Cheukting/mathqa huggingface dataset:
Question (general): in a class , 20 % of the students were absent for an exam . 30 % failed by 20 marks and 10 % just passed . find the average score of the class if the remaining students scored an average of 65 marks and the cut off for passing the exam is 40 .
Options: a ) 36 , b ) 302 , c ) 272 , d ) 292 , e ) 271
Rationale: explanation : let total students be 100 . hence , marks of 20 students is 0 as they were absent . 30 students scored 20 marks ( as they failed by 20 marks ) 10 students scored 40 marks ( just passed ) 40 students scored 65 marks ( average of 65 ) therefore , average score of the class is : ( 0 + 600 + 400 + 2600 ) / 100 = 3600 / 100 = 36 answer : a
Answer: a
Question (general): a library has an average of 510 visitors on sundays and 240 on other days . the avearge number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 150 , b ) 225 , c ) 285 , d ) 315 , e ) 374
Rationale: "since the month begin with sunday , so there will be five sundays in the month required average = ( 510 * 5 + 240 * 25 ) / 30 = 8550 / 30 = 285 answer is c"
Answer: c
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 40 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 85 , d ) 95 , e ) 60
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 40 = > 20 = x - 40 = > x = 20 + 40 = 60 answer is e ."
Answer: e
Question (physics): how long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length ?
Options: a ) 16.5 , b ) 16.0 , c ) 16.4 , d ) 14 , e ) 16.1
Rationale: "d = 110 + 170 = 280 m s = 72 * 5 / 18 = 20 t = 280 * 1 / 20 = 14 sec answer : d"
Answer: d
Question (general): find large number from below question the difference of two numbers is 250 . on dividing the larger number by the smaller , we get 5 as quotient and the 14 as remainder
Options: a ) 120 , b ) 135 , c ) 140 , d ) 309 , e ) 369
Rationale: "let the smaller number be x . then larger number = ( x + 250 ) . x + 250 = 5 x + 14 4 x = 236 x = 59 large number = 59 + 250 = 309 d"
Answer: d
Question (probability): what is the probability of drawn an ace or a space or both from a dew of cards .
Options: a ) 14 / 52 , b ) 15 / 52 , c ) 16 / 52 , d ) 17 / 52 , e ) 18 / 52
Rationale: "there are 13 spades in a standard deck of cards . there are four aces in a standard deck of cards . one of the aces is a spade . so , 13 + 4 - 1 = 16 spades or aces to choose from . since we have a total of 52 cards , the probability of selecting an ace or a spade is 16 / 52 answer : c"
Answer: c
Question (gain): the water level in a reservoir has been dropping at the rate of 14 inches per day . exactly 4 days ago , the water level was at w inches . what will be the water level exactly 4 days from now if the rate at which the level is dropping remains the same ?
Options: a ) w − 126 , b ) w − 112 , c ) w − 14 , d ) w + 14 , e ) w + 126
Rationale: "drop = 14 inches / day 4 days ago = w , means now it ' s equal w - 56 and in 4 days = w - 56 - 56 = w - 112 answer b"
Answer: b
Question (gain): thirty percent of the women in a college class are science majors , and the non - science majors make up 80 % of the class . what percentage of the men are non - science majors if 40 % of the class are men ?
Options: a ) 2 % , b ) 5 % , c ) 28 % , d ) 30 % , e ) 95 %
Rationale: "3 / k + 2 / m = 6 / t assuming total # is 100 : [ science - women ] will have - 0.3 * 60 = 18 [ non - science - women ] will have - 42 [ science - men ] will have = 20 - 18 = 2 [ non - science - men ] will have - 38 s 0 38 / 40 * 100 = 95 % answer - e"
Answer: e
Question (general): an amount of rs . 1000 is to be distributed amongst p , q , r and s such that “ p ” gets twice as that of “ q ” and “ s ” gets 4 times as that of “ r ” . if “ q ” and “ r ” are to receive equal amount , what is the difference between the amounts received by s and p ?
Options: a ) 2378 , b ) 2697 , c ) 250 , d ) 5000 , e ) 6971
Rationale: explanation : we have , p = 2 q & s = 4 r further q = r & p + q + r + s = 1,000 thus we get , 2 q + q + q + 4 q = 1,000 8 q = 1,000 or q = rs . 125 thus , r = rs . 125 , p = 250 & s = rs . 500 hence , the required difference = ( s – p ) = ( 500 – 250 ) = rs . 250 answer : c
Answer: c
Question (general): a certain galaxy is known to comprise approximately 4 x 10 ^ 10 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "total no . of stars on galaxy = 4 * 10 ^ 10 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 4 * 10 ^ 10 / 50 * 10 ^ 6 = 40 * 10 ^ 2 / 5 = 800 therefore answer is a"
Answer: a
Question (physics): ajay can walk 6 km in 1 hour . in how many hours he can walk 45 km ?
