Problem: the area of a rectangular field is equal to 800 square meters . its perimeter is equal to 120 meters . find the width of this rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "l * w = 800 : area , l is the length and w is the width . 2 l + 2 w = 120 : perimeter l = 60 - w : solve for l ( 60 - w ) * w = 800 : substitute in the area equation w = 20 and l = 40 correct answer d"
Answer: d
Problem: lisa and robert have taken the same number of photos on their school trip . lisa has taken 3 times as many photos as claire and robert has taken 20 more photos than claire . how many photos has claire taken ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "l = r l = 3 c r = c + 20 3 c = c + 20 c = 10 the answer is c ."
Answer: c
Problem: in a company , 48 percent of the employees are men . if 60 percent of the employees are unionized and 70 percent of these are men , what percent of the non - union employees are women ?
Options: a ) 85 % , b ) 80 % , c ) 75 % , d ) 70 % , e ) 65 %
Rationale: "the percent of employees who are unionized and men is 0.7 * 0.6 = 42 % the percent of employees who are unionized and women is 60 - 42 = 18 % 52 % of all employees are women , so non - union women are 52 % - 18 % = 34 % 40 % of all employees are non - union . the percent of non - union employees who are women is 34 % / 40 % = 85 % the answer is a ."
Answer: a
Problem: by weight , liquid x makes up 0.8 percent of solution a and 1.8 percent of solution b . if 500 grams of solution a are mixed with 700 grams of solution b , then liquid x accounts for what percent of the weight of the resulting solution ?
Options: a ) 1.66 % , b ) 1.96 % , c ) 10 % , d ) 15 % , e ) 19 %
Rationale: "i think there is a typo in question . it should have been ` ` by weight liquid ' x ' makes up . . . . . ` ` weight of liquid x = 0.8 % of weight of a + 1.8 % of weight of b when 500 gms of a and 700 gms of b is mixed : weight of liquid x = ( 0.8 * 500 ) / 100 + ( 1.8 * 700 ) / 100 = 16.6 gms % of liquid x in resultant mixture = ( 16.6 / 1000 ) * 100 = 1.66 % a"
Answer: a
Problem: what number has a 5 : 1 ratio to the number 9 ?
Options: a ) 45 , b ) 50 , c ) 88 , d ) 52 , e ) 12
Rationale: "5 : 1 = x : 9 x = 45 answer : a"
Answer: a
Problem: there are 100 employees in a room . 99 % are president . how many managers must leave the room to bring down the percentage of president to 98 % ?
Options: a ) 1 , b ) 2 , c ) 46 , d ) 50 , e ) 97
Rationale: "we have 99 presidents and 1 director . that 1 director to compose 2 % of the total number of people , there must be 50 people in the room , hence 50 presidents must leave . answer : b ."
Answer: b
Problem: what is the compound interest paid on a sum of rs . 3000 for the period of 3 years at 10 % per annum .
Options: a ) 900 , b ) 930 , c ) 990 , d ) 993 , e ) none of these
Rationale: "solution = interest % for 1 st year = 10 interest % for 2 nd year = 10 + 10 % of 10 = 10 + 10 * 10 / 100 = 11 interest % for 3 rd year = 10 + 10 % ( 10 + 11 ) = 10 + 2.1 = 12.1 total % of interest = 10 + 11 + 12.1 = 33.1 total interest = 33.1 % 3000 = 3000 * ( 33.1 / 100 ) = 993 answer d"
Answer: d
Problem: how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 35 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 10 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 10 x = 15 since you need a 15 l solution , you must evaporate 35 of the original 50 l solution to get a 10 % solution . answer is a ."
