Cheukting/mathqa huggingface dataset:
Question (physics): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (probability): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (geometry): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (general): ( ( - 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (other): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (geometry): 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
Question (physics): 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