Options: a ) 5 hrs , b ) 10 hrs , c ) 7.5 hrs , d ) 20 hrs , e ) 30 hrs
Rationale: "1 hour he walk 6 km he walk 45 km in = 45 / 6 * 1 = 7.5 hours answer is c"
Answer: c
Question (gain): a man sells a car to his friend at 13 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 21724.14 , b ) rs . 31724.14 , c ) rs . 51724.14 , d ) rs . 61724.14 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 13 % . now s . p = rs . 45000 and loss = 13 % c . p . rs . [ 100 / 87 ã — 45000 ] = rs . 51724.14 . correct option : c"
Answer: c
Question (general): n 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b the present age of b is
Options: a ) 22 , b ) 897 , c ) 268 , d ) 20 , e ) 48
Rationale: a + 10 = 2 ( b - 10 ) . . . . . . . . ( 1 ) a = b + 9 . . . . . . . . . ( 2 ) from equations . 1 & 2 we get b = 39 a will be 39 + 9 = 48 years old . answer : e
Answer: e
Question (general): rs . 700 is divided among a , b , c so that a receives half as much as b and b half as much as c . then c ' s share is
Options: a ) rs 429 , b ) rs 412 , c ) rs 400 , d ) rs 129 , e ) rs 122
Rationale: "let c = x . then b = x / 2 and a = x / 4 a : b : c = 1 : 2 : 4 . c ' s share rs . [ ( 4 / 7 ) * 700 ) = 400 answer : c"
Answer: c
Question (geometry): if the height of a cone is increased by 130 % then its volume is increased by ?
Options: a ) 100 , b ) 777 , c ) 998 , d ) 729 , e ) 130
Rationale: "100 % answer : e"
Answer: e
Question (general): the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 5 ?
Options: a ) 10 ^ 6 , b ) 10 ^ 7 , c ) 10 ^ 8 , d ) 10 ^ 9 , e ) 10 ^ 10
Rationale: "0.1 = 10 ^ - 1 ( 0.01 ) ^ 5 = ( 10 ^ - 2 ) ^ 5 = 10 ^ - 10 10 ^ 9 * 10 ^ - 10 = 10 ^ - 1 the answer is d ."
Answer: d
Question (general): a number exceeds by 15 from its 3 / 8 part . then the number is ?
Options: a ) a ) 32 , b ) b ) 24 , c ) c ) 39 , d ) d ) 40 , e ) e ) 45
Rationale: x – 3 / 8 x = 15 x = 24 answer : b
Answer: b
Question (general): yearly subscription to professional magazines cost a company $ 940.00 . to make a 20 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 752 , c ) 656 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 20 / 100 = 188 so the cut in amount is 188 the less amount to be spend is 940 - 188 = 752 answer : b"
Answer: b
Question (general): a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are
Options: a ) 600 , b ) 500 , c ) 400 , d ) 300 , e ) none of these
Rationale: explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark = > total mark × ( 33 / 100 ) = 165 = > total mark = 16500 / 33 = 500 answer : option b
Answer: b
Question (gain): find the number of shares that can be bought for rs . 8800 if the market value is rs . 20 each with brokerage being 2.5 % .
Options: a ) 429.3 , b ) 270 , c ) 177 , d ) 166 , e ) 111
Rationale: explanation : cost of each share = ( 20 + 2.5 % of 20 ) = rs . 20.5 therefore , number of shares = 8800 / 20.5 = 429.3 answer : a
Answer: a
Question (general): 1 / 0.08 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 12.5 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.08 = ( 1 * 100 ) / 8 = 100 / 8 = 12.5 option c"
Answer: c
Question (general): when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: when a certain number x is divided by 52 , the remainder is 19 . what is the remainder when x is divided by 7 ? putting a value say x = 19 we get remainder as 19 when divided by 52 . when 19 divided by 7 we get 5 as remainder . d is the answer .
Answer: d
Question (other): the simple form of the ratio 5 / 8 : 3 / 2 is ?
