Cheukting/mathqa huggingface dataset:
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (other): 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
Question (other): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (physics): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (physics): 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
Question (gain): 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