Cheukting/mathqa huggingface dataset:
Question (gain): a man ' s speed with the current is 18 km / hr and the speed of the current is 3.4 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10.4 , c ) 11.2 , d ) 12.5 , e ) 13
Rationale: "man ' s rate in still water = ( 18 - 3.4 ) km / hr = 14.6 km / hr . man ' s rate against the current = ( 14.6 - 3.4 ) km / hr = 11.2 km / hr . answer : c"
Answer: c
Question (gain): in town p , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the percent of the population who are employed females is 60 - 48 = 12 % the percent of employed people who are female is 12 % / 60 % = 20 % . the answer is a ."
Answer: a
Question (general): average monthly income of a family of 4 earning members was rs . 782 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 1178 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 782 x 4 - 650 x 3 rs . = 1178 rs . correct option : a"
Answer: a
Question (general): how many words , with or without meaning , can be formed using all letters of the word equation using each letter exactly once ?
Options: a ) 38,320 , b ) 39,320 , c ) 40,320 , d ) 38,400 , e ) 39,400
Rationale: "the word equation has exactly 8 letters which are all different . therefore the number of words that can be formed = number of permutations of 8 letters taken all at a time . = p ( 8 , 8 ) = 8 ! = 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 40,320 answer : c"
Answer: c
Question (physics): a train 350 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 9 sec , c ) 12 sec , d ) 21 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 350 m at 50 / 3 m / sec = 350 * 3 / 50 sec = 21 sec answer : d"
Answer: d
Question (general): what is remainder of the division ( 1125 * 1127 * 1129 ) / 12 ?
Options: a ) 0 , b ) 3 , c ) 1 , d ) 2 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : b"
Answer: b
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 8000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 7 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 8000 x 7 ) + 6000 ( x - 7 ) x = 7 . answer d"
Answer: d
Question (general): 0.0005 ? = 0.01
Options: a ) 5 , b ) 0.05 , c ) 0.5 , d ) 50 , e ) none of these
Rationale: "explanation : required answer = 0.0005 / 0.01 = 0.05 / 1 = 0.05 . answer : option b"
Answer: b
Question (general): a library has an average of 140 visitors on sundays and 80 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 90 , b ) 100 , c ) 105 , d ) 110 , e ) 125
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 140 * 5 + 80 * 25 ) / 30 = 2700 / 30 = 90 answer : a ) 90"
Answer: a
Question (geometry): the diagonal of a rhombus are 62 m and 80 m . its area is :
Options: a ) 1940 , b ) 2480 , c ) 2460 , d ) 2500 , e ) 1980
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 62 ã — 80 ) cm ( power ) 2 = 62 ã — 40 = 2480 cm ( power ) 2 answer is b ."
Answer: b
Question (physics): the distance from city a to city b is 180 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 180 / 40 = 4.5 hours . alice needs to take less than 4 hours for the trip . alice needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is a ."
Answer: a
Question (general): a soccer store typically sells replica jerseys at a discount of 30 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 = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer"
Answer: d
Question (general): find the least number must be added to 228712 so that remaining no . is divisible by 9 ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2
Rationale: on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a
Answer: a
Question (physics): how many revolutions will a circular wheel make to travel a distance of 3 km , given that the radius is 2.4 m ?
Options: a ) 11085.7 , b ) 15085.7 , c ) 35085.7 , d ) 15015.7 , e ) 15083.7
Rationale: 2 * 22 / 7 * 2.4 * x = 15085.7 x = 1000 answer : a
Answer: a
Question (general): if 4 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 4 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 4 = > ( 3 / 20 ) c = 4 = > c = ( 4 * 20 ) / 3 = 26.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 4 = 19.99 + 4 = 23.99 = 24 answer b"
Answer: b
Question (general): a drink vendor has 50 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 237 , c ) 281 , d ) 300 , e ) 380
Rationale: "the number of liters in each can = hcf of 50 , 144 and 368 = 2 liters . number of cans of maaza = 50 / 2 = 25 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 25 + 72 + 184 = 281 cans . answer : c"
Answer: c
Question (physics): express a speed of 36 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "36 * 5 / 18 = 10 mps answer : a"
Answer: a
Question (other): lily shop runs a sale on goldfish and platys . if one customer buys 13 goldfish and 12 platys for $ 5.60 , and another buys 14 goldfish and 21 platys for $ 8.05 , what is the ratio of the price of goldfish to platys ?
Options: a ) 0.8 , b ) 0.75 , c ) c ) 8 / 9 , d ) 5 / 7 , e ) 6 / 8
Rationale: the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lily shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
Answer: d
Question (gain): a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,051 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1051 / 1000 ) - 1 = 0.051 = 5.1 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.051 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.051 - 0.01 x = - 0.009 x = - 0.009 / - 0.01 = 9 / 10 = 90 % so x = 90 % of the 1000 which is 900 answer : d"
Answer: d
Question (other): in a class , 9 students like to play basketball and 8 like to play cricket . 6 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 11 , c ) 16 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 9 + 8 - 6 = 11 b )"
Answer: b
Question (gain): in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7000 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2520
Rationale: "e number of valid votes = 80 % of 7000 = 5600 . valid votes polled by other candidate = 45 % of 6000 = ( 45 / 100 x 5600 ) = 2520 ."
