Cheukting/mathqa huggingface dataset:
Question (general): in an election , candidate douglas won 60 percent of the total vote in counties x and y . he won 72 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 18 % , b ) 30 % , c ) 36 % , d ) 48 % , e ) 54 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 72 % voted means 72 * 200 = 144 votes combined for xy has 300 voters and voted 60 % so total votes = 180 balance votes = 180 - 144 = 36 as y has 100 voters so 36 votes means 36 % of votes required ans c"
Answer: c
Question (general): a ferry can transport 50 tons of vehicles . automobiles range in weight from 1600 to 3200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 62 , e ) 86
Rationale: to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 50 tons will be 100,000 pounds from the answer choices : let max number of vehicles be 62 total weight will be = 62 * 1600 = 99200 pounds , which is lesser than the maximum weight allowed . ans : d
Answer: d
Question (general): how much time does a train 150 metres long running at 54 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 7.6 s , e ) 10 s
Rationale: "explanation : 54 km / hr = 54 * 5 / 18 = 15 m / s speed = distance / time ; v = d / t 15 = 150 / t t = 10 s answer : e"
Answer: e
Question (general): the cash realised on selling a 14 % stock is rs . 104.25 , brokerage being 1 / 4 % is
Options: a ) 123 , b ) 106 , c ) 100 , d ) 156 , e ) 104
Rationale: "explanation : cash realised = rs . ( 104.25 - 0.25 ) = rs . 104 . answer : e"
Answer: e
Question (gain): by selling 12 pencils for a rupee a man loses 12 % . how many for a rupee should he sell in order to gain 18 % ?
Options: a ) 12 , b ) 9 , c ) 10 , d ) 89 , e ) 81
Rationale: "88 % - - - 12 112 % - - - ? 88 / 112 * 12 = 9 answer : a"
Answer: a
Question (general): ages of two persons differ by 4 years . if 3 years ago , the elder one was 3 times as old the younger one , find their present age
Options: a ) 5,9 , b ) 14,18 , c ) 16,20 , d ) 18,22 , e ) 19,23
Rationale: "explanation : let the age of the younger person be x , then the elder person ' s age is ( x + 4 ) = > 3 ( x - 3 ) = ( x + 4 - 3 ) [ 3 years before ] = > 3 x - 9 = x + 1 = > x = 5 . so the elder person ' s age is x + 4 = 9 answer : option a"
Answer: a
Question (general): a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 23 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 280 , e ) 312
Rationale: "so 12.2 * 23 = 280 . . imo option d is correct answer . ."
Answer: d
Question (physics): if 12 men or 20 women can do a piece of work in 54 days , then in how many days can 9 men and 21 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "b 30 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 21 women = 15 women + 21 women = 36 women 20 women can do the work in 54 days . so , 36 women can do it in ( 20 * 54 ) / 36 = 30 days ."
Answer: b
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 70 to incur a loss 20 % ?
Options: a ) 45 , b ) 35 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 70 * ( 100 % + 20 % ) = $ 84 number of articles to be sold for $ 84 to incur a 20 % loss : $ 84 / $ 2.40 = 35 thus , solution b is correct ."
Answer: b
Question (gain): solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 60 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 30 % , c ) 40 % , d ) 50 % , e ) 60 %
Rationale: "60 % is 20 % - points below 80 % and 5 % - points above 55 % . so the ratio of solution p to solution q is 1 : 4 . mixture p is 1 / 5 = 20 % of the volume of mixture pq . the answer is a ."
Answer: a
Question (general): how many integers from 0 to 50 inclusive have a remainder of 3 when divided by 11 ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the numbers should be of the form 11 c + 3 . the minimum is 3 when c = 0 . the maximum is 47 when c = 4 . there are 5 such numbers . the answer is a ."
Answer: a
Question (general): find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number .
Options: a ) 3 , b ) 5 , c ) 7 , d ) 12 , e ) 15
Rationale: "sol . let the number be x . then , x + 17 = 60 / x ⇔ x 2 + 17 x - 60 = 0 ⇔ ( x + 20 ) ( x - 3 ) = 0 ⇔ x = 3 . answer a"
Answer: a
Question (geometry): the largest five digit number which is a perfect cube , is :
Options: a ) 85184
b ) 91125
c ) 97336
d ) 96806
e ) 99999
Rationale: explanation : 46 * 46 * 46 = 97336 answer : c
Answer: c
Question (physics): in one hour , a boat goes 15 km / hr along the stream and 11 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 15 + 11 ) kmph = 13 kmph . answer : option b"
Answer: b
Question (general): a no . when divided by the sum of 555 and 445 gives 2 times their difference as quotient & 80 as remainder . find the no . is ?
