Cheukting/mathqa huggingface dataset:
Question (physics): calculate the circumference of a circular field whose radius is 8 centimeters .
Options: a ) 17 π cm , b ) 18 π cm , c ) 1 π cm , d ) 16 π cm , e ) 6 π cm
Rationale: "circumference c is given by c = 2 π r = 2 π * 8 = 16 π cm answer : d"
Answer: d
Question (general): the average score in an examination of 10 students of a class is 60 . if the scores of the top 5 students are not considered , the average score of the remaining students falls by 5 . the pass mark was 40 and the maximum mark was 100 . it is also known that none of the students failed . if each of the top 5 scorers had distinct integral scores , the maximum possible score of the topper is . . . . . .
Options: a ) 99 , b ) 100 , c ) 87 , d ) 95 , e ) 90
Rationale: detailed solution 10 students have scored 600 marks amongst them , and no one is allowed to score lesser than 40 or higher than 100 . the idea now is to maximize what the highest scorer gets . the 5 least scores have an average of 55 , which means that they have scored 55 x 5 = 275 marks amongst them . this leaves 325 marks to be shared amongst the top 5 students . lets call them a , b , c , d and e . now , in order to maximize what the top scorer “ e ” gets , all the others have to get the least possible scores ( and at the same time , they should also get distinct integers . ) the least possible score of the top 5 should be at least equal to the highest of the bottom 5 . now we want to make sure that the highest of the bottom 5 is the least possible . this can be done by making all scores equal to 55 . if some scores are less than 55 , some other scores have to be higher than 55 to compensate and make the average 55 . thus the highest score is the least only when the range is 0 . so now , we have the lowest value that the top 5 can score , which is 55 . the others have to get distinct integer scores , and as few marks as possible , so that “ e ” gets the maximum . so , 55 + 56 + 57 + 58 + e = 325 e = 99 marks . answer choice ( a )
Answer: a
Question (general): 5 + 3 + 2 = 151022 9 + 2 + 4 = 183652 8 + 6 + 3 = 482466 5 + 4 + 5 = 202541 then ; 7 + 2 + 5 = ?
Options: a ) 253547 , b ) 143681 , c ) 143547 , d ) 147614 , e ) 255547
Rationale: c 143547
Answer: c
Question (physics): on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 45 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 212 , c ) 283 , d ) 296 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 45 cm . : 45 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 45 / ( 3.81 ) = 283 answer will be c ."
Answer: c
Question (physics): a labourer was engaged for 25 days on the condition that for every day , he works , he will be paid rs . 2 and for every day , he is absent he will be fined 50 p . if he receives only rs . 37 • 50 , find the no . of days he was absent is _____
Options: a ) 3 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 7 days
Rationale: if a labour worked for 25 days he should get 50 rs . but in this he is getting 13 rs less . if he do n ' t go for work for 1 day he will loose 2.5 rs then no of days ( absent ) = 13 / 2.5 = 5.2 . means he was absent for 5 days answer : c
Answer: c
Question (gain): a cycle is bought for rs . 930 and sold for rs . 1210 , find the gain percent ?
Options: a ) 70 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 80 %
Rationale: "explanation : 930 - - - - 280 100 - - - - ? = > 30 % answer : b"
Answer: b
Question (physics): bob finishes the first half of an exam in two - sixth the time it takes him to finish the second half . if the whole exam takes him an hour , how many minutes does he spend on the first half of the exam ?
Options: a ) 15 , b ) 24 , c ) 27 , d ) 36 , e ) 40
Rationale: many times , it is easiest to think of problems like this conceptually ( as opposed to formulaically ) . conceptually , if the first half of the exam takes 2 / 6 ' s the time of the second half ( 6 / 6 ' s ) , we can see that the hour the entire exam took to finish can be broken down into eight ' s . ( another way to look at this problem is via ratio ' s - first half is 2 : 8 and the second half is 6 : 8 ) . with each sixth of an hour being 15 / 2 minutes ( 60 / 8 ) , the first half of the exam would have taken 15 minutes . correct answer is a .