Answer: e
Question (physics): if daily wages of a man is double to that of a woman , how many men should work for 10 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 20 , e ) 40
Rationale: "explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 2 / 40 ã — 30 wages of 1 man for 10 days = 21600 ã — 2 ã — 10 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 2 ã — 10 / 40 ã — 30 ) = 144 / ( 216 ã — 20 / 40 ã — 30 ) = 40 answer : option e"
Answer: e
Question (other): two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 91 , b ) 59 , c ) 53 , d ) 47 , e ) 45
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 - 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 98 - 45 = 53 answer : c"
Answer: c
Question (physics): the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 1600 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 1600 x = ( 2 ^ 6 * 25 ) / 2 ^ 9 = 25 / 8 the answer is c ."
Answer: c
Question (general): last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 40 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 781 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 790 * 20 ) / 26 = 781 answer is a . posted from my mobile device"
Answer: a
Question (general): if two different solutions of alcohol with a respective proportion of water to alcohol of 3 : 1 and 2 : 3 were combined , what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts ?
Options: a ) 30.0 % , b ) 36.6 % , c ) 42.5 % , d ) 44.4 % , e ) 60.0 %
Rationale: alcohol : water first mixture - - 3 : 1 - - 15 : 5 second mixture - - 2 : 3 - - 8 : 12 equal amounts of the mixture were combined , hence the final mixture will be in the ratio - - ( 15 + 8 ) : ( 5 + 12 ) - - 23 : 17 % of alcohol - - 17 / ( 23 + 17 ) * 100 = ( 17 / 40 ) * 100 = 42.5 answer : c
Answer: c
Question (general): if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ?
Options: a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01
Rationale: answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest number is 24 . answer : a
Answer: a
Question (physics): a man swims downstream 72 km and upstream 45 km taking 9 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 1.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 72 - - - 9 ds = 8 ? - - - - 1 45 - - - - 9 us = 5 ? - - - - 1 s = ? s = ( 8 - 5 ) / 2 = 1.5 answer : option b"
Answer: b
Question (gain): solution y is 30 percent liquid x and 70 percent water . if 4 kilograms of water evaporate from 8 kilograms of solution y and 4 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 40 % , b ) 41 1 / 2 % , c ) 44 % , d ) 45 % , e ) 46 %
Rationale: "in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 4 kilograms of water are replaced by 4 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 4 = 1.2 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 1.2 = 3.6 kilograms of solution x , which is 3.6 / 8 * 100 = 45 % of this new solution . answer : d ."
Answer: d
Question (general): a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6600 ?
Options: a ) s . 4991 , b ) s . 5591 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6600 * 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 . answer : b"
Answer: b
Question (physics): a can run 3 kms in 3 min 18 sec and b can run same distance in 3 min 40 sec , then by how much distance a can beat b ?
Options: a ) 300 m , b ) 220 m , c ) 280 m , d ) 195 m , e ) 295 m
Rationale: distance travelled = 3000 m time taken by a = 3 m 18 s time taken by b = 3 m 40 sec = 220 sec speed of b = 3000 m / 220 s = 150 / 11 m / s difference between time of a and b = 22 sec when time will be 3 m 18 s a will have travelled 3000 m but b need 22 sec more to finish . distance travelled by b in 22 sec = ( 150 / 11 ) * 22 = 300 m hence , a beat b by 300 m answer : a
Answer: a
Question (physics): 22 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 28 m , c ) 120 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 22 ⇔ = [ 22 * 20 * 20 * 7 / 22 ] = 2800 cm = 28 m . answer b"
Answer: b
Question (physics): two cyclists are moving towards each other at 10 miles / hour . they are now 50 miles apart . at this instance a fly starts from one cyclist and move towards other and moves to and fro till the two cyclist meet each other . if the fly is moving at 15 miles / hour , what is the total distance covered by the fly ?
Options: a ) 37.5 miles , b ) 38.5 miles , c ) 39.5 miles , d ) 36.5 miles , e ) 35.5 miles
Rationale: time taken by cyclists to meet = 50 / 20 2.5 hrs distance covered by fly during 2.5 hrs = 15 * 2.5 = 37.5 miles answer : a
Answer: a
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio s of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) s = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Question (general): the maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 1001 and 910 . ‹ = › 91 . answer a"
Answer: a
Question (physics): when a train travels at a speed of 100 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 15 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: let x be the time reached with the speed 100 km / h 50 km / h - - - - > x + 15 distance is equal so 100 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 100 x = 50 x + 750 so the would be in km and x = 15 answer : a
Answer: a
Question (gain): a circle graph shows how the megatech corporation allocates its research and development budget : 10 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 50 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 10 + 24 + 15 + 29 + 8 = 86 % . so remaining 14 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 14 % will be 50 degrees . . imo option e ."