Options: a ) 220880 , b ) 145778 , c ) 220081 , d ) 220080 , e ) 220030
Rationale: ( 555 + 445 ) * 2 * 110 + 80 = 220000 + 80 = 220080 d
Answer: d
Question (general): the sum of two number is 120 and their difference is 30 . find the numbers .
Options: a ) 9525 , b ) 5565 , c ) 7545 , d ) 6555 , e ) 8535
Rationale: let the two number be x and y . x + y = 120 . . . . . . . ( 1 ) x - y = 30 . . . . . . . . . ( 2 ) = > 2 x = 150 = > x = 75 . x - y = 30 = > y = 45 . the two numbers are 7545 ans : c
Answer: c
Question (general): the prices of tea and coffee per kg were the same in june . in july the price of coffee shot up by 10 % and that of tea dropped by 20 % . if in july , a mixture containing equal quantities of tea and coffee costs 50 / kg . how much did a kg of coffee cost in june ?
Options: a ) 50 , b ) 45 , c ) 52.63 , d ) 40 , e ) 35
Rationale: "let the price of tea and coffee be x per kg in june . price of tea in july = 1.1 x price of coffee in july = 0.8 x . in july the price of 1 / 2 kg ( 500 gm ) of tea and 1 / 2 kg ( 500 gm ) of coffee ( equal quantities ) = 50 1.1 x ( 1 / 2 ) + 0.8 x ( 1 / 2 ) = 50 = > x = 52.63 c"
Answer: c
Question (gain): a dishonest person wants to make a profit on the selling of milk . he would like to mix water ( costing nothing ) with milk costing 33 $ per litre so as to make a profit of 30 % on cost when he sells the resulting milk and water mixture for 36 $ . in what ratio should he mix the water and milk ?
Options: a ) 1 : 20 , b ) 1 : 10 , c ) 1 : 120 , d ) 23 : 4 , e ) 23 : 120
Rationale: "first of all , let ' s consider 1 liter of the stuff he is going to sell - - - naive customers think it ' s pure milk , but we know it ' s some milk - water mixture . he is going to sell this liter of milk - water for $ 36 . this $ 36 should be a 30 % increase over cost . here , we need to think about percentage increases as multipliers . using multipliers ( cost ) * 1.30 = $ 36 cost = 36 / 1.3 = 360 / 12 = $ 27.69 if he wants a 30 % increase over cost on the sale of one liter of his milk - water , the cost has to be $ 27.69 . well , a liter of milk costs $ 33 , so if he is going to use just $ 30 of milk in his mixture , that ' s 27.69 / 33 = 120 / 143 of a liter . if milk is 120 / 143 of the liter , then water is 23 / 143 of the liter , and the ratio of water to milk is 23 : 120 . answer choice ( e )"
Answer: e
Question (physics): a train 110 m long is running at 50 kmph . in how much time will it pass a platform 210 m long ?
Options: a ) 14.15 seconds , b ) 15.24 seconds , c ) 16.28 seconds , d ) 13.30 seconds , e ) 10.24 seconds
Rationale: distance travelled = 110 + 210 m = 320 m speed = 50 * 5 / 8 = 125 / 4 m time = 320 * 4 / 125 = 10.24 seconds answer : e .
Answer: e
Question (gain): a man buys an article for $ 100 . and sells it for $ 115 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 115 gain = $ 15 gain % = 15 / 100 * 100 = 25 % answer is b"
Answer: b
Question (general): there was a cycle race going on . 1 / 5 th of the those in front of a person and 5 / 6 th of those behind him gives the total number of participants . how many people took part in the race ?
Options: a ) 31 , b ) 39 , c ) 30 , d ) 33 , e ) 34
Rationale: explanation : let total participants be ( x + 1 ) then = > ( 1 / 5 ) * x + ( 5 / 6 ) * x = x + 1 = > 31 x / 30 = x + 1 = > x = 30 so total participants ( x + 1 ) = 31 hence ( a ) is the correct answer . answer : a
Answer: a
Question (gain): at what rate percent on simple interest will rs . 1750 amount to rs . 2000 in 2 years ?
