Cheukting/mathqa huggingface dataset:
Question (general): what is the sum of the digits of integer k , if k = ( 10 ^ 40 - 79 )
Options: a ) 345 , b ) 340 , c ) 343 , d ) 349 , e ) 338
Rationale: "there are 41 digits in 10 ^ 40 when we subtract 79 from it , there will be 40 digits left . 10 ^ 40 can be written as 9999999 . . . . ( 40 times ) + 1 so , 10 ^ 40 - 79 = 9999999 . . . . ( 40 times ) + 1 - 79 = 9999999 . . . . ( 40 times ) - 78 consider the last 2 digits , 99 - 78 = 21 the last 2 digits will be 21 . and our number would be 99999 . . . . . . 99921 with 2 less 9 s after subtraction . number of 9 s left are 38 and the last two digits are 21 the sum of the digits will be ( 38 * 9 ) + 2 + 1 = 345 answer : - a"
Answer: a
Question (gain): by investing in 16 % stock at 64 , one earns rs . 1500 . the investment made is :
Options: a ) 5760 , b ) 7667 , c ) 4445 , d ) 4566 , e ) 3344
Rationale: "explanation : to earn rs . , investment = rs . 64 . to earn rs . 1500 , investment = = rs . 5760 . answer : c ) 5760"
Answer: c
Question (general): if 80 percent of 600 is 50 percent of x , then x = ?
Options: a ) 960 , b ) 1000 , c ) 1020 , d ) 1080 , e ) 1075
Rationale: 0.8 * 600 = 0.5 * x x = 8 / 5 * 600 = 960
Answer: a
Question (general): if a 2 + b 2 + c 2 = 560 and ab + bc + ca = 8 , then a + b + c is
Options: a ) 4 , b ) 52 , c ) 16 , d ) 24 , e ) 64
Rationale: "by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 560 and ab + bc + ca = 8 , ( a + b + c ) ^ 2 = 560 + 2 ( 8 ) = 576 = 24 ^ 2 therefore : a + b + c = 24 answer : d"
Answer: d
Question (general): a man whose speed is 6.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 5.5 kmph , d ) 4 kmph , e ) 7 kmph
Rationale: "explanation : speed of man = 6.5 kmph speed of stream = 2.5 kmph speed in downstream = 9 kmph speed in upstream = 4 kmph average speed = ( 2 x 9 x 4 ) / 13 = 5.5 kmph . answer : c"
Answer: c
Question (gain): a shopkeeper buys two articles for rs . 1000 each and then sells them , making 15 % profit on the first article and 15 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 150 , d ) 280 , e ) 279
Rationale: "profit on first article = 150 % of 1000 = 150 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : c"
Answer: c
Question (physics): a and b can do a work in 8 days , b and c can do the same work in 12 days . a , b and c together can finish it in 6 days . a and c together will do it in how many days ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 8 , e ) 9
Rationale: "let the total units of work be 48 . units of work completed by a and b in one day = 6 . units of work completed by b and c in one day = 4 units of work completed by a , b , and c in one day = 8 . from the above information we get the work completed by a and c in one day is 6 units . therefore , the number of days taken by a and c to complete the whole work = 48 / 6 = 8 days . answer : d"
Answer: d
Question (geometry): the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 288 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 10,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 288 pi r = 6 so area = 4 . pi . r ^ 2 = 144 . pi = 324 x 3.14 = 400 ( approx ) c"
Answer: c
Question (geometry): the percentage increase in the area of rectangle , if each of its side is increased by 10 % is ?
Options: a ) 21 % , b ) 30 % , c ) 25 % , d ) 40 % , e ) 50 %
Rationale: "let original length = x meters original breadth = y meters original area = xy m ^ 2 new length = 110 x / 100 new breadth = 110 y / 100 = 11 y / 10 new area = 11 x / 10 * 11 y / 10 = 121 xy / 100 m ^ 2 increase percent = 21 xy / 100 * 1 / xy * 100 = 21 % answer is a"
Answer: a
Question (physics): a fill pipe can fill 1 / 2 of cistern in 35 minutes . in how many minutes , it can fill 1 / 2 of the cistern ?
