Cheukting/mathqa huggingface dataset:
Question (general): if the farmer sells 75 of his chickens , his stock of feed will last for 20 more days than planned , but if he buys 100 more chickens , he will run out of feed 15 days earlier than planned . if no chickens are sold or bought , the farmer will be exactly on schedule . how many chickens does the farmer have ?
Options: a ) 60 , b ) 120 , c ) 240 , d ) 275 , e ) 300
Rationale: let v denote the volume of feed one chicken consumes per day . then the total volume of feed in stock will be v ∗ d ∗ c where d is the number of days the feed will last if the number of chickens does not change and cc is the current number of chickens . from the question it follows that v ( d + 20 ) ( c − 75 ) = vdc v ( d − 15 ) ( c + 100 ) = vdc the first equation simplifies to 20 c − 75 d = 1500 . the second equation simplifies to ( − 15 ) c + 100 d = 1500 after dividing everything by 5 we get the linear system : 4 c − 15 d = 300 ( − 3 ) c + 20 d = 300 solving it we get c = 300 d = 60 answer : e
Answer: e
Question (general): if the average of t , b , c , 14 and 15 is 12 . what is the average value of t , b , c and 29
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: t + b + c + 14 + 15 = 12 * 5 = 60 = > t + b + c = 60 - 29 = 31 t + b + c + 29 = 31 + 29 = 60 average = 60 / 4 = 15 answer d
Answer: d
Question (geometry): a square of 2 unit is given and four circles are made on its corners having equal radius of each . and another circle of equal radius is made on the center of the square . find out the area of square which is not covered by circles ?
Options: a ) 0.76
b ) 0.86
c ) 0.96
d ) 1.16
e ) 1.26
Rationale: let the radius of circle is ' r ' area of the circle which is at corner = ( 22 / 7 * r ^ 2 ) / 4 hence the area of all four circles are = 22 / 7 * r ^ 2 areaof circle which is made on center of suare is = 22 / 7 * r ^ 2 total area of all circles are = 2 * 22 / 7 * r ^ 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) if we construct the diagram we get the relation 4 r = 2 sqrt 2 r = 1 / sqrt 2 put the value of r in eqn 1 and we get 2 * 22 / 7 * 1 / 2 = 22 / 7 = 3.14 area of suare = 2 ^ 2 = 4 area of remaining part = 4 - 3.14 = 0.86 answer : b
Answer: b
Question (other): sachin is younger than rahul by 6 years . if the ratio of their ages is 7 : 9 , find the age of sachin
Options: a ) 24.58 , b ) 14 , c ) 15 , d ) 24.9 , e ) 24.1
Rationale: "if rahul age is x , then sachin age is x - 6 , so ( x - 6 ) / x = 7 / 9 = > 9 x - 42 = 7 x = > 2 x = 42 = > x = 21 so sachin age is 21 - 6 = 15 answer : c"
Answer: c
Question (physics): 31 of the scientists that attended a certain workshop were wolf prize laureates , and 13 of these 31 were also nobel prize laureates . of the scientists that attended that workshop and had not received the wolf prize , the number of scientists that had received the nobel prize was 3 greater than the number of scientists that had not received the nobel prize . if 51 of the scientists attended that workshop , how many of them were nobel prize laureates ?
Options: a ) a ) 11 , b ) b ) 18 , c ) c ) 24 , d ) d ) 25 , e ) d ) 36
Rationale: "lets solve by creating equation . . w = 31 . . total = 52 . . not w = 52 - 31 = 21 . . now let people who were neither be x , so out of 19 who won nobel = x + 3 . . so x + x + 3 = 21 or x = 9 . . so who won nobel but not wolf = x + 3 = 12 . . but people who won both w and n = 13 . . so total who won n = 12 + 13 = 25 . . d"
Answer: d
Question (geometry): a rectangular lawn of length 200 m by 120 m has two roads running along its center , one along the length and the other along the width . if the width of the roads is 5 m what is the area covered by the two roads ?
