Cheukting/mathqa huggingface dataset:
Question (general): a certain protective additive increases from 50 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 20 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 50 / 50 ∗ 100 = 20 answer : e ."
Answer: e
Question (general): given that 268 * 74 = 19832 , find the values of 2.68 * 0.74 .
Options: a ) 1.9328 , b ) 1.9832 , c ) 1.9823 , d ) 1.9382 , e ) none of them
Rationale: sum of decimal places = ( 2 + 2 ) = 4 2.68 * 0.74 = 1.9832 . answer is b .
Answer: b
Question (other): the probability of two events a and b are 0.25 and 0.40 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: "we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 40 - . 15 = . 50 but the probability of neither a nor b = 1 - . 50 = 0.50 answer : c"
Answer: c
Question (physics): a pump can fill a tank with a water in 2 hours . because of a leak , it took 3 and 1 / 3 hours to fill the tank . the leak can drain all the water of the full tank in how many hours ?
Options: a ) 5 hrs , b ) 7 hrs , c ) 12 hrs , d ) 14 hrs , e ) 16 hrs
Rationale: "the rate of the pump + leak = 3 / 10 1 / 2 - leak ' s rate = 3 / 10 leak ' s rate = 1 / 5 the leak will empty the tank in 5 hours . the answer is a ."
Answer: a
Question (general): if henry were to add 9 gallons of water to a tank that is already 3 / 4 full of water , the tank would be 7 / 8 full . how many gallons of water would the tank hold if it were full ?
Options: a ) 25 , b ) 40 , c ) 64 , d ) 72 , e ) 96
Rationale: "7 / 8 x - 3 / 4 x = 9 galls 1 / 8 * x = 9 gallons x = 72 gallons answer d"
Answer: d
Question (physics): bruce and anne can clean their house in 4 hours working together at their respective constant rates . if anne ’ s speed were doubled , they could clean their house in 3 hours working at their respective rates . how many w hours does it currently take anne to clean the house on her own ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 14
Rationale: "lets suppose anne and bruce take a and b hrs working separately so in 1 hour they can together finish 1 / a + 1 / b portion of the work which equals 1 / 4 ( as the work is completed in 4 hours ) after anne doubles her rate of work the portion completed by the both is 1 / a + 2 / b which is w equal to 1 / 3 ( as the work is completed in w = 3 hours ) solving these 2 equations we can find b as 12 so , d"
Answer: d
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 10 percent , and on day 3 , it is discounted an additional 30 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 63 % , c ) 64.8 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 10 % discount = 810 price in day 3 after 30 % discount = 567 so , price in day 3 as percentage of the sale price on day 1 will be = 567 / 900 * 100 = > 63 % answer will definitely be ( b )"
Answer: b
Question (gain): the price of a book is increased from $ 300 to $ 330 . what is the % of increase in its price ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 35 % , e ) 45 %
Rationale: explanation : change in the price = rs 330 – rs 300 = rs 30 percentage of increase = change in the price initial price * 100 . percentage increase in price = ( 30 / 300 ) * 100 = 10 % a
Answer: a
Question (gain): a sum of 14,800 amounts to 19,800 in 3 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 12 % , b ) 11 % , c ) 16 % , d ) 15 % , e ) 18 %
Rationale: "b 11 % s . i . = ( 19800 - 14800 ) = 5000 . rate = ( 100 x 5000 ) / ( 14800 x 3 ) % = 11 %"
Answer: b
Question (physics): a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 360 - mile journey ? assume that the train makes no intermediate stops .
Options: a ) 8 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: "a train travels at the rate of 10 miles / hr for the first hour of a trip , at 20 miles / hr for the second hour , at 30 miles / hr for the third hour and so on . how many hours will it take the train to complete a 360 - mile journey ? assume that the train makes no intermediate stops . i think the easiest way to solve this problem would be simply to count the number of miles it travels per hour ( and in total ) hour miles / hour total miles 1 10 10 2 20 30 3 30 60 4 40 100 5 50 150 6 60 210 7 70 280 8 80 360 it takes a total of eight hours to cover the 360 mile distance . answer : a"
Answer: a
Question (geometry): in the figure given below , abc and cde are two identical semi - circles of radius 2 units . b and d are the mid points of the arc abc and cde respectively . what is the area of the shaded region ?