Options: a ) 5 : 8 , b ) 5 : 5 , c ) 5 : 9 , d ) 5 : 3 , e ) 5 : 1
Rationale: "5 / 8 : 3 / 2 = 5 : 8 answer : a"
Answer: a
Question (gain): a reduction of 40 % in the price of bananas would enable a man to obtain 50 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.34 , b ) 2.84 , c ) 3.84 , d ) 4.34 , e ) 5
Rationale: "40 * ( 40 / 100 ) = 16 - - - 50 ? - - - 12 = > rs . 3.84 answer : c"
Answer: c
Question (probability): two unbiased coins are tossed . find the probability of getting two heads ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 3 / 5
Rationale: "s = { hh , ht , th , tt } e = event of getting two heads e = { tt } p ( e ) = 1 / 4 answer is c"
Answer: c
Question (physics): a student traveled 30 percent of the distance of the trip alone , continued another 20 miles with a friend , and then finished the last half of the trip alone . how many miles long was the trip ?
Options: a ) 240 , b ) 200 , c ) 160 , d ) 100 , e ) 50
Rationale: "let x be the total length of the trip . 0.3 x + 20 miles + 0.5 x = x 20 miles = 0.2 x x = 100 miles the answer is d ."
Answer: d
Question (physics): two pipes a and b can fill a tank in 12 and 24 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 6 minutes , b ) 8 minutes , c ) 5 minutes , d ) 2 minutes , e ) 7 minutes
Rationale: "required time = 12 * 24 / 12 + 12 = 12 * 24 / 36 = 24 / 3 = 8 minutes answer : b"
Answer: b
Question (gain): the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 10 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 35 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 67.5 . 4 ) now 67.5 has to be added by x % in order to equal the original price . 67.5 + ( x % ) 67.5 = 100 . solving this eq for x , we get x = 48.1 answer is c ."
Answer: c
Question (general): a man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 2.0 , b ) 2.5 , c ) 3.0 , d ) 2.1 , e ) 4.0
Rationale: "m = 3.5 s = 1.5 ds = 5 us = 2 as = ( 2 * 5 * 2 ) / 5 = 4 answer : e"
Answer: e
Question (general): if a , b , c , and d are integers ; w , x , y , and z are prime numbers ; w < x < y < z ; and ( wa ) ( xb ) ( yc ) ( zd ) = 660 ( wa ) ( xb ) ( yc ) ( zd ) = 660 , what is the value of ( a + b ) – ( c + d ) ?
Options: a ) – 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: 660660 = 2 ^ 2 x 3 ^ 1 x 5 ^ 1 x 11 ^ 1 w < x < y < z = 2 < 3 < 5 < 11 so , can can say - w = 2 x = 3 y = 5 z = 11 hence a = 2 , b = c = d = 1 ( a + b ) – ( c + d ) will be ( 2 + 1 ) – ( 1 + 1 ) = 1 answer will be ( c )
Answer: c
Question (gain): a man gains 50 % by selling an article for a certain price . if he sells it at double the price , the percentage of profit will be .
Options: a ) 130 % , b ) 300 % , c ) 150 % , d ) 160 % , e ) 170 %
Rationale: explanation : let the c . p . = x , then s . p . = ( 150 / 100 ) x = 3 x / 2 new s . p . = 2 ( 3 x / 2 ) = 3 x / 1 profit = 3 x / 1 - x = 3 x / 1 profit % = ( profit / c . p . ) * 100 = > ( 3 x / 1 ) * ( 1 / x ) * 100 = 300 % option b
Answer: b
Question (general): | 14 - 5 | - | 8 - 12 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 5 , e ) 4
Rationale: | 14 - 5 | - | 8 - 12 | = | 9 | - | - 4 | = 9 - 4 = 5 correct answer d
Answer: d
Question (general): in kaya ' s teacher ' s desk there are 3 pink highlighters , 7 yellow highlighters , and 5 blue highlighters . how many highlighters are there in all ?
Options: a ) 11 , b ) 15 , c ) 77 , d ) 33 , e ) 88
Rationale: "add the numbers of highlighters . 3 + 7 + 5 = 15 . answer is b ."
Answer: b
Question (general): the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum w of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just w = 900 : the answer is c ."
Answer: c
Question (gain): the difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4 % per annum is rs 1 . find the sum
Options: a ) rs 600 , b ) rs 625 , c ) rs 650 , d ) rs 675 , e ) none of these
Rationale: explanation : let the sum be p s . i . = p ∗ 4 ∗ 2 / 100 = 2 p / 25 c . i . = p ( 1 + 4 / 100 ) 2 − p = 676 p / 625 − p = 51 p / 625 as , c . i . - s . i = 1 = > 51 p / 625 − 2 p / 25 = 1 = > 51 p − 50 p / 625 = 1 p = 625 option b
Answer: b
Question (gain): the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 8.4 . the true discount is
Options: a ) rs . 70 , b ) rs . 36 , c ) rs . 54 , d ) rs . 50 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 8.4 x 100 / 12 x 1 ) = rs . 70 . answer a"
Answer: a
Question (general): in a basketball game , tim scored 20 points more than joe , but only half as many points as ken . if the 3 players scored a combined total of 100 points , how many points did tim score ?
