Cheukting/mathqa huggingface dataset:
Question (general): working simultaneously and independently at an identical constant rate , 20 machines of a certain type can produce a total of x units of product p in 4 days . how many of these machines , working simultaneously and independently at this constant rate , can produce a total of 3 x units of product p in 8 days ?
Options: a ) 30 , b ) 32 , c ) 35 , d ) 38 , e ) 40
Rationale: "the rate of 20 machines is rate = job / time = x / 4 units per day - - > the rate of 1 machine 1 / 20 * ( x / 4 ) = x / 80 units per day ; now , again as { time } * { combined rate } = { job done } then 8 * ( m * x / 80 ) = 3 x - - > m = 30 . answer : a ."
Answer: a
Question (general): the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 13 and 31 inclusive .
Options: a ) 220 , b ) 364 , c ) 410 , d ) 424 , e ) 450
Rationale: we ' re dealing with a sequence of consecutive odd integers : 13 to 31 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 13 + 31 = 44 2 ) now look at the ' next smallest ' and the ' next biggest ' : 15 + 29 = 44 now we have proof that there is no middle term . we have 5 bunches of 44 5 ( 44 ) = 220 a
Answer: a
Question (physics): find the l . c . m of 15 , 18 , 28 and 30 .
Options: a ) 1800 , b ) 1260 , c ) 1460 , d ) 1600 , e ) 960
Rationale: "explanation : 2 x 3 x 5 x 3 x 14 = 1260 answer : option b"
Answer: b
Question (geometry): if o is the center of the circle in the figure above and the area of the unshaded sector is 5 , what is the area of the shaded region ?
Options: a ) 25 / √ π
b ) 30 / √ π
c ) 20
d ) 25
e ) 30
Rationale: 60 / 360 = 1 / 6 1 / 6 of total area = 5 5 / 6 of total area = 5 * 5 = 25 answer : d
Answer: d
Question (general): the smallest value of n , for which 2 n is not a prime number , is
Options: a ) 2 , 3,4 , b ) 1 , 3,5 , c ) 2 , 5,6 , d ) 4 , 8,9 , e ) 12 , 14,16
Rationale: "( 2 ã — 1 ) = 2 . ( 2 ã — 2 ) = 4 . ( 2 ã — 3 ) = 6 . ( 2 ã — 4 ) = 8 . which is not prime , n = 2 , 3,4 . answer : a"
Answer: a
Question (general): if a mixture is 5 ⁄ 9 alcohol by volume and 4 ⁄ 9 water by volume , what is the ratio of the volume of alcohol to the volume of water in this mixture ?
Options: a ) 1 / 4 , b ) 3 / 4 , c ) 5 / 4 , d ) 6 / 4 , e ) 7 / 4
Rationale: "should be a sub - 600 level q . . volume = { 5 / 9 } / { 4 / 9 } = 5 / 4 c"
Answer: c
Question (physics): two spherical balls lie on the ground touching . if one of the balls has a radius of 8 cm , and the point of contact is 12 cm above the ground , what is the radius of the other ball ( in centimeters ) ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "a straight line will join the two centers and the point of contact , thus making similar triangles . 4 / 8 = ( r - 12 ) / r 4 r = 8 r - 96 r = 24 the answer is b ."
Answer: b
Question (general): s = { 12 , 35 , 69 } t = { 45 , 67 , 13 } what is the probability that x chosen from s and y chosen from t will result x * y = even
Options: a ) 5 / 9 , b ) 3 / 2 , c ) 1 / 2 , d ) 5 / 6 , e ) 6 / 5
Rationale: p : the probability that x * y is even , then p = 1 - p ( x * y is odd ) p ( x * y odd ) = p ( x odd ) * p ( y odd ) = 4 / 6 * 4 / 6 = 16 / 36 = 4 / 9 and p = 1 - 4 / 9 = 5 / 9 option : a
Answer: a
Question (other): a certain music store stocks 800 cellos and 600 violas . of these instruments , there are 110 cello - viola pairs , such that a cello and a viola were both made with wood from the same tree ( each tree can make at most one viola and one cello , so there are no pairs other than these 90 ) . if one viola and one cello are chosen at random , what is the probability that the two instruments are made with wood from the same tree ?
Options: a ) 11 / 48,000 , b ) 1 / 8,100 , c ) 3 / 1,600 , d ) 1 / 90 , e ) 2 / 45
Rationale: "solution provided by stanford 2012 is correct : 110 / 800 choosing one of the cellos which has a pair viola , 1 / 600 choosing the viola which is the pair of chosen cello - - > p = 110 / 800 * 1 / 600 = 311 / 48,000 . answer : a ."