Options: a ) 4 π - 1
b ) 3 π - 1
c ) 2 π - 4
d ) ½ ( 3 π - 1 )
e ) 2 π - 2
Rationale: solution p and q are the centers of the two semicircles . draw bp perpendicular to ac . bp is radius to the semi - circle . so are ap and pc . therefore , bp = ap = pc = 2 units . in semicircle abc , area of the shaded portion is the difference between the area of half the semicircle pbc and the area of the triangle pbc . triangle pbc is a right triangle because pb is perpendicular to pc . pb and pc are radii to the circle and are equal . so , triangle pbc is an isosceles triangle . therefore , triangle pbc is a right isosceles triangle . area of half the semicircle - area of region pbc area of the semicircle abc = ½ area of the circle of radius 2 . so , area of half the semicircle , pbc = ¼ area of the circle of radius 2 . area of half the semicircle , pbc = ¼ * π * 22 area of half the semicircle , pbc = π sq units area of right isosceles triangle pbc area of right triangle pbc = ½ pc * pb area of triangle pbc = ½ * 2 * 2 = 2 sq units area of shaded region area of shaded region in one of the semi circles abc = ( π - 2 ) sq units therefore , area of the overall shaded region = 2 ( π - 2 ) sq units choice c
Answer: c
Question (gain): from the sale of sleeping bags , a retailer made a gross profit of 16 % of the wholesale cost . if each sleeping bag was sold for $ 28 , what was the wholesale cost per bag ?
Options: a ) 3.0 , b ) 3.36 , c ) 24.13 , d ) 25.0 , e ) 31.36
Rationale: "cost price * 1.16 = selling price - - > cost price * 1.16 = $ 28 - - > cost price = $ 24.13 . answer : c ."
Answer: c
Question (general): a number is doubled and 5 is added . if the resultant is trebled , it becomes 129 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 19 , e ) 99
Rationale: explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 129 6 x + 15 = 129 6 x = 114 x = 19 answer : d
Answer: d
Question (physics): the average temperature for tuesday , wednesday and thursday was 42 ° c . the average temperature for wednesday , thursday and friday was 44 ° c . if the temperature on friday be 43 ° c , what was the temperature on tuesday ?
Options: a ) 39 ° c , b ) 44 ° c , c ) 37 ° c , d ) 42 ° c , e ) none of these
Rationale: "explanation : t + w + t = 42 × 3 = 126 ° c w + t + f = 44 × 3 = 132 ° c also , temperature on friday = 43 ° c temperature on tuesday = 126 + 43 - 132 = 37 ° c answer : option c"
Answer: c
Question (general): 72519 x 9999 = ?
Options: a ) 725117481 , b ) 674217481 , c ) 685126481 , d ) 696217481 , e ) none of them
Rationale: "= 7259 x 9999 = 7259 x ( 10000 - 1 ) = 72519 x 10000 - 72519 x 1 = 725190000 - 72519 = 725117481 answer is a"
Answer: a
Question (general): on a certain date , pat invested $ 5,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 20,000 , in how many years total will the total value of the investment plus interest increase to $ 40,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "5,000 ( 1 + x ) ^ 10 = 20,000 ( 1 + x ) ^ 10 = 4 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 5000 ( 1 + x ) ^ n = 40,000 ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Question (general): if a , b , and c are positive real numbers such that a ( b + c ) = 152 , b ( c + a ) = 162 , and c ( a + b ) = 170 , then abc is
Options: a ) a ) 672 , b ) b ) 688 , c ) c ) 704 , d ) d ) 720 , e ) e ) 750
Rationale: ab + bc = 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1 ) bc + ba = 162 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 ) ac + ab = 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 3 ) re - writing equation 3 as follows : ac + cb = 162 + 8 ac + cb = bc + ba + 8 ac = ba + 8 . . . . . . . . . . . . . . . ( 4 ) adding ( 1 ) ( 4 ) 2 ac = 160 ac = 80 abc has to be multiple of 80 , only 720 fits in answer = d
Answer: d
Question (general): s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is
Options: a ) 198 , b ) 154 , c ) 199 , d ) 102 , e ) 105
Rationale: "last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 50 consecutive multiples of 2 . if the smallest number in s is 56 , then the greatest number in s is first term = 56 ; total terms = 50 ; difference = 2 56 + ( 49 ) 2 = 154 ans b"
Answer: b
Question (general): the total number of digit used in numbering the pages of a book having 366 pages , is :
Options: a ) 732 , b ) 990 , c ) 1098 , d ) 1305 , e ) none of these
Rationale: solution total number of digits = ( no . of digits in 1 - digits page nos . + no . of digits in 2 - digits page nos . + no . of digits i 3 - digits page nos . ) = ( 1 * 9 + 2 * 90 + 3 * 267 ) = ( 9 + 180 + 801 ) = 990 . answer b
Answer: b
Question (general): 5.511 / 10.02 =
Options: a ) 0.35 , b ) 0.55 , c ) 0.3509 , d ) 0.351 , e ) 0.3527
Rationale: "5.511 / 10.02 5511 / 1002 = 5.5 move the comma two places to the left as we have 2 decimal places from the divisor : 0.55 . answer : b"
Answer: b
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 240 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1,800 , c ) 1,600 , d ) 10,800 , e ) 64,800
Rationale: "6 machines produce 240 bottles per minute ; 1 machine produces 240 / 6 = 40 bottles per minute ; 10 machines produce 40 * 10 = 400 bottles per minute ; in 4 minutes 10 machines produce 400 * 4 = 1,600 bottles . answer : c ."
