Cheukting/mathqa huggingface dataset:
Question (gain): in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 20 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 27.5 %
Rationale: "since 20 % of the customers who sample the candyare notcaught , then 80 % of the customers who sample the candyarecaught : { % of customers who sample candy } * 0.80 = 0.22 ; { % of customers who sample candy } = 0.275 answer : e ."
Answer: e
Question (gain): if the selling price of 50 articles is equal to the cost price of 40 articles , then the loss or gain percent is ?
Options: a ) 20 % , b ) 80 % , c ) 90 % , d ) 22 % , e ) 24 %
Rationale: "let c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 40 . loss % = 10 / 50 * 100 = 20 % . answer : a"
Answer: a
Question (general): 3 students appear at an examination of mathematics . the probability of their success are 1 / 2 , 1 / 4 , 1 / 5 respectively . find the probability of success of at least two .
Options: a ) 1 / 60 , b ) 2 / 50 , c ) 9 / 40 , d ) 3 / 40 , e ) 4 / 50
Rationale: the probability of success of at least two students will involve the following possibilities . the first two students are successful , the last two students are successful , the first and third students are successful and all the three students are successful . therefore , the required probability = 1 / 2 x 1 / 4 x 4 / 5 + 1 / 4 x 1 / 5 x 1 / 2 + 1 / 2 x 1 / 5 x 3 / 4 + 1 / 2 x 1 / 4 x 1 / 5 = 9 / 40 answer : c
Answer: c
Question (general): if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 2 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 8 , e ) 1 / 4
Rationale: "say a = 3 . then : a / b = 1 / 3 - - > b = 9 ; b / c = 2 - - > c = 9 / 2 ; c / d = 1 / 2 - - > d = 9 ; d / e = 3 - - > e = 3 ; e / f = 1 / 2 - - > f = 6 . abc / def = ( 3 * 9 * 9 / 2 ) / ( 9 * 3 * 6 ) = 3 / 4 . answer : c ."
Answer: c
Question (physics): a train leaves delhi at 9 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 42 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
Options: a ) 229 , b ) 288 , c ) 787.5 , d ) 888 , e ) 121
Rationale: "d = 30 * 5 = 150 rs = 42 – 30 = 8 t = 150 / 8 = 18.75 d = 42 * 18.75 = 787.5 km answer : c"
Answer: c
Question (general): a man performs 1 / 2 of the total journey by rail , 1 / 3 by bus and the remaining 2 km on foot . his total journey is
Options: a ) 16 km , b ) 10 km , c ) 12 km , d ) 24 km , e ) 25 km
Rationale: "explanation : let the journey be x km then , 1 x / 2 + 1 x / 3 + 2 = x 5 x + 12 = 6 x x = 12 km answer : option c"
Answer: c
Question (general): the average of 7 consecutive numbers is 33 . the highest of these numbers is :
Options: a ) 28 , b ) 30 , c ) 33 , d ) 36 , e ) 28
Rationale: "the average of 7 consecutive numbers will be the 4 th number which is given to be = 33 5 th number = 34 , 6 th number = 35 , 7 th number = 36 answer : d ."
Answer: d
Question (probability): in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 6 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 116 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 6 = 5 / 6 , so of 200 newborn 200 * 5 / 6 * 5 / 6 * 5 / 6 = ~ 116 is expected to survive . answer : a ."
Answer: a
Question (physics): find the circumference of radius 7 cm .
Options: a ) 44 , b ) 55 , c ) 66 , d ) 77 , e ) 88
Rationale: "circumference of circle = 2 π r = 2 × 22 / 7 × 7 = 44 cm answer : a"
Answer: a
Question (physics): in what time will a train 50 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 1.25 sec , b ) 2.75 sec , c ) 3.5 sec , d ) 2.39 sec , e ) 9.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 50 / 40 = 1.25 sec . answer : a"
Answer: a
Question (geometry): a square carpet with an area 169 m 2 must have 2 metres cut - off one of its edges in order to be a perfect fit for a rectangular room . what is the area of rectangular room ?