Answer: a
Question (general): 4 , 10 , ( ? ) , 82 , 244 , 730
Options: a ) 26 , b ) 24 , c ) 40 , d ) 48 , e ) 28
Rationale: "4 × 3 - 2 = 10 10 × 3 - 2 = 28 28 × 3 - 2 = 82 82 × 3 - 2 = 244 244 × 3 - 2 = 730 answer is e ."
Answer: e
Question (physics): the capacity of a cylindrical tank is 246.4 litres . if the height is 4 metres , what is the diameter of the base ?
Options: a ) 1.4 metres , b ) 2.8 metres , c ) 28 metres , d ) 14 metres , e ) none of these
Rationale: capacity ( volume ) of a cylindrical tank = π r 2 h ( here r = radius and h = height of the tank ) now , from the question , 246.4 × 0.001 = 22 ⁄ 7 × r 2 × 4 [ ∵ 1 litre = 1000 cm 3 = 0.001 m 3 ] or , 0.2464 × 7 / 22 × 4 = r 2 or , r = 0.14 m or , diameter = 2 r = 0.28 m answer e
Answer: e
Question (general): calculate the ratio between x and y if 80 % of x equal to 20 % of y ?
Options: a ) 1 : 1 , b ) 3 : 1 , c ) 4 : 5 , d ) 4 : 3 , e ) 4 : 1
Rationale: explanation : 80 x = 20 y x : y = 80 : 20 = 4 : 1 answer : e
Answer: e
Question (general): the remainder of the division of a number by 63 is 27 . what will be the remainder when that number is divided by 6 ? please explain
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 0
Rationale: the easiest way to solve this question is by plugging in a number . here are the steps i followed : 1 ) choose a number x that when divided by 63 gives you 27 as a remainder . so i did x = 63 + 27 = 90 . ( 90 / 63 = 1 r 27 ) 2 ) divide that number by 6 . 90 / 5 = 15 r 0 since the remainder is 0 , the correct answer is choice e .
Answer: e
Question (physics): a cistern which could be filled in 9 hours takes one hour more to be filled owing to a leak in its bottom . if the cistern is full in what time will the leak empty it ?
Options: a ) 76 hrs , b ) 99 hrs , c ) 55 hrs , d ) 90 hrs , e ) 11 hrs
Rationale: "1 / 9 - 1 / x = 1 / 10 = > 90 hrs answer : d"
Answer: d
Question (geometry): how many odd numbers between 10 and 1600 are the squares of integers ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 21
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 39 which includes 18 numbers . the answer is d ."
Answer: d
Question (physics): aaron will jog from home at 6 miles per hour and then walk back home by the same route at 12 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 15 , e ) 11
Rationale: "xyt / ( x + y ) x = 6 , y = 12 t = 3 6 * 12 * 3 / 6 + 12 = 12 answer : a"
Answer: a
Question (other): if n is the greatest positive integer for which 2 ^ n is a factor of 6 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "6 ! = 720 e . 2 ^ 10 = 512 ( 720 / 512 ) - this is not a factor of 6 ! d . 2 ^ 8 = 256 ( 720 / 256 ) - this is not a factor of 6 ! c . 2 ^ 6 = 64 ( 720 / 64 ) - this is not a factor of 6 ! b . 2 ^ 4 = 16 ( 720 / 16 ) - this is a factor of 6 ! b is answer"
Answer: b
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 , $ 1.85 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.85 , 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 , $ 1.85 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.85 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b"
Answer: b
Question (general): find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 9 x + 3 = 0 ?
Options: a ) 28.3 , b ) 1.45 , c ) 2.78 , d ) 6.84 , e ) 7.23
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 9 / 1 = - 9 ab = 3 / 1 = 3 hence a / b + b / a = [ ( - 9 ) 2 - 2 ( 3 ) ] / 3 = 56 / 4 = 28.3 . a )"
Answer: a
Question (physics): if 20 men can build a water fountain 56 metres long in 6 days , what length of a similar water fountain can be built by 35 men in 3 days ?
