regisss/math_qa huggingface dataset:
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 5 kmph , what time will he take to cover 60 metres ?
Options: a ) 16 seconds , b ) 76 seconds , c ) 10.8 seconds , d ) 12 seconds , e ) 18 seconds
Rationale: "speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5 / 18 = 50 / 9 m / s hence time taken to cover 60 m = 60 * 9 / 50 = 10.8 seconds . answer : c"
Answer: c
Problem: find the cube root of 185193 .
Options: a ) 33 , b ) 57 , c ) 99 , d ) 17 , e ) 01
Rationale: "observe unit digit here is 3 so unit digit of the answer is 7 . now omit 193 . now find after which perfect cube 193 lies . it is 125 . so our tenth place is 5 . so answer is 57 . answer : b"
Answer: b
Problem: david and lewis leave chennai for hyderabad simultaneously at 8 p . m in the night driving in two cars at speeds of 50 mph and 70 mph respectively . as soon as lewis reaches hyderabad he returns back to chennai along the same route and meets david on the way back . if the distance between the two cities is 350 miles , how far from chennai did david and lewis meet ?
Options: a ) 250 miles , b ) 240 miles , c ) 230 miles , d ) 235 miles , e ) 75 miles
Rationale: time taken by lewis to reach hyderabad = 350 / 70 = 5 hours in 5 hours , david travels 50 * 5 = 250 miles so distance at which they meet should be greater than 250 miles . only a satisfies . answer is a .
Answer: a
Problem: divide $ 600 among a , b in the ratio 1 : 2 . how many $ that a get ?
Options: a ) $ 50 , b ) $ 500 , c ) $ 150 , d ) $ 250 , e ) $ 600
Rationale: sum of ratio terms = 1 + 2 = 3 a = 600 * 1 / 3 = $ 200 answer is e
Answer: e
Problem: how many three digit numbers w are divisible by 78 or 91 ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "the answer will be 19 . explanation : 78 = 2 * 3 * 13 now multiples of 78 , 156 . . . . 780 , now 1000 - 780 = 220 only two more muktiples of 78 can exists . so total number of 3 digit multiples of 78 are 9 + 2 = 11 91 = 13 * 7 - - total number of three digit multiples - - 9 no remember we have a common multiples as well - - 13 * 7 * 6 = 91 * 6 = 546 so total number of multiples w - - 11 + 9 - 1 = 19 . hence answer is 19 . b"
Answer: b
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 5
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 5 - 4 ) / ( 10 - 5 ) = 1 / 5 so they should be mixed in the ratio 1 : 5 answer - e"
Answer: e
Problem: what is the hcf of 2 / 3 , 4 / 9 and 6 / 18
Options: a ) 7 / 45 , b ) 2 / 45 , c ) 1 / 9 , d ) 8 / 45 , e ) 9 / 45
Rationale: explanation : hcf of fractions = hcf of numerators / lcm of denominators = ( hcf of 2 , 4 , 6 ) / ( lcm of 3 , 9 , 18 ) = 2 / 18 = 1 / 9 answer : option c
Answer: c
Problem: the mean proportional between 234 and 104 is
Options: a ) 12 , b ) 39 , c ) 54 , d ) 156 , e ) none
Rationale: "sol . required mean proportional = √ 234 x 104 = √ 13 x 9 x 2 x 13 x 8 = ( 13 x 3 x 4 ) = 156 . answer d"
Answer: d
Problem: a man sells an article at a profit of 25 % . if he had bought it at 20 % less and sold it for rs . 6.30 less , he would have gained 30 % . find the cost of the article .
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: "let c . p = 100 gain = 25 % s . p = 125 supposed c . p = 80 gain = 30 % s . p = ( 130 * 80 ) / 100 = 104 diff = ( 125 - 104 ) = 21 diff 21 when c . p = 100 then diff 6.30 when c . p = ( 100 * 6.30 ) / 21 = 30 answer : a"
Answer: a
Problem: a bus starts from city x . the number of women in the bus is half of the number of men . in city y , 16 men leave the bus and 8 women enter . now , number of men and women is equal . in the beginning , how many passengers entered the bus ?
Options: a ) 15 , b ) 30 , c ) 36 , d ) 72 , e ) 46
Rationale: explanation : originally , let number of women = x . then , number of men = 2 x . so , in city y , we have : ( 2 x - 16 ) = ( x + 8 ) or x = 24 . therefore total number of passengers in the beginning = ( x + 2 x ) = 3 x = 72 . answer : d
Answer: d
Problem: at tea factory , each employee working the second shift produced 2 / 3 as many widgets as each employee working the first shift . if the first shift has 3 / 4 as many employees , what fraction of the total widgets did the second shift produce ?
Options: a ) 8 / 17 , b ) 1 / 2 , c ) 8 / 9 , d ) 9 / 8 , e ) 17 / 8
Rationale: at tea factory , let the first shift have 3 employee and each produce 3 widgets , so the total number of widgets produced by the first shift is 3 * 3 = 9 ; then the second shift would have 4 employees and each second shift employee would produce 3 * 2 / 3 = 2 widgets , so the total number of widgets produced by the second shift employees would be 4 * 2 = 8 ; the ratio of the second shift production to the total is 8 / ( 9 + 8 ) = 8 / 17 . answer : a .