Answer: a
Question (general): a certain roller coaster has 3 cars , and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster . if a certain passenger is to ride the roller coaster 3 times , what is the probability that the passenger will ride in each of the 3 cars ?
Options: a ) 0 , b ) 1 / 9 , c ) 2 / 9 , d ) 1 / 3 , e ) 1
Rationale: "probability = ( favorable cases ) / ( total number of cases ) total number of ways in which a person can ride car = 3 * 3 * 3 = 27 ( in first ride he has 3 options to sit , in second right again he has 3 seats available to sit and so on ) number of favorable cases , i . e . , when he rides on different cars ; he can choose seat car in 3 ways in his 1 st ride . he can choose seat car in 2 ways in his 2 nd ride . he can choose seat car in 1 ways in his 3 rd ride . so , 3 * 2 * 1 = 6 ways thus , probability of choosing different seats = 6 / 27 = 2 / 9 answer : c"
Answer: c
Question (general): of the 100 people in a room , 4 / 5 are women . if 3 / 5 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 32 , b ) 34 , c ) 36 , d ) 38 , e ) 40
Rationale: "women = 4 / 5 * 100 = 80 married = 3 / 5 * 100 = 60 unmarried = 40 max ( un - married women ) = 40 e"
Answer: e
Question (physics): one copy machine can make 25 copies a minute , and a second copy machine makes 35 copies a minute . if the two copiers work together , how long would it take them to make 4,800 copies ?
Options: a ) 30 minutes , b ) 40 minutes , c ) 60 minutes , d ) 70 minutes , e ) 80 minutes
Rationale: "total work done by both machines in a minute = 25 + 35 = 60 copies total number of copies required = 6000 time = 4800 / 60 = 80 mins answer e"
Answer: e
Question (general): a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 20 gallons of water and 40 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 300 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 40 gallons salt is added and 20 gallons of water is added . so salt now becomes - > ( 0.2 x + 40 ) and water - - > ( 0.6 x + 20 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 40 ) = ( 0.6 x + 20 ) / 2 = > 0.4 x + 80 = 0.6 x + 20 = > 0.2 x = 60 solving , x = 300 answer : a"
Answer: a
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 w 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 w = 1000 + 600 - 25 = 1575 answer : option c"
Answer: c
Question (general): each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 53 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 48 , b ) 50 , c ) 52 , d ) 54 , e ) 56
Rationale: "annie earned 40 x + 13 ( 2 x ) = 66 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 66 x ( 1.5 x ) ( h ) = 81 x h = 54 hours the answer is d ."
Answer: d
Question (geometry): the diagonals of a rhombus are 18 cm and 22 cm . find its area ?
Options: a ) 277
b ) 266
c ) 198
d ) 288
e ) 212
Rationale: 1 / 2 * 18 * 22 = 198 answer : c
Answer: c
Question (general): if 20 liters of chemical x are added to 80 liters of a mixture that is 25 % chemical x and 75 % chemical y , then what percentage of the resulting mixture is chemical x ?
Options: a ) 28 % , b ) 32 % , c ) 36 % , d ) 40 % , e ) 44 %
Rationale: the amount of chemical x in the solution is 20 + 0.25 ( 80 ) = 40 liters . 40 liters / 100 liters = 40 % the answer is d .
Answer: d
Question (gain): a number increased by 20 % gives 600 . the number is
Options: a ) 250 , b ) 400 , c ) 450 , d ) 500 , e ) 520
Rationale: "formula = total = 100 % , increse = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 20 % = 120 % 120 % - - - - - - - > 600 ( 120 × 5 = 600 ) 100 % - - - - - - - > 500 ( 100 × 5 = 500 ) d )"
Answer: d
Question (gain): when a laptop is sold for rs . 49,000 , the owner loses 30 % . at what price must that laptop be sold in order to gain 30 % ?
Options: a ) 87000 , b ) 88000 , c ) 89000 , d ) 90000 , e ) 91000
Rationale: 70 : 49000 = 130 : x x = ( 49000 x 130 ) / 70 = 91000 . hence , s . p . = rs . 91,000 . answer : option e
Answer: e
Question (physics): if a and b together can finish a work in 16 days . a can finish same work alone in 24 days then b alone can finish same work alone in how many days ?