Options: a ) 400
b ) 1550
c ) 1575
d ) 1600
e ) 1625
Rationale: area covered by road along the length = 5 * 200 = 1000 square meter area covered by road along the width = 5 * 120 = 600 square meter common area in both roads ( where the roads intersect ) = square with side 5 meter = 5 * 5 = 25 total area of the roads = 1000 + 600 - 25 = 1575 answer : option c
Answer: c
Question (general): if p # q denotes the least common multiple of p and q , then q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = ?
Options: a ) 216 , b ) 180 , c ) 144 , d ) 108 , e ) 72
Rationale: "there are several ways to find the least common multiple of two numbers . in this case , the most efficient method is to use the greatest common factor : ( a * b ) / ( gcf ab ) = lcm ab the greatest common factor of 12 and 16 is 4 . so , 12 # 16 = 12 * 16 / 4 = 48 . the greatest common factor of 18 and 24 is 6 . so , 18 # 24 = 18 * 24 / 6 = 72 finally , the greatest common factor of 48 and 72 is 24 . so , q = ( ( 12 # 16 ) # ( 18 # 24 ) ) = 48 # 72 = ( 48 * 72 ) / 24 = 2 * 72 = 144 the correct answer is c ."
Answer: c
Question (general): the difference between a two - digit number and the number obtained by interchanging the digits is 9 . what is the difference between the two digits of the number ?
Options: a ) 8 , b ) 2 , c ) 7 , d ) can not be determined , e ) none of these
Rationale: "suppose the two - digit number be 10 x + y . then we have been given l 0 x + y – ( 10 y + x ) = 9 ⇒ 9 x – 9 y = 9 ⇒ x – y = 1 hence , the required difference = 1 note that if the difference between a two - digit number and the number obtained by interchanging the digits is d , then the difference between the two digits of the number = d ⁄ 9 answer e"
Answer: e
Question (general): 81 , 64 , 27 , 16 . . .
Options: a ) 12 , b ) 4 , c ) 9 , d ) 3 , e ) 1
Rationale: "81 / 3 = 27 64 / 4 = 16 27 / 3 = 9 answer : c"
Answer: c
Question (general): set x consists of all two - digit primes and set y consists of all positive odd multiples of 7 less than 100 . if the two sets are combined into one , what will be the range of the new set ?
Options: a ) 84 , b ) 89 , c ) 90 , d ) 92 , e ) 95
Rationale: set x = { 11 , 13 , 17 , . . . . . . . . . . . . . , 83 , 89 , 97 } set y = { 7 , 21 , 35 , . . . . . . . . . . . . . . . , 77 , 91 , } combining two sets , say set z set z = { 7 , 11 , 13 , 17,21 , . . . . . . . . . . . . . . . . . . . , 77 , 83 , 89 , 91 , 97 } range = max value - min value range ( z ) = 97 - 7 = 90 oa c is the answer .
Answer: c
Question (gain): a shopkeeper sold an article offering a discount of 10 % and earned a profit of 25 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 39 % , b ) 52 % , c ) 15 % , d ) 21 % , e ) 28 %
Rationale: "let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 90 / 100 * x = 125 x = 12500 / 90 = $ 139 now , s . p . = $ 139 , c . p . = rs . 100 profit % = 39 % . answer : a"
Answer: a
Question (other): a certain high school has 500 students . of these students , 30 are taking music , 20 are taking art , and 10 are taking both music and art . how many students are taking neither music nor art ?