Answer: a
Problem: there are two concentric circles with radii 6 and 4 . if the radius of the outer circle is increased by 50 % and the radius of the inner circle decreased by 25 % , by what percent does the area between the circles increase ?
Options: a ) 160 , b ) 210 , c ) 260 , d ) 310 , e ) 360
Rationale: "the area of a circle is pir ^ 2 , where r is the radius . the area of the big circle is 36 pi . the area of the small circle is 16 pi . the area a 1 between the circles is 20 pi . when the big circle ' s radius increases , the new area is 81 pi . when the small circle ' s radius decreases , the new area is 9 pi . the area a 2 between the circles is 72 pi . the ratio of a 2 / a 1 is 72 / 20 = 3.6 which is an increase of 260 % . the answer is c ."
Answer: c
Problem: john works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 6 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 8 , b ) 1 / 7 , c ) 1 / 2 , d ) 1 / 4 , e ) 1 / 6
Rationale: first notice the number of months for which he worked - march to sept i . e . 7 months avg of monthly totals in tips for months other than august = x tips in august = 6 x total tips for all months = 6 * x + 6 x = 12 x tips for august / total tips for all months = 6 x / 12 x = 1 / 2 answer : c
Answer: c
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 192,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,500 , d ) $ 2,050 , e ) $ 2,250
Rationale: "number of boxes = total volume / volume of one box = 192,000 / ( 8 * 10 * 12 ) = 200 one box costs 7.50 , so 200 box will cost = 200 * 7.5 = 1500 c is the answer"
Answer: c
Problem: x does a work in 15 days . y does the same work in 45 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 11.25 , e ) 15
Rationale: "x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 45 ) = 1 / 11.25 both together will finish the work in 11.25 days . correct option is d"
Answer: d
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 75 percent of the republicans and 15 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 15 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 3 : 2 = = 60 : 40 represents the number ratio of republicans : democrats . if 75 % of republicans ( which is ( 60 * 0.75 ) = 45 ) and 15 % of democrats ( 40 * 0.15 = 6 ) voted for candidate x , means that out of total of 100 voters ; 51 ( 45 + 6 ) voters voted for candidate x and 49 voted for candidate y . thus we can infer that candidate x is expected to win the election by 2 ( 51 - 49 ) votes . therefore candidate x is expected to win the election by ( 2 / 100 ) votes which is equivalent to 2 % . i think the answer is a ."
Answer: a
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 4000 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 1,600 / 3 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 4000 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 4000 2 = 2000 d = s * t d = 2000 * ( 1 / 2 ) d = 1000 answer : c"
Answer: c
Problem: a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 500 million ) / ( 10 billion ) ] * 100 = [ ( 500 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"
Answer: c
Problem: if 0.75 : x : : 3 : 8 , then x is equal to :
Options: a ) a ) 2.12 , b ) b ) 2.2 , c ) c ) 1.25 , d ) d ) 1.3 , e ) e ) 2.0
Rationale: ( x * 3 ) = ( 0.75 * 8 ) x = 6 / 3 x = 2 answer = e
Answer: e
Problem: a train 280 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 50 kmph , e ) 18 kmph
Rationale: "length = speed * time speed = l / t s = 280 / 20 s = 14 m / sec speed = 14 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 50 kmph answer : d"
Answer: d
Problem: the tax on a commodity is diminished by 25 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 12 % decrease , b ) 18 % decrease , c ) 19 % decrease , d ) 13.75 % decrease , e ) 12.5 % decrease
Rationale: "100 * 100 = 10000 75 * 115 = 9200 - - - - - - - - - - - 10000 - - - - - - - - - - - 1375 100 - - - - - - - - - - - ? = > 13.75 % decrease answer : c"
Answer: c
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 83200 ?
Options: a ) 81000 , b ) 81028 , c ) 105300 , d ) 29889 , e ) 22312
Rationale: 83200 * 9 / 8 * 9 / 8 = 105300 . answer : c
Answer: c
Problem: the length of a side of a hexagon is 2 inches . what is the perimeter ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "hexagon . it means 6 equal sides . p = 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 = 8 + 4 = 12 inches answer b"
Answer: b
Problem: a student is ranked 12 th from right and 6 th from left . how many students are there in totality ?
Options: a ) 17 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 12 , from left 6 total = 12 + 6 - 1 = 17 answer : b"
Answer: b
Problem: what is the square root of 3,249 ?
Options: a ) a ) 18 , b ) b ) 9 , c ) c ) 45 , d ) d ) 62 , e ) e ) 57
Rationale: "a square root of a number is a number times itself equals the original number . ex ) the square root of 81 is 9 because 9 times itself ( 9 ) equals the original number ( 81 ) . 57 * 57 = 3,249 3249 divided by x = 57 x = 57 ( e ) 57"
Answer: e
Problem: x starts a business with rs . 35000 . y joins in the business after 3 months with rs . 25000 . what will be the ratio in which they should share the profit at the end of the year ?