Options: a ) 40 m , b ) 44 m , c ) 47 m , d ) 49 m , e ) 50 m
Rationale: explanation : let the required length be x metres more men , more length built ( direct proportion ) less days , less length built ( direct proportion ) men 20 : 35 days 6 : 3 : : 56 : x therefore ( 20 x 6 x x ) = ( 35 x 3 x 56 ) x = ( 35 x 3 x 56 ) / 120 = 49 hence , the required length is 49 m . answer : d
Answer: d
Question (other): each factor of 230 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 46 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 4
Rationale: "so the # of factors 230 has 8 ( see below ) ; so out of 8 factors only two are multiples of 46 : 46 and 230 , itself ; so , the probability is 2 / 8 = 1 / 4 . answer : e ."
Answer: e
Question (general): a certain psychologist charges $ 25 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 250 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 115 , b ) $ 135 , c ) $ 150 , d ) $ 165 , e ) $ 192
Rationale: "let the charge for first hour = x + 25 then charge for each additional hour = x x + 25 + 4 x = 250 = > 5 x = 225 = > x = 45 total charge for patient for 3 hours of therapy = x + 25 + x = 2 x + 25 = 115 $ answer a"
Answer: a
Question (general): there are 8 stores in town that had a total of 23 visitors on a particular day . however , only 12 people went shopping that day ; some people visited more than one store . if 8 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "8 people visited 2 stores each for 16 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 23 - 16 - 3 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Question (gain): if difference between compound interest and simple interest on a sum at 10 % p . a . for 2 years is rs . 61 then sum is
Options: a ) s . 6100 , b ) s . 5100 , c ) s . 5800 , d ) s . 6000 , e ) s . 6200
Rationale: "p ( r / 100 ) ^ 2 = c . i - s . i p ( 10 / 100 ) ^ 2 = 61 6100 answer : a"
Answer: a
Question (gain): a sum of money at simple interest amounts to rs . 815 in 4 years and to rs . 854 in 5 years . the sum is :
Options: a ) 659 , b ) 698 , c ) 780 , d ) 910 , e ) none
Rationale: "sol . s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 4 years = rs . ( 39 * 4 ) = rs . 156 . â ˆ ´ principal = rs . ( 815 - 156 ) = rs . 659 answer a"
Answer: a
Question (general): according to the directions on a can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 4 cans of water to make orange juice . how many 12 ounce cans of concentrate are required to prepare 120 6 - ounce servings of orange juice ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 1 x 12 ounce can of concentrate + 4 x 12 ounce cans of water = 60 ounces of the mixture . 60 ounces of mixture gives ( 60 / 6 ) = 10 servings . thus 1 x 12 ounce can of concentrate is used to produce 10 servings of the mixture . to make 120 servings of the mixture , we need 120 / 10 = 12 cans of the concentrate . the answer is b .
Answer: b
Question (general): at a certain restaurant , the price of a sandwich is $ 4.00 more than the price of a cup of coffee . if the price of a sandwich and a cup of coffee is $ 7.35 , including a sales tax of 5 % , what is the price of a cup of coffee , excluding the sales tax ?
Options: a ) $ 1.50 , b ) $ 3.00 , c ) $ 4.00 , d ) $ 5.50 , e ) $ 7.00
Rationale: let the price of sandwich = s price of coffee = c s = c + 4 = > s - c = 4 - - 1 the price of a sandwich and a cup of coffee is $ 7.35 , including a sales tax of 5 % , 1.05 ( s + c ) = 7.35 = > s + c = 7 - - 2 from equations 1 and 2 , we get s = 5.5 $ c = 1.5 $ answer a
Answer: a
Question (geometry): what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 30 % ?
