regisss/math_qa huggingface dataset:
Problem: oy started cycling along the boundaries of a square field from corner point a . after half an hour he reached the corner point c , diagonally opposite to a . if his speed was 8 km / hr , the area of the filed in square km is ?
Options: a ) 64
b ) 4
c ) 16
d ) 9
e ) 5
Rationale: explanation : distance covered by roy in 1 / 2 hr = 4 kmtherefore , side of the square = 4 / 2 = 2 kmhence , area = 2 × 2 = 4 square km answer : b
Answer: b
Problem: how many 4 - digit numbers are there such that all 3 digits are different and the first digit and last digit is not zero ?
Options: a ) 2128 , b ) 3458 , c ) 4207 , d ) 5184 , e ) 8104
Rationale: all three digits are different and first digit is not zero . so first digit can be filled in 8 ways . and , second digit can be filled in 9 ways . and , third digit can be filled in 9 ways . and , fourth digit can be filled in 8 ways . total ways = 8 * 9 * 9 * 8 = 5184 hence option ( d ) .
Answer: d
Problem: the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 80 inclusive is the digital sum a multiple of 7 ?
Options: a ) 7 , b ) 9 , c ) 14 , d ) 16 , e ) 20
Rationale: "is there other way than just listing ? 25 34 43 52 59 61 68 70 77 9 ways . . b"
Answer: b
Problem: 32 = a + 2 b | a | > 2 if ‘ a ’ and ‘ b ’ are both integers , then what is the smallest possible values of ‘ a ’ that can be used to solve the above equation .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: let us understand the meaning of | a | > 2 mod is very easy concept if you solve mod question by considering as a distance . when a mod is written as | x - ( a ) | = b , this means the distance from point ' a ' ( both side left and right of ' a ' on number line ) is b . | x - ( a ) | < b means the distance is between the two extreme distance ( left and right side of ' a ' on number line , considering the max distance is ' b ' from ' a ' - as per this scenario . . . . . hence the value of ' a ' must be between these two extremes . | x - ( a ) | > b means the distance is greater than the distance of ' b ' . . i . e the value of a could be anywhere more than ' b ' ( i . e . current case ) . now come to the question . first its given | a | > 2 = = > a > 2 i . e . a can have any value bigger than 2 ( i . e . 3 , 4 , 5 … ) . now , lets move to equation a + 2 b = 32 = = > b = ( 32 – a ) / 2 = = > b = 16 – ( a / 2 ) . according to question , b is an integer , hence to make ‘ b ’ integer a must be divisible by 2 . minimum possible value of ‘ a ’ that is divisible by 2 is 4 ( a is greater than 2 so the next number that is divisible by 2 is 4 ) . so the answer is c ( value 4 ) .
Answer: c
Problem: a salesman ' s income consists of a commission and a base salary of $ 350 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 495 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 315 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 730
Rationale: total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 495 = $ 2170 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2170 = $ 1330 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1330 - $ 700 = $ 730 for 2 weeks avg weekly commission = $ 315 answer a
Answer: a
Problem: at company x , senior sales representatives visit the home office once every 15 days , and junior sales representatives visit the home office once every 10 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 30 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 99 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 35 , b ) 40 , c ) 45 , d ) 50 , e ) 55
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 / 15 ) + 1 = 7 total : 19 + 32 - 7 = 44 hence , widgets not inspected : 99 - 44 = 55 option e"
Answer: e
Problem: the guests at a football banquet consumed a total of 411 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 165 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 164 * 2.5 ( max possible amount of food a guest could consume ) = 410 pounds , so there must be more than 164 guests , next integer is 165 . answer : a ."
Answer: a
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ?
