Cheukting/mathqa huggingface dataset:
Question (gain): a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 190 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.2
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 190 / 45 = $ 4.2 answer : e ."
Answer: e
Question (physics): a train is travelling at 48 kmph . it crosses another train having half of its length , travelling in opposite direction at 42 kmph , in 12 seconds . it also passes a railway platform in 45 seconds . what is the length of the platform ?
Options: a ) 400 m , b ) 500 m , c ) 600 m , d ) 550 m , e ) 700 m
Rationale: speed of i train = 48 kmph length of i train = 2 x m speed of sec train = 42 kmph length of seconf train = x m dist = ( 2 x + x ) = 3 x m time = 12 sec = 90 * 5 / 18 = 25 m / s x = 100 length of first train = 2 x = 200 m time taken = 45 sec speed of first train = 48 kmph = 48 * 5 / 18 = 40 / 3 m / s length of the platform = y metre 200 + y = 45 * 45 / 3 = 600 y = 400 answer a
Answer: a
Question (general): if 3 / p = 6 and 3 / q = 15 then p – q = ?
Options: a ) 3 / 19 , b ) 3 / 11 , c ) 3 / 17 , d ) 3 / 10 , e ) 3 / 13
Rationale: explanation : 3 p 3 p = 6 , p = 3636 = 1212 and 3 q 3 q = 15 , q = 315315 = 1515 then p – q = 1 / 2 – 1 / 5 = 3 / 10 answer : d
Answer: d
Question (general): light glows for every 13 seconds . how many max . times did it glow between 1 : 57 : 58 and 3 : 20 : 47 am .
Options: a ) 380 times , b ) 381 times , c ) 382 times , d ) 392 times , e ) 482 times
Rationale: "time difference is 1 hr , 22 min , 49 sec = 4969 sec . so , light glows floor ( 4969 / 13 ) = 382 times . answer : c"
Answer: c
Question (gain): in an election , candidate a got 80 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 380800 , c ) 356500 , d ) 356800 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 b )"
Answer: b
Question (other): what is the square root of 239,121 ?
Options: a ) 476 , b ) 489 , c ) 497 , d ) 511 , e ) 524
Rationale: "according to divisibility rules , 239,121 is divisible by 9 . 2 + 3 + 9 + 1 + 2 + 1 = 18 this means , that the answer choice must be divisible by 3 a ) 4 + 7 + 6 = 17 no b ) 4 + 8 + 9 = 21 yes c ) 4 + 9 + 7 = 20 no d ) 5 + 1 + 1 = 7 no e ) 5 + 2 + 4 = 11 no b is the only answer"
Answer: b
Question (general): if n = 2 ^ 0.1 and n ^ b = 16 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3
Rationale: 10 / 100 = 1 / 10 n = 2 ^ 1 / 10 n ^ b = 2 ^ 4 ( 2 ^ 1 / 10 ) ^ b = 2 ^ 4 b = 40 answer : c
Answer: c
Question (geometry): find the perimeter and area of the rectangle of length 11 cm and breadth 7 cm .
Options: a ) 77 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 11 cm , breadth = 7 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 11 + 7 ) cm = 2 × 16 cm = 32 cm we know that the area of rectangle = length × breadth = ( 11 × 7 ) cm 22 = 77 cm 2 answer : a"
Answer: a
Question (general): the maximum number 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 ) 37 , c ) 99 , d ) 277 , e ) 19
Rationale: explanation : required number of students = h . c . f of 1001 and 910 = 9 answer : a ) 91
Answer: a
Question (general): a will states that the estate would be divided among 6 sons with the remainder donated to charity . one stipulation in the will is that no one among the sons can receive an amount within 12 % of another ' s amount . if one of the beneficiaries received $ 30000 , what is the smallest possible range between the highest and lowest amounts ( rounded to the nearest dollar ) among the 6 sons ?
Options: a ) $ 4096 , b ) $ 14043 , c ) $ 7892 , d ) $ 17736 , e ) $ 15336
Rationale: 1 st - 30000 . 2 nd - 0.88 * 30000 = 26400 3 rd - 0.88 * 26400 = 23232 4 th - 0.88 * 23232 = 20 , 444.16 5 th - 0.88 * 20 , 444.16 = ~ 17 , 990.86 6 th - 0.88 * 17 , 990.86 = ~ 15 , 831.96 range = 30000 - 15831 = 14168 answer : b .
