Cheukting/mathqa huggingface dataset:
Question (general): q - 2 : how many two digit numbers of distinct digits can be formed by using digits 1 , 2 , 3 , 4 , 5 , 6 and 7 such that the numbers are divisible by 3 ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: concept : a number will be divisible by 3 if sum of all the digits of the number is divisible by 3 here the possible sum of the two distinct digits can be 3 , 6 , 9 and 12 only in order to satisfy the given condition if sum of digits = 3 , no . = 12 , 21 - - - 2 cases if sum of digits = 6 , no . = 15 , 24 , 42 , 51 - - - 4 cases if sum of digits = 9 , no . = 27 , 36 , 45 , 54 , 63 , 72 - - - 6 cases if sum of digits = 12 , no . = 57 , 75 - - - 2 cases total cases = 2 + 4 + 6 + 2 = 14 cases answer : option e
Answer: e
Question (physics): car x began traveling at an average speed of 35 miles per hour . after 72 minutes , car y began traveling at an average speed of 65 miles per hour . when both cars had traveled the same distance , both cars stopped . how many miles did car x travel from the time car y began traveling until both cars stopped ?
Options: a ) 15 , b ) 20 , c ) 40 , d ) 47 , e ) 49
Rationale: "car y began travelling after 72 minutes or 1.2 hours . let t be the time for which car y travelled before it stopped . both cars stop when they have travelled the same distance . so , 35 ( t + 1.2 ) = 65 t t = 1.4 distance traveled by car x from the time car y began traveling until both cars stopped is 35 x 1.4 = 49 miles answer : - e"
Answer: e
Question (other): the l . c . m . of two numbers is 42 . the numbers are in the ratio 2 : 3 . then sum of the number is :
Options: a ) 28 , b ) 32 , c ) 35 , d ) 53 , e ) 54
Rationale: let the numbers be 2 x and 3 x . then , their l . c . m . = 6 x . so , 6 x = 42 or x = 7 . the numbers are 14 and 21 . hence , required sum = ( 14 + 21 ) = 35 . answer : option c
Answer: c
Question (gain): if 20 % of a = b , then b % of 20 is the same as :
Options: a ) 4 % of a , b ) 8 % of a , c ) 12 % of a , d ) 9 % of a , e ) 1 % of a
Rationale: "20 % of a = b b % of 20 = = = = 4 % of a . answer : a"
Answer: a
Question (general): a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 150 . find the unknown rate of two towels ?
Options: a ) 400 , b ) 450 , c ) 500 , d ) 550 , e ) 600
Rationale: "10 * 150 = 1500 3 * 100 + 5 * 150 = 1050 1500 – 1050 = 450 b"
Answer: b
Question (gain): a present value of a machine is $ 400 . its value depletiation rate is 25 % per annum then find the machine value after 2 years ?
Options: a ) $ 125 , b ) $ 100 , c ) $ 200 , d ) $ 215 , e ) $ 225
Rationale: "p = $ 400 r = 25 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 400 * 3 / 4 * 3 / 4 = $ 225 approximately answer is e"
Answer: e
Question (gain): a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 60.50 , his capital is ?