Options: a ) 20 min , b ) 25 min , c ) 30 min , d ) 35 min , e ) 40 min
Rationale: "required time = 35 * 2 * 1 / 2 = 20 minutes answer is d"
Answer: d
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 1 per sq m ?
Options: a ) 675 , rs . 1350 , b ) 575 , rs . 675 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 1 = rs . 675 answer : b"
Answer: b
Question (geometry): the diameter of a cylindrical tin is 6 cm and height is 5 cm . find the volume of the cylinder ?
Options: a ) 33
b ) 45
c ) 66
d ) 77
e ) 21
Rationale: r = 3 h = 5 π * 3 * 3 * 5 = 45 π cc answer : b
Answer: b
Question (physics): b completes a work in 9 days . a alone can do it in 10 days . if both work together , the work can be completed in how many days ?
Options: a ) 3.75 days , b ) 4.73 days , c ) 5.75 days , d ) 6.75 days , e ) 7.73 days
Rationale: "1 / 9 + 1 / 10 = 19 / 90 90 / 19 = 4.73 days answer : b"
Answer: b
Question (general): if a ( a + 7 ) = 18 and b ( b + 7 ) = 18 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) − 7 , d ) 46 , e ) 48
Rationale: "a ( a + 7 ) = 18 = > we have a = 2 or - 9 also b ( b + 7 ) = 18 = > b = 2 or - 9 given a ≠ b 1 ) when a = 2 , b = - 9 and a + b = - 7 1 ) when a = - 9 , b = 2 and a + b = - 7 answer choice c"
Answer: c
Question (general): the average ( arithmetic mean ) of the even integers from 0 to 80 inclusive is how much greater than the average ( arithmetic mean ) of the even integers from 0 to 40 inclusive ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 36 , e ) 40
Rationale: "the sum of even numbers from 0 to n is 2 + 4 + . . . + n = 2 ( 1 + 2 + . . . + n / 2 ) = 2 ( n / 2 ) ( n / 2 + 1 ) / 2 = ( n / 2 ) ( n / 2 + 1 ) the average is ( n / 2 ) ( n / 2 + 1 ) / ( n / 2 + 1 ) = n / 2 the average of the even numbers from 0 to 80 is 80 / 2 = 40 the average of the even numbers from 0 to 40 is 40 / 2 = 20 the answer is a ."
Answer: a
Question (other): the number of sailors on a ship is 80 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 9 : 5 , c ) 47 : 25 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.80 * officer sailor / officer = 1.80 / 1 = 180 / 100 = 9 / 5 answer will be b"
Answer: b
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 1,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 23,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "let the weekly sales of both = x 550 + ( x − 1000 ) 8 / 100 = 10 / 100 x x = 23500 answer : a"
Answer: a
Question (gain): a small college reduced its faculty by approximately 20 percent to 195 professors . what was the original number of faculty members ?
Options: a ) 182 , b ) 208 , c ) 224 , d ) 254 , e ) 244
Rationale: "if x is the original number of faculty members , then after 20 % reduction in faculty members number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of faculty members is 244 correct answer - e"
Answer: e
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 15.5 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15.5 - 2 * 1.5 = 12.5 . answer : e ."
Answer: e
Question (general): the greatest number that divides 180 , 565 and 705 leaving remainder 5 , 5 and 5 respectively is :
Options: a ) 31 , b ) 33 , c ) 35 , d ) 38 , e ) 39
Rationale: "explanation : 180 - 5 = 175 , 565 - 5 = 560 and 705 - 5 = 700 highest number that divides 175 , 560 and 700 is hcf of numbers . hcf of 175 , 560 and 700 = 35 answer : c"
Answer: c
Question (general): how many positive integers less than 100 have a remainder of 4 when divided by 13 ?
Options: a ) 6 , b ) 7 , c ) 4 , d ) 9 , e ) 10
Rationale: "we have to include 4 also . as 13 * 0 + 4 = 2 if somebody says to divide 4 by 13 , we will be telling we have 0 quotient and remainder as 4 . answer is c"
Answer: c
Question (general): how many of the positive divisors f of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . f = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Question (geometry): a circle is inscribed in a triangle of side 6 cm . and a square is inscribed in the circle . what is the area of square ?