Options: a ) 30 days , b ) 48 days , c ) 40 days , d ) 36 days , e ) 50 days
Rationale: ( a + b ) work in 1 day = 1 / 16 , a work in 1 day = 1 / 24 b work in 1 day = [ 1 / 16 - 1 / 24 ] = 1 / 48 . b alone can finish same work in 48 days . answer b
Answer: b
Question (general): if 5 a + 7 b = m , where a and b are positive integers , what is the largest possible value of m for which exactly one pair of integers ( a , b ) makes the equation true ?
Options: a ) 35 , b ) 48 , c ) 69 , d ) 70 , e ) 74
Rationale: 5 * a 1 + 7 * b 1 = m 5 * a 2 + 7 * b 2 = m 5 * ( a 1 - a 2 ) = 7 * ( b 2 - b 1 ) since we are dealing with integers we can assume that a 1 - a 2 = 7 * q and b 2 - b 1 = 5 * q where q is integer , so whenever we get a pair for ( a ; b ) we can find another one by simply adding 7 to a and subtracting 5 from b or vice versa , subtracting 7 from a and adding 5 to b . lets check how it works for our numbers , starting from the largest : e ) 74 = 5 * 12 + 7 * 2 ( a 1 = 12 , b 1 = 2 ) , subtract 7 from a and add 5 to b respectively , so a 2 = 5 and b 2 = 7 , second pair - bad d ) 70 = 5 * 7 + 7 * 5 ( a 1 = 7 , b 1 = 5 ) , if we add 7 toawe will have to subtract 5 from b but b ca n ' t be 0 , so - no pair , if we subtract 7 froma , we ' ll get a = 0 which also is n ' t allowed - no pair , thus this is the only pair for ( a ; b ) that works , good ! , thus d is the answer
Answer: d
Question (gain): the cost price of an article is 64 % of the marked price . calculate the gain percent after allowing a discount of 15 % ?
Options: a ) 32.8 % , b ) 37.6 % , c ) 38.5 % , d ) 17.5 % , e ) 37.2 %
Rationale: "let marked price = rs . 100 . then , c . p . = rs . 64 , s . p . = rs . 85 gain % = 21 / 64 * 100 = 32.8 % . answer : a"
Answer: a
Question (gain): the calendar of the year 2028 can be used again in the year ?
Options: a ) 2041 , b ) 1951 , c ) 2056 , d ) 1971 , e ) 1973
Rationale: "explanation : given year 2028 when divided by 4 , leaves a remainder 0 . note : when remainder is 0 , 28 is added to the given year to get the result . so , 2028 + 28 = 2056 answer : c"
Answer: c
Question (probability): a man speaks truth 3 out of 4 times . he throws a die and reports it to be a 6 . what is the probability of it being a 6 ?
Options: a ) 3 / 5 , b ) 1 / 2 , c ) 3 / 4 , d ) 3 / 8 , e ) 3 / 6
Rationale: explanation : there are two cases 1 ) he is telling truth that the die reports 6 , its probability = 3 / 4 * 1 / 6 = 1 / 8 2 ) he is telling lie that the die reports 6 , its probability = 1 / 4 * 5 / 6 = 5 / 24 so required probability = ( 1 / 8 ) / ( 1 / 8 ) + ( 5 / 24 ) = ( 1 / 8 ) / ( 1 / 3 ) = 3 / 8 hencer ( d ) is the correct answer answer : d
Answer: d
Question (probability): a fair coin is tossed 11 times . what is the probability of getting more heads than tails in 11 tosses ?
Options: a ) 1 / 2 , b ) 63 / 128 , c ) 4 / 7 , d ) 61 / 256 , e ) 63 / 64
Rationale: "on each toss , the probability of getting a head is 1 / 2 and the probability of getting a tail is 1 / 2 . there is no way to get the same number of heads and tails on an odd number of tosses . there will either be more heads or more tails . then there must be more heads on half of the possible outcomes and more tails on half of the possible outcomes . p ( more heads ) = 1 / 2 the answer is a ."
Answer: a
Question (gain): on a sum of money , simple interest for 2 years is rs 660 and compound interest is rs 696.30 , the rate of interest being the same in both cases .
Options: a ) 8 % , b ) 9 % , c ) 10 % , d ) 11 % , e ) none of these
Rationale: explanation : difference between c . i and s . i for 2 years = 36.30 s . i . for one year = 330 . s . i . on rs 330 for one year = 36.30 so r % = \ frac { 100 * 36.30 } { 330 * 1 } = 11 % answer : d
Answer: d
Question (general): an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 19404 / - in 3 years at the same rate of interest . find the rate percentage ?