Answer: b
Question (general): calculate 469111 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4690640889
Rationale: answer 469111 x 9999 = 469111 x ( 10000 - 1 ) = 4691110000 - 469111 = 4690640889 . option : e
Answer: e
Question (gain): simple interest on a certain sum at a certain annual rate of interest is 1 / 25 of the sum . if the numbers representing rate percent and time in years be equal , then the rate of interest is :
Options: a ) 5 % , b ) 2 % , c ) 6 % , d ) 8 % , e ) 3 %
Rationale: "explanation : let sum = x . then , s . i . = x / 25 let rate = r % and time = r years . [ x * r * r / 100 ] = x / 25 ? r ^ 2 = 100 / 25 = 4 r = 2 hence , rate of interest = 2 % . answer : b"
Answer: b
Question (other): two numbers are in the ratio of 1 : 2 . if 9 be added to both , their ratio changes to 3 : 5 . the greater number is
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the ratio be x : y , given x / y = 1 / 2 , ( x + 9 ) / ( y + 9 ) = 3 / 5 = > x = 18 and y = 36 answer : e"
Answer: e
Question (general): bookman purchased 60 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 660 , how many paperback copies were sold ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "the bookman had 10 hardback ad 60 - 10 = 50 paperback copies ; 14 copies were sold , hence 60 - 14 = 46 copies were left . let # of paperback copies left be p then 10 p + 20 ( 46 - p ) = 660 - - > 10 p = 260 - - > p = 26 # of paperback copies sold is 50 - 26 = 24 answer : b"
Answer: b
Question (general): last year manfred received 26 paychecks . each of his first 6 paychecks was $ 760 ; each of his remaining paychecks was $ 30 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 ) $ 752 , b ) $ 755 , c ) $ 765 , d ) $ 783 , e ) $ 775
Rationale: "= ( 760 * 6 + 790 * 20 ) / 26 = 783 answer is d . posted from my mobile device"
Answer: d
Question (gain): two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 30 km apart , if they walk in the same direction ?
Options: a ) 15 hours , b ) 6 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 30 = 15 hours answer is a"
Answer: a
Question (general): if a ' s salary is 20 % less than b ' s salary , by how much percentage is b ' s salary more than a ' s ?
Options: a ) 25 % , b ) 15 % , c ) 30 % , d ) 32 % , e ) 40 %
Rationale: "required percentage = [ 100 * 20 / ( 100 - 20 ) ] % = 25 % answer is a"
Answer: a
Question (geometry): the area of a square is equal to three times the area of a rectangle of dimensions 15 cm * 5 cm . what is the perimeter of the square ?
Options: a ) 30 , b ) 80 , c ) 50 , d ) 60 , e ) 70
Rationale: "area of the square = s * s = 3 ( 15 * 5 ) = > s = 15 cm perimeter of the square = 4 * 15 = 60 cm . answer : option d"
Answer: d
Question (gain): a reduction of 20 % in the price of salt enables a lady to obtain 5 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 6 , b ) 1 , c ) 5 , d ) 4 , e ) 7
Rationale: "100 * ( 20 / 100 ) = 20 - - - 5 ? - - - 1 = > rs . 4 100 - - - 80 ? - - - 4 = > rs . 5 answer : c"
Answer: c
Question (general): find 103 × × 10
Options: a ) 106 / 19 , b ) 108 / 12 , c ) 108 / 19 , d ) 108 / 15 , e ) 108 / 11
Rationale: "by taking 100 as a base we can easily get the answer for the above question within seconds . 103 is 3 more than 100 and 105 is 5 more than 100 so we will write add the excess of the second number to first number or excess of first number to second number as show below to get left most digits and multiply the excesses to get the right most two digits . note : always remember if you get a single digit number put zero in the left two make it a two digit number to get the right most two digits . answer : d"
Answer: d
Question (gain): a worker is paid a regular rate of rs . 10 for completing a survey . the worker completes 100 surveys per week . for any survey involving the use of her cellphone , she is paid at a rate of that is 30 % higher than her regular rate . if she completed 60 surveys involving the use of her cellphone , how much did she get that week ?