Options: a ) 28 : 15 , b ) 29 : 16 , c ) 25 : 23 , d ) 14 : 15 , e ) none of these
Rationale: "explanation : ratio in which they should share the profit = ratio of the investments multiplied by the time period = 35000 * 12 : 25000 * 9 = 35 * 12 : 25 * 9 = 7 * 4 : 5 * 3 = 28 : 15 . answer : option a"
Answer: a
Problem: how many 3 digit even numbers do not use any digit more than once
Options: a ) 280 , b ) 216 , c ) 2240 , d ) 246 , e ) 2520
Rationale: the way i solved it is a b c ( hundreds , tens , units ) c can be 0 2 4 6 8 ( any of the 5 digits ) a can be anything except ( d or 0 ) so 8 possibilities b can be anything execpt ( a d c ) so 7 possibilities total ways are 7 * 8 * 5 = 280 ans : a
Answer: a
Problem: a circular path of 19 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 49.25 , b ) rs . 40.50 , c ) rs . 44.20 , d ) rs . 62.85 , e ) rs . 43.10
Rationale: "explanation : π ( 21 ^ 2 - 19 ^ 2 ) = 22 / 7 * ( 441 - 361 ) = 251.43 251.43 * 1 / 4 = rs . 62.85 answer : option d"
Answer: d
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1200 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 3.88 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1200 xtx 5 / 100 ) = 350 â † ’ t = 3.88 answer c
Answer: c
Problem: mother , her daughter and her grand child weighs 130 kg . daughter and her daughter ( child ) weighs 60 kg . child is 1 / 5 th of her grand mother . what is the age of the daughter ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 50
Rationale: mother + daughter + child = 130 kg daughter + child = 60 kg mother = 130 - 60 = 70 kg child = 1 / 5 th of mother = ( 1 / 5 ) * 70 = 14 kg so now daughter = 130 - ( mother + child ) = 130 - ( 70 + 14 ) = 46 kg answer : a
Answer: a
Problem: an aeroplane covers a certain distance at a speed of 1500 kmph in 2 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed of :
Options: a ) 2200 kmph , b ) 1800 kmph , c ) 1900 kmph , d ) 2100 kmph , e ) none
Rationale: "explanation : distance = ( 1500 x 2 ) = 3000 km . speed = distance / time speed = 3000 / ( 5 / 3 ) km / hr . [ we can write 1 2 / 3 hours as 5 / 3 hours ] required speed = 3000 x 3 / 5 km / hr = 1800 km / hr . answer : option b"
Answer: b
Problem: the length of a room is 10 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 42750 , e ) 55725
Rationale: "area = 10 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 10 × 4.75 × 900 = 10 × 4275 = rs . 42750 answer is d ."
Answer: d
Problem: two stations a and b are 200 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 200 45 x = 225 x = 5 . so , they meet at 12 a . m . answer : option d"
Answer: d
Problem: a certain box has 13 cards and each card has one of the integers from 1 to 13 inclusive . each card has a different number . if 2 different cards are selected at random , what is the probability that the sum of the numbers written on the 2 cards is less than the average ( arithmetic mean ) of all the numbers written on the 13 cards ?
Options: a ) 1 / 7 , b ) 1 / 13 , c ) 1 / 15 , d ) 1 / 22 , e ) 1 / 26
Rationale: "the average of the numbers is 7 the total number of ways to choose 2 cards from 13 cards is 13 c 2 = 78 . the ways to choose 2 cards with a sum less than the average are : { 1,2 } , { 1,3 } , { 1,4 } , { 1,5 } , { 2,3 } , { 2,4 } the probability is 6 / 78 = 1 / 13 the answer is b ."
Answer: b
Problem: the value of ( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 * 0.025 * 8.1 ) is
Options: a ) 0.3825 , b ) 3.825 , c ) 38.25 , d ) 382.5 , e ) 0.0382
Rationale: ( 0.625 * 0.0729 * 28.9 ) / ( 0.0017 ) * 0.025 * 8.1 = { ( 625 / 1000 ) * ( 729 / 10000 ) * ( 289 / 10 ) } / { ( 17 / 10000 ) * ( 25 / 1000 ) * ( 81 / 10 ) = 382.5 answer : d
Answer: d
Problem: the length of a rectangle is increased by 25 % and its breadth is decreased by 20 % . what is the effect on its area ?
Options: a ) 10000
b ) 10008
c ) 10005
d ) 10004
e ) 10001
Rationale: 100 * 100 = 10000 125 * 80 = 10000 no change answer : a
Answer: a
Problem: the effective annual rate of interest corresponding to a nominal rate of 10 % per annum payable half - yearly is ?
Options: a ) 10.06 % , b ) 10.25 % , c ) 10.35 % , d ) 16.09 % , e ) 16.19 %
Rationale: "amount of rs . 100 for 1 year when compounded half - yearly = [ 100 * ( 1 + 5 / 100 ) 2 ] = rs . 110.25 effective rate = ( 110.25 - 100 ) = 10.25 % answer : b"
Answer: b
Problem: in a certain parking lot , 5 % of the cars are towed for parking illegally . however 80 % of the cars which are parked illegally are not towed . what percentage of cars in the parking lot are parked illegally ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "let x be the number of cars and let y be the number of cars parked illegally . 5 % * x = 20 % * y y / x = 1 / 4 = 25 % the answer is b ."
