Cheukting/mathqa huggingface dataset:
Question (gain): in an institute , 60 % of the students are boys and the rest are girls . further 15 % of the boys and 7.5 % of the girls are getting a fee waiver . if the number of those getting a fee waiver is 90 , find the total number of students getting 50 % concessions if it is given that 50 % of those not getting a fee waiver are eligible to get half fee concession ?
Options: a ) 360 , b ) 280 , c ) 320 , d ) 330 , e ) 350
Rationale: solution : let us assume there are 100 students in the institute . then , number of boys = 60 and , number of girls = 40 further , 15 % of boys get fee waiver = 9 boys 7.5 % of girls get fee waiver = 3 girls total = 12 students who gets fee waiver but , here given 90 students are getting fee waiver . so we compare 12 = 90 so , 1 = 90 / 12 = 7.5 now number of students who are not getting fee waiver = 51 boys and 37 girls . 50 % concession = 25.5 boys and 18.5 girls ( i . e . total 44 ) . hence , required students = 44 * 7.5 = 330 . answer : option d
Answer: d
Question (general): if n = 2 ^ 0.15 and n ^ b = 64 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 40 , d ) 5 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 6 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 6 b = 40 answer : c"
Answer: c
Question (geometry): each of the 9 squares shown is to contain one number chosen from 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 . no number is to be repeated . suppose the sum of the 5 squares aligned vertically on the right is 32 and that the sum of the 5 squares aligned horizontally on the bottom is 20 . what number goes in the shared corner square ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: if x is the number in the corner square , then the sum of all the numbers in the squares is equal to the sum of the numbers in the five squares aligned vertically plus the sum of the numbers in the five squares aligned horizontally minus x . hence , 1 + 2 + · · · + 9 = 32 + 20 − x . the sum on the left is 45 , so x = 52 − 45 = 7 . correct answer e
Answer: e
Question (general): in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 7 ohms ?
Options: a ) 3 / 5 , b ) 1 / 7 , c ) 12 / 35 , d ) 31 / 12 , e ) 35 / 12
Rationale: "1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 7 = 12 / 35 r = 35 / 12 the answer is e ."
Answer: e
Question (general): a envelop weight 8.5 gm , if 850 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.6 kg , b ) 7.225 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: 850 * 8.5 7225.0 gm 7.225 kg answer : b
Answer: b
Question (physics): a can give b 90 meters start and c 200 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 120.88 , b ) 120.13 , c ) 111.22 , d ) 120.0 , e ) 111.12
Rationale: "a runs 1000 m while b runs 910 m and c runs 800 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 800 ) / 910 = 879.12 m . b can give c = 1000 - 879.12 = 120.88 m . answer : a"
Answer: a
Question (gain): a man buys 12 lts of liquid which contains 10 % of the liquid and the rest is water . he then mixes it with 10 lts of another mixture with 30 % of liquid . what is the % of water in the new mixture ?
Options: a ) 80.91 , b ) 76.45 , c ) 77.45 , d ) 74.45 , e ) 73.45
Rationale: 10 % in 12 lts is 1.2 . so water = 12 - 1.2 = 10.8 lts . 30 % of 10 lts = 3 . so water in 2 nd mixture = 10 - 3 = 7 lts . now total quantity = 12 + 10 = 22 lts . total water in it will be 10.8 + 7 = 17.8 lts . % of water = ( 100 * 17.8 ) / 22 = 80.91 . answer : a
Answer: a
Question (probability): a jar contains 6 black and 2 white balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 15 , e ) 3 / 14
Rationale: "p ( 1 st black , 2 nd white ) = 6 / 8 * 2 / 7 = 12 / 56 ; p ( 1 st white , 2 nd black ) = 2 / 8 * 6 / 7 = 12 / 56 . p = 12 / 56 + 12 / 56 = 24 / 112 = 12 / 56 = 6 / 28 = 3 / 14 . answer : e ."