Options: a ) 180 , b ) 1180 , c ) 280 , d ) 580 , e ) 2080
Rationale: "amount earned using her cell phone = 60 * 13 = 780 earned for remaining surveys = 40 * 10 = 400 total earning = 1180 answer : b"
Answer: b
Question (general): if the price of sugar rises from rs . 2 per kg to rs . 5 per kg , a person , to have no increase in the expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 15 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 60 %
Rationale: "sol . let the original consumption = 100 kg and new consumption = x kg . so , 100 x 2 = x × 5 = x = 40 kg . ∴ reduction in consumption = 60 % . answer e"
Answer: e
Question (general): what is the 124 th digit to the right of the decimal point in the decimal form of 24 / 44 ?
Options: a ) 8 , b ) 9 , c ) 6 , d ) 4 , e ) 2
Rationale: "to solve this question , we first have to use some long division . this long division allows us to get 24 / 44 in decimal form , which is 0.545454 … where “ 54 ” is repeating . we can see that the 1 st , 3 rd , 5 th digit to the right of the decimal point is a 5 and that the 2 nd , 4 th , 6 th digit to the right of the decimal point is a 4 . in other words , each odd - positioned digit is a 5 , and each even - positioned digit is a 4 . then the 124 digit to the right of the decimal point and we see that 124 is even , we know that the 124 th digit is a 4 . answer d ."
Answer: d
Question (general): a palindrome is a number that reads the same forward and backward , such as 145 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 80 , d ) 90 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 16 = 80 ways c"
Answer: c
Question (general): when n is divided by 25 , the remainder is 4 . what is the remainder when n + 15 is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "assume n = 29 remainder ( n / 24 ) = 4 n + 15 = 44 remainder ( 44 / 5 ) = 4 option c"
Answer: c
Question (gain): find the 25 % of rs . 500 .
Options: a ) s . 50 , b ) s . 70 , c ) s . 100 , d ) s . 125 , e ) s . 60
Rationale: "explanation : 25 % of 500 = > 25 / 100 * 500 = rs . 125 answer : d"
Answer: d
Question (general): what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 200 inclusive ?
Options: a ) 190 , b ) 105 , c ) 200 , d ) 205 , e ) 210
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 200 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 20 ( 10 ) = 200 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 200 = 210 20 + 190 = 210 30 + 180 = 210 etc . since there are 20 total terms , this pattern will create 10 ' pairs ' of 210 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 10 ) ( 210 ) / ( 20 ) = 105 answer : b"
Answer: b
Question (general): the ages of two persons differ by 12 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,8 , c ) 25,15 , d ) 30,10 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 12 ) years . 5 ( x - 5 ) = ( x + 12 - 5 ) or 4 x = 32 or x = 8 . their present ages are 20 years and 8 years option b"
Answer: b
Question (geometry): if n is the smallest integer such that 54 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 1 , c ) 6 , d ) 12 , e ) 24
Rationale: "54 can written as = 2 * 3 * 3 * 3 - - > 2 ^ 1 * 3 ^ 3 - - - ( 1 ) so for 54 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 1 in ( 1 ) even option b is correct"
Answer: b
Question (physics): two trains a and b are 150 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 150 + 150 = 300 m . time taken = 300 / 25 = 12 s . correct answer e ."
Answer: e
Question (general): if 4 a = 5 b = 30 , then 40 ab =
Options: a ) 900 , b ) 1800 , c ) 2250 , d ) 1650 , e ) 1250
Rationale: "4 a * 5 b = 30 * 30 = 900 20 ab = 900 i . e . 30 ab = 1800 answer : option b"
Answer: b
Question (physics): if a train , travelling at a speed of 18 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 281 m , b ) 25 m , c ) 50 m , d ) 125 m , e ) 75 m
Rationale: "b b = 18 * 5 / 18 * 5 = 25 m"
Answer: b
Question (physics): a train speeds past a pole in 15 seconds and a platform 110 meters long in 25 seconds . what is the length of the train ?
Options: a ) 100 m , b ) 125 m , c ) 130 m , d ) 150 m , e ) 165 m
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 110 = 25 * ( x / 15 ) 10 x = 1650 x = 165 meters the answer is e ."