Answer: b
Problem: in n is a positive integer less than 200 , and 14 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: "14 n / 60 must be an integer . = > 7 n / 30 must be an integer . hence n must be a multiple of 2 * 3 * 5 . = > n has 3 different prime integers and can not have more than 3 different prime integers because 2 * 3 * 5 * 7 = 210 > 200 answer : b"
Answer: b
Problem: if x is to be chosen at random from the integers between 1 to 6 , inclusive , and y is to be chosen at random from the integers between 7 and 11 , inclusive , what is the probability that x + y will be even ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: "x + y will be even if x and y are both even or both odd . p ( x and y are both even ) = 3 / 6 * 2 / 5 = 1 / 5 p ( x and y are both odd ) = 3 / 6 * 3 / 5 = 3 / 10 p ( x + y is even ) = 1 / 5 + 3 / 10 = 1 / 2 the answer is a ."
Answer: a
Problem: how long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 290 m in length ?
Options: a ) 18.9 sec , b ) 88.9 sec , c ) 22.9 sec , d ) 24.00 sec , e ) 72.0 sec
Rationale: "d = 110 + 290 = 400 m s = 60 * 5 / 18 = 50 / 3 t = 400 * 3 / 50 = 24.00 sec answer : d"
Answer: d
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 8 th year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 45 , b ) 40 , c ) 35 , d ) 30 , e ) 25
Rationale: 1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 7 th year : 6 - 7 ( age ) , we take age = 6 8 th year : 7 - 8 ( age ) , we take age = 7 thus for the 3 rd year = 50 , 4 th year = 50 - 3 = 47 5 th year = 47 - 4 = 43 6 th year = 43 - 5 = 38 . 7 th year = 38 - 6 = 32 8 th year = 32 - 7 = 25 the correct answer is e .
Answer: e
Problem: a man covers a distance of 180 km at 72 kmph and next 190 km at 88 kmph . what is his average speed for his whole journey of 370 km ?
Options: a ) 77 kmph , b ) 77.15 kmph , c ) 77.25 kmph , d ) 79 kmph , e ) 80 kmph
Rationale: formula = 2 * f . s * s . p / f . s + s . p = 2 * 72 * 88 / 88 + 72 = 79.2 kmph option ' c '
Answer: c
Problem: find the sum of first 16 natural numbers
Options: a ) 136 , b ) 468 , c ) 465 , d ) 463 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 16 ( 16 + 1 ) / 2 = 16 ( 17 ) / 2 = 136 answer : option a"
Answer: a
Problem: in a zoo , the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same 5 years ago . if the increase in the number of cheetahs in the zoo since then is 2 , then what is the increase in the number of pandas ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 15
Rationale: one short cut to solve the problem is c : p = 1 : 3 c increased to 3 = > 1 : 3 = 3 : x = > x = 9 = > p increased by 6 d is the answer
Answer: d
Problem: ramesh purchased a refrigerator for rs . 16500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 22899 , d ) 23100 , e ) 32778
Rationale: "price at which the tv set is bought = rs . 16,500 discount offered = 20 % marked price = 16500 * 100 / 80 = rs . 20625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 20625 + 375 = rs . 21000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 21000 * 110 / 100 = rs . 23100 answer : d"
Answer: d
Problem: john bought a total of 16 mangoes and oranges . each mango costs 80 cents and each orange costs 60 cents . if the average price of the 16 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: let number of mangoes be x , number of oranges be 16 - x 0.80 x + ( 16 - x ) 0.60 / 16 = 0.65 solving for x , we get x = 4 - - > mangoes 4 , oranges 12 now , number of oranges to be returned be y 0.80 * 4 + ( 12 - y ) * 0.60 / 16 - y = 0.72 solving for y , y = 10 ans : e
Answer: e
Problem: 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 30 meters deep by working for 6 hours ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 30 x = 60 total workers 60 - 45 = 15 new workers the answer is b ."
Answer: b
Problem: the cost of 8 pens and 4 pencils is rs . 200 and the cost of 2 pens and 2 pencils is rs . 48 . find the cost of each pen ?
Options: a ) rs . 32 , b ) rs . 36 , c ) rs . 42 , d ) rs . 26 , e ) rs . 104
Rationale: "let the cost of each pen and pencil be ' p ' and ' q ' respectively . 8 p + 4 q = 200 - - - ( 1 ) 2 p + 2 q = 48 4 p + 4 q = 96 - - - ( 2 ) ( 1 ) - ( 2 ) = > 4 p = 104 = > p = 26 answer : d"
Answer: d
Problem: if the product of 4 integers is negative , at most how many of the integers can be negative ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: the product of 4 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 3 correct option : b
Answer: b
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . how far is the place ?
Options: a ) 4.32 , b ) 4.42 , c ) 4.52 , d ) 4.62 , e ) 4.72
Rationale: "m = 9 s = 1.2 ds = 9 + 1.2 = 10.2 us = 9 - 1.2 = 7.8 x / 10.2 + x / 7.8 = 1 x = 4.42 . answer : b"
Answer: b
Problem: if 12 men can reap 120 acres of land in 36 days , how many acres of land can 44 men reap in 54 days ?