Options: a ) 5 % , b ) 7 % , c ) 9 % , d ) 10 % , e ) 12 %
Rationale: explanation : the difference of two successive amounts must be the simple interest in 1 year on the lower amount of money . s . i = 19404 / - - 17640 / - = rs . 1764 / - rate of interest = ( 1764 / 17640 ) × ( 100 / 1 ) = > 10 % answer : option d
Answer: d
Question (gain): a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 30 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 41
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 30 % discount then the original price of it was x * 0.7 = $ 14 - - > x = $ 20 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 20 + 21 = $ 41 . answer : e ."
Answer: e
Question (general): a man is 22 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 22 ) + 2 = 2 ( x + 2 ) x + 24 = 2 x + 4 x = 20 . answer : c"
Answer: c
Question (physics): a is twice as good a work man as b and together they finish the work in 10 days . in how many days a alone can finish the work ?
Options: a ) 23 , b ) 15 , c ) 77 , d ) 92 , e ) 61
Rationale: "wc = 2 : 1 2 x + x = 1 / 10 = > x = 1 / 30 2 x = 1 / 15 a can do the work in 15 days . answer : b"
Answer: b
Question (physics): pumps a , b , and c operate at their respective constant rates . pumps a and b , operating simultaneously , can fill a certain tank in 1 / 2 hours ; pumps a and c , operating simultaneously , can fill the tank in 1 / 2 hours ; and pumps b and c , operating simultaneously , can fill the tank in 2 hours . how many hours does it take pumps a , b , and c , operating simultaneously , to fill the tank .
Options: a ) 1 / 3 , b ) 1 / 2 , c ) 1 / 4 , d ) 1 , e ) 5 / 6
Rationale: "a + b = 1 / 2 ; a + c = 1 / 2 , b + c = 2 ; add then 2 * ( a + b + c ) = 3 a + b + c = 3 / 2 hrs e"
Answer: e
Question (general): if y > 0 , ( 10 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to y / 2 + 3 y / 10 = 4 y / 5 = 80 % e"
Answer: e
Question (general): the ages of two persons differ by 16 years . if 6 years ago , the elder one be 3 times as old as the younger one , find their present ages .
Options: a ) 10 years and 18 years , b ) 18 years and 26 years , c ) 20 years and 28 years , d ) 14 years and 30 years , e ) 16 years and 25 years
Rationale: "explanation : sol . let the age of the younger person be xx years then , age of the elder person = ( x + 16 ) ( x + 16 ) years â ˆ ´ â ˆ ´ 3 ( x â ˆ ’ 6 ) = ( x + 16 â ˆ ’ 6 ) 3 ( x - 6 ) = ( x + 16 - 6 ) â ‡ ” 3 x â ˆ ’ 18 = x + 10 â ‡ ” 3 x - 18 = x + 10 â ‡ ” 2 x = 28 â ‡ ” 2 x = 28 â ‡ ” x = 14 â ‡ ” x = 14 hence , their present age are 14 years and 30 years . answer is d"
Answer: d
Question (general): let the number which when multiplied by 11 is increased by 300 .
Options: a ) 14 , b ) 20 , c ) 26 , d ) 28 , e ) 30
Rationale: solution let the number be x . then , 11 x - x = 300 ‹ = › 10 x = 300 x ‹ = › 30 . answer e
Answer: e
Question (general): in a division , a student took 78 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 52 , e ) 38
Rationale: "x / 78 = 24 . x = 24 * 78 . so correct answer would be , ( 24 * 78 ) / 36 = 52 . answer : d"
Answer: d
Question (physics): an athlete takes 10 seconds to run 100 m . what is his avg . speed in miles per hour ?
Options: a ) 22.37 , b ) 26.66 , c ) 24.35 , d ) 36.0 , e ) 42.44
Rationale: his average speed is 10 m / s . which is 36 km / hr . but 36 km = 22.37 miles . the average speed of the athlete is 22.37 mph answer : a
Answer: a
Question (general): chris age after 13 years will be 5 times his age 5 years back . what is the present age of chris ?
Options: a ) a ) 20 , b ) b ) 25 , c ) c ) 15 , d ) d ) 22 , e ) e ) 12
Rationale: "chris present age = x after 13 years = x + 13 5 years back = x - 5 x + 13 = 5 ( x - 5 ) x = 12 answer is e"
Answer: e
Question (gain): a pair of articles was bought for $ 50 at a discount of 50 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 12.50 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 50 % of x = 25 x = 25 * . 5 = $ 12.50 answer is b"
Answer: b
Question (gain): a tank is filled to one quarter of its capacity with a mixture consisting of water and sodium chloride . the proportion of sodium chloride in the tank is 40 % by volume and the capacity of the tank is 24 gallons . if the water evaporates from the tank at the rate of 0.5 gallons per hour , and the amount of sodium chloride stays the same , what will be the concentration of water in the mixture in 6 hours ?