Options: a ) 180 m 2
b ) 164 m 2
c ) 152 m 2
d ) 143 m 2
e ) none of these
Rationale: side of square carpet = √ area = √ 169 = 13 m after cutting of one side , measure of one side = 13 – 2 = 11 m and other side = 13 m ( remain same ) ∴ area of rectangular room = 13 × 11 = 143 m 2 answer d
Answer: d
Question (general): a “ sophie germain ” prime is any positive prime number p for which 2 p + 1 is also prime . the product of all the possible units digits of sophie germain primes greater than 3 is
Options: a ) 3 , b ) 189 , c ) 221 , d ) 227 , e ) 230
Rationale: "in that case , the sophie prime numbers greater than 5 are 7 , 11,23 , 47,59 , . . which yields units digit as 1 , 3,7 and 9 product would be 1 x 3 x 7 x 9 = 189 answer should be b ."
Answer: b
Question (general): a number x is multiplied by 5 , and this product is then divided by 7 . if the positive square root of the result of these two operations equals x , what is the value of x if x ≠ 0 ?
Options: a ) 25 / 9 , b ) 9 / 5 , c ) 5 / 7 , d ) 3 / 5 , e ) 9 / 25
Rationale: "sqrt ( 5 x / 7 ) to be perfect square x has to 5 / 7 ans : c"
Answer: c
Question (physics): the center of a circle lies on the origin of the coordinate plane . if a point ( x , y ) is randomly selected inside of the circle , what is the probability that y > 0 or y > x ?
Options: a ) 5 / 8 , b ) 1 / 6 , c ) 3 / 8 , d ) 1 / 2 , e ) 3 / 4
Rationale: "the line y = x divides the circle into two equal areas . all the points above the line y = x satisfy the condition that y > x . all the points above the x - axis satisfy the condition that y > 0 . the union of these two areas is 5 / 8 of the circle . the answer is a ."
Answer: a
Question (physics): in a kilometer race , a beats b by 25 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 167 sec , b ) 190 sec , c ) 390 sec , d ) 716 sec , e ) 123 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 25 = 400 sec . time taken by a = 400 - 10 = 390 sec . answer : c"
Answer: c
Question (general): one week , a certain truck rental lot had a total of 26 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 14 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 24 , e ) 4
Rationale: "n - not rented trucks ; r - rented trucks n + r = 26 n + r / 2 = 14 r = 24 d"
Answer: d
Question (general): each week , harry is paid x dollars per hour for the first 15 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 33 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: 42 x = 15 x + 1.5 x ( h - 15 ) = = > 42 = 15 + 1.5 ( h - 15 ) = = > h - 15 = 27 / 1.5 = 18 = = > h = 33 answer is a
Answer: a
Question (gain): shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $ 200 as interest . he invested the remaining in a bond that paid compound interest , interest being compounded annually , for the same 2 years at the same rate of interest and received $ 245 as interest . what was the value of his total savings before investing in these two bonds ?
Options: a ) 4000 , b ) 3500 , c ) 2500 , d ) 3000 , e ) 2000
Rationale: "so , we know that shawn received 20 % of the amount he invested in a year . we also know that in one year shawn received $ 100 , thus 0.2 x = $ 100 - - > x = $ 1,000 . since , he invested equal sums in his 2 bonds , then his total savings before investing was 2 * $ 1,000 = $ 2,000 answer e"
Answer: e
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 160 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 25 , d ) 82 , e ) 27
Rationale: "explanation : d = 100 + 160 = 260 s = 36 * 5 / 18 = 10 mps t = 260 / 10 = 26 sec answer : option a"
Answer: a
Question (general): at a bank , the service charges for transactions were us dollar 1 for every 5 transactions . the bank recently revised the charges to us dollar 0.75 for every 3 transactions . by approximately what percent did the ratio of price to transactions increase from the previous charge ?