Options: a ) 24,200 , b ) 28,888 , c ) 24,600 , d ) 24,628 , e ) 24,6012
Rationale: "let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 60.50 32 x - 31 x = 6050 * 4 x = 24,200 . answer : a"
Answer: a
Question (gain): a merchant purchased a jacket for $ 60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 20 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "actual cost = $ 60 sp = actual cost + mark up = actual cost + 20 % sp = 60 * 100 / 80 on sale sp = 80 / 100 ( 60 * 100 / 80 ) = 60 gross profit = $ 0 answer is a"
Answer: a
Question (gain): a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: "2240 = x * 1.4 = x * ( 7 / 5 ) . therefore , x = 2240 * 5 / 7 . 2240 is easily divided by 7 to be 320 , which is then easily multiplied by 5 to give x = 1600 . to get 50 % profit , you need 1600 * 1.5 = 2400 . answer : a"
Answer: a
Question (physics): two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 80 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 8 : 5
b ) 9 : 25
c ) 5 : 8
d ) 25 : 9
e ) can not be determined from the information provided
Rationale: same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 40 / speed b since the times are same , 50 pi / speed a = 80 pi / speed b speeda / speed b = 50 pi / 80 pi = 5 / 8 correct option : c
Answer: c
Question (general): what is the area inscribed by the lines y = 3 , x = 2 , y = x + 3 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 6 , e ) e ) 10
Rationale: "first , let ' s graph the lines y = 3 and x = 2 at this point , we need to find the points where the line y = x + 3 intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = x + 3 to get y = 2 + 3 = 5 perfect , when x = 2 , y = 5 , so one point of intersection is ( 2,5 ) for the horizontal line , we know that y = 3 , so we ' ll plug y = 3 into the equation y = x + 3 to get 3 = x + 3 . solve to get : x = 0 so , when y = 3 , x = 0 , so one point of intersection is ( 0,3 ) now add these points to our graph and sketch the line y = x + 3 at this point , we can see that we have the following triangle . the base has length 2 and the height is 2 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 2 ) = 2 answer : b"
Answer: b
Question (general): tough and tricky questions : distance / rate . on a reconnaissance mission , a state - of - the - art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier . this journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster . what was the average speed , in miles per hour , for the actual journey ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 50
Rationale: say , if speed is 60 , 300 / 50 = 6 hrs and 300 / 60 = 5 hrs ( a reduction of 1 hr - > correct answer ) answer ( e )
Answer: e
Question (gain): a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 12000 . a ' s share is ?
Options: a ) 2500 , b ) 3500 , c ) 4500 , d ) 2800 , e ) 4000
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 12000 = 4000 answer : e"
Answer: e
Question (physics): one computer can upload 100 megabytes worth of data in 3 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 30 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 10 , c ) 9 , d ) 11 , e ) 13
Rationale: since the first computer can upload 100 megabytes worth of data in 3 seconds then in 3 * 10 = 30 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 30 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 10 seconds . answer : b .
Answer: b
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 40 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 140 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 140 - 90 ) / 90 * 100 = 40 % answer : d ."
Answer: d
Question (physics): two trains 130 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.44 , e ) 10.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 130 + 160 = 290 m . required time = 290 * 9 / 250 = 261 / 25 = 10.44 sec . ' answer : d"
Answer: d
Question (general): in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number w of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible w : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer
Answer: d
Question (physics): how many pieces of 75 cm can be cut from a rope 57 meters long ?
Options: a ) 30 , b ) 40 , c ) 76 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 57 meters long is = ( 57 meters ) / ( 75 cm ) = ( 57 meters ) / ( 0.75 meters ) = 76 answer : c"
Answer: c
Question (general): if r is a positive integer and r ^ 2 is divisible by 12 , then the largest positive integer that must divide r ^ 3 is
Options: a ) 2 ^ 3 , b ) 2 ^ 6 , c ) 3 ^ 3 , d ) 6 ^ 3 , e ) 12 ^ 2
Rationale: since r is an integer so r can not have a 2 and sqrt 3 ( because squaring this will give us a 2 ^ 2 and 3 ( making the product as 12 , and making r ^ 2 as a multiple of 12 ) ) r ^ 2 is divisible by 12 ( 12 = 2 * 2 * 3 ) , so , r should have at least one 2 and one 3 so that r ^ 2 has a 2 ^ 2 and two 3 so , r will have a 2 and a 3 . or r will be a multiple of 6 so , largest possible integer than should divide r ^ 3 is 6 ^ 3 so , answer will be d
Answer: d
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "soln : - ( 406 / 116 ) 110 = 385 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 11 = 385 ( 350 + 35 ) answer : c"
Answer: c
Question (general): what is the average of first 21 multiples of 6 ?
Options: a ) a ) 66 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82
Rationale: "required average = 6 ( 1 + 2 + . . . . + 21 ) / 21 ( 6 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 66 a"
Answer: a
Question (physics): a contractor undertook to do a piece of work in 8 days . he employed certain number of laboures but 3 of them were absent from the very first day and the rest could finish the work in only 14 days . find the number of men originally employed ?