Answer: c
Question (general): there are 5 boxes in a cargo . the weight of the 1 st box is 200 kg , the weight of the 2 nd box is 20 % higher than the third box , whose weight is 25 % higher than the 1 st box weight . the 4 th box which weighs 350 kg is 30 % lighter than the 5 th box . find the difference in average weight of the 4 heaviest boxes and the 4 lightest boxes .
Options: a ) 22 , b ) 75 , c ) 25 , d ) 70 , e ) 11
Rationale: weight of 1 st box = 200 weight of 3 rd box = ( 125 / 100 ) * 200 = 250 weight of 2 nd box = ( 120 / 100 ) * 250 = 300 weight of 4 th box = 350 weight of 5 th box = ( 10 / 7 ) * 350 = 500 average of 4 highest weighted boxes = ( 500 + 350 + 300 + 250 ) / 4 = 350 average of 4 lightest boxes = ( 350 + 300 + 250 + 200 ) / 4 = 275 therefore difference = 350 - 275 = 75 answer : b
Answer: b
Question (other): veena ranks 73 rd from the top in a class of 198 . what is her rank from the bottom if 22 students have failed the examination ?
Options: a ) 88 , b ) 104 , c ) 110 , d ) 90 , e ) 93
Rationale: "total student = 198 failed = 22 paasd student = 198 - 22 = 176 from bottom her rank is = 176 - 73 + 1 = 104 answer : b"
Answer: b
Question (gain): if each side of a square is increased by 20 % , find the percentage change in its area ?
Options: a ) 40 % , b ) 42 % , c ) 46 % , d ) 44 % , e ) 38 %
Rationale: "let each side of the square be a , then area = a x a new side = 120 a / 100 = 6 a / 5 new area = ( 6 a x 6 a ) / ( 5 x 5 ) = ( 36 a ² / 25 ) increased area = = ( 36 a ² / 25 ) - a ² increase % = [ ( 11 a ² / 25 ) x ( 1 / a ² ) x 100 ] % = 44 % answer : d"
Answer: d
Question (gain): by selling 20 pencils for a rupee a man loses 30 % . how many for a rupee should he sell in order to gain 30 % ?
Options: a ) 8.56 , b ) 10.75 , c ) 14.5 , d ) 16.5 , e ) 11.4
Rationale: "70 % - - - 20 130 % - - - ? 70 / 130 * 20 = 10.75 answer : b"
Answer: b
Question (general): how many positive integers less than 100 are neither multiples of 2 or 3 ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "1 ) multiples of 2 till 100 = 100 / 2 = 50 2 ) multiples of 3 till 100 = 100 / 3 = 33.33 = 33 add the two 50 + 33 = 83 ; subtract common terms that are multiple of both 2 and 3 . . lcm of 2 and 3 = 6 multiples of 6 till 100 = 100 / 6 = 16.66 = 16 so total multiples of 2 and 3 = 83 - 16 = 67 100 - 67 = 33 answer : d"
Answer: d
Question (gain): an article is bought for rs . 675 and sold for rs . 775 , find the gain percent ?
Options: a ) 73 % , b ) 14.8 % , c ) 33 1 / 3 % , d ) 93 1 / 3 % , e ) 33 1 / 3 %
Rationale: "explanation : 675 - - - - 100 100 - - - - ? = > 14.8 % answer : b"
Answer: b
Question (gain): a man buys 60 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 29.13 % , d ) 33.6 % , e ) 37.82 %
Rationale: explanation : let marked price be re . 1 each c . p . of 60 pens = rs . 46 s . p . of 60 pens = 99 % of rs . 60 = rs . 59.4 profit % = ( profit / c . p . ) x 100 profit % = ( 13.4 / 46 ) x 100 = 29.13 % answer : c
Answer: c
Question (gain): a sells a bicycle to b and makes a profit of 25 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 144
Rationale: "explanation : let cp be 100 a sells at 25 % profit so sp = 125 b sells at 25 % profit = 125 x ( 1 + 25 / 100 ) = 156.25 cp sp 100 - - - 156.25 x - - - 225 cp = 225 x 100 / 156.25 = 144 answer : e"
Answer: e
Question (geometry): what is the area of a regular hexagon with sides 1 in . long ?