Options: a ) 18 % , b ) 20 % , c ) 22 % , d ) 24 % , e ) 26 %
Rationale: the number of gallons in the tank is ( 1 / 4 ) 24 = 6 gallons the amount of sodium chloride is 0.4 ( 6 ) = 2.4 gallons at the start , the amount of water is 0.6 ( 6 ) = 3.6 gallons after 6 hours , the amount of water is 3.6 - 0.5 ( 6 ) = 0.6 gallons the concentration of water is 0.6 / ( 2.4 + 0.6 ) = 2 / 10 = 20 % the answer is b .
Answer: b
Question (general): in what proportion must rice at rs 3.10 per kg be mixed with rice at rs 3.75 per kg , so that the mixture be worth rs 3.25 a kg ?
Options: a ) 7 / 3 , b ) 5 / 3 , c ) 10 / 3 , d ) 3 / 7 , e ) 11 / 5
Rationale: c . p of 1 kg of cheaper rice = rs 3.10 c . p of 1 kg of expensive rice = rs 3.75 the mixture be worth for 1 kg = rs 3.25 by the alligation rule : quantity of cheaper rice / quantity of expensive rice = ( 3.75 - 3.25 ) / ( 3.25 - 3.10 ) = ( 0.50 ) / ( 0.15 ) = 10 / 3 c
Answer: c
Question (physics): the distance between 2 cities a and b is 1000 km . a train starts from a at 12 p . m . and travels towards b at 100 km / hr . another starts from b at 1 p . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 5 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 12 p . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 10 + 5 = 5 p . m . answer is c"
Answer: c
Question (general): in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 300 points , how many points is the third question worth ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 300 10 x = 120 x = 12 3 rd question = x + 8 = 12 + 8 = 20 answer d"
Answer: d
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 256 sq . feet , how many feet of fencing will be required ?
Options: a ) 45.6 , b ) 40 , c ) 68 , d ) 88 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 256 breadth = 12.8 feet area to be fenced = 2 b + l = 2 ( 12.8 ) + 20 = 45.6 feet answer : a"
Answer: a
Question (other): there are 180 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?
Options: a ) 100 , b ) 104 , c ) 108 , d ) 112 , e ) 116
Rationale: "the number of nurses at the hospital is ( 3 / 5 ) * 180 = 108 . the answer is c ."
Answer: c
Question (gain): a reduction of 40 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 80 , b ) 72 , c ) 64 , d ) 56 , e ) 48
Rationale: "800 * ( 40 / 100 ) = 320 - - - - 5 ? - - - - 1 = > rs . 64 answer : c"
Answer: c
Question (gain): a tank contains 6,500 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.12 % , b ) 6.12 % , c ) 7.12 % , d ) 8.12 % , e ) 9.12 %
Rationale: "we start with 6,500 gallons of a solution that is 5 % sodium chloride by volume . this means that there are 0.05 x 6,500 = 325 gallons of sodium chloride . when 2,500 gallons of water evaporate we are left with 4,000 gallons of solution . from here we can determine what percent of the 4,000 gallon solution is sodium chloride . ( sodium chloride / total solution ) x 100 = ? ( 325 / 4,000 ) x 100 = ? 0.0812 x 100 = ? = 8.12 % answer is d ."
Answer: d
Question (other): the l . c . m . of 2 numbers is 72 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 60 , e ) 56
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 72 x = 12 the numbers are = 24 and 36 required sum = 24 + 36 = 60 answer is d"
Answer: d
Question (general): if a farmer sells 15 of his chickens , his stock of feed will last for 4 more days than planned , but if he buys 25 more chickens , he will run out of feed 3 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 ) 12 , b ) 24 , c ) 48 , d ) 55 , e ) 49
Rationale: "say farmer has n chicken and he is good for d days . : - we have 3 equations given in question : - ( n - 15 ) * d + 4 = ( n + 25 ) * ( d - 3 ) = n * d solving these : ( you can solve 1 st and 3 rd and 2 nd and 3 rd together ) we get : 25 d - 3 n = 75 4 n - 15 d = 60 = > n ~ 49 ans e it is !"
Answer: e