Options: a ) 820 acres , b ) 660 acres , c ) 620 acres , d ) 720 acres , e ) 920 acres
Rationale: "12 men 120 acres 36 days 44 men ? 54 days 120 * 44 / 12 * 54 / 36 10 * 44 * 3 / 2 44 * 15 = 660 answer : b"
Answer: b
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 3 years ?
Options: a ) 3277 , b ) 2977 , c ) 16875 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 ( 34 ) 3 = 1687540,000 ( 34 ) 3 = 16875 answer : c"
Answer: c
Problem: the wages earned by robin is 50 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 7 %
Rationale: "let wage of erica = 10 wage of robin = 1.5 * 10 = 15 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 15 ) / 15 * 100 % = 1 / 15 * 100 % = 7 % answer e"
Answer: e
Problem: a 20 litre mixture of milk and water contains milk and water in the ratio 3 : 2 . 10 litres of the mixture is removed and replaced with pure milk and the operation is repeated once more . at the end of the two removal and replacement , what is the ratio r of milk and water in the resultant mixture ?
Options: a ) 17 : 3 , b ) 9 : 1 , c ) 3 : 17 , d ) 5 : 3 , e ) 11 : 2
Rationale: "he 20 litre mixture contains milk and water in the ratio of 3 : 2 . therefore , there will be 12 litres of milk in the mixture and 8 litres of water in the mixture . step 1 . when 10 litres of the mixture is removed , 6 litres of milk is removed and 4 litres of water is removed . therefore , there will be 6 litres of milk and 4 litres of water left in the container . it is then replaced with pure milk of 10 litres . now the container will have 16 litres of milk and 4 litres of water . step 2 . when 10 litres of the new mixture is removed , 8 litres of milk and 2 litres of water is removed . the container will have 8 litres of milk and 2 litres of water in it . now 10 litres of pure milk is added . therefore , the container will have 18 litres of milk and 2 litres of water in it at the end of the second step . therefore , the ratio of milk and water is 18 : 2 or 9 : 1 . shortcut . we are essentially replacing water in the mixture with pure milk . let w _ o be the amount of water in the mixture originally = 8 litres . let w _ r be the amount of water in the mixture after the replacements have taken place . then , { w _ r } / { w _ o } = ( 1 - r / m ) ^ n where r is the amount of the mixture replaced by milk in each of the steps , m is the total volume of the mixture and n is the number of times the cycle is repeated . hence , { w _ r } / { w _ o }   = ( 1 / 2 ) ^ 2   = 1 / 4 therefore r , w _ r   = { w _ o } / 4 = 8 / 4   = 2 litres . b"
Answer: b
Problem: reb normally drives to work in 45 minutes at an average speed of 40 miles per hour . this week , however , she plans to bike to work along a route that decreases the total distance she usually travels when driving by 20 % . if reb averages between 12 and 16 miles per hour when biking , how many minutes earlier will she need to leave in the morning in order to ensure she arrives at work at the same time as when she drives ?
Options: a ) 135 , b ) 105 , c ) 95 , d ) 75 , e ) 45
Rationale: reb normally drives to work in 45 minutes at an average speed of 40 miles per hour . use formula d = rt car : t 1 : 45 min r 1 : 40 mph d 1 : [ ( 40 * 45 ) / 60 ] = 30 miles bike : t 1 : ? r 2 : 12 - 16 mph d 2 : 08 * d 1 = 24 miles t 1 : [ ( 24 * 60 ) / 12 ] = 120 min ( only 12 mph speed yields an answer given in the choices ) therefore , deb has to leave 120 min - 45 min = 75 min early answer : d
Answer: d
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 20 percent of the cost . what percent p of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "let the market price of the product is mp . let the original cost price of the product is cp . selling price ( discounted price ) = 100 % of mp - 20 % mp = 80 % of mp . - - - - - - - - - - - - - - - - ( 1 ) profit made by selling at discounted price = 20 % of cp - - - - - - - - - - - - - - ( 2 ) apply the formula : profit = selling price - original cost price = > 20 % of cp = 80 % of mp - 100 % cp = > mp = 120 cp / 80 = 3 / 2 ( cp ) now if product is sold without any discount , then , profit = selling price ( without discount ) - original cost price = market price - original cost price = mp - cp = 3 / 2 cp - cp = 1 / 2 cp p = = 50 % of cp thus , answer should bec ."
Answer: c
Problem: a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 10 % next year . this year , the total amount paid for type a products was $ 4500 and the total price paid for type b products was $ 8300 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
Options: a ) $ 14,305 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
Rationale: "cost of type a products next year = 1.15 * 4500 = 5175 cost of type b products next year = 1.1 * 8300 = 9130 total 5175 + 9130 = 14305 option a"
Answer: a
Problem: the area of one square is x ^ 2 + 8 x + 16 and the area of another square is 4 x ^ 2 − 28 x + 49 . if the sum of the perimeters of both squares is 72 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 4 ) ^ 2 and ( 2 x - 7 ) ^ 2 . the lengths of the sides are x + 4 and 2 x - 7 . if we add the two perimeters : 4 ( x + 4 ) + 4 ( 2 x - 7 ) = 72 12 x = 84 x = 7 the answer is e ."