Answer: a
Problem: a person borrows rs . 6000 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 ) 120 rs , b ) 150 rs , c ) 160 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 6000 * 6 * 2 ) / 100 ] - [ ( 6000 * 4 * 2 ) / 100 ] 720 - 480 = 240 gain in 1 year = ( 240 / 2 ) = 120 rs answer : a"
Answer: a
Problem: a person crosses a 1440 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 7.2
Rationale: "speed = 1440 / ( 12 x 60 ) m / sec = 2 m / sec . converting m / sec to km / hr = 2 x ( 18 / 5 ) km / hr = 7.2 km / hr . answer : e"
Answer: e
Problem: an object thrown directly upward is at a height of h feet after t seconds , where h = - 14 ( t - 3 ) ^ 2 + 140 . at what height , in feet , is the object 2 seconds after it reaches its maximum height ?
Options: a ) 62 , b ) 68 , c ) 76 , d ) 84 , e ) 96
Rationale: "we see that h will be a maximum h = 140 when t - 3 = 0 , that is when t = 3 . at t = 5 , h = - 14 ( 5 - 3 ) ^ 2 + 140 = - 14 ( 4 ) + 140 = 84 the answer is d ."
Answer: d
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage x .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: "given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % x = ( 97 / 556 ) * 100 = 17.4 % answer : b"
Answer: b
Problem: the amount of time that three people worked on a special project was in the ratio of 2 to 3 to 4 . if the project took 90 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 18 hours , b ) 22 hours , c ) 25 hours , d ) 26 hours , e ) 20 hours
Rationale: "let the persons be a , b , c . hours worked : a = 2 * 90 / 9 = 20 hours b = 3 * 90 / 9 = 30 hours c = 4 * 90 / 9 = 40 hours c is the hardest worker and a worked for the least number of hours . so the difference is 40 - 20 = 20 hours . answer : e"
Answer: e
Problem: a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 9 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 9 ) x solve for r , r = 33 33 - 9 = 24 mpg d"
Answer: d
Problem: the ratio of the radius of two circles is 2 : 7 , and then the ratio of their areas is ?
Options: a ) 1 : 7 , b ) 2 : 9 , c ) 1 : 9 , d ) 4 : 49 , e ) 3 : 4
Rationale: "r 1 : r 2 = 2 : 7 î r 1 ^ 2 : î r 2 ^ 2 r 1 ^ 2 : r 2 ^ 2 = 4 : 49 answer : d"
Answer: d
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many q miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) q = 24 miles . d is the correct answer ."
Answer: d
Problem: there are 7 thieves . they stole diamonds from a diamond merchant and ran away . while running , night sets in and they decide to rest in the jungle . when everybody was sleeping , two of them woke up and decided to divide the diamonds equally among themselves . but when they divided the diamonds equally , one diamond is left . so they woke up the 3 rd thief and tried to divide the diamonds equally again but still one diamond was left . then they woke up the 4 th thief to divide the diamonds equally again , and again one diamond was left . this happened with the 5 th and 6 th thief – one diamond was still left . finally , they woke up the 7 th thief and this time the diamonds were divided equally . how many diamonds did they steal in total ?
Options: a ) 1560 , b ) 1561 , c ) 1559 , d ) 1557 , e ) none of the above
Rationale: we need a number that is a multiple of 7 that will give a remainder of 1 when divided by 2 , 3 , 4 , 5 , and 6 . the least common multiple of these numbers is 60 . so , we need a multiple of 7 that is 1 greater than a multiple of 60 . answer b
Answer: b
Problem: in a race where 15 cars are running , the chance that car x will win is 1 / 4 , that y will win is 1 / 8 and that z will win is 1 / 12 . assuming that a dead heat is impossible , find the chance that one of them will win .
Options: a ) 1 / 140 , b ) 1 / 180 , c ) 11 / 24 , d ) 10 / 15 , e ) 57 / 120
Rationale: "required probability = p ( x ) + p ( y ) + p ( z ) ( all the events are mutually exclusive ) . = 1 / 4 + 1 / 8 + 1 / 12 = 11 / 24 answer : c"
Answer: c
Problem: find the compound interest on $ 26,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532.93 , b ) 2552.26 , c ) 2524.23 , d ) 4098.25 , e ) 2512.23
Rationale: "principal = $ 26000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 26000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 30098.25 ci . = $ ( 30098.25 - 26000 ) = $ 4098.25 answer d ."