Answer: e
Question (physics): if a car had traveled 10 kmh faster than it actually did , the trip would have lasted 30 minutes less . if the car went exactly 30 km , at what speed did it travel ?
Options: a ) 20 kmh , b ) 25 kmh , c ) 30 kmh , d ) 35 kmh , e ) 40 kmh
Rationale: "time = distance / speed difference in time = 1 / 2 hrs 30 / x - 30 / ( x + 10 ) = 1 / 2 substitute the value of x from the options . - - > x = 20 - - > 30 / 20 - 30 / 30 = 3 / 2 - 1 = 1 / 2 answer : a"
Answer: a
Question (general): a man is 28 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 ) 26 years
Rationale: "let present age of the son = x years then , present age the man = ( x + 28 ) years given that , in 2 years , man ' s age will be twice the age of his son â ‡ ’ ( x + 28 ) + 2 = 2 ( x + 2 ) â ‡ ’ x = 26 answer : e"
Answer: e
Question (general): how many numbers from 10 to 100 are exactly divisible by 9 ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "option ' c ' 10 / 9 = 1 and 100 / 9 = 11 = = > 11 - 1 = 10 . therefore 10 digits ."
Answer: c
Question (general): what is the units digit of the expression 7 ^ 75 + 6 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "7 in power repeats pattern of 4 : 7 - 9 - 3 - 1 . as 75 = 4 * 18 + 3 then the last digit of 7 ^ 75 is the same as the last digit of 7 ^ 3 , which is 3 . units digit of 7 ^ 75 + 6 will be : 3 + 6 = 9 . answer is e"
Answer: e
Question (general): a certain list consists of 21 different numbers . if n is in the list and n is 8 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 2 / 7 , d ) 4 / 21 , e ) 5 / 21
Rationale: "series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 8 * x hence , a 1 + a 2 + . . + a 20 + n = 28 x so , the fraction asked = 8 x / 28 x = 2 / 7 c"
Answer: c
Question (physics): two tains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 14 , c ) 10.9 , d ) 20 , e ) 18
Rationale: "sol . speed of the first train = [ 120 / 10 ] m / sec = 12 m / sec . speed of the second train = [ 120 / 12 ] m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = m / sec = 22 m / sec . ∴ required time = ( 120 + 120 ) / 22 secc = 10.9 sec . answer c"
Answer: c
Question (geometry): 108 . triangle a ’ s base is 8 % greater than the base of triangle b , and a ’ s height is 8 % less than the height of triangle b . the area of triangle a is what percent less or more than the area of triangle b ?
Options: a ) 9 % less , b ) 1 % less , c ) equal to each other , d ) 1.6 % more , e ) 9 % more
Rationale: "wish the question specified that we are talking about corresponding height . base of a = 9 / 8 * base of b height of a = 7 / 8 * height of b area of a = ( 1 / 2 ) * base of a * height of a = 9 / 8 * 7 / 8 * area of b = 63 / 64 * area of b area of a is 1.6 % more than the area of b . answer ( d )"
Answer: d
Question (gain): an agent , gets a commission of 4 % on the sales of cloth . if on a certain day , he gets rs . 12.50 as commission , the cloth sold through him on that day is worth
Options: a ) 312 , b ) 500 , c ) 887 , d ) 299 , e ) 132
Rationale: "explanation : let the total sale be rs . x . then , 4 % . of x = 12.50 = ( 4 / 100 * x ) = 12.5 < = > x = 312.5 . answer : a"
Answer: a
Question (other): a certain university will select 3 of 7 candidates eligible to fill a position in the mathematics department and 5 of 8 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42232 , b ) 42170 , c ) 14008 , d ) 16510 , e ) 41160
Rationale: "7 c 3 * 8 c 5 = 35 * 56 = 41160 the answer is ( e )"
Answer: e
Question (physics): a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 2 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 4 4 / 5 days , d ) 3 days , e ) 9 days
Rationale: "work done by a in 2 days = 2 / 10 = 1 / 5 remaining work = 4 / 5 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 4 / 5 * 6 / 1 = 24 / 5 = 4 4 / 5 days . answer : c"
Answer: c
Question (geometry): the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m . what is the area of the field ?