Answer: e
Problem: a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 65 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 50
Rationale: "there are 10 books less ( 75 - 65 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 50 answer e"
Answer: e
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 95 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 155 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 186
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 186 min * leg a - b - - - > d = 95.186 / 60 = 17670 / 60 * leg b - a - - - - > d = 155 * 114 / 60 = 17670 / 60 so the correct ans . ise"
Answer: e
Problem: the owner of a furniture shop charges his customer 24 % more than the cost price . if a customer paid rs . 8091 for a computer table , then what was the cost price of the computer table ?
Options: a ) 7297 , b ) 2977 , c ) 2871 , d ) 6725 , e ) 6525
Rationale: "explanation : cp = sp * ( 100 / ( 100 + profit % ) ) = 8091 ( 100 / 124 ) = rs . 6525 . answer : e"
Answer: e
Problem: what is the smallest number which when diminished by 10 , is divisible 2 , 6 , 12 and 24 ?
Options: a ) 35 , b ) 34 , c ) 20 , d ) 35 , e ) 342
Rationale: "required number = ( lcm of 2 , 6 , 12 and 24 ) + 12 = 24 + 10 = 34 option b"
Answer: b
Problem: the cash realised on selling a 14 % stock is rs . 108.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 108 , d ) 192 , e ) 122
Rationale: "cash realised = rs . ( 108.25 - 0.25 ) = rs . 108 . answer : c"
Answer: c
Problem: if n is the greatest positive integer for which 4 ^ n is a factor of 8 ! , then n = ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "8 ! = 40320 e . 4 ^ 10 = 1048576 ( 40320 / 1048576 ) - this is not a factor of 8 ! d . 4 ^ 8 = 65536 ( 40320 / 65536 ) - this is not a factor of 8 ! c . 4 ^ 6 = 4096 ( 40320 / 4096 ) - this is not a factor of 8 ! b . 4 ^ 4 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! a . 4 ^ 2 = 16 ( 40320 / 16 ) - this is a factor of 8 !"
Answer: a
Problem: if the average ( arithmetic mean ) of a and b is 215 , and the average of b and c is 160 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) 110 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 215 = = = > a + b = 430 ( b + c ) / 2 = 160 = = = > b + c = 320 ( a + b ) - ( b + c ) = 430 - 320 = = = > a + b - b - c = 110 = = = > a - c = 110 answer : d"
Answer: d
Problem: 3 boys are ages 4 , 6 and 7 respectively . 3 girls are ages 5 , 8 and 9 , respectively . if two of the boys and two of the girls are randomly selected and the sum of the selected children ' s ages is w , what is the difference between the probability that w is even and the probability that w is odd ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 9 , d ) 1 / 4 , e ) 1 / 2
Rationale: age of boys w : 4 , 6 , 7 sum of ages taken 2 at a time : 10 , 1311 ages of girls : 5 , 8 , 9 sum of ages taken 2 at a time : 13 , 1714 9 combinations of sum between sets ( 10 , 1211 ) ( 13 , 1714 ) = 23 , 2724 - 16 , 3017 - 24 , 2825 prob ( even ) = 5 / 9 prob ( odd ) = 4 / 9 answer = 5 / 9 - 4 / 9 = 1 / 9
Answer: a
Problem: a can do a job in 30 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 26 days , c ) 30 days , d ) 31 days , e ) 39 days
Rationale: "c 1 / 30 + 1 / 30 = 1 / 15 15 * 2 = 30 days"
Answer: c
Problem: 8 x 2.25 - 5 x 0.85 / 2.5 = ?
Options: a ) 3.8 , b ) 10 , c ) 5 , d ) 5.5 , e ) 7.5
Rationale: "given expression = ( 18 - 4.25 / 2.5 = 13.75 / 2.5 = 137.5 / 25 = 5.5 answer is d ."
Answer: d
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 20000 and b rs . 25000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4800 , e ) 7291
Rationale: 20 : 25 = > 4 : 5 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 4 / 9 = 3840 + 960 = 4800 answer : d
Answer: d
Problem: if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 170 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 86 , c ) 92 , d ) 98 , e ) 104
Rationale: "l + k = 170 and so k = 170 - l l + 10 = 1.5 k = 1.5 ( 170 - l ) 2.5 l = 245 l = 98 the answer is d ."
Answer: d
Problem: 12 * 18 * 6 is the volume of some material . how many cubes of edge 3 can be insert into it ?
Options: a ) 48
b ) 49
c ) 50
d ) 51
e ) 52
Rationale: no . of such cubes = volume of material / volume of one cube ( 12 * 18 * 6 ) / ( 3 * 3 * 3 ) = 48 answer : a
Answer: a
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.63 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.63 - - > 15 p - 13.5 p = 63 - - > p = 42 . answer : d ."
Answer: d
Problem: 1904 x 1904 = ?
Options: a ) 3623216 , b ) 3624216 , c ) 3624316 , d ) 3625116 , e ) 3625216
Rationale: "1904 x 1904 = ( 1904 ) 2 = ( 1900 + 4 ) 2 = ( 1900 ) 2 + ( 4 ) 2 + ( 2 x 1900 x 4 ) = 3610000 + 16 + 15200 . = 3625216 . e )"
Answer: e
Problem: at what rate percent per annum will sum of money double in 20 years ?