Options: a ) 430 , b ) 440 , c ) 450 , d ) 460 , e ) 470
Rationale: "we ' re given a series of facts to work with : 1 ) a certain high school has 500 students . 2 ) of these students : x are taking music , y are taking art , and z are taking both music and art . we ' re asked how many students are taking neither music nor art ? let ' s test x = 30 y = 20 z = 10 so , we have 30 students taking music , 20 taking art and 10 taking both music and art . 20 student taking just music 10 student taking just art 10 student taking both music and art total = 40 students we ' re asked for the total number of students who are taking neither course . that is 500 - 40 = 460 . d"
Answer: d
Question (general): a ranch has both horses and ponies . exactly 3 / 10 of the ponies have horseshoes , and exactly 5 / 8 of the ponies with horseshoes are from iceland . if there are 3 more horses than ponies , what is the minimum possible combined number of horses and ponies on the ranch ?
Options: a ) 130 , b ) 141 , c ) 152 , d ) 163 , e ) 174
Rationale: "3 / 10 * p are ponies with horseshoes , so p is a multiple of 10 . 5 / 8 * 3 / 10 * p = 3 / 16 * p are icelandic ponies with horseshoes , so p is a multiple of 16 . the minimum value of p is 80 . then h = p + 3 = 83 . the minimum number of horses and ponies is 163 . the answer is d ."
Answer: d
Question (physics): two bullet trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 13 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "c 12 sec . speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 15 m / sec = 8 m / sec . relative speed = ( 12 + 8 ) = 20 m / sec . required time = ( 120 + 120 ) / 20 sec = 12 sec ."
Answer: c
Question (physics): there is food for 760 men for 22 days . how many more men should join after two days so that the same food may last for 8 days more ?
Options: a ) 1122 , b ) 1140 , c ) 1199 , d ) 1188 , e ) 1166
Rationale: 760 - - - - 22 760 - - - - 20 x - - - - - 8 x * 8 = 760 * 20 x = 1900 760 - - - - - - - 1140 answer : b
Answer: b
Question (general): if the price of a tv is first decreased by 20 % and then increased by 55 % , then the net change in the price will be :
Options: a ) 4 % increase , b ) 24 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 155 % of ( 80 % of 100 ) = rs . 155 / 100 * 80 / 100 * 100 = rs . 124 . . ' . increase = 24 % answer : b"
Answer: b
Question (general): what is the smallest integer c for which 27 ^ c > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ c > 3 ^ 24 converting into the same bases : 27 ^ c > 27 ^ 8 therefore for the equation to hold true , c > 8 or c = 9 option c"
Answer: c
Question (gain): in order to obtain an income of rs . 600 from 12 % stock at rs . 106 , one must make an investment of
Options: a ) 5363 , b ) 6240 , c ) 2368 , d ) 7632 , e ) 7732
Rationale: "to obtain rs . 10 , investment = rs . 106 . to obtain rs . 600 , investment = = rs . 7632 answer : d"
Answer: d
Question (physics): speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7200 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 905 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7200 / 18 + 7200 / 14 = 400 + 514.2 = 914.2 hours answer : option a"
Answer: a
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 7000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 400 , c ) s . 600 , d ) s . 800 , e ) s . 875
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 7000 ) = rs . 875 answer = e"
Answer: e
Question (general): what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 400 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 210
Rationale: "we ' re asked for the average of all of the multiples of 10 from 10 to 400 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 40 ( 10 ) = 400 so we know that there are 40 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 400 = 410 20 + 390 = 410 30 + 380 = 410 etc . since there are 40 total terms , this pattern will create 20 ' pairs ' of 410 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 20 ) ( 410 ) / ( 40 ) = 410 / 2 = 205 final answer : d"
Answer: d
Question (physics): a train 130 m long is running with a speed of 60 km / hr . in what time will it pass a man who is running at 4 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 10 , b ) 6.5 , c ) 7 , d ) 7.13 , e ) 10.2
Rationale: "speed of train relative to man = 60 + 4 = 64 km / hr . = 64 * 5 / 18 = 160 / 9 m / sec . time taken to pass the men = 130 * 9 / 160 = 7.13 sec . answer : option d"
Answer: d
Question (gain): after giving a discount of rs . 80 the shopkeeper still gets a profit of 10 % , if the cost price is rs . 200 . find the markup % ?