Options: a ) 6 , b ) 7.5 , c ) 5 , d ) 6 , e ) 7
Rationale: "let the number of men originally employed be x . 8 x = 14 ( x â € “ 3 ) or x = 7 answer e"
Answer: e
Question (general): what is the sum of two consecutive even numbers , the difference of whose squares is 84 ?
Options: a ) 42 , b ) 84 , c ) 48 , d ) 24 , e ) 43
Rationale: let the numbers be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 4 x + 4 = 84 4 x = 80 x = 20 . the required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer a 42
Answer: a
Question (physics): a man rows his boat 90 km downstream and 40 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 15
Rationale: "speed downstream = d / t = 90 / ( 2 1 / 2 ) = 36 kmph speed upstream = d / t = 40 / ( 2 1 / 2 ) = 16 kmph the speed of the stream = ( 36 - 16 ) / 2 = 15 kmph answer : e"
Answer: e
Question (general): in the youth summer village there are 300 people , 200 of them are not working , 100 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 150 , b ) 125 , c ) 175 , d ) 200 , e ) 100
Rationale: "total = 300 not working = 200 having family = 100 like to sing in shower = 125 working = 300 - 200 = 100 not having family = 300 - 100 = 200 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 e"
Answer: e
Question (geometry): a 15 by 20 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 5 π , b ) 10 π , c ) 15 π , d ) 20 π , e ) 25 π
Rationale: "the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : e"
Answer: e
Question (general): if x > 0 , x / 5 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 24 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 5 + 100 / 25 = 20 + 4 = 24 24 is 24 % of 100 = b"
Answer: b
Question (gain): each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 102 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 3400 , b ) $ 3200 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 102 x = 3400 answer a"
Answer: a
Question (general): if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2017 ) = ?
Options: a ) 2018 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2017 ) = 2018 ans : a"
Answer: a
Question (other): the h . c . f . of two numbers is 32 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 448 , b ) 299 , c ) 421 , d ) 460 , e ) 365
Rationale: "clearly , the numbers are ( 32 x 13 ) and ( 32 x 14 ) . larger number = ( 32 x 14 ) = 448 . answer : option a"
Answer: a
Question (general): a solution is 90 % glycerin . if there are 4 gallons of the solution , how much water , in gallons must be addded to make a 75 % glycerin solution
Options: a ) 1.8 , b ) 1.4 , c ) 1.2 , d ) 1.0 , e ) 0.8
Rationale: in 4 gallons of the solution there are 0.9 ∗ 4 = 3.80 gallons of glycerin . we want to add ww gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75 % of new solution : 0.9 ∗ 4 = 0.75 ( 4 + w ) - - > w = 0.8 answer : e .
Answer: e
Question (gain): of the 120 passengers on flight 750 , 30 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 28 , c ) 50 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 3 * 120 = 36 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 36 - 8 = 28 answer b"
Answer: b
Question (physics): 1240 men have provisions for 12 days . if 300 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 9.7 , d ) 8.6 , e ) 12.1
Rationale: "1240 * 12 = 1540 * x x = 9.7 answer : c"
Answer: c
Question (gain): on a certain transatlantic crossing , 15 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 37.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: 0.15 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.15 p = 0.40 ( rt ) rt / p = 37.5 % answer - a
Answer: a
Question (physics): in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 150 / 10 = 15 seconds the answer is c ."
Answer: c
Question (physics): two numbers n and 16 have lcm = 48 and gcf = 4 . find n .
Options: a ) 35 , b ) 56 , c ) 76 , d ) 87 , e ) 12
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 4 n = 48 * 4 / 16 = 12 correct answer e"
Answer: e
Question (general): every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 65000 ?