Options: a ) $ 280,000 , b ) $ 320,000 , c ) $ 360,000 , d ) $ 400,000 , e ) $ 540,000
Rationale: "the amount of an investment will double in approximately 70 / p years , where p is the percent interest , compounded annually . if thelma invests $ 50,000 in a long - term cd that pays 5 percent interest , compounded annually , what will be the approximate total value of the investment when thelma is ready to retire 42 years later ? the investment gets doubled in 70 / p years . therefore , the investment gets doubled in 70 / 5 = every 14 years . after 42 years , the investment will get doubled 42 / 14 = 3 times . so the amount invested will get doubled thrice . so , 50000 * 2 ^ 3 = 400000 hence , the answer is d ."
Answer: d
Problem: a man buys an article for $ 110 . and sells it for $ 125 . find the gain percent ?
Options: a ) 10 % , b ) 13.6 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 110 s . p . = $ 125 gain = $ 15 gain % = 15 / 110 * 100 = 13.6 % answer is b"
Answer: b
Problem: the slant height of a cone is 10 cm and radius of the base is 5 cm , find the curved surface of the cone ?
Options: a ) 150 , b ) 155 , c ) 158 , d ) 157 , e ) 190
Rationale: "π * 10 * 5 = 157 answer : d"
Answer: d
Problem: excluding stoppages , the speed of a train is 54 kmph and including stoppages it is 36 kmph . of how many minutes does the train stop per hour ?
Options: a ) 20 , b ) 17 , c ) 15 , d ) 18 , e ) 12
Rationale: "t = 18 / 54 * 60 = 20 answer : a"
Answer: a
Problem: a rectangular region has a fence along three sides and a wall along the fourth side . the fenced side opposite the wall is twice the length of each of the other two fenced sides . if the area of the rectangular region is 200 square feet , what is the total length of the fence , in feet ?
Options: a ) 10
b ) 20
c ) 30
d ) 40
e ) 80
Rationale: two sides each = x the third = 2 x and the wall length is thus 2 x too x * 2 x = 2 x ^ 2 = 200 ie x ^ 2 = 100 ie x = 10 l = 20 w = 10 total lenght of fence = 2 * 10 + 20 = 40 my answer is d
Answer: d
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 3 ¤ √ 3 =
Options: a ) 0 , b ) 5 , c ) 12 , d ) 15 , e ) 20
Rationale: "x = √ 3 and y also = √ 3 applying the function ( √ 3 + √ 3 ) ^ 2 - ( √ 3 - √ 3 ) ^ 2 = ( 2 √ 3 ) ^ 2 - 0 = 4 x 3 = 12 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 3 and y = √ 3 you get the answer 12 . answer c"
Answer: c
Problem: a palindrome is a number that reads the same forward and backward , such as 124 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 60 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 12 = 60 ways d"
Answer: d
Problem: hillary and eddy are climbing to the summit of mt . everest from a base camp 5,000 ft from the summit . when they depart for the summit at 06 : 00 , hillary climbs at a rate of 800 ft / hr with eddy lagging behind at a slower rate of 500 ft / hr . if hillary stops 1000 ft short of the summit and then descends at a rate of 1,000 ft / hr , at what time do hillary and eddy pass each other on her return trip ?
Options: a ) 11.0 , b ) 12.0 , c ) 13.0 , d ) 14.0 , e ) 15.0
Rationale: solution : h stopped 1000 ft before reaching the final point , time taken to reach 4000 ft = 4000 / 800 = 5 hrs . this means she reached there at 11 : 00 . speed difference between them is 800 - 500 = 300 ft / hr so by the time h stops they have 1500 ft of distance so now here we use relative speed formula they both are travelling toward each other with speed of 1000 and 500 total 1500 ft / hr and distance bwn them is 1500 ft so time taken to meet = 1 hr from 11 : 00 means 12 : 00 is the answer . b
Answer: b
Problem: a car drives 60 miles on local roads at 20 mph , and 120 miles on the highway at 60 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 52 mph , e ) 58 mph
Rationale: "so the answer is plainly a . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 120 to 60 to find the needed time to cover 120 miles , so t = 2 hours so the total time for covering total distance would be 3 + 2 = 5 hours and total distance is 60 + 120 = 180 miles final stage : average speed is total distance divide to total time : 180 / 5 = 36 miles per hour . . . ."