Answer: d
Problem: some of 50 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 1 / 3 , b ) 1 / 5 , c ) 2 / 3 , d ) 3 / 4 , e ) 4 / 5
Rationale: "40 % is 20 % - points above 20 % and 10 % - points below 50 % . thus the ratio of 20 % - solution to 50 % - solution is 1 : 2 . 1 / 3 of the original paint was replaced . the answer is a ."
Answer: a
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 50 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 40 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 38 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 40 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 46 hence answer is e"
Answer: e
Problem: how many three digit numbers r are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples r - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Problem: the malibu country club needs to drain its pool for refinishing . the hose they use to drain it can remove 60 cubic feet of water per minute . if the pool is 60 feet wide by 150 feet long by 10 feet deep and is currently at 80 % capacity , how long will it take to drain the pool ?
Options: a ) 1800 , b ) 1000 , c ) 1200 , d ) 1400 , e ) 1600
Rationale: "volume of pool = 60 * 150 * 10 cu . ft , 80 % full = 60 * 150 * 10 * 0.8 cu . ft water is available to drain . draining capacity = 60 cu . ft / min therefore time taken = 60 * 150 * 10 * 0.8 / 60 min = 1200 min c"
Answer: c
Problem: a shopkeeper labeled the price of his articles so as to earn a profit of 50 % on the cost price . he then sold the articles by offering a discount of 10 % on the labeled price . what is the actual percent profit earned in the deal ?
Options: a ) 35 % , b ) 20 % , c ) 17 % , d ) 18 % , e ) none of these
Rationale: "explanation : let the cp of the article = rs . 100 . then labeled price = rs . 150 . sp = rs . 150 - 10 % of 150 = rs . 150 - 15 = rs . 135 . gain = rs . 135 â € “ rs . 100 = rs . 35 therefore , gain / profit percent = 35 % . answer : option a"
Answer: a
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 770 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 193 , c ) 195 , d ) 212 , e ) 213
Rationale: "total movies submitted are 770 . as per question we need to take 1 / 4 of 770 to be considered for top 10 movies = 192.25 approximate the value we 193 imo option b is the correct answer . . ."
Answer: b
Problem: 1 / 3 of girls , 1 / 2 of boys go to canteen . what factor and total number of classmates go to canteen .
Options: a ) 1 / 5 , b ) 1 / 4 , c ) 1 / 3 , d ) 2 / 5 , e ) 2 / 3
Rationale: let total girls be 3 . . . and total boys be 2 . . . so total girls going to canteen = 1 boys going to canteen = 1 total no . of classmates = 5 ( only suppose . . . . . . to find out the factor of students going to canteen . . . ) factor of classmates going to canteen = 2 / 5 . answer : d
Answer: d
Problem: suraj has a certain average of runs for 9 innings . in the 10 th innings he scores 200 runs thereby increasing his average by 8 runs . what is his average after the 10 th innings ?
Options: a ) 149 , b ) 190 , c ) 128 , d ) 178 , e ) 190
Rationale: "to improve his average by 8 runs per innings he has to contribute 9 x 8 = 72 runs for the previous 8 innings . thus , the average after the 9 th innings = 200 - 72 = 128 . answer : c"
Answer: c
Problem: at a particular graduation party with 220 guests , 70 % of the guests brought gifts , and 40 % of the female guests brought gifts . if 12 males did not bring gifts to the party , how many females did bring gifts ?