Options: a ) 28 , b ) 24 , c ) 23 , d ) 22 , e ) 25
Rationale: initial charge / transaction ratio = 1 / 5 = 3 / 15 revised charge / transaction ratio = . 75 / 3 = 3.75 / 15 answer : e
Answer: e
Question (physics): convert 800 miles into meters ?
Options: a ) 1287472 , b ) 845796 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 800 mile = 800 * 1609.34 = 1287472 meters answer is a"
Answer: a
Question (physics): nil and ethan are brothers . they left their home at the same time and drove to the same beach . nil drove at a speed of 80 miles per hour . ethan drove at a speed of 20 miles per hour . nil arrived at the beach 0.5 hour earlier than ethan . what is the distance between their home and the beach ?
Options: a ) 70 miles , b ) 80 miles , c ) 90 miles , d ) 100 miles , e ) 110 miles
Rationale: every hour , nil gets ahead of ethan 80 - 20 = 60 miles . when nil arrived at the beach , ethan is only 20 × 0.5 = 10 miles behind . that tells us they only drove 1 hour when nil arrived at the beach . the distance between their home and the beach is nil ’ s speed × nil ’ s time = 80 × 1 = 80 miles . correct answer b
Answer: b
Question (other): if m = 3 ^ n , what is the greatest value of n for which m is a factor of 19 !
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: solution - consider multiples of 25 ! = > 3,6 , 9,12 , 15,18 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 - - - - count 3 ' s = 8 so answer is 8 answer : a
Answer: a
Question (gain): a reduction of 15 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 1200 , what is the reduced price for kg ?
Options: a ) 43 , b ) 55 , c ) 35 , d ) 45 , e ) 40
Rationale: "1200 * ( 15 / 100 ) = 180 - - - - 4 ? - - - - 1 = > rs . 45 answer : d"
Answer: d
Question (general): x , y , and z are different prime numbers . the product x ^ 2 * y ^ 2 * z is divisible by how many different positive numbers ?
Options: a ) 6 , b ) 8 , c ) 12 , d ) 18 , e ) 24
Rationale: "the exponents of x ^ 2 * y ^ 2 * z are 2 , 2 , and 1 . the number of factors is ( 2 + 1 ) ( 2 + 1 ) ( 1 + 1 ) = 18 the answer is d ."
Answer: d
Question (general): a car travels from point a to point b . the average speed of the car is 60 km / hr and it travels the first half of the trip at a speed of 48 km / hr . what is the speed of the car in the second half of the trip ?
Options: a ) 72 , b ) 75 , c ) 80 , d ) 84 , e ) 90
Rationale: "let d be the distance and let v be the speed in the second half . the total time = t 1 + t 2 d / 60 = d / 96 + ( d / 2 ) / v 8 d / 480 - 5 d / 480 = ( d / 2 ) / v d / 160 = d / 2 v and so v = 80 km / hr the answer is c ."
Answer: c
Question (general): a soccer store typically sells replica jerseys at a discount of 60 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 50 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , e is the answer"
Answer: e
Question (general): how many real solutions does the equation x 5 + 2 x 3 + 8 x 2 + 16 = 0 have ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: note that x 5 + 2 x 3 + 8 x 2 + 16 = ( x 3 + 8 ) ( x 2 + 2 ) = ( x + 2 ) ( x 2 - 2 x + 4 ) ( x 2 + 2 ) . since the quadratic equations x 2 - 2 x + 4 = 0 and x 2 + 2 = 0 have no real solutions , the original equation has just one real solution , x = - 2 . correct answer b
Answer: b
Question (general): a man is 20 years older than his son . in two years , his age will be twice the age of his son . what is the present age of his son ?
Options: a ) 23 years , b ) 22 years , c ) 21 years , d ) 20 years , e ) 18 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 20 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 20 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 18 answer : e"
Answer: e
Question (gain): a man can row downstream at the rate of 10 km / hr and upstream at 6 km / hr . find man ' s rate in still water and the rate of current ?