Options: a ) 4 % , b ) 7.14 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
Rationale: "explanation : 250 = ( 1750 x 2 xr ) / 100 r = 7.14 % answer : option b"
Answer: b
Question (general): what is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder ?
Options: a ) 1108 , b ) 1683 , c ) 2007 , d ) 3363 , e ) 1436
Rationale: "lcm of 5 , 6 , 7 and 8 = 840 hence the number can be written in the form ( 840 k + 3 ) which is divisible by 9 . if k = 1 , number = ( 840 × 1 ) + 3 = 843 which is not divisible by 9 . if k = 2 , number = ( 840 × 2 ) + 3 = 1683 which is divisible by 9 . hence 1683 is the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder . answer : b"
Answer: b
Question (general): what is the difference between the largest number and the least number written with the digits 7 , 3 , 1 , 4 ?
Options: a ) 6084 , b ) 6184 , c ) 5084 , d ) 6048 , e ) 6049
Rationale: "1347 7431 - - - - - - - - - - - - 6084 answer : a"
Answer: a
Question (physics): if a light flashes every 30 seconds , how many times will it flash in 1 / 2 of an hour ?
Options: a ) 30 , b ) 42 , c ) 61 , d ) 59 , e ) 45
Rationale: "there are 60 minutes in an hour . in 1 / 2 of an hour there are ( 60 * 1 / 2 ) minutes = 30 minutes . in 1 / 2 of an hour there are ( 60 * 30 ) seconds = 1800 seconds . light flashed for every 30 seconds . in 1800 seconds 1800 / 30 = 60 times . the count start after the first flash , the light will flashes 61 times in 1 / 2 of an hour . answer : c"
Answer: c
Question (general): what is the smallest positive integer k such that the product of 720 x k is a perfect square ?
Options: a ) 5 , 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 , 720 = 3 ^ 2 * 4 ^ 2 * 5 , so if k = 5 then 720 k = ( 3 * 4 * 5 ) ^ 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
Question (other): the ratio of two numbers is 2 : 3 and their h . c . f . is 6 . their l . c . m . is
Options: a ) 48 , b ) 22 , c ) 36 , d ) 27 , e ) 67
Rationale: explanation : let the numbers be 2 x and 3 x . then , their h . c . f . = x . so , x = 6 . so , the numbers 12 and 18 l . c . m . of 12 and 18 = 36 option c
Answer: c
Question (physics): the speed at which a girl can row a boat in still water is 90 kmph . if she rows downstream , where the speed of current is 18 kmph , what time will he take to cover 330 metres ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "speed of the boat downstream = 90 + 18 = 108 kmph = 108 * 5 / 18 = 30 m / s hence time taken to cover 330 m = 330 / 30 = 11 seconds . answer : a"
Answer: a
Question (physics): one hour after matthew started waking from q to y , a distance of 45 km , johnny started walking along the same road from y to q . matthew ' s walking rate was 3 km per hour and johnny ' s was 4 km per hour , how many km had johnny walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 19.5
Rationale: just an alternative method . . . after the first hour the distance q is 42 km ( 45 - 3 ) . now the problem can be treated as if bothof them started at the same time . since the speeds are in the ratio 3 : 4 , the distances will also be in the same ratio . splitting 42 in that ratio we get 18 : 24 . so answer is 24 . hence a .
Answer: a
Question (general): if 2 / w + 2 / x = 2 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 2 / w + 2 / x = 2 / ywx = y find : ( w + x ) / 2 = ? 2 ( 1 / w + 1 / x ) = 2 ( 1 / y ) - divide both sides by 2 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 810 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 84 , e ) none
Rationale: "explanation we have : l = 30 ft and lb = 810 sq . ft . so , b = 27 ft . length of fencing = ( l + 2 b ) = ( 30 + 54 ) ft = 84 ft . answer d"
Answer: d
Question (physics): the food in a camp lasts for 40 men for 45 days . if fifteen more men join , how many days will the food last ?