Options: a ) 81000 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 82265.6
Rationale: "65000 * 9 / 8 * 9 / 8 = 82265.6 answer : e"
Answer: e
Question (physics): a track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute . the ratio of their speeds is :
Options: a ) 4 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 50 : 3 , e ) none
Rationale: solution : speed of track = 550 per minute . speed of bus = 33 kms / 45 = 33000 / 45 = 733.33 m / minute ratio of their speeds = 550 / 733.33 = 3 : 4 . answer : option c
Answer: c
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 64 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 192 sq m , c ) 452 sq m , d ) 428 sq m , e ) 528 sq m
Rationale: "2 ( 3 x + x ) = 64 l = 24 b = 8 lb = 24 * 8 = 192 answer : b"
Answer: b
Question (general): the instructions state that cheryl needs 3 / 8 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 15 / 40 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 / 3 , e ) 2 1 / 9
Rationale: "total bought = 3 / 8 + 1 / 3 left part 15 / 40 - - - > 3 / 8 so used part 3 / 8 + 1 / 3 - 3 / 8 = 1 / 3 ans d"
Answer: d
Question (other): what number has a 1 : 20 ratio to the number 10 ?
Options: a ) 10 , b ) 1 / 2 , c ) 2 , d ) 1 / 4 , e ) 20
Rationale: "1 : 20 = x : 10 20 x = 10 ; x = 10 / 20 x = 1 / 2 answer : b"
Answer: b
Question (gain): running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 10 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 4200 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: 8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 10 machine produce 560 * 6 * ( 10 / 8 ) in 6 minutes 560 * 6 * 10 / 8 = 4200 answer is b .
Answer: b
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7020 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 891.4 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7020 / 18 + 7020 / 14 = 390 + 501.4 = 891.4 hours answer : option d"
Answer: d
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 4.20 ° is
Options: a ) 0 ° , b ) 5 ° , c ) 10 ° , d ) 20 ° , e ) none
Rationale: "sol . angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min . = ( 360 / 60 x 20 ) ° = 120 ° ∴ required angle = ( 130 - 120 ) ° = 10 ° answer c"
Answer: c
Question (other): a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 96 / 9 ) = rs . 32 / 3 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 120 / 12 ) = rs . 10 . ∴ ratio of investments = 32 / 3 : 10 = 32 : 30 = 16 : 15 answer d"
Answer: d
Question (general): at 6 ' o clock clock ticks 6 times . the time between first and last ticks was 30 sec . how much time it takes at 8 ' o clock .
Options: a ) 54 sec , b ) 48 sec , c ) 42 sec , d ) 70 sec , e ) 60 sec
Rationale: at 6 ' 0 clock , clock ticks 6 times . so , there must be 5 intervals between clock ticks . time between first and last ticks = 30 sec so , 1 interval = 30 / 5 = 6 sec so 6 ' o clock 5 * 6 = 30 sec 7 ' o clock 6 * 6 = 36 sec 8 ' o clock 7 * 6 = 42 sec so , 42 sec at 8 ' o clock . answer : c
Answer: c
Question (general): 9 fencers participate in a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?
Options: a ) 72 , b ) 75 , c ) 81 , d ) 84 , e ) 88
Rationale: 9 * 8 = 72 the answer is a .
Answer: a
Question (general): what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "( 2222 ^ 333 ) * ( 3333 ^ 222 ) = 2222 ^ 111 * ( 2222 ^ 222 * 3333 ^ 222 ) here please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 ( 2222 ^ 222 * 3333 ^ 222 ) . since 6 powered in any number more than 0 results in 6 as a units digit , as a result we have - 6 * 2222 ^ 111 2 has a cycle of 4 . 111 = 27 * 4 + 3 . 2 ^ 3 = 8 6 * 8 = 48 so the units digit is 8 , and the answer is e"
Answer: e
Question (general): in a factory , an average of 70 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 68 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 58
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 68 - 25 x 70 = 290 ∴ average for last 5 days = 290 / 5 = 58 e"
Answer: e
Question (general): alex has 4 pens worth of { 22 , 25 , 30 , 40 } , what is the total mean and median of the worth of pens ?
Options: a ) 3.42 , b ) 6.16 , c ) 8.32 , d ) 2.0 , e ) 1.75
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 22 + 25 + 30 + 40 ) / 4 = 29.25 median = ( 25 + 30 ) / 2 = 27.5 total = 1.75 option e
Answer: e