Options: a ) 18750 sq . m
b ) 37500 sq . m
c ) 40000 sq . m
d ) 48000 sq . m
e ) none of these
Rationale: solution so length = 250 m ; breadth = 150 m area = ( 250 x 150 ) m ² = 37500 m ² answer b
Answer: b
Question (general): if | 20 x - 10 | = 170 , then find the product of the values of x ?
Options: a ) - 45 , b ) 50 , c ) - 72 , d ) 35 , e ) - 30
Rationale: "| 20 x - 10 | = 170 20 x - 10 = 170 or 20 x - 10 = - 170 20 x = 180 or 20 x = - 160 x = 9 or x = - 8 product = - 8 * 9 = - 72 answer is c"
Answer: c
Question (general): 5 liters of a 20 percent solution of alcohol in water are mixed with 3 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
Options: a ) 16.7 % , b ) 17.0 % , c ) 17.3 % , d ) 17.6 % , e ) 17.9 %
Rationale: "the total amount of alcohol is 0.2 ( 5 ) + 0.12 ( 3 ) = 1.36 liters . the percentage is 1.36 / 8 = 136 / 800 = 17 / 100 which is 17 % the answer is b ."
Answer: b
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 50 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 120 - 80 ) / 80 * 100 = ~ 50 % answer : d ."
Answer: d
Question (gain): compare the rates of two trains , one travelling at 45 km / hr and other is at 10 m / s ?
Options: a ) 5 : 4 , b ) 3 : 2 , c ) 1 : 5 , d ) 2 : 7 , e ) 3 : 5
Rationale: "speed of the 1 st train = 45 km / hr speed of the 2 nd train = 10 m / s = 10 * 18 / 5 = 36 km / hr ratio of the speeds of the train = 45 : 36 = 5 : 4 answer is a"
Answer: a
Question (gain): a scuba diver descends at a rate of 32 feet per minute . a diver dive from a ship to search for a lost ship at the depth of 6400 feet below the sea level . . how long will he take to reach the ship ?
Options: a ) 200 minutes , b ) 240 minutes , c ) 220 minutes , d ) 210 minutes , e ) 77 minutes
Rationale: "time taken to reach = 6400 / 32 = 200 minutes answer : a"
Answer: a
Question (physics): a clock shows the time as 9 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 6 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: "there are 9 hours in between 9 a . m . to 6 p . m . 9 * 5 = 45 minutes . answer : c"
Answer: c
Question (other): three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 300 . what is their h . c . f . ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 60 , e ) 75
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 300 x = 25 hcf of 2 x , 3 x and 4 x = x = 25 the answer is b ."
Answer: b
Question (general): for what values of k will the pair of equations 3 x + 4 y = 12 and ( kx + 12 y ) / 2 = 15 does not have a unique solution ?
Options: a ) 12 , b ) 9 , c ) 3 , d ) 7.5 , e ) 2.5
Rationale: "we have 2 equations 1 . 3 x + 4 y = 12 - - > 9 x + 12 y = 36 2 . ( kx + 12 y ) / 2 = 15 - - > kx + 12 y = 30 substract 1 - 2 , we get ( 9 - k ) x = 6 i . e . x = 6 / ( 9 - k ) then , by looking at options , we get some value of x except for b . when we put k = 9 , x becomes 6 / 0 and hence answer is b"
Answer: b
Question (gain): what will be the compound interest on a sum of rs . 30,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 10123.28 , e ) s : 12147.84
Rationale: "amount = [ 30000 * ( 1 + 12 / 100 ) 3 ] = 30000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 42147.84 c . i . = ( 42147.84 - 30000 ) = rs : 12147.84 answer : e"
Answer: e
Question (general): a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 65 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 65 % = 65 = b + c total number of flags = a + b + c = 100 ( since all the flags have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 65 - c = 100 c = 25 option e ."