Options: a ) 1.2 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) none of these
Rationale: "explanation : hint : if sum of money becomes ( z times ) in ( t ) years at simple interest , then rate of interest ( r ) can be calculated using the formula : rate of interest ( r ) % = 100 ( z – 1 ) / t here , principal amount is not given . hence , we can directly use the trick to calculate the rate of interest . rate of interest ( r ) % = 100 ( 2 – 1 ) / 20 rate of interest ( r ) % = 5 % p . a . answer is d"
Answer: d
Problem: n is a positive integer . when n + 1 is divided by 3 , the remainder is 2 . what is the remainder when n is divided by 3 ?
Options: a ) 1 , b ) 5 , c ) 4 , d ) 3 , e ) 2
Rationale: "n + 1 = 3 a + 2 i . e . n + 1 = 5 , 8 , 11 , 14 , . . . etc . i . e . n = 4 , 7 , 10 , 13 , . . . etc . when n is divided by 3 remainder is always 1 answer : a"
Answer: a
Problem: i bought two books ; for rs . 490 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337.83 , b ) 285.83 , c ) 284.83 , d ) 266.83 , e ) 299.83
Rationale: "x * ( 85 / 100 ) = ( 490 - x ) 119 / 100 x = 285.83 answer : b"
Answer: b
Problem: if 13 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 42 days , d ) 48 days , e ) 52 days
Rationale: "13 * 80 = 20 * x x = 52 days answer : e"
Answer: e
Problem: 9773 + x = 13200 , then x is ?
Options: a ) 3427 , b ) 3237 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: "answer x = 13200 - 9773 = 3427 option : a"
Answer: a
Problem: when 5 + 6 = 305 , 6 + 7 = 425 , 7 + 8 = 565 , then 8 + 9 = ?
Options: a ) 705 , b ) 735 , c ) 685 , d ) 665 , e ) 725
Rationale: 5 + 6 = > 5 ã — 6 = 30 = > 30 ã — 10 + 5 = 305 6 + 7 = > 6 ã — 7 = 42 = > 42 ã — 10 + 5 = 425 7 + 8 = > 7 ã — 8 = 56 = > 56 ã — 10 + 5 = 565 then 8 + 9 = > 8 ã — 9 = 72 = > 72 ã — 10 + 5 = 725 answer : e
Answer: e
Problem: the population of a town is 7800 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9600 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7800 ã — 100 / 90 ã — 100 / 90 = 9629 a )"
Answer: a
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls , the volume of hall is ?
Options: a ) 1100
b ) 1200
c ) 1300
d ) 1400
e ) 1500
Rationale: area of 4 wall = sum of area of floor and celling 2 ( l + b ) * h = 2 ( l * b ) ( 15 + 12 ) * h = 2 ( 12 * 15 ) on solving h = 20 / 3 m volume = l * b * h = 12 * 15 * 20 / 3 = 1200 m ^ 3 answer : b
Answer: b
Problem: when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 4 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 4 x = 56 4 x / 9 = 9 * 6 + 2 remainder is 2 . answer is c"
Answer: c
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 8 mat weavers in 8 days ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : please always remember , that what exactly we need to calculate before applying chain formula . as in this question we need to find how many mats , right ! so we will compare everything with ` ` number of mats ' ' as , more men , more number of mats ( direct proportion ) more days , more number of mats ( direct proportion ) so , it can be solved as , [ weavers 4 4 days 8 8 ] : : 4 : x = > x ∗ 4 ∗ 4 = 8 ∗ 8 ∗ 4 = > x = 16 option c"
Answer: c
Problem: the floor of a rectangular room is 21 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 124 m 2 , b ) 128 m 2 , c ) 138 m 2 , d ) 148 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 25 ã — 16 = 400 m 2 area of the inner rectangle = 21 ã — 12 = 252 m 2 required area = ( 400 â € “ 252 ) = 148 m 2 answer d"
Answer: d
Problem: two bullet trains of equal lengths take 10 seconds and 20 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 11 sec . , b ) 15 sec . , c ) 13.3 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 20 m / sec = 6 m / sec . relative speed = ( 12 + 6 ) = 18 m / sec . required time = ( 120 + 120 ) / 18 sec = 13.3 sec . c"
Answer: c
Problem: in a tree , 3 / 7 of the birds are robins while the rest are bluejays . if 1 / 3 of the robins are female and 3 / 5 of the bluejays are female , what fraction of the birds in the tree are male ?
Options: a ) 11 / 35 , b ) 14 / 35 , c ) 18 / 35 , d ) 31 / 70 , e ) 37 / 70
Rationale: "the fraction of birds that are male robins is ( 2 / 3 ) ( 3 / 7 ) = 2 / 7 . the fraction of birds that are male bluejays is ( 2 / 5 ) ( 4 / 7 ) = 8 / 35 . the total fraction of male birds is 2 / 7 + 8 / 35 = 18 / 35 . the answer is c ."
Answer: c
Problem: the length of a rectangular landscape is 8 times its breadth . there is a playground in it whose area is 1200 square mtr & which is 1 / 6 rd of the total landscape . what is the length of the landscape ?