Options: a ) 31 % , b ) 33 % , c ) 28 % , d ) 30 % , e ) 32 %
Rationale: "cost price = 180 s . p = 200 * 110 / 100 = 220 disc = 80 so . . . mark price = 216 + 80 = 296 . . . . . . mark up % = 261 - 200 / 200 = 61 / 200 = 0.305 or 31 % answer : a"
Answer: a
Question (general): if the digits 27 in the decimal 0.00027 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00027 ) ?
Options: a ) 0.27 , b ) 0.027 , c ) 27 , d ) 0.0027 , e ) 2.7 e - 06
Rationale: "99 * 0.27 = 26.73 approx . 27 answer : c"
Answer: c
Question (gain): one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 200 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 80 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 80 2.5 h = 80 h = 80 . a is the answer ."
Answer: a
Question (geometry): in the coordinate plane , one of the vertices of a square is the point ( - 3 , - 4 ) . if the diagonals of that square intersect at point ( 5 , 3 ) , what is the area of that square ?
Options: a ) 100 , b ) 169 , c ) 225 , d ) 324 , e ) 256
Rationale: "one point ( - 3 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 3 - 5 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 e"
Answer: e
Question (general): in a school with 652 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
Options: a ) 150 , b ) 200 , c ) 250 , d ) 163 , e ) none
Rationale: "sol . let the number of grils be x . then , number of boys = ( 652 - x ) . then , ( 11 3 / 4 × 652 ) ⇔ 11 x + 12 ( 652 - x ) ⇔ x = 7824 - 7661 ⇔ 163 . answer d"
Answer: d
Question (general): ( 35423 + 7164 + 41720 ) - ( 317 x 89 ) = ?
Options: a ) 28213 , b ) 84307 , c ) 50694 , d ) 54094 , e ) none of them
Rationale: "= ( 84307 ) - 317 x 89 = 84307 - ( 317 x ( 90 - 1 ) ) = 84307 - ( 317 x 90 - 317 ) = 84307 - 28213 = 54094 answer is d"
Answer: d
Question (probability): in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 2 / 3 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 6 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 2 / 3 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 3 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 1 / 3 * 1 / 2 = 1 / 6 , or a ."
Answer: a
Question (general): how many words , with or without meaning , can be formed using all letters of the word beautiful using each letter exactly once ?
Options: a ) 388,620 , b ) 388,260 , c ) 362,880 , d ) 352,880 , e ) 342,880
Rationale: "the word beautiful has exactly 9 letters which are all different . therefore the number of words that can be formed = number of permutations of 9 letters taken all at a time . = p ( 9 , 9 ) = 9 ! = 9 x 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 362,880 answer : c"
Answer: c
Question (gain): a shopkeeper sells his goods at cost price but uses a faulty meter that weighs 940 grams . find the profit percent .
Options: a ) 7.38 , b ) 5.38 , c ) 4.38 , d ) 6.38 , e ) 3.38
Rationale: explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 940 100 + g / 100 + 0 = 1000 / 940 100 + g = 100 / 94 * 100 g = 6.38 answer : d
Answer: d
Question (general): the average of first six multiples of 4 is :
Options: a ) 14 , b ) 9 , c ) 12 , d ) 15 , e ) 17
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 + 6 ) / 6 = 84 / 6 = 14 answer a"
Answer: a
Question (physics): a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 20 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 96 km , d ) 12 km , e ) 15 km
Rationale: "speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 20 2 x + 3 x = 480 x = 96 km answer is c"
Answer: c
Question (gain): during a sale , the price of a pair of shoes is marked down 20 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 15 % , e ) 25 %
Rationale: "assume the price = 100 price during sale = 80 price after sale = 100 percent increase = 20 / 80 * 100 = 25 % approx . correct option : e"
Answer: e
Question (physics): in what time will a train 320 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 8.0 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 320 / 40 = 8.0 sec . answer : b"
Answer: b
Question (other): among 200 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 30 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 172 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 60 using your analysis : we see that the total number of students who study either maths or sociology = 88 + 112 - 60 = 140 so , in the image we know that the number of students in the zone with the black boundary = 140 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 200 , we can write : 140 + b + w = 200 or , b + w = 200 - 140 = 60 that is , b = 60 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 60 a"
Answer: a
Question (physics): a person can row at 10 kmph in still water . if the velocity of the current is 2 kmph and it takes him 5 hour to row to a place and come back , how far is the place ?