Options: a ) 18 , b ) 36 , c ) 42 , d ) 68 , e ) 70
Rationale: "the correct method total = 220 . . 70 % of 220 = 154 got gifts . . 66 did not get gift , out of which 12 are males , so remaining 60 - 12 = 54 are females . . but 40 % females brought gift , so 60 % did not get it . . so 60 % = 54 , 100 % = 54 * 100 / 60 = 90 . . ans 40 % of 90 = 36 b"
Answer: b
Problem: if ( 1 / 5 ) ^ m * ( 1 / 4 ) ^ 3 = 1 / ( 2 * ( 10 ) ^ 3 ) , then m =
Options: a ) 4 , b ) 3 , c ) 1 , d ) 6 , e ) 8
Rationale: "1 / 5 ^ m * 1 / 4 ^ 3 = 2 * 1 / 2 ^ 3 * 5 ^ 3 * 8 2 ^ 3 * 5 ^ 3 * 8 / 4 ^ 3 = 5 ^ m or 5 ^ 3 = 5 ^ m m = 3 b"
Answer: b
Problem: in town x , 64 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 34 % , e ) 52 %
Rationale: "we are asked to find the percentage of females in employed people . total employed people 64 % , out of which 42 are employed males , hence 22 % are employed females . ( employed females ) / ( total employed people ) = 22 / 64 = 34 % answer : d ."
Answer: d
Problem: if n divided by 7 has a remainder of 1 , what is the remainder when 3 times n is divided by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "as per question = > n = 7 p + 1 for some integer p hence 3 n = > 21 q + 3 = > remainder = > 6 for some integer q alternatively = > n = 2 > 3 n = > 3 = > 3 divided by 7 will leave a remainder 3 hence c"
Answer: c
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 53 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 3 . so , one more solution , where a = b is not possible . so , answer will be c ."
Answer: c
Problem: in a house , there are 4 birds , 3 dogs , and 18 cats living with the human family . if the total number of feet in the house are 74 more than the number of heads in the house , how many family members are there ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: explanation : let number of family members be x . then , total number of feet = 2 x 4 + 4 x 3 + 4 x 18 + 2 x = 2 x + 92 . total number of heads = 4 + 3 + 18 + x = 25 + x . therefore ( 2 x + 92 ) = ( 25 + x ) + 74 or x = 7 . answer : d
Answer: d
Problem: what will be the fraction of 33.33 %
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 3 , d ) 1 / 8 , e ) none of above
Rationale: "explanation : it will 33.33 * 1 / 100 = 1 / 3 answer : option c"
Answer: c
Problem: the ratio of the adjacent angles of a parallelogram is 6 : 9 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 6 x + 9 x = 180 ° or , 15 x = 180 ° or , x = 12 ° hence the angles of the parallelogram are 72 ° and 108 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 72 ° + 84 ° = 156 ° answer : c"
Answer: c
Problem: the h . c . f . of two numbers is 12 and their difference is 12 . the numbers are
Options: a ) 66 , 78 , b ) 70 , 82 , c ) 94 , 106 , d ) 84 , 96 , e ) none
Rationale: "solution out of the given numbers , the two with h . c . f . 12 and difference 12 are 84 and 96 answer d"
Answer: d
Problem: if the length and breadth of a room are increased by y feet each , the perimeter increases by 16 feet . find y
Options: a ) 8
b ) 2
c ) 6
d ) 4
e ) 3
Rationale: 2 ( l + b ) = x ; 2 ( l + y + b + y ) = x + 16 ; 2 ( l + b ) + 4 y = x + 16 ; x + 4 y = x + 16 ; y = 4 answer : d
Answer: d
Problem: jack and paul are running 1000 m . jack runs 1.5 km / hr faster than paul but also finishes the race 1.5 sec earlier . what is the speed of jack ? ?
Options: a ) 19.6 , b ) 20.6 , c ) 21.6 , d ) 22.6 , e ) 23.6
Rationale: distance ( given ) 1000 m paul speed ( let ) = x m / s time ( paul take ) = 1000 / x sec jack speed = x + 1.5 * ( 5 / 18 ) m / s tym ( jack ) = 1000 / ( x + 7.5 / 18 ) s tym ( paul ) - tym ( jack ) = 1.5 solving for x we get 20.20 speed of jack is 20.20 + 7.5 / 18 = 20.61 answer : b
Answer: b
Problem: the speed of boat in still water is 20 km / hr . if it travels 26 km downstream and 14 km upstream in same time , what is the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 2
Rationale: explanation : let x be speed of stream speed of boat downstream = ( 20 + x ) speed of boat upstream = ( 20 – x ) it is given that boat takes same time to travel 26 km downstream and 14 km upstream [ 26 / ( 20 + x ) ] = [ 14 / ( 20 – x ) ] 520 – 26 x = 280 + 14 x 40 x = 240 x = 6 km / hr answer : a
Answer: a
Problem: on my sister ' s birthday , she was 147 cm in height , having grown 5 % since the year before . how tall was she the previous year ?