Options: a ) 9,6 , b ) 8,2 , c ) 9,3 , d ) 6,6 , e ) none of these
Rationale: "explanation : rate of still water = 1 / 2 ( 10 + 6 ) = 8 km / hr rate of current = 1 / 2 ( 10 - 6 ) = 2 km / hr answer : option b"
Answer: b
Question (general): in a can , there is a mixture of milk and water in the ratio 8 : 5 . if it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 12 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 18.4 , c ) 48 , d ) 50 , e ) 56
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 8 / 13 ( t - 8 ) after adding milk , quantity of milk in the mixture = 12 / 17 t . 12 t / 17 - 8 = 8 / 13 ( t - 8 ) 20 t = 1456 - 1088 = > t = 18.4 . answer : b"
Answer: b
Question (physics): matt and peter can do together a piece of work in 20 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 8 days . in how many days peter complete the work separately .
Options: a ) 21 , b ) 24 , c ) 20 , d ) 25 , e ) 30
Rationale: "together they complete the job in 20 days means they complete 12 / 20 of the job after 12 days . peter completes the remaining ( 8 / 20 ) of the job in 8 days which means that the whole job ( 1 ) can be completed in x days . x = 8 / ( 8 / 20 ) = 20 c"
Answer: c
Question (gain): if 40 % of a number exceeds 25 % of it by 18 , then find the number ?
Options: a ) 120 , b ) 150 , c ) 200 , d ) 64 , e ) 100
Rationale: "use the elimination method to find the correct option . of all the options only 120 fits 40 % of 120 = 48 25 % of 120 = 30 48 - 30 = 18 required number is 180 . answer : a"
Answer: a
Question (physics): jack rode his bicycle at an average speed of 5 mph for some time and then at an average speed of 15 mph for the rest of the journey . if he made no stops during the trip , and his average speed for the entire journey was 10 miles per hour , for what fraction of the total time did he ride at 15 mph ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 3 , d ) 2 / 5 , e ) 1 / 2
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . the average speed for the entire journey is 10 mph ; so , he rode at 5 mph and 15 mph for an equal duration of time . difference is 5 and 5 , respectively . 5 - - - - 10 - - - - 15 this shows that you can divide the entire journey into 2 equal parts . thus , 1 / 2 of the journey he rode at 10 mph , and 1 / 2 of the journey he rode at 15 mph . answer : e
Answer: e
Question (other): of the female students at barkely university , 1 / 6 are on the honor roll . of the male students , 2 / 5 are on the honor roll . if 3 / 5 of the students are female , what is ratio of male to female students on honor roll ?
Options: a ) 8 / 5 , b ) 3 / 15 , c ) 23 / 30 , d ) 43 / 60 , e ) 53 / 90
Rationale: "let the total students be 100 given 3 / 5 of the students are females = 60 then males = 2 / 5 = 40 1 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 5 = 16 ratio of m : f students on honor roll = 16 / 10 = 8 / 5 a"
Answer: a
Question (general): if ( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) and a and b are positive integers , what is the value of a ?
Options: a ) 22 , b ) 11 , c ) 9 , d ) 6 , e ) 7
Rationale: "( 18 ^ a ) * 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) = 2 ^ a . 9 ^ a . 9 ^ ( 3 a – 1 ) = ( 2 ^ 7 ) ( 3 ^ b ) just compare powers of 2 from both sides answer = 7 = e"
Answer: e
Question (general): the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 85 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 105 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 85 + 20 ) kg = 105 kg the answer is e ."
Answer: e
Question (general): if it takes a tub 6 minutes to drain 5 / 7 of its content , how much more time will it take for the tub to be empty ?
Options: a ) 48 seconds , b ) 1 minute , 12 seconds , c ) 1 minute , 50 seconds , d ) 2 minutes , 24 seconds , e ) 4 minutes , 12 seconds
Rationale: if 5 / 7 of tub ' s content is drained 2 / 7 th of tub still needs to be drained . if it takes 6 minutes to drain 5 / 7 th of tub it takes 6 * ( 7 / 5 ) minutes to drain the entire tub and 6 * ( 7 / 5 ) * ( 2 / 7 ) min to drain 2 / 7 th of the tub which is 2.4 minutes or 12 / 5 minutes or 2 minute 24 seconds so answer is d
Answer: d
Question (other): the compound ratio of 5 : 6 , 5 : 2 and 4 : 5 ?