Answer: e
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 3 sec . what is the length of the train ?
Options: a ) 50 , b ) 75 , c ) 100 , d ) 120 , e ) 25
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 3 = 50 m answer : a"
Answer: a
Question (gain): if the compound interest on a certain sum of money for 3 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 3 yrs = ( 3000 x 10 x 3 ) / 100 = 900 / - answer : d .
Answer: d
Question (general): what least number must be subtracted from 427398 so that remaining no . is divisible by 13
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "explanation : on dividing 427398 by 13 we get the remainder 10 , so 10 should be subtracted answer : option e"
Answer: e
Question (general): if k is the greatest positive integer such that 3 ^ k is a divisor of 24 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "24 / 3 = 8 24 / 9 = 2 8 + 2 = 10 k = 10 answer : e"
Answer: e
Question (gain): the present worth of a certain bill due sometime hence is rs . 800 and the true discount is rs . 36 . the banker ’ s discount is
Options: a ) rs . 34.38 , b ) rs . 38.98 , c ) rs . 37 , d ) rs . 37.62 , e ) none
Rationale: "solution b . g = [ ( t . d ) ² / p . w ] = rs . ( 36 x 36 / 800 ) = rs . 1.62 b . d given , t . d = 36 = ( t . d + b . g ) = rs . ( 36 + 1.62 ) = rs . 37.62 . answer d"
Answer: d
Question (general): an old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 81 times the difference between the two numbers . how many coins did the old man have ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 81 , e ) 40
Rationale: let the number of coins one son got be x and the number of coins another got be y . total = x + y . x ^ 2 - y ^ 2 = 81 ( x - y ) - - > x + y = 81 . answer : d .
Answer: d
Question (general): how much is it cost $ 0.50 each tire for 8 tires ?
Options: a ) $ 3.00 , b ) $ 9.00 , c ) $ 2.00 , d ) $ 4.00 , e ) $ 7.00
Rationale: d . $ 4.00
Answer: d
Question (physics): it takes avery 4 hours to build a brick wall while tom can do it in 2 hours . if the two start working together and after an hour avery leaves , how much time will it take tom to complete the wall on his own ?
Options: a ) 20 , b ) 40 , c ) 30 , d ) 50 , e ) 60
Rationale: "avery takes 4 hours tom takes 2 hours efficiency of avery is 1 / 4 units / hr efficiency of tom is 1 / 2 units / hr combined efficiency of tom and avery is 1 / 4 + 1 / 2 = 3 / 4 units / hr since they worked for 1 hour they completed 3 / 4 units of work and 1 / 4 units of work is left which is to be completed by tom ( since avery left ) so time taken by tom to complete the remaining work will be 1 / 4 / 1 / 2 hours = > 1 / 2 * 60 = 30 minutes . . . answer will be ( c )"
Answer: c
Question (physics): two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 4 seconds . the length of the faster train is
Options: a ) 80 m , b ) 100 m , c ) 90 m , d ) 180 m , e ) none
Rationale: solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 4 ) m = 90 m . answer c
Answer: c
Question (general): set x consists of 15 integers and has median of 20 and a range of 20 . what is the value of the greatest possible integer that can be present in the set ?
Options: a ) 32 , b ) 37 , c ) c . 40 , d ) 60 , e ) 50
Rationale: "note that both median and range do not restrict too many numbers in the set . range is only concerned with the smallest and greatest . median only cares about the middle . quick check of each option starting from the largest : ( e ) 50 range of 20 means the smallest integer will be 30 . so 20 can not lie in between and hence can not be the median . ( d ) 43 range of 20 means the smallest integer will be 23 . so 20 can not lie in between and hence can not be the median . ( c ) 40 range of 20 means the smallest integer will be 20 . 20 can lie in between such as : 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 20 , 40 , 40 , 40 , 50 , 60 this is possible . hence it is the greatest such number . answer ( d )"
Answer: d
Question (general): if x / 2 years ago roger was 18 years old and x / 2 years from now he will be 4 x years old , how old will he be 5 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 51 , e ) 28
Rationale: "assume the current age = a a - x / 2 = 18 ( i ) a + x / 2 = 4 x or a = 7 x / 2 ( ii ) putting the value of a from ( ii ) in ( i ) 7 x / 2 - x / 2 = 18 or 6 x / 2 = 18 therefore x = 6 and a = 21 5 x years from now , age will be 21 + 5 * 6 = 51 option d"
Answer: d
Question (gain): a small college reduced its faculty by approximately 23 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 253 , b ) 208 , c ) 224 , d ) 254 , e ) 302
Rationale: "if x is the original number of faculty members , then after 23 % reduction in faculty members number is . 77 x but we are given . 77 x = 195 x = 253 so the original number of faculty members is 253 correct answer - a"
Answer: a