Options: a ) 70 %
b ) 69 %
c ) 80 %
d ) 82 %
e ) 55 %
Rationale: the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 30 % increase a surface = 6 * ( ( 1.3 a ) ^ 2 ) = 6 * 1.69 * a ^ 2 the increase in the surface area = ( 6 * 1.69 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.69 - 1 ) ) / ( 6 * a ^ 2 ) = 1.69 - 1 = 0.69 = 69 % answer : b
Answer: b
Question (general): if a , b , c , d , e and f are integers and ( ab + cdef ) < 0 , then what is the maximum number a of integers that can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: minimuum should be 1 maximum should be 4 : 1 out of a or b to make the multiplication negative 3 out of c , d , e or f to make the multiplication negative . negative + negative < 0 answer : c maximum will be 5 . . you dont require both the multiplicatin to be negative for entire equation to be negative . . . any one a or b can be negative to make ab negative and it can still be more ( away from 0 ) than the multiplication of 4 other - ve numbers . . . actually by writing minimum required as 1 out of 6 , you are actually meaning 5 out of 6 also possible as you will see a = 5 or 1 will give you same equation . . ans d
Answer: d
Question (gain): ritesh and co . generated revenue of rs . 1,500 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 12.5 % , b ) 20.83 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,500 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1250 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1500 . = > 12,000 . hence , the total revenue by end of 2007 is rs . 12,000 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 12000 ) × 100 . = > 20.83 % . answer : b"
Answer: b
Question (general): if x is a number such that x ^ 2 + 4 x - 5 = 0 and x ^ 2 - 5 x + 4 = 0 , then x =
Options: a ) 5 , b ) 4 , c ) 1 , d ) - 4 , e ) - 5
Rationale: "x ^ 2 + 4 x - 5 = ( x + 5 ) ( x - 1 ) = 0 then x = - 5 or x = 1 . x ^ 2 - 5 x + 4 = ( x - 4 ) ( x - 1 ) = 0 then x = 4 or x = 1 . thus x = 1 . the answer is c ."
Answer: c
Question (other): if the ratio of two number is 3 : 4 and lcm of the number is 180 then what is the number .
Options: a ) 15 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 3 x * 4 x = 180 * x x = 15 answer : a"
Answer: a
Question (general): calculate the average marks of a student who obtained 56 , 60 , 72 , 85 and 80 marks ( out of 100 ) in geography , history and government , art , computer science and modern literature ?
Options: a ) 71.6 , b ) 70.6 , c ) 80.6 , d ) 60.6 , e ) 50.6
Rationale: explanation : average = ( 56 + 60 + 72 + 85 + 80 ) / 5 = 70.6 . answer : b ) 70.6
Answer: b
Question (general): find the 21 th term of an arithmetic progression whose first term is 3 and the common difference is 5 .
Options: a ) 100 , b ) 102 , c ) 103 , d ) 150 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 3 + ( 21 - 1 ) * 5 , = 3 + 100 = 103 . answer : c"
Answer: c
Question (general): in δ pqs above , if pq = 6 and ps = 7 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 21 / 4
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 6 * 7 / 2 = pr * 8 / 2 pr = 21 / 4 e"
Answer: e
Question (physics): it was calculated that 75 men could complete a piece of work in 30 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 20 days . , b ) 30 days . , c ) 25 days . , d ) 28 days . , e ) 45 days .
Rationale: "one day work = 1 / 30 one man ’ s one day work = 1 / ( 30 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 30 * 75 ) the total no . of days required to complete the work = ( 75 * 30 ) / 50 = 45 answer : e"
Answer: e
Question (general): a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction w of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose w 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Question (geometry): the slant height of a cone is 13 cm and radius of the base is 9 cm , find the curved surface of the cone ?
Options: a ) 367 , b ) 378 , c ) 365 , d ) 26 , e ) 28
Rationale: "π * 13 * 9 = 367 answer : a"
Answer: a
Question (gain): a number increased by 20 % gives 480 . the number is
Options: a ) 200 , b ) 400 , c ) 300 , d ) 450 , e ) 500
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 480 ( 120 × 4 = 480 ) 100 % - - - - - - - > 400 ( 100 × 4 = 400 ) b )"
Answer: b
Question (general): a person spends 1 / 3 rd of the money with him on clothes , 1 / 5 th of the remaining on food and 1 / 4 th of the remaining on travel . now , he is left with rs 400 . how much did he have with him in the beginning ?