Options: a ) 4 cm ^ 2
b ) 6 cm ^ 2
c ) 5 cm ^ 2
d ) 7 cm ^ 2
e ) 8 cm ^ 2
Rationale: the radius of the incircle in a equilateral triangle is a / 2 ( sqrt ) 3 where a = side of triangle = 6 cm so the diameter of the circle would be the diagonal of square so diagonal = 2 * a / 2 ( sqrt ) 3 = a / ( sqrt ) 3 so area of square = 1 / 2 * ( diagonal ) ^ 2 = 6 * 6 / 2 * 3 = 6 cm ^ 2 answer : b
Answer: b
Question (physics): two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 60 km and the other at the rate of 90 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 6.85 , d ) 5.85 , e ) 6.62
Rationale: "t = ( 111 + 165 ) / ( 60 + 90 ) * 18 / 5 t = 6.62 answer : e"
Answer: e
Question (general): what is the average of first 20 multiples of 7 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 84 , e ) e ) 82
Rationale: "required average = 7 ( 1 + 2 + . . . . + 20 ) / 20 ( 8 / 20 ) x ( ( 20 x 21 ) / 2 ) ( because sum of first 21 natural numbers ) = 84 d"
Answer: d
Question (general): all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 148 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1184 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a 1184 b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 148 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 148 = 3 k + 148 = > 2 k = 296 = > k = 148 the initial quantity of milk in a = 8 k = 8 * 148 = 1184 liters ."
Answer: a
Question (general): in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the dividend is
Options: a ) 5336 , b ) 4306 , c ) 4236 , d ) 4336 , e ) none
Rationale: sol . divisor = ( 5 × 46 ) = 230 . also , 10 × q = 230 ⇒ q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer a
Answer: a
Question (gain): in one alloy there is 12 % chromium while in another alloy it is 8 % . 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy . find the percentage of chromium in the new alloy .
Options: a ) 8.8 % , b ) 9 % , c ) 9.2 % , d ) 9.1 % , e ) 8.4 %
Rationale: "the amount of chromium in the new 15 + 40 = 55 kg alloy is 0.12 * 15 + 0.08 * 40 = 5 kg , so the percentage is 5 / 55 * 100 = 9.1 % . answer : d ."
Answer: d
Question (gain): the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 5750 for a computer table , then what was the cost price of the computer table ?
Options: a ) 2299 , b ) 2699 , c ) 2670 , d ) 6725 , e ) 5000
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 5750 ( 100 / 115 ) = rs . 5000 answer : e"
Answer: e
Question (general): when positive integer n is divided by 5 , the remainder is 1 . when n is divided by 7 , the remainder is 3 . what is the smallest positive integer k such that k + n is a multiple of 36 .
Options: a ) 5 , b ) 4 , c ) 12 , d ) 32 , e ) 35
Rationale: "first , let us say i have a number n which is divisible by 5 and by 7 . we all agree that it will be divisible by 35 , the lcm of 5 and 7 . now , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1 , we can say the number is of the form n = 5 a + 1 e . g . 5 + 1 , 10 + 1 , 15 + 1 , 20 + 1 , 25 + 1 , 30 + 1 , 35 + 1 etc and n = 7 b + 1 e . g . 7 + 1 , 14 + 1 , 21 + 1 , 28 + 1 , 35 + 1 etc so when it is divided by the lcm , 35 , it will give 1 as remainder ( as is apparent above ) next , if i have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3 , we can say the number is of the form n = 5 a + 1 and n = 7 b + 3 now , the only thing you should try to understand here is that when n is divided by 5 and if i say the remainder is 1 , it is the same as saying the remainder is - 4 . e . g . when 6 is divided by 5 , remainder is 1 because it is 1 more than a multiple of 5 . i can also say it is 4 less than the next multiple of 5 , ca n ' t i ? 6 is one more than 5 , but 4 less than 10 . therefore , we can say n = 5 x - 4 and n = 7 y - 4 ( a remainder of 3 when divided by 7 is the same as getting a remainder of - 4 ) now this question is exactly like the question above . so when you divide n by 36 , remainder will be - 4 i . e . n will be 4 less than a multiple of 36 . so you must add 5 to n to make it a multiple of 36 a"
Answer: a
Question (gain): on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 4 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on october 1 than were in stock on january 1 ?