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 45
Rationale: let joe scored point = x then tim scored = x + 20 ken scored = 2 * ( x + 20 ) = 2 x + 40 as given , x + x + 20 + 2 x + 40 = 100 points 4 x + 60 = 100 x = 100 - 60 / 4 = 10 so tim scored = x + 20 i . e ) 10 + 20 = 30 answer : d
Answer: d
Question (general): if taxi fares were $ 2.00 for the first 1 / 5 mile and $ 0.60 for each 1 / 5 mile there after , then the taxi fare for a 8 - mile ride was
Options: a ) $ 2.40 , b ) $ 25.20 , c ) $ 25.40 , d ) $ 25.60 , e ) $ 25.50
Rationale: "in 8 miles , initial 1 / 5 mile charge is $ 2 rest of the distance = 8 - ( 1 / 5 ) = 39 / 5 rest of the distance charge = 39 ( 0.6 ) = $ 23.4 ( as the charge is 0.6 for every 1 / 5 mile ) = > total charge for 4 miles = 2 + 23.4 = 25.4 answer is c"
Answer: c
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 670 then loss of pyarelal ?
Options: a ) 603 , b ) 703 , c ) 800 , d ) 903 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 670 , loss of pyarelal = 670 * 9 x / 10 x = 603 answer : a"
Answer: a
Question (general): 40 % of the population of a village is 23040 . the total population of the village is ?
Options: a ) 57600 , b ) 44000 , c ) 34936 , d ) 25640 , e ) none
Rationale: "answer ∵ 40 % of p = 23040 ∴ p = ( 23040 x 100 ) / 40 = 57600 correct option : a"
Answer: a
Question (physics): what distance will be covered by a bus moving at 54 kmph in 30 seconds ?
Options: a ) 287 , b ) 900 , c ) 289 , d ) 276 , e ) 207
Rationale: "54 kmph = 54 * 5 / 18 = 30 mps d = speed * time = 30 * 30 = 900 m . answer : b"
Answer: b
Question (general): if ( 1 / 2 ) ^ 22 ( 1 / 81 ) ^ k = 1 / 18 ^ 22 , then k =
Options: a ) 8 , b ) 12 , c ) 16 , d ) 24 , e ) 11
Rationale: i ' m going to focus on denominator only . . ( 2 ^ 22 ) . ( ( 3 ^ 4 ) ^ k = 18 ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 . 3 ^ 2 ) ^ 22 ( 2 ^ 22 ) . ( ( 3 ^ 4 k ) = ( 2 ^ 24 ) . ( 3 ^ 2 ) ^ 22 hence 4 k = 44 k = 11 answer e i hope it ' s quite clear
Answer: e
Question (physics): two pipes a and b can separately fill a tank in 10 and 15 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 ) 450 , b ) 540 , c ) 542 , d ) 829 , e ) 279
Rationale: "1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 45 = 450 answer : a"
Answer: a
Question (general): a baker makes chocolate cookies and peanut cookies . his recipes allow him to make chocolate cookie in batches of 7 and peanut cookies in batches of 6 . if he makes exactly 97 cookies , what is the minimum number of chocolate chip cookies he makes ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 35 , e ) 49
Rationale: "7 c + 6 p = 97 we need to maximize p to minimize c so that the eq is also satisfied try substitution for cp to solve so that eqn is satisfied the least value of c for which equation gets satisfied is 5 i . e . 7 * 1 + 6 * 15 = 7 + 90 = 97 hence a is the answer"
Answer: a
Question (geometry): a cube of edge 17 cm is immersed completely in a rectangular vessel containing water . if the dimensions of the base of vessel are 20 cm * 15 cm , find the rise in water level ?
Options: a ) 6 cm , b ) 8.25 cm , c ) 11.25 cm , d ) 16.37 cm , e ) 20.62 cm
Rationale: "increase in volume = volume of the cube = 17 * 17 * 17 cm ^ 3 rise in water level = volume / area = 17 * 17 * 17 / 20 * 15 = 16.37 cm answer is d"
Answer: d
Question (gain): find the simple interest on rs . 520 for 7 months at 8 paisa per month ?
Options: a ) 277 , b ) 270 , c ) 291 , d ) 266 , e ) 121
Rationale: "i = ( 520 * 7 * 8 ) / 100 = 291 answer : c"
Answer: c
Question (gain): a person incurs 10 % loss by selling a laptop for $ 900 . at what price should the watch be sold to earn 10 % profit ?