Options: a ) s 200 , b ) s 1000 , c ) s 300 , d ) s 450 , e ) s 550
Rationale: "suppose the amount in the beginning was rs ’ x ’ money spent on clothes = rs 1 x / 3 balance = rs 2 x / 3 money spent on food = 1 / 5 of 2 x / 3 = rs 2 x / 15 balance = 2 x / 3 - 2 x / 15 = rs 8 x / 15 money spent on travel = 1 / 4 of 8 x / 15 = rs 2 x / 15 = 8 x / 15 - 2 x / 15 = 6 x / 15 = rs 2 x / 5 therefore 2 x / 5 = 400 = 1000 answer : b"
Answer: b
Question (physics): in what time will a train 200 metres long cross an electric pole , if its speed be 124 km / hr ?
Options: a ) 4.8 sec , b ) 5.9 sec , c ) 5.0 sec , d ) 5.4 sec , e ) 5.8 sec
Rationale: "solution speed = ( 124 x 5 / 18 ) m / sec = 34.44 m / sec time taken = ( 200 / 34.44 ) sec = 5.8 sec . answer e"
Answer: e
Question (other): the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 15 and 16 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 368 , e ) 121
Rationale: clearly , the numbers are ( 23 * 15 ) and ( 23 * 16 ) . larger number = ( 23 * 16 ) = 368 . answer : d
Answer: d
Question (physics): a train of 45 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4.2 , d ) 9 , e ) 4
Rationale: "d = 45 * 60 + 1500 = 4200 m t = 4200 / 60 * 18 / 5 = 252 sec = 4.2 mins answer : c"
Answer: c
Question (gain): mike needs 30 % to pass . if he scored 212 marks and falls short by 13 marks , what was the maximum marks he could have got ?
Options: a ) 343 , b ) 377 , c ) 750 , d ) 367 , e ) 232
Rationale: "if mike had scored 13 marks more , he could have scored 30 % therefore , mike required 212 + 13 = 225 marks let the maximum marks be m . then 30 % of m = 225 ( 30 / 100 ) × m = 225 m = ( 225 × 100 ) / 30 m = 22500 / 30 m = 750 answer : c"
Answer: c
Question (gain): a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 7,000 meters of fabric ?
Options: a ) $ 13,360 , b ) $ 14,450 , c ) $ 15,720 , d ) $ 16,780 , e ) $ 17,240
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 3500 = $ 6510 the total price is $ 4000 + $ 2850 + $ 6510 = $ 13,360 the answer is a ."
Answer: a
Question (general): when 100 is divided by positive integer x , the remainder is 4 . what is the remainder when 196 is divided by x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "f 100 / x leaves a reminder 4 then ( 100 - 4 ) i . e . 96 is divisible by x so ( 100 + 96 ) / x leaves a reminder rem ( 100 / x ) + rem ( 96 / x ) = > 4 + 0 = 4 answer : c"
Answer: c
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 50 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 45 % , c ) 32 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 50 . s . p . of each item = rs . 1.10 total sale = 1.10 * 50 = rs . 55 hence , loss % = 45 / 100 * 100 = 45 % answer : b"
Answer: b
Question (gain): a sum was put a simple interest at a certain rate for 4 years . had it been put at 3 % higher rate , it would have fetched rs . 120 more . the sum is :
Options: a ) s . 750 , b ) s . 1000 , c ) s . 1250 , d ) s . 1500 , e ) s . 1750
Rationale: explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 3 ) ã — 4 / 100 â ˆ ’ x ã — r ã — 4 / 100 = 120 â ‡ ’ x ã — 3 ã — 4 / 100 = 120 â ‡ ’ x ã — 4 / 100 = 40 â ‡ ’ 4 x = 4000 â ‡ ’ x = 1000 answer : option b
Answer: b
Question (general): √ ( 14 ) ^ 2
Options: a ) 7 , b ) 14 , c ) 49 , d ) 21 , e ) none of these
Rationale: "explanation √ ( 14 ) ^ 2 = ? or , ? = 14 answer b"
Answer: b
Question (other): in a graduating class of 236 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 117 , e ) 31
Rationale: "greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 236 = 27 greatest - smallest is 144 - 27 = 117 so answer must be d . 117"
Answer: d
Question (gain): bruce purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) 1040 , b ) 1050 , c ) 1055 , d ) 1065 , e ) 1075
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 560 + 490 = 1055 c"
Answer: c
Question (other): initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many r women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d