Options: a ) 8 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: jan 1 = c feb 1 = c - 4 march 1 = c - 8 april 1 = c - 12 may 1 = c - 16 june 1 = c - 20 july 1 = c - 24 aug 1 = c - 28 sept 1 = c - 32 oct 1 = c - 36 difference between stock on october 1 than were in stock on january 1 will be - c - ( c - 36 ) = 36 hence answer will be ( e )
Answer: e
Question (general): when positive integer n is divided by positive integer j , the remainder is 5 . if n / j = 105.20 , what is value of j ?
Options: a ) 10 , b ) 50 , c ) 30 , d ) 15 , e ) 25
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 105.20 here 105 is the quotient . given that remainder = 5 so , 105.20 = 105 + 5 / j so , j = 25 answer : e"
Answer: e
Question (physics): the speed at which a man can row a boat in still water is 9.5 kmph . if he rows downstream , where the speed of current is 8.5 kmph , what time will he take to cover 45.5 metres ?
Options: a ) 18 seconds , b ) 8.4 seconds , c ) 5 seconds , d ) 9.1 seconds , e ) 9.5 econds
Rationale: "speed of the boat downstream = 9.5 + 8.5 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 45.5 m = 45.5 / 5 = 9.1 seconds . answer : d"
Answer: d
Question (physics): in what time will a railway train 65 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 8 sec , b ) 7 sec , c ) 2 sec , d ) 6.5 sec , e ) 9 sec
Rationale: "t = 65 / 36 * 18 / 5 = 6.5 sec answer : d"
Answer: d
Question (general): of 70 players on a football team , 46 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 62
Rationale: "total = 70 thrower = 46 rest = 70 - 46 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 46 + 16 = 62 so e . 62 is the right answer"
Answer: e
Question (physics): how many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards ? ( 1 mile = 1,160 yards )
Options: a ) 2 , b ) 5 , c ) 4 , d ) 3.61 , e ) 4.3
Rationale: speed = 9 miles / hr = 4.4 yard / s = 29.33 yards / min distance = 106 yards time = distance / speed = 106 / 29.33 = 3.61 minutes ans - d
Answer: d
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 8 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 8 = 4 / 9 ( t - 8 ) 10 t = 792 - 352 = > t = 44 . answer : b"
Answer: b
Question (physics): in a race of 1000 m , a can beat by 100 m , in a race of 800 m , b can beat c by 100 m . by how many meters will a beat c in a race of 800 m ?
Options: a ) 122.9 m , b ) 170 m . , c ) 122.2 m , d ) 222.9 m , e ) 12289 m
Rationale: "when a runs 1000 m , b runs 900 m and when b runs 800 m , c runs 700 m . when b runs 900 m , distance that c runs = ( 900 * 700 ) / 800 = 6300 / 8 = 787.5 m . in a race of 1000 m , a beats c by ( 1000 - 787.5 ) = 212.5 m to c . in a race of 800 m , the number of meters by which a beats c = ( 800 * 212.5 ) / 1000 = 170 m . answer : b"
Answer: b
Question (general): 5 ^ 100 is divided by 18 then what is the remainder ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 15 , e ) 16
Rationale: here n = 18 = 2 × 32 ϕ ( 18 ) = 18 ( 1 − 12 ) ( 1 − 13 ) = 6 so 56 when divided by 18 , remainder is 1 . so we can write the given expression 5100 = ( 56 ) 16 × 54 = ( 1 ) 16 × 54 = 52 × 52 = 7 × 7 = 49 now 49 when divided by 18 , remainder is 13 . c
Answer: c
Question (general): if ( a + b ) = 4 , ( b + c ) = 7 and ( c + d ) = 5 , what is the value of ( a + d ) ?
Options: a ) 16 . , b ) 8 . , c ) 7 . , d ) 2 . , e ) - 2 .
Rationale: "given a + b = 4 b + c = 7 c + d = 5 ( a + b ) - ( b + c ) + ( c + d ) = ( a + d ) = > 4 - 7 + 5 = 2 . option d . . ."
Answer: d
Question (general): the average of 45 results is 8 . the average of first 22 of them is 15 and that of last 22 is 20 . find the 23 result ?