Options: a ) 1.59 square inch , b ) 2.59 square inch , c ) 3.59 square inch , d ) 4.59 square inch , e ) 2.69 square inch
Rationale: "a regular hexagon of side 1 inch can be divided in to 6 equilateral triangle of side 1 inch . area of each triangle = ( root 3 / 4 ) * side ^ 2 = ( root 3 / 4 ) area of 6 triangles = 6 * ( root 3 / 4 ) = 1.5 root 3 = 2.59 square inch answer : b"
Answer: b
Question (other): ratio between rahul and deepak is 4 : 2 , after 10 years rahul age will be 26 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 12 , d ) 22 , e ) 8
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 10 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 answer : option e"
Answer: e
Question (physics): two trains running in opposite directions cross a man standing on the platform in 37 seconds and 27 seconds respectively and they cross each other in 29 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 3 : 25 , e ) 1 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 37 x meters , and length of the second train = 27 y meters . ( 37 x + 27 y ) / ( x + y ) = 29 = = > 37 x + 27 y = 29 x + 29 y = = > 8 x = 2 y = = > x / y = 2 / 8 = 1 / 4 answer : option e"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 160 in 5 years ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 2 % , e ) 4 %
Rationale: "160 = ( 800 * 5 * r ) / 100 r = 4 % answer : e"
Answer: e
Question (general): if 2 + 2 / x = 3 - 3 / x , then x =
Options: a ) - 5 , b ) 2 / 3 , c ) 1 , d ) 3 / 2 , e ) 5
Rationale: "we ' re given the equation 2 + 2 / x = 3 - 3 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we have to multiple 2 of the numbers to give them that denominator . . . 2 x / x + 2 / x = 3 x / x - 3 / x we can then eliminate that denominator , which gives us . . . . 2 x + 2 = 3 x - 3 5 = x final answer : e"
Answer: e
Question (other): how many factors of 2475 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 17 , d ) 6 , e ) 7
Rationale: "prime factors of 330 are 2 ^ 1,3 ^ 2,5 ^ 2 and 11 ^ 1 total divisors = ( power if a prime factor + 1 ) total no . of odd factors ( 3 , 5,11 ) = ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 since we need odd divisors other than 1 = > 18 - 1 = 17 odd divisors c is the answer"
Answer: c
Question (general): harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 2 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 1 / 4 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 2 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 2 x = 8 x august tips as a fraction of total tips = 2 x / 8 x = 1 / 4 . so c"
Answer: c
Question (physics): a plant manager must assign 12 new workers to one of five shifts . she needs a first , second , and third shift , and two alternate shifts . each of the shifts will receive 3 new workers . how many different ways can she assign the new workers ?
Options: a ) 2430 , b ) 2640 , c ) 3300 , d ) 4860 , e ) 5400
Rationale: "whatever : my take selecting team of 3 out of 12 to assign to the shifts = 12 c 3 = 220 ways . now 3 out of 12 means total of 4 group possible . so putting them in shifts = counting methode : first , second , third , alt , alt = 4 * 3 * 2 * 1 = 24 here alt and alt are the same : so 24 / 2 = 12 ways . total ways of selecting = ( selecting 3 out of 12 ) * arranging those teams in shifts = 220 * 24 = 2640 ans : b"
Answer: b
Question (gain): a and b invests rs . 5000 and rs . 6000 in a business . after 6 months , a withdraws two - fifth of his capital and 2 months later , b withdraws one - third of his capital . in what ratio should they share the profits at the end of the year ?
Options: a ) 3 : 5 , b ) 7 : 8 , c ) 5 : 6 , d ) 3 : 4 , e ) 7 : 9
Rationale: "a : b ( 5000 * 6 ) + ( 3000 * 6 ) : ( 6000 * 8 ) + ( 4000 * 4 ) 48000 : 64000 3 : 4 answer : d"
Answer: d
Question (general): in a maths test , students were asked to find 5 / 16 of a certain number . one of the students by mistake found 5 / 6 th of that number and his answer was 150 more than the correct answer . find the number .
Options: a ) 125 , b ) 288 , c ) 384 , d ) 400 , e ) 500
Rationale: "explanation : let the number be x . 5 * x / 6 = 5 * x / 16 + 150 25 * x / 48 = 150 x = 288 answer b"
Answer: b
Question (gain): a , b and c enter into a partnership by investing $ 7000 , $ 11000 and $ 18000 respectively . at the end of 8 months , b receives $ 880 as his share . find the share of a .