Options: a ) 80 days , b ) 33 days , c ) 35 days , d ) 16 days , e ) 15 days
Rationale: one man can consume the same food in 40 * 45 = 1800 days . 15 more men join , the total number of men = 55 the number of days the food will last = 1800 / 55 = 33 days . answer : b
Answer: b
Question (physics): lionel left his house and walked towards walt ' s house , 48 miles away . four hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 3 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "in the first 4 hours lionel at the rate of 3 miles per hour covered distance = rate * time = 4 * 3 = 12 miles . so , the distance between him and walt was 48 - 12 = 36 miles when walt left his house . now , their combined rate to cover this distance was 3 + 6 = 9 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 36 / 9 = 4 hours . total time that lionel was walking is 4 + 4 = 8 hours , which means that he covered in that time interval distance = rate * time = 3 * 8 = 24 miles . answer : d ."
Answer: d
Question (physics): a certain car can travel 72 kilometers on a liter of fuel . if the fuel tank ’ s contents decrease by 3.9 gallons over a period of 5.7 hours as the car moves at a constant speed , how fast is the car moving , in miles per hour ? ( 1 gallon = 3.8 liters ; 1 mile = 1.6 kilometers )
Options: a ) 52 , b ) 65 , c ) 117 , d ) 91 , e ) 104
Rationale: "fuel used 3.9 gallons ; convert to liters - - > 3.9 x 3.8 liters time = 5.7 hours 1 mile = 1.6 kilometers ; convert to miles - - > 1 km = 1 / 1.6 mile speed ( km / hour ) = d / t = 72 ( km * ) x 3.9 x 3.8 / 5.7 replace ( km * ) to miles ; multiply by 1 / 1.6 mile speed ( miles / hour ) = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 78 miles / hour ans : c ps : i felt the factors were easy to cancel out , so did n ' t require much rounding off = 72 x 3.9 x 3.8 / 5.7 x 1.6 = 117 c"
Answer: c
Question (probability): find the probability that a leap year selected at random will have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays we should have either { sat , sun } or { sun , mon } case . the probability of that is 2 / 7 . answer : e ."
Answer: e
Question (physics): a tank is 25 m long , 12 m wide and 6 m deep . the cost of plastering its walls and bottom at 75 paise per sq . m , is :
Options: a ) rs . 456 , b ) rs . 458 , c ) rs . 558 , d ) rs . 568 , e ) none of these
Rationale: explanation : area to be plastered = [ 2 ( l + b ) x h ] + ( l x b ) = { [ 2 ( 25 + 12 ) x 6 ] + ( 25 x 12 ) } m 2 = ( 444 + 300 ) m 2 = 744 m 2 . cost of plastering = rs . 744 x 75 / 100 = rs . 558 answer : c
Answer: c
Question (general): if p is the product of the integers from 1 to 38 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of p ?
Options: a ) 13 , b ) 15 , c ) 17 , d ) 19 , e ) 21
Rationale: "38 ! has 3 , 6 , 9 , . . . . 30 , 33 , 36 as factors , which are 12 multiples of 3 . we need to add 5 more to these 12 because of 9 , 18 , 27 , and 36 . the greatest integer of k is 17 . the answer is c ."
Answer: c
Question (general): find the average increase rate , if increase in the population in the first year is 30 % and that in the second year is 40 % .
Options: a ) 41 , b ) 56 , c ) 40 , d ) 38 , e ) 39
Rationale: solution : let 100 be the original population . 1 st year ' s population increased = 30 % so , population after first year = ( 100 + 30 % of 100 ) = 130 . population in second year increases by 40 % , then population = ( 130 + 40 % of 130 ) = 182 . the final population become 182 which was originally at 100 . it means there is 82 % increment in the population in 2 years so , average increment = 82 / 2 = 41 % . mind calculation method : increase in population is given by , 100 = = 30 % ↑ = = > 130 = = 40 % ↑ = = > 182 . hence , average increase = 82 / 2 = 41 % answer : option a
Answer: a
Question (gain): rs . 6000 is lent out in two parts . one part is lent at 4 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 7 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 4 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 4 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 2500 amount lent at 10 % = 3500 required ratio = 5 : 7 answer : b"
Answer: b
Question (physics): the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of $ 800 per sq . metre .