Options: a ) 600 , b ) 470 , c ) 750 , d ) 650 , e ) 560
Rationale: "23 th result = sum of 45 results - sum of 44 results 8 * 45 - 15 * 22 + 20 * 22 = 360 - 330 + 440 = 470 answer is b"
Answer: b
Question (physics): a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 20 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 4200 , b ) 5400 , c ) 6600 , d ) 7800 , e ) 8900
Rationale: "the distance the sound traveled to the man is 20 * 330 = 6600 meters the answer is c ."
Answer: c
Question (general): in the set of positive integers from 1 to 70 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 245 , c ) 240 , d ) 200 , e ) 190
Rationale: "reduce 1 - 70 5 - 15 - 25 - 35 - 45 + 55 + 65 are valid multiples 0 f 5 . add them - - > 245 b"
Answer: b
Question (geometry): if the area of a triangle with base 6 cm is equal to the area of a square with side 6 cm , then the altitude of the triangle is
Options: a ) 12 cm
b ) 10 cm
c ) 11 cm
d ) 15 cm
e ) 20 cm
Rationale: area of square = 6 ^ 2 = 36 area of triangle = 36 1 / 2 bh = 36 h = 12 cm answer a
Answer: a
Question (general): what is the remainder when 1014 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 6 , c ) 30 , d ) 21 , e ) 18
Rationale: "oa is ' c ' . oe : take the remainder from each of 1044 / 33 , 1047 / 33 and so on . . 1014 / 33 gives remainder = 24 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 24 * 24 * 27 * 30 break them into pairs 24 * 24 / 33 gives remainder 15 and 27 * 30 / 33 gives remainder 18 so 15 * 18 / 33 gives remainder 6 . b"
Answer: b
Question (physics): a train 600 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 279 m , c ) 500 m , d ) 289 m , e ) 700 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 600 + x ) / 60 = 65 / 3 x = 700 m . answer : e"
Answer: e
Question (physics): walking at 3 / 4 of his usual place , a man reaches his office 20 minute late . find his usual time ?
Options: a ) 2 hr , b ) 1 hr , c ) 3 hr , d ) 1.5 hr , e ) 2.5 hr
Rationale: let the original speed be s and time be t if new speed = s ã — 3 / 4 , then new time would be t ã — 4 / 3 ( d = st = constant ) . given , 3 t / 4 â ˆ ’ t = 20 t / 3 â ‡ ’ t = 60 minutes = 1 hour answer : a
Answer: a
Question (general): andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.86 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.86 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: "ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.86 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.86 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Question (geometry): how many odd numbers between 10 and 1,100 are the squares of integers ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "the square of an odd number is an odd number : 10 < odd < 1,000 10 < odd ^ 2 < 1,000 3 . something < odd < 31 . something ( by taking the square root ) . so , that odd number could be any odd number from 5 to 31 , inclusive : 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19 , 21 , 23 , 25 , 27 , 29 , and 31 . 15 numbers . answer : d ."
Answer: d
Question (gain): a man deposits $ 1000 in a bank at 2 % per annum and $ 1500 in uti at 7 % per annum . find the rate of interest for the whole sum .
Options: a ) 5 % , b ) 8 % , c ) 3 % , d ) 7 % , e ) 1 %
Rationale: "following the above formula , we have the rate of interest for the whole sum = ( 1000 * 2 ) + ( 1500 * 7 ) / 1000 + 1500 = 12500 / 2500 = 5 % . answer is a"
Answer: a
Question (physics): a pump can fill a tank with water in 6 hours . because of a leak , it took 12 hours to fill the tank . the leak can drain all the water in ?
Options: a ) 12 hr , b ) 11 hr , c ) 13 hr , d ) 14 hr , e ) 16 hr
Rationale: work done by the leak in 1 hour = 1 / 6 - 1 / 12 = 1 / 12 leak will empty the tank in 12 hours answer is a
Answer: a
Question (general): if 10 x = 8 y = 14 z , then what is a possible sum of positive integers x , y , and z ?
Options: a ) 52 , b ) 166 , c ) 84 , d ) 122 , e ) 168
Rationale: "10 x = 8 y = 14 z 5 x = 4 y = 7 z 5 ( 4 * 7 ) = 4 ( 5 * 7 ) = 7 ( 5 * 4 ) addition = 28 + 20 + 35 = 83 answer would be multiple of 83 which is 166 answer : b"
Answer: b