Options: a ) 145 cm , b ) 140 cm , c ) 142 cm , d ) 138 cm , e ) 135 cm
Rationale: "let the previous year ' s height be x . 1.05 x = 147 x = 140 the answer is b ."
Answer: b
Problem: if the sum of the 4 th term and the 12 th term of an arithmetic progression is 10 , what is the sum of the first 15 terms of the progression ?
Options: a ) 65 , b ) 75 , c ) 60 , d ) 55 , e ) 50
Rationale: "4 th term + 12 th term = 10 i . e . , ( a + 3 d ) + ( a + 11 d ) = 10 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 10 - - - - - - - - - - - - - - - from ( 1 ) = 75 answer : b"
Answer: b
Problem: during a certain season , a team won 65 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 75 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 65 percent of its first 100 games . this means the team won 0.65 x 100 = 65 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 65 + 0.5 t – 50 = 0.7 t 15 = 0.2 t 150 = 2 t 75 = t answer is b ."
Answer: b
Problem: worker a takes 8 hours to do a job . worker b takes 10 hours to do a job . how long should it take both a and b , working together to do same job .
Options: a ) 4 / 9 , b ) 2 4 / 9 , c ) 3 4 / 9 , d ) 4 4 / 9 , e ) none of these
Rationale: "explanation : in this type of questions , first we need to calculate 1 hours work , then their collective work as , a ' s 1 hour work is 1 / 8 b ' s 1 hour work is 1 / 10 ( a + b ) ' s 1 hour work = 1 / 8 + 1 / 10 = 9 / 40 so both will finish the work in 40 / 9 hours = 4 4 / 9 option d"
Answer: d
Problem: a man can row downstream at 18 kmph and upstream at 12 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 4 , e ) 9
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 18 - - - ( 1 ) and x - y = 12 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 30 = > x = 15 , y = 3 . answer : a"
Answer: a
Problem: the weight of a glass of jar is 25 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 7 / 15
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 25 g weight of coffee beans = 75 g weight of jar and remaining beans = 60 g weight of remaining beans = 35 g fraction remaining = 35 / 75 = 7 / 15 answer is e ."
Answer: e
Problem: one ton has 2500 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 2000 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2500 pound = 13 * 2500 * 16 ounces . hence the answer is ( 13 * 2500 * 16 ) / 260 = 2000 . answer : a ."
Answer: a
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 28 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 70.20 % , e ) none of these
Rationale: girls = 900 , boys = 1100 passed = ( 28 % of 1100 ) + ( 32 % of 900 ) = 308 + 288 = 596 failed = 2000 - 596 = 1404 failed % = [ ( 1404 / 2000 ) x 100 ] % = 70.2 % . answer : d
Answer: d
Problem: for what value of x , is | x – 5 | + | x + 4 | + | x | = 14 ?
Options: a ) 0 , b ) 3 , c ) 4 , d ) - 4 , e ) 5
Rationale: "for what value of x , is | x – 5 | + | x + 4 | + | x | = 14 ? it ' s easiest just to plug in answer choices : ( e ) : 5 | x – 5 | + | x + 4 | + | x | = 14 ? | 5 - 5 | + | 5 + 4 | + | 5 | = 14 ? | 0 | + | 9 | + | 5 | = 14 ( e )"
Answer: e
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 3 : 7 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 2000 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 3 x and r = 7 x . then , 5 x = 1500 ? x = 500 . p = 1500 , q = 1500 and r = 3500 . hence , ( r - p ) = ( 3500 - 1500 ) = 2000 answer : d"
Answer: d
Problem: a , b and c are employed to do apiece of work for rs . 529 . a and c are supposed to finish 19 / 23 of the work together . how much shall be paid to b ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 16
Rationale: c 12 12 men can complete a work in 18 days . six days after they started working , 4 more men joined them . how many days will all of them together complete the remaining work ?