Options: a ) $ 320 , b ) $ 440 , c ) $ 560 , d ) $ 670 , e ) $ 780
Rationale: "the ratio of capital of a , b and c = 7000 : 11000 : 18000 = 7 : 11 : 18 a ' s share = ( 7 / 11 ) * 880 = $ 560 the answer is c ."
Answer: c
Question (general): bill downloads the movierevenge of the avengersto his computer in 2.5 hours , using a download manager that downloads from 3 sources marked a , b and c . each source provides download at a constant rate , but the rates of different sources are not necessarily identical . if the movie was downloaded from sources a and c alone , it would take 4 hours to complete the download . the next day , source b is available , but the other sources are inactive . how long will it take to download the trailer of the movie , a file that is 10 times smaller , from source b alone ?
Options: a ) 40 minutes , b ) 15 minutes , c ) 12 minutes , d ) 10 minutes , e ) 3 minutes
Rationale: let the movie size be 400 u . given , a + c = 4 hrs . a + c = 100 u / hr and a + b + c = 2.5 hrs or 400 / 2.5 = 160 u / hr b alone = 160 - 100 = 60 u / hr trailer = 40 times smaller or 400 / 10 = 40 u b will take 40 / 60 hrs or 40 minutes . ans a
Answer: a
Question (gain): a bowl of fruit contains 14 apples and 21 oranges . how many oranges must be removed so that 70 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 15 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 14 number of oranges = 23 let number of oranges that must be removed so that 70 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 14 + ( 21 - x ) = 35 - x 14 / ( 35 - x ) = 7 / 10 = > 20 = 35 - x = > x = 15 answer b"
Answer: b
Question (gain): the present worth of rs . 2310 due 2 years hence , the rate of interest being 15 % per annum , is :
Options: a ) 1689 , b ) 1680 , c ) 1682 , d ) 1681 , e ) 1686
Rationale: "p . w . = rs . 100 x 2310 = rs . 1680 . 100 + 15 x 5 2 answer : b"
Answer: b
Question (gain): after decreasing 24 % in the price of an article costs rs . 684 . find the actual cost of an article ?
Options: a ) 218 , b ) 777 , c ) 900 , d ) 2688 , e ) 1991
Rationale: "cp * ( 76 / 100 ) = 684 cp = 9 * 100 = > cp = 900 answer : c"
Answer: c
Question (physics): a man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream . the ratio of the speed of the boat in still water and stream is
Options: a ) 3 : 1 , b ) 1 : 3 , c ) 2 : 4 , d ) 4 : 2 , e ) none of these
Rationale: "explanation : let speed downstream = x kmph then speed upstream = 2 x kmph so ratio will be , ( 2 x + x ) / 2 : ( 2 x - x ) / 2 = > 3 x / 2 : x / 2 = > 3 : 1 option a"
Answer: a
Question (gain): ritesh and co . generated revenue of rs . 1,600 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 ) 19.53 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: explanation : given , ritesh and co . generated revenue of rs . 1,600 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1600 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1600 . = > 12,800 . hence , the total revenue by end of 2007 is rs . 12,800 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 12800 ) × 100 . = > 19.53 % . answer : b
Answer: b
Question (general): the average ( arithmetic mean ) of the integers from 100 to 400 , inclusive , is how much greater than the average of the integers from 50 to 250 , inclusive ?
Options: a ) 100 , b ) 175 , c ) 200 , d ) 125 , e ) 300
Rationale: for an ap the mean or average of series is average of first and last term . so , average of numbers between 100 to 400 , inclusive = ( 100 + 400 ) / 2 = 250 average of numbers between 50 to 250 , inclusive = ( 50 + 250 ) / 2 = 150 difference = 250 - 150 = 100 answer is a
Answer: a
Question (general): a tourist does not have to pay tax on the first $ 600 of goods he purchases in country b , but does have to pay a 11 percent tax on the portion of the total value that is in excess of $ 600 . what tax must be paid by a tourist if he buys goods with a total value of $ 1720 ?
Options: a ) $ 54.00 , b ) $ 64.80 , c ) $ 90.00 , d ) $ 100.80 , e ) $ 123.20
Rationale: "correct answer : e the tourist must pay tax on $ 1720 - $ 600 = $ 1120 . thus , the amount of tax he has to pay is 0.11 ( $ 1120 ) = $ 123.20 . the correct answer is e ."
Answer: e