Options: a ) 180 , b ) 270 , c ) 340 , d ) 140 , e ) 240
Rationale: "sol . x * 8 x = 6 * 1200 x = 30 length = 8 * 30 = 240 e"
Answer: e
Problem: ratio and proportion 215 : 474 : : 537 : ?
Options: a ) 26 , b ) 27 , c ) 25 , d ) 22 , e ) 23
Rationale: 2 + 1 + 5 + 4 + 7 + 4 = 23 5 + 3 + 7 + x = 23 = > x = 8 combination that match 8 is 26 since 2 + 6 = 8 answer : a
Answer: a
Problem: sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 288 per week . how much does she earn in dollars per hour ?
Options: a ) 11 , b ) 10 , c ) 9 , d ) 8 , e ) 7
Rationale: "let sheila earn x dollars per hour so , on monday , wednesday and friday , she earns 8 x each and , on tuesday and thursday , she earns 6 x each in total , over the week she should earn , 3 ( 8 x ) + 2 ( 6 x ) = 36 x she earns $ 288 per week 36 x = 288 x = 8 correct option : d"
Answer: d
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 200 kg . in the first week 20 percent is cut away . in the second week 25 percent of the remainder is cut away . in the third week the statue is completed when 35 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 97.5 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "a 97.5 kg 250 ã — 0.8 ã — 0.75 ã — 0.65 = 97.5 kg ."
Answer: a
Problem: an offshore company sells two products , l and m . last year , seventy percent of the units sold were product l , and the price of product l was 25 percent greater than the price of product m . approximately what percent of the total revenue the company received last year was from the sale of product l ?
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 65 % , e ) 74 %
Rationale: percentage of total units that is product l = 70 % price of product l = 25 percent greater than price of product m . now , we can consider this as a weighted average scenario . if the price of both the products l and m was equal , then contribution of product l to total sales would be = 70 % but since , price of product l is greater than m , then contribution of product l to total sales will be greater than 70 % the only option is 74 % answer e
Answer: e
Problem: if x , y , and z are positive integers , and 4 x = 5 y = 8 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 23 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 4,5 and 8 = 40 now 4 x = 40 = > x = 10 5 y = 40 = > y = 8 8 z = 40 = > z = 5 10 + 8 + 5 = 23 . option b ."
Answer: b
Problem: find the principal which yields a simple interest of rs . 20 and compound interest of rs . 28 in two years , at the same percent rate per annum ?
Options: a ) s . 25 , b ) s . 48 , c ) s . 42 , d ) s . 20 , e ) s . 60
Rationale: "explanation : si in 2 years = rs . 20 , si in 1 year = rs . 10 ci in 2 years = rs . 28 % rate per annum = [ ( ci – si ) / ( si in 1 year ) ] * 100 = [ ( 28 – 20 ) / 20 ] * 100 = 40 % p . a . let the principal be rs . x time = t = 2 years % rate = 40 % p . a . si = ( prt / 100 ) 20 = ( x * 40 * 2 ) / 100 x = rs . 25 answer : a"
Answer: a
Problem: joshua and jose work at an auto repair center with 2 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 15 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 4 probability of chosing jose second = 1 / 3 total = 1 / 12 probability of chosing jose first = 1 / 4 probability of chosing josh second = 1 / 3 total = 1 / 12 final = 1 / 12 + 1 / 12 = 1 / 6 d"
Answer: d
Problem: in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 60 % , and the students on the make - up date had an average score of 90 % , what was the average score for the entire class ?
Options: a ) 65 % , b ) 67 % , c ) 69 % , d ) 72 % , e ) 75 %
Rationale: "70 % of the class scored 60 % and 30 % of the class scored 90 % . the difference between 60 % and 90 % is 30 % . the average will be 60 % + 0.3 ( 30 % ) = 69 % . the answer is c ."
Answer: c
Problem: of 90 applicants for a job , 42 had at least 4 years ' experience , 54 had degrees , and 8 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 10 , b ) 8 , c ) 14 , d ) 16 , e ) 12
Rationale: "90 - 8 = 82 82 - 42 - 54 = - 14 then 14 are in the intersection between 4 years experience and degree . answer : c"
Answer: c
Problem: a shopkeeper sold an article at $ 1110 and gained a 20 % profit . what was the cost price ?
Options: a ) $ 850 , b ) $ 875 , c ) $ 900 , d ) $ 925 , e ) $ 950
Rationale: "let x be the cost price . 1.2 x = 1110 x = 1110 / 1.2 = 925 the answer is d ."
Answer: d
Problem: two trains running in opposite directions cross a pole placed on the platform in 47 seconds and 31 seconds respectively . if they cross each other in 33 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 7 , b ) 8 : 7 , c ) 6 : 7 , d ) 6 : 5 , e ) 4 : 7
Rationale: explanation : let the speed of the trains be x and y respectively length of train 1 = 47 x length of train 2 = 31 y relative speed = x + y time taken to cross each other = 33 s = > = 33 = > ( 47 x + 31 y ) = 33 ( x + y ) = > 14 x = 2 y = > x / y = 2 / 14 = 1 / 7 = 1 : 7 answer : a
Answer: a