Options: a ) 24 km , b ) 30 km , c ) 48 km , d ) 12 km , e ) 15 km
Rationale: speed of down stream = 10 + 2 = 12 kmph speed of upstream = 10 - 2 = 8 kmph let the required distance be xkm x / 12 + x / 8 = 5 2 x + 3 x = 120 x = 24 km answer is a
Answer: a
Question (physics): what is the cost of leveling the field in the form of parallelogram at the rate of rs . 70 / 10 sq . metre , whose base & perpendicular distance from the other side being 84 m & 24 m respectively ?
Options: a ) s . 2400 , b ) s . 2016 , c ) s . 1400 , d ) s . 3480 , e ) s . 2000
Rationale: "area of the parallelogram = length of the base * perpendicular height = 84 * 24 = 2016 m . total cost of levelling = rs . 2016 b"
Answer: b
Question (general): during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 5 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) a / 14 , b ) 5 a / 7 , c ) 7 a / 5 , d ) 14 a , e ) 35 a
Rationale: "total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 5 * action = 30 - - > action = a = 5 . comedies = 70 = 14 a . answer : d ."
Answer: d
Question (general): country x taxes each of its citizens an amount equal to 11 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 56,000 , c ) $ 64,000 , d ) $ 58,000 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.11 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 4,400 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 11,600 - - > x = 58,000 . answer : d ."
Answer: d
Question (general): list k consists of 14 consecutive integers . if - 4 is the least integer in list k , what is the range of the positive integers in list k ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: answer = d = 8 if least = - 4 , then largest = 9 range = 9 - 1 = 8
Answer: d
Question (physics): a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 40 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 2.55 km
Rationale: "e 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 40 / 60 47 x / 60 = 40 / 60 = > x = 0.85 . total distance = 3 * 0.85 = 2.55 km ."
Answer: e
Question (general): the average of 20 results is 65 and the average of other 65 results is 20 . what is the average of all the results ?
Options: a ) 30 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 85 result = sum of 20 result + sum of 65 result . = 20 x 65 + 65 x 20 = 2600 correct option : a"
Answer: a
Question (gain): by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at
Options: a ) 46 , b ) 96 , c ) 35 , d ) 87 , e ) 13
Rationale: "to earn rs . 135 , investment = rs . 1620 . to earn rs . 8 , investment = rs . 96 . market value of rs . 100 stock = rs . 96 . answer : b"
Answer: b
Question (gain): in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 192 votes . find the total number of valid votes ?
Options: a ) 430 , b ) 438 , c ) 436 , d ) 480 , e ) 422
Rationale: "let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 192 = > 4 x / 10 = 192 = > 4 x = 1920 = > x = 480 . answer : d"
Answer: d
Question (gain): how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ?
Options: a ) 45 , b ) 33 1 / 3 , c ) 27 , d ) 16 2 / 3 , e ) 15
Rationale: "how many liters of water must be evaporated from 50 liters of a 3 - percent sugar solution to get a 20 - percent solution ? 3 % of a 50 liter solution is 1.5 l . so you are trying to determine how many liters must a solution be for the 1.5 l to represent 20 % of the solution . set up an inequality and solve for x : 1.5 / x = 1 / 20 x = 30 since you need a 15 l solution , you must evaporate 45 of the original 50 l solution to get a 20 % solution . answer is a ."
Answer: a