Answer: a
Problem: how many kg of pure salt must be added to 100 kg of 10 % solution of salt and water to increase it to a 20 % solution ?
Options: a ) 6.7 , b ) 1.3 , c ) 9.6 , d ) 12.5 , e ) 7.9
Rationale: "amount salt in 100 kg solution = 10 * 100 / 100 = 10 kg let x kg of pure salt be added then ( 10 + x ) / ( 100 + x ) = 20 / 100 100 + 10 x = 200 + 2 x 8 x = 100 x = 12.5 answer is d"
Answer: d
Problem: a train 200 m long passes a man , running at 6 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 36 , b ) 50 , c ) 78 , d ) 66 , e ) 22
Rationale: "speed of the train relative to man = ( 200 / 10 ) m / sec = 20 m / sec . [ 20 * ( 18 / 5 ) ] km / hr = 72 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 6 ) km / hr . x - 6 = 72 = = > x = 78 km / hr . answer : c"
Answer: c
Problem: if a triangle in the xy - coordinate system has vertices at ( - 2 , - 3 ) , ( 4 , - 3 ) and ( 28 , 7 ) , what is the area of the triangle ?
Options: a ) 30
b ) 36
c ) 48
d ) 60
e ) 65
Rationale: ( - 2 , - 3 ) is in 3 rd quadrant , ( 4 , - 3 ) is in 4 th quadrant while ( 28,7 ) is in 1 st quadrant . also , y coordinate of ( - 2 , - 3 ) and ( 4 , - 3 ) is same so they lie on same horizontal line . so base of triangle = sqrt [ ( - 3 + 3 ) ^ 2 + ( 4 + 2 ) ^ 2 ] = 6 and height of triangle = 7 - ( - 3 ) = 10 so area of triangle = 1 / 2 * 6 * 10 = 30 hence option ( a ) ,
Answer: a
Problem: a man can row upstream at 20 kmph and downstream at 80 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 50 kmph , c ) 30 kmph , d ) 45 kmph , e ) 65 kmph
Rationale: "us = 20 ds = 80 m = ( 20 + 80 ) / 2 = 50 answer : b"
Answer: b
Problem: in a tree , 1 / 5 of the birds are robins while the rest are bluejays . if 1 / 2 of the robins are female and 2 / 5 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 9 / 25 , b ) 12 / 25 , c ) 17 / 25 , d ) 29 / 50 , e ) 33 / 50
Rationale: "the fraction of birds that are male robins is ( 1 / 2 ) ( 1 / 5 ) = 1 / 10 . the fraction of birds that are male bluejays is ( 3 / 5 ) ( 4 / 5 ) = 12 / 25 . the total fraction of male birds is 1 / 10 + 12 / 25 = 29 / 50 . the answer is d ."
Answer: d
Problem: salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of b ' s total sales for that week . for what amount of total weekly sales would both salespeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 4,500 , e ) $ 4,000
Rationale: "360 + 0.06 ( x - 1000 ) = 0.08 x or 360 - 60 = 0.08 x or 300 / 0.02 = x or 15000 = x answer : c"
Answer: c
Problem: a crate measures 7 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2
b ) 4
c ) 6
d ) 7
e ) 12
Rationale: we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 7 for the surface 8 * 12 face . volume = 343 pi answer d
Answer: d
Problem: in a fuel station the service costs $ 2.30 per vehicle and every liter of fuel costs $ 0.70 . assuming that you fill up 4 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 396 , b ) $ 400 , c ) $ 404 , d ) $ 408 , e ) $ 412
Rationale: "the service cost of 4 vans and 2 trucks is 6 * 2.30 $ 13.80 the fuel in 4 vans is 4 * 65 = 260 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 546 liters the total fuel cost is 546 * 0.7 = $ 382.20 the total cost is $ 382.20 + $ 13.80 = $ 396 the answer is a ."