Answer: c
Problem: a train 990 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 2898 , b ) 277 , c ) 310 , d ) 297 , e ) 435
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 990 + x ) / 60 = 65 / 3 x = 310 m . answer : c"
Answer: c
Problem: calculate how many days it will take for 5 boys to paint a 30 m long fence if 2 boys can paint a 20 m long fence in 3 days ,
Options: a ) 6.80 days , b ) 4.80 days , c ) 3.80 days , d ) 2 days , e ) 1.80 days
Rationale: "the length of wall painted by one boy in one day = 20 / 2 * 1 / 3 = 3.33 m no . of days required to paint 50 m cloth by 8 boys = 30 / 5 * 1 / 3.33 = 1.80 days . e"
Answer: e
Problem: find the value of ( 28 + 48 / 69 ) × 69
Options: a ) 1980 , b ) 1982 , c ) 1930 , d ) 1988 , e ) 1680
Rationale: "= ( 28 + 48 / 69 ) × 69 = ( 1932 + 48 ) / 69 × 69 = 1980 / 69 × 69 = 1980 answer is a ."
Answer: a
Problem: a soccer store typically sells replica jerseys at a discount of 20 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 4 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 30 , d ) 31 / 45 , e ) 11 / 15
Rationale: "i think d - 31 / 45 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 4 x so old = x , new = 3 x now 1 / 3 of x are occupied and 1 / 5 of 3 x are occupied which simplifies to ( 3 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 3 / 5 of x occupied in the new ward . add them up to get 14 / 15 of x there are 3 x beds in new tower so ratio is : ( 14 / 15 ) x / 3 x = 14 / 45 of x subtract that from 45 / 45 of x and you get the number of un - occupied beds to total capacity of new tower = 31 / 45 d"
Answer: d
Problem: if jake loses 32 pounds , he will weigh twice as much as his sister . together they now weigh 212 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 152 , e ) 188
Rationale: lets say j is the weight of jack and s is the wt of his sister . if he loses 32 pounds , he s twice as heavy as his sister . j - 32 = 2 * s also , together they weight 212 pounds j + s = 212 solvong the 2 equation , we get j = 152 pounds ! d
Answer: d
Problem: a train 125 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 sec . the speed of the train is ?
Options: a ) 225 km / hr , b ) 50 km / hr , c ) 99 km / hr , d ) 88 km / hr , e ) 66 km / hr
Rationale: "speed of the train relative to man = 125 / 10 = 25 / 2 m / sec . = 25 / 2 * 18 / 5 = 45 km / hr let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 45 = > x = 50 km / hr . answer : b"
Answer: b
Problem: how many cuboids of length 6 m , width 4 m and height 3 m can be farmed from a cuboid of 18 m length , 15 m width and 2 m height .
Options: a ) 2.6 , b ) 5.8 , c ) 6.2 , d ) 7.5 , e ) 1.2
Rationale: "( 18 ã — 15 ã — 2 ) / ( 6 ã — 4 ã — 3 ) = 7.5 answer is d ."
Answer: d
Problem: how many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 28 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 180 = 280 s = 36 * 5 / 18 = 10 mps t = 280 / 10 = 28 sec answer : option c"
Answer: c
Problem: there are 36 students in a certain geometry class . if one third of the students are boys and one fourth of the boys are under 6 feet tall , how many boys in the class are under 6 feet tall ?
Options: a ) 3 , b ) 12 , c ) 18 , d ) 24 , e ) 27
Rationale: total students = 36 one third of the students are boys = 1 / 3 * 36 = 12 one fourth of the boys are under six feet tall = 1 / 4 * 12 = 3 . . . therefore number of boys in the class under six feet tall = 3 . . . answer a . . . . alternatively . . . number of boys in the class under six feet tall = 1 / 4 of 1 / 3 of total students = 1 / 4 * 1 / 3 * 36 = 3 . . . answer a
Answer: a