Options: a ) $ 12500 , b ) $ 13500 , c ) $ 16500 , d ) $ 14500 , e ) $ 18500
Rationale: "c $ 16500 area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = $ 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = $ 16500"
Answer: c
Question (gain): ? % of 360 = 115.2
Options: a ) 277 , b ) 36 , c ) 64 , d ) 32 , e ) none of these
Rationale: ? % of 360 = 115.2 or , ? = 115.2 × 100 / 360 = 32 answer d
Answer: d
Question (gain): walking 7 / 6 of his usual rate , a boy reaches his school 2 min early . find his usual time to reach the school ?
Options: a ) 14 , b ) 28 , c ) 99 , d ) 77 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 2 - - - - - - - - - ? 14 m answer : a"
Answer: a
Question (general): what least number must be subtracted from 427398 so that remaining no . is divisible by 11
Options: a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "explanation : on dividing 427398 by 11 we get the remainder 4 , so 4 should be subtracted answer : option b"
Answer: b
Question (general): 4 milkmen rented a pasture . a grazed 24 cows for 3 months , b 10 cows for 5 months , c 35 cows for 4 months and d 21 cows for 3 months . if a ’ s share of rent is rs . 720 , find the total rent of the field .
Options: a ) rs . 3250 , b ) rs . 3350 , c ) rs . 3450 , d ) rs . 3550 , e ) rs . 3650
Rationale: ratio of shares of a , b , c , d = ( 24 * 3 ) : ( 10 * 5 ) : ( 35 * 4 ) : ( 21 * 3 ) = 72 : 50 : 140 : 63 let total rent be rs . x . then , a ’ s share = rs . 72 x / 325 . therefore , 72 x / 325 = 720 = > x = 720 * 325 / 72 = 3250 . hence , total rent of the field is rs . 3250 . answer : a
Answer: a
Question (general): 500 , 250 , 750 , 375 . . .
Options: a ) 875 , b ) 1050 , c ) 950 , d ) 1125 , e ) 925
Rationale: "500 / 2 = 250 x 3 = 750 / 2 = 375 x 3 = 1125 answer is d"
Answer: d
Question (other): at present , the ratio between the ages of shekhar and shobha is 4 : 3 . after 6 years , shekhar ' s age will be 26 years . find out the age of shobha at present ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 20
Rationale: after 6 years , shekhar ' s age will be 26 years therefore , present age of shekhar = 26 − 6 = 20 let present age of shobha = x then , 20 x = 43 x = 20 × 34 = 15 answer is d .
Answer: d
Question (general): if ( a - b - c + d = 12 ) and ( a + b - c - d = 6 ) , what is the value of ( b - d ) ^ 2 ?
Options: a ) 4 . , b ) 9 . , c ) 12 . , d ) 16 . , e ) 64 .
Rationale: "eq 1 : a - b - c + d = 12 eq 2 : a + b - c - d = 6 ( 1 ) subtract eq 1 from eq 2 a - b - c + d = 12 - a + b - c - d = 6 - - - - - - - - - - - - - - - - - - - - - - - - - 2 b + 2 d = 6 ( 2 ) simplify - b + d = 3 b - d = - 3 ( b - d ) ^ 2 = ( - 3 ) ^ 2 = 9 my answer : b"
Answer: b
Question (gain): ashok and pyarelal invested money together in a business and share a capital of ashok is 1 / 9 of that of pyarelal . if the incur a loss of rs 1000 then loss of pyarelal ?
Options: a ) 600 , b ) 700 , c ) 800 , d ) 900 , e ) 1000
Rationale: "let the capital of pyarelal be x , then capital of ashok = x / 9 so ratio of investment of pyarelal and ashok = x : x / 9 = 9 x : x hence out of the total loss of 1000 , loss of pyarelal = 1000 * 9 x / 10 x = 900 answer : d"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 81 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 2287 , c ) 2977 , d ) 2088 , e ) 1298
Rationale: "let the side of the square plot be a ft . a 2 = 81 = > a = 9 length of the fence = perimeter of the plot = 4 a = 36 ft . cost of building the fence = 36 * 58 = rs . 2088 . answer : d"
Answer: d
Question (gain): in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 30 percent , but profits were 16 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Question (physics): while driving from a - ville to b - town , harriet drove at a constant speed of 105 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 145 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 ) 174
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 = 174 min * leg a - b - - - > d = 105.174 / 60 = 18270 / 60 * leg b - a - - - - > d = 145 * 126 / 60 = 18270 / 60 so the correct ans . ise"
Answer: e