Answer: a
Problem: evaluate : 6502.5 + 650.25 + 65.025 + 6.5025 + 0.65025
Options: a ) 6819.59775 , b ) 6981.59775 , c ) 7224.92775 , d ) 6198.59775 , e ) 6891.59775
Rationale: "6502.5 650.25 65.025 6.5025 + 0.65025 - - - - - - - - - - - - - - - 7224.92775 answer is c ."
Answer: c
Problem: what is the smallest positive integer k such that the product of 450 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 450 = 3 ^ 2 * 5 ^ 2 * 3 , so if k = 3 then 450 k = ( 3 * 5 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Problem: log 3 n + log 5 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 125 , e ) 727
Rationale: "no of values n can take is 1 5 ^ 3 = 125 answer : d"
Answer: d
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 14 meters . what is the length of the yard if the area of the yard is 6 meters squared ?
Options: a ) 8 , b ) 6 , c ) 2 , d ) 4 , e ) 3
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 14 - - > l + b = 7 area = l * b = 6 b = 7 - l l ( 7 - l ) = 6 7 l - l ^ 2 = 6 l ^ 2 - 7 l + 6 = 0 upon simplifying we get l = 1 or 6 . only 6 is there in the answer choice . answer : b"
Answer: b
Problem: if a and b are positive integers , and a = 4 b + 16 , the greatest common divisor of a and b can not be
Options: a ) 2 , b ) 9 , c ) 4 , d ) 8 , e ) 16
Rationale: "if b is 2 , 4 , 8 , or 16 , then gcd of a and b is 2 , 4 , 8 , and 16 respectively . so , by poe the answer must be b . still : if b is a multiple of 9 , then a is 16 greater than a multiple of 9 , so not a multiple of 9 , so both of them can not be divisive by 9 . answer : b ."
Answer: b
Problem: find large number from below question the difference of two numbers is 1375 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1234 , b ) 1265 , c ) 1350 , d ) 1467 , e ) 1647
Rationale: "let the smaller number be x . then larger number = ( x + 1375 ) . x + 1375 = 6 x + 15 5 x = 1360 x = 272 large number = 272 + 1375 = 1647 e"
Answer: e
Problem: 3 pumps , working 8 hours a day , can empty a tank in 2 days . how many hours a day must 6 pumps work to empty the tank in 1 day ?
Options: a ) 8 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "3 pumps take 16 hrs total ( 8 hrs a day ) if 1 pump will be working then , it will need 16 * 3 = 48 hrs 1 pump need 48 hrs if i contribute 6 pumps then 48 / 6 = 8 hrs . answer : a"
Answer: a
Problem: at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 18 th highest price and the 25 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: "there were 17 items sold at a higher price than the radio and 24 items sold at a lower price than the radio . including the radio , there were 17 + 24 + 1 = 42 items sold . the answer is b ."
Answer: b
Problem: tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 3 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 7 / 15 , e ) 9 / 25
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 5 / 6 ) = 2 / 5 hours peter worked for 7 / 5 hours so he painted 7 / 5 * 1 / 3 = 7 / 15 of the room . the answer is d ."
Answer: d
Problem: if x ^ 2 + 1 / x ^ 2 = 3 , what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 7 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = 3 andsquareboth sides : ( x ² + 1 / x ² ) ² = 9 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 9 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 9 simplify : x ⁴ + 1 / x ⁴ = 7 answer : a"
Answer: a
Problem: find the value of 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ]
Options: a ) 800 , b ) 500 , c ) 2800 , d ) 1600 , e ) none
Rationale: answer 3.5 x [ ( 3.6 x 0.48 x 2.50 ) / ( 0.12 x 0.09 x 0.5 ) ] = 3.5 x [ ( 36 x 48 x 250 ) / ( 12 x 9 x 5 ) ] = 3.5 x 4 x 4 x 50 = 2800 correct option : c
Answer: c
Problem: a and b can do a piece of work in 3 days . with the help of c they finish the work in 2 days . c alone can do that piece of work in ?