Answer: e
Question (general): how many multiples of 6 are less than 3600 , and also multiples of 36 ?
Options: a ) 94 , b ) 100 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 6 and 36 is 36 . divide 3600 / 36 = 100 . xxx . so b is your answer .
Answer: b
Question (general): 17 times a positive integer is more than its square by 70 , then the positive integer is
Options: a ) 13 , b ) 10 , c ) 11 , d ) 12 , e ) 14
Rationale: "explanation : let the number be x . then , 17 x = x 2 + 70 = > x 2 - 17 x + 70 = 0 = > ( x - 7 ) ( x - 10 ) = 0 = > x = 7 or 10 answer : b"
Answer: b
Question (gain): the profit earned by selling an article for rs . 832 is equal to the loss incurred when the same article is sold for rs . 448 . what should be the sale price for making 80 % profit ?
Options: a ) 1152 , b ) 230 , c ) 960 , d ) 780 , e ) 400
Rationale: "c . p . = rs . x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 180 % of rs . 640 = 180 / 100 * 640 = rs . 1152 . a"
Answer: a
Question (physics): find the distance covered by a man walking for 30 min at a speed of 5 km / hr ?
Options: a ) 1 km , b ) 3 km , c ) 4 km , d ) 2.5 km , e ) 6 km
Rationale: "distance = 5 * 30 / 60 = 2.5 km answer is d"
Answer: d
Question (general): dacid obtained 96 , 95 , 82 , 87 and 92 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 67 , b ) 26 , c ) 87 , d ) 26 , e ) 90
Rationale: "average = ( 96 + 95 + 82 + 87 + 92 ) / 5 = 452 / 5 = 90 . answer : e"
Answer: e
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 15 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 ) 72 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 = 15 2 x + 3 x = 360 x = 72 km answer is d"
Answer: d
Question (general): of the 80 people in a room , 2 / 5 are women . if 1 / 2 of the people are married , what is the maximum number of women in the room who could be unmarried ?
Options: a ) 20 , b ) 22 , c ) 26 , d ) 30 , e ) 32
Rationale: "women = 2 / 5 * 80 = 32 married = 1 / 2 * 80 = 40 unmarried = 40 max ( un - married women ) = 32 e"
Answer: e
Question (general): the value of x . 1234 - x = 4234 - 3361
Options: a ) 671 , b ) 371 , c ) 361 , d ) 248 , e ) 246
Rationale: "1234 - x = 4234 - 3361 x = 1234 - 4234 + 3361 = 361 x = 361 correct answer : c"
Answer: c
Question (general): in a group of ducks and cows , the total number of legs are 32 more than twice the no . of heads . find the total no . of buffaloes .
Options: a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 32 = > 2 x = 32 = > x = 16 d"
Answer: d
Question (physics): two pipes a and b can fill a tank in 24 hours and 36 hours respectively . if both the pipes are opened simultaneously , how much time will be taken to fill the tank ?
Options: a ) 20 hours , b ) 15 hours , c ) 14 2 / 5 hours , d ) 12 hours , e ) 8 hours
Rationale: "part filled by a in 1 hour = 1 / 24 part filled by b in 1 hour = 1 / 36 part filled by ( a + b ) in 1 hour = 1 / 24 + 1 / 36 = 5 / 72 both the pipes together fill the tank in 72 / 5 = 14 2 / 5 hours answer is c"
Answer: c
Question (physics): maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 20 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 12 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 20 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 20 / 10 = 2 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 2 = 12 kms . . . answer - a"
Answer: a
Question (general): in 1 kg mixture of iron and manganese 20 % of manganese . how much iron should be added so that the proportion of manganese becomes 10 %
Options: a ) 1.5 kg , b ) 2 kg , c ) . 5 kg , d ) 1 kg , e ) none of these
Rationale: explanation : by the rule of alligation , we have percentage concentration of manganese in the mixture : 20 percentage concentration of manganese in pure iron : 0 percentage concentration of manganese in the final mixture 10 10 - 0 = 10 20 - 10 = 10 = > quantity of the mixture : quantity of iron = 10 : 10 = 1 : 1 given that quantity of the mixture = 1 kg hence quantity of iron to be added = 1 kg answer : option d
Answer: d
Question (general): a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes john can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
Answer: a
Question (general): a meal cost $ 36.50 and there was no tax . if the tip was more than 10 pc but less than 15 pc of the price , then the total amount paid should be :
Options: a ) 40 - 42 , b ) 39 - 41 , c ) 38 - 40 , d ) 37 - 39 , e ) 36 - 37
Rationale: "10 % ( 36.5 ) = 3.65 15 % ( 36.5 ) = 5.475 total amount could have been 36.5 + 3.65 and 36.5 + 5.475 = > could have been between 40.15 and 41.975 = > approximately between 40 and 42 answer is a ."