Options: a ) 1 : 1 , b ) 5 : 3 , c ) 1 : 6 , d ) 1 : 9 , e ) 1 : 2
Rationale: "5 / 6 * 5 / 2 * 4 / 5 = 5 / 3 5 : 3 answer : b"
Answer: b
Question (general): the average of 10 numbers is 60 . out of 10 numbers the average of first 6 no . is 68 , and last 6 numbers is 75 then find 7 th number ?
Options: a ) a ) 78 , b ) b ) 65 , c ) c ) 258 , d ) d ) 62 , e ) e ) 48
Rationale: "7 th number = sum of 1 st 6 no . s + sum of last 6 no . s - sum of 11 no . s answer = 6 * 68 + 6 * 75 - 10 * 60 = 258 answer is c"
Answer: c
Question (general): for a certain exam , a score of 42 was 5 standard deviations below mean and a score of 67 was 2.5 standard deviations above mean . what was the mean score for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 58.67 , e ) 82.2
Rationale: "mean - 5 sd = 42 mean + 2.5 sd = 67 by solving above equations we get , sd ( absolute value ) = 3.33 mean = 58.67 ans . d"
Answer: d
Question (general): how many integers between 1 and 1,050 are divisible by 10 , 25 , and 35 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "prime factorization of given numbers 10 = 2 * 5 25 = 5 ^ 2 35 = 5 * 7 lcm of the given numbers = 2 * 5 ^ 2 * 7 = 50 * 7 = 350 therefore , number of integers = 1050 / 350 = 3 answer : option e"
Answer: e
Question (physics): a cistern 4 meters long and 4 meters wide contains water up to a depth of 1 meter 25 cm . what is the total area of the wet surface ?
Options: a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 4 x 1.25 ) + 4 x 4 ] = 36 the answer is c ."
Answer: c
Question (general): an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 16 - meter platform and caught it after it had traveled 32.5 meters . how many times did the ball bounce ?
Options: a ) 2 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "ans : 2 division of total diatance travelled will be 16 + 16 + 0.5 a"
Answer: a
Question (general): a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 146 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 146 / 25 = 5 . . . . so the max is 5 146 / 20 = 7 . . . so the max is 7 146 - 145 = 1 ( 6 small box + 1 big box ) answer : d"
Answer: d
Question (gain): each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 111 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 6000 , d ) $ 6400 , e ) $ 3700
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 111 x = 3700 answer e"
Answer: e
Question (general): in the graduating class of a certain college , 48 percent of the students are male and 52 percent are female . in this class 40 percent of the male and 40 percent of the female students are 25 years old or older . if one student in the class is randomly selected , approximately what is the probability that he or she will be less than 25 years old ?
Options: a ) a ) 0.9 , b ) b ) 0.6 , c ) c ) 0.45 , d ) d ) 0.3 , e ) e ) 0.25
Rationale: "percent of students who are 25 years old or older is 0.4 * 48 + 0.4 * 52 = 40 , so percent of people who are less than 25 years old is 100 - 40 = 60 . answer : b ."
Answer: b
Question (physics): two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 4 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: let x be the total time it takes for the cistern to fill . 4 / 12 + x / 15 = 1 x / 15 = 2 / 3 x = 10 after the first pipe is turned off , it takes 6 more minutes to fill the cistern . the answer is a .
Answer: a
Question (geometry): the edge of a cube is 5 a cm . find its surface ?
Options: a ) 150 a 2 cm 2 , b ) 170 a 2 cm 2 , c ) 125 a 2 cm 2 , d ) 175 a 2 cm 2 , e ) 120 a 2 cm 2
Rationale: "6 a 2 = 6 * 5 a * 5 a = 150 a 2 answer : a"
Answer: a
Question (general): 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container q ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c