Options: a ) 6 days , b ) 5 days , c ) 4 days , d ) 3 days , e ) 2 days
Rationale: "c = 1 / 2 – 1 / 3 = 1 / 6 = > 6 days answer : a"
Answer: a
Problem: dacid obtained 91 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 29 , b ) 78 , c ) 39 , d ) 37 , e ) 75
Rationale: "average = ( 91 + 65 + 82 + 67 + 85 ) / 5 = 78 answer : b"
Answer: b
Problem: harkamal purchased 8 kg of grapes at the rate of 80 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1135 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 80 × 8 = 640 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 640 + 495 = 1135 . d )"
Answer: d
Problem: the average of 9 observations was 4 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 54 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 4 = 36 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 36 = 54 option a"
Answer: a
Problem: 60 percent of movie theatres in town x have 1 screens or less . 20 % of those theatres sell an average of more than $ 300 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 300 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 40 ( 44 - 12 ) must be those with four screens or more d is the answer"
Answer: d
Problem: a man can row his boat with the stream at 26 km / h and against the stream in 12 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 4 kmph , c ) 5 kmph , d ) 7 kmph , e ) 8 kmph
Rationale: "ds = 26 us = 12 s = ? s = ( 26 - 12 ) / 2 = 7 kmph answer : d"
Answer: d
Problem: in n is a positive integer less than 200 , and 10 n / 60 is an integer , then n has how many different positive prime factors ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "( a ) . 10 n / 60 must be an integer . = > 1 n / 6 must be an integer . hence n must be a multiple of 2 * 3 . = > n has 2 different prime integers ."
Answer: a
Problem: a retailer bought a machine at a wholesale price of $ 117 and later on sold it after a 10 % discount of the retail price . if the retailer made a profit equivalent to 20 % of the whole price , what is the retail price of the machine ?
Options: a ) 81 , b ) 100 , c ) 120 , d ) 135 , e ) 159
Rationale: "my solution : wholesale price = 117 retail price , be = x he provides 10 % discount on retail price = x - 10 x / 100 this retail price = 20 % profit on wholesale price x - 10 x / 100 = 117 + 1 / 5 ( 117 ) x = 156 ; answer : e"
Answer: e
Problem: what sum of money put at c . i amounts in 2 years to rs . 8000 and in 3 years to rs . 9261 ?
Options: a ) 5969.72 , b ) 8877.72 , c ) 2877.72 , d ) 2678.72 , e ) 1011.72
Rationale: 8000 - - - - 1261 100 - - - - ? = > 15.76 % x * 115.76 / 100 * 115.76 / 100 = 8000 x * 1.34 = 8000 x = 8000 / 1.34 = > 5969.72 answer : a
Answer: a
Problem: carol spends 1 / 4 of her savings on a stereo and 1 / 6 less than she spent on the stereo for a television . what fraction of her savings did she spend on the stereo and television ?
Options: a ) 1 / 4 , b ) 2 / 7 , c ) 5 / 12 , d ) 1 / 2 , e ) 11 / 24
Rationale: "total savings = s amount spent on stereo = ( 1 / 4 ) s amount spent on television = ( 1 - 1 / 6 ) ( 1 / 4 ) s = ( 5 / 6 ) * ( 1 / 4 ) * s = ( 5 / 24 ) s ( stereo + tv ) / total savings = s ( 1 / 4 + 5 / 24 ) / s = 11 / 24 answer : e"
Answer: e
Problem: if x and y are both odd prime numbers and x < y , how many distinct positive integer t factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime t factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Problem: how many kg of pure salt must be added to 30 kg of 2 % solution of salt and water to increase it to 10 % solution ?
Options: a ) 3 / 5 , b ) 4 / 3 , c ) 5 / 7 , d ) 2 / 3 , e ) 8 / 3
Rationale: "amount of salt in 30 kg solution = [ ( 20 / 100 ) * 30 ] kg = 0.6 kg let x kg of pure salt be added then , ( 0.6 + x ) / ( 30 + x ) = 10 / 100 60 + 100 x = 300 + 10 x 90 x = 240 x = 8 / 3 . answer is e ."
Answer: e