Options: a ) 1200 , b ) 1000 , c ) 1100 , d ) 1050 , e ) 1250
Rationale: "let the new s . p . = x then ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) ( 100 - 10 ) / 900 = ( 100 + 10 ) / x x = 110 * 900 / 90 = 1100 new price = $ 1100 correct option is c"
Answer: c
Question (general): product of two natural numbers is 11 . then , the sum of reciprocals of their squares is
Options: a ) 290 / 289 , b ) 122 / 121 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 17 , as 17 is a prime number , so a = 1 , b = 17 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 11 ( 2 ) = 122 / 121 option b"
Answer: b
Question (gain): a survey of employers found that during 1993 employment costs rose 3.5 percent , where employment costs consist of salary costs and fringe - benefit costs . if salary costs rose 3 percent and fringe - benefit costs rose 4.5 percent during 1993 , then fringe - benefit costs represented what percent of employment costs at the beginning of 1993 ?
Options: a ) 16.5 % , b ) 20 % , c ) 33 % , d ) 55 % , e ) 65 %
Rationale: "the amount by which employment costs rose is equal to 0.035 ( salary costs + fringe benefit costs ) ; on the other hand the amount by which employment costs rose is equal to 0.03 * salary costs + 0.045 * fringe benefit costs ; so , 35 ( s + f ) = 30 s + 45 f - - > s = 2 f - - > f / s = 1 / 2 - - > f / ( s + f ) = 1 / ( 1 + 2 ) = 1 / 3 = 0.33 . answer : c ."
Answer: c
Question (general): sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum . sandy attempts 30 sums and obtains 45 marks . how many sums did sandy get correct ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 28
Rationale: let x be the correct sums and ( 30 - x ) be the incorrect sums . 3 x - 2 ( 30 - x ) = 45 5 x = 105 x = 21 the answer is b .
Answer: b
Question (physics): bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many q hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is equal to q = 1 / 3 ( as the work is completed in q = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Question (general): if the average ( arithmetic mean ) of a and b is 160 , and c – a = 200 , what is the average of b and c ?
Options: a ) 260 , b ) 250 , c ) 150 , d ) 225 , e ) 325
Rationale: "a + b / 2 = 160 = > a + b = 320 a = c - 200 . . . sub this value c - 200 + b = 320 = > c + b = 520 = > c + b / 2 = 260 answer : a"
Answer: a
Question (general): the sum of all the integers k such that – 24 < k < 24 is
Options: a ) 0 , b ) - 2 , c ) - 45 , d ) - 49 , e ) - 51
Rationale: "- 23 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 23 - 22 sum of which is - 45 . hence option d . c"
Answer: c
Question (general): a student is ranked 21 th from right and 11 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 31 , e ) 22
Rationale: "from right 21 , from left 11 total = 21 + 11 - 1 = 31 answer : d"
Answer: d
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 13 and 19 . the larger of the two numbers is :
Options: a ) 437 , b ) 299 , c ) 322 , d ) 345 , e ) 355
Rationale: "clearly , the numbers are ( 23 x 13 ) and ( 23 x 19 ) . larger number = ( 23 x 19 ) = 437 . answer : option a"
Answer: a
Question (general): find the sum of the number of combinations possible by using 12 , 34 such that no number is repeated ( ex : - 12234322 are invalid 12344321 are valid ) more than once .
Options: a ) 66660 , b ) 66760 , c ) 66860 , d ) 66960 , e ) 67660
Rationale: total no . formed = 4 ! = 4 * 3 * 2 * 1 = 24 each digit will be used at each positions , 6 times sum of digits at unit place = 6 * 1 + 6 * 2 + 6 * 3 + 6 * 4 = 6 * ( 1 + 2 + 3 + 4 ) = 60 this sum will be same for hundred , tens & unit places sum of all 4 digit numbers formed using digits 12 , 34 = 1000 * 60 + 100 * 60 + 10 * 60 + 60 = 60 * ( 1000 + 100 + 10 + 1 ) = 60 * 1111 = 66660 answer : a
Answer: a
Question (general): linda spent 3 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 240 , what were her original savings ?
Options: a ) $ 900 , b ) $ 800 , c ) $ 960 , d ) $ 700 , e ) $ 1500
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 3 / 4 = 1 / 4 on a tv but the tv cost her $ 240 . so 1 / 4 of her savings is $ 240 . so her original savings are 4 times $ 240 = $ 960 correct answer c"
Answer: c