Answer: a
Question (physics): imagine an analog clock set to 12 o ' clock . note that the hour and minute hands overlap . how many times each day do both the hour and minute hands overlap ? how would you determine the exact times of the day that this occurs ?
Options: a ) 11 , b ) 12 , c ) 22 , d ) 24 , e ) 44
Rationale: 22 times in a day . 12,1 hours 60 / 11 minutes , 2 hours 120 / 11 minutes , . . . so on till 12 ( 11 hours 660 / 11 minutes ) answer : c
Answer: c
Question (general): a basketball is dropped from a height of 30 feet . if it bounces back up to a height that is exactly half of its previous height , and it stops bouncing after hitting the ground for the fourth time , then how many total feet will the ball have traveled after 2 full bounces .
Options: a ) 50 , b ) 55 , c ) 60 , d ) 75 , e ) 80
Rationale: "initial distance = 30 feet first bounce = 15 feet up + 15 feet down = 30 feet second bouche = 7.5 feet up + 7.5 feet down = 15 feet total distance covered = 30 + 30 + 15 = 75 answer : d"
Answer: d
Question (physics): jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 7 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 14 hours , d ) 21 hours , e ) 32 hours
Rationale: "i believe the answer is d . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 7 = > 1 / 21 working alone taimour can do the job in 1 = 1 / 21 * hours = > 21 answer d"
Answer: d
Question (physics): to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 1 / 5 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 62.5 , e ) 125
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 1 x / 5 hence , number of buckets needed = 25 x / ( 1 x / 5 ) = ( 25 × 5 ) / 1 = 125 answer is e ."
Answer: e
Question (physics): 12 buckets of water fill a tank when the capacity of each bucket is 81 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 9 litres ?
Options: a ) 96 , b ) 110 , c ) 100 , d ) 90 , e ) 108
Rationale: "capacity of the tank = ( 12 ã — 81 ) litre number of buckets required of capacity of each bucket is 17 litre = 12 ã — 81 / 9 = 12 ã — 9 = 108 answer is e"
Answer: e
Question (geometry): the number 83 can be written as the sum of the squares of 3 different positive integers . what is the sum of these 3 integers ?
Options: a ) 17
b ) 16
c ) 15
d ) 14
e ) 13
Rationale: 7 ^ 2 + 5 ^ 2 + 3 ^ 2 = 49 + 25 + 9 = 83 7 + 5 + 3 = 15 hence answer is c
Answer: c
Question (geometry): one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 24 cm 2 . find the lengths of all sides .
Options: a ) 10 and 3
b ) 7 and 10
c ) 10 and 7
d ) 3 and 10
e ) 13 and 10
Rationale: let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm 2 , which is 24 cm 2 more than the first area . therefore a 1 + 24 = a 2 x ( x − 3 ) + 24 = ( x + 1 ) ( x − 2 ) x 2 − 3 x + 24 = x 2 + x − 2 x − 2 2 x = 26 x = 13 . so , the sides of the rectangle are 13 cm and ( 13 − 3 ) = 10 cm long . so answer is e .
Answer: e