Answer: e
Question (physics): a train covers a distance at a speed of 150 kmph in 3 hours . to cover the same distance in 1 hours , it must travel at a speed of ?
Options: a ) 320 , b ) 250 , c ) 560 , d ) 400 , e ) 450
Rationale: distance = 150 * 3 = 450 km required speed = 450 / 1 = 450 km / hr answer is e
Answer: e
Question (general): find the quotient : 0.63 / 9
Options: a ) 0.5 , b ) 0.3 , c ) 0.9 , d ) 0.1 , e ) 0.7
Rationale: "63 / 9 = 7 . dividend contains 2 places decimal . 0.63 / 9 = 0.7 answer is e ."
Answer: e
Question (geometry): the ratio of boys to girls in a class is 2 : 3 . the career preference of the students in the class are to be represented in a circle graph . if the area of the graph allocated to each career preference is to be proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one third of the boys and two - third of the girls in the class ?
Options: a ) a ) 160 degree
b ) b ) 168 degree
c ) c ) 191 degree
d ) d ) 272 degree
e ) e ) 192 degree
Rationale: let the common ratio be x . . so b = 2 x and g = 3 x and total = 5 x 1 / 3 of m = 2 x / 3 and 2 / 3 of f = 2 x . . total preferring that carrer = 2 x / 3 + 2 x = 8 x / 3 . . now 5 x = 360 , so x = 360 / 5 = 72 . . so x * 8 / 3 = 72 * 8 / 3 = 192 ans 192 e
Answer: e
Question (general): x , y , and z are different prime numbers . the product x ^ 2 * y * z is divisible by how many different positive numbers ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: the exponents of x ^ 2 * y * z are 2 , 1 , and 1 . the number of factors is ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 the answer is e .
Answer: e
Question (physics): due to construction , the speed limit along an 10 - mile section of highway is reduced from 55 miles per hour to 25 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 6.24 , b ) b ) 13.1 , c ) c ) 10 , d ) d ) 15 , e ) e ) 24
Rationale: "old time in minutes to cross 10 miles stretch = 10 * 60 / 55 = 10 * 12 / 11 = 10.9 new time in minutes to cross 10 miles stretch = 10 * 60 / 25 = 10 * 12 / 5 = 24 time difference = 13.1 ans : b"
Answer: b
Question (physics): a 120 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 108 , c ) 278 , d ) 72 , e ) 112
Rationale: "s = 120 / 6 * 18 / 5 = 72 kmph answer : d"
Answer: d
Question (general): peter takes a loan of $ 100000 with 12 % annual interest : the interest is paid once , at the end of the year . martha takes a loan of $ 100000 with 12 % annual interest , compounding monthly at the end of each month . at the end of one full year , compared to peter ' s loan interest , approximately how much more does martha have to repay ?
Options: a ) $ 68.25 , b ) zero , c ) $ 6825.00 , d ) $ 6.82 , e ) $ 682.50
Rationale: peters interest = $ 100000 * 0.12 = $ 12000 or $ 1000 each month . martha ’ s interest , 12 % / 12 = 1 % each month : for the 1 st month = $ 100000 * 0.01 = $ 1000 ; for the 2 nd month = $ 1000 + 1 % of 1000 = $ 1010 , so we would have interest earned on interest ( very small amount ) ; for the 3 rd month = $ 1010 + 1 % of 1010 = ~ $ 1020 ; for the 4 th month = $ 1020 + 1 % of 1020 = ~ $ 1030 ; . . . for the 12 th month = $ 1100 + 1 % of 1100 = ~ $ 1110 . the difference between peters interest and martha ’ s interest = ~ ( 10 + 20 + . . . + 110 ) = $ 660 . answer : e .
Answer: e
Question (gain): the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 15 % . 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 ) 56.8 , 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 $ 63.75 . 4 ) now 63.75 has to be added byx % in order to equal the original price . 63.75 + ( x % ) 63.75 = 100 . solving this eq for x , we get x = 56.8 ans is d ."
Answer: d
Question (physics): 3 numbers are randomly selected , with replacement , from the set of integers { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } . if the first number selected is w , the second number selected is x , and the third number is y , what is the probability that w < x < y ?
Options: a ) 3 / 40 , b ) 28 / 243 , c ) 3 / 25 , d ) 33 / 100 , e ) 64 / 125
Rationale: solution : total possible ways = 10 * 10 * 10 = 1000 case 1 : w = 0 . if x = 1 , then y can have 8 ways . if x = 2 , then y can have 7 ways and so on . so , no . of ways = 8 + 7 + . . + 1 case 2 : w = 1 . if x = 2 , then y can have 7 ways . if x = 3 , then y can have 6 ways and so on . so , no . of ways = 7 + 6 + . . + 1 there will be 8 cases in this way and they will follow a pattern which looks like this : no . of ways for case 1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 no . of ways for case 2 : 1 + 2 + 3 + 4 + 5 + 6 + 7 no . of ways for case 3 : 1 + 2 + 3 + 4 + 5 + 6 no . of ways for case 4 : 1 + 2 + 3 + 4 + 5 no . of ways for case 5 : 1 + 2 + 3 + 4 no . of ways for case 6 : 1 + 2 + 3 no . of ways for case 7 : 1 + 2 no . of ways for case 8 : 1 ____________________________________________________________ total number of ways : 8 ( 1 ) + 7 ( 2 ) + 6 ( 3 ) + 5 ( 4 ) + 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) = 2 ( 4 ( 5 ) + 3 ( 6 ) + 2 ( 7 ) + 1 ( 8 ) ) = 2 ( 60 ) = 120 therefore , ans is 120 / 1000 = 3 / 25 . option c .
Answer: c
Question (physics): two trains a and b are 200 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 14 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 200 + 150 = 350 m . time taken = 350 / 25 = 14 s . correct answer c ."
Answer: c
Question (general): if 20 % of a class averages 80 % on a test , 50 % of the class averages 60 % on the test , and the remainder of the class averages 40 % on the test , what is the overall class average ?
Options: a ) 80 % , b ) 74 % , c ) 58 % , d ) 56 % , e ) 50 %
Rationale: 2 students scored 80 % 5 students scored 60 % 3 students scored 40 % ( 2 ) ( 80 ) + 5 ( 60 ) + 3 ( 40 ) = 160 + 300 + 120 = 580 580 / 10 students = 58 - - > 58 % average answer : c
Answer: c
Question (general): a man whose bowling average is 12.4 , takes 6 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 113 , b ) 114 , c ) 115 , d ) 116 , e ) 117
Rationale: "12.4 * x + 26 = ( 6 + x ) 12 solve equation x = 115 answer : c"
Answer: c
Question (other): of the 200 stamps in a collection , 90 are foreign and 70 are more than 10 years old . if 20 stamps are both foreign and more than 10 years old , how many stamps are neither foreign nor more than 10 years old ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 150
Rationale: 20 stamps are both foreign and more than 10 years old . 70 stamps are foreign only . 50 stamps are 10 years old only . the number of remaining stamps is 200 - ( 20 + 70 + 50 ) = 60 the answer is a .
Answer: a
Question (general): the average age of 20 students in a class is 5 years . if teacher ' s age is also included then average increases 1 year then find the teacher ' s age ?
Options: a ) 28 , b ) 24 , c ) 20 , d ) 22 , e ) 18
Rationale: "total age of 50 students = 20 * 5 = 100 total age of 51 persons = 20 * 6 = 120 age of teacher = 120 - 100 = 20 years answer is c"
Answer: c
Question (general): how many zeroes are there at the end of the number n , if n = 80 ! + 160 ! ?
Options: a ) 15 , b ) 19 , c ) 23 , d ) 27 , e ) 31
Rationale: "the number of zeroes at the end of 80 ! will be less than the number of zeroes at the end of 160 ! hence it is sufficient to calculate the number of zeroes at the end of 80 ! the number of zeroes = [ 80 / 5 ] + [ 80 / 25 ] + [ 80 / 125 ] = 16 + 3 + 0 = 19 the answer is b ."
Answer: b
Question (gain): the principal that amounts to rs . 4913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) 288 , b ) 267 , c ) 200 , d ) 4096 , e ) 2771
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 4913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 4096 . answer : d"
Answer: d