Cheukting/mathqa huggingface dataset:
Question (gain): the cash difference between the selling prices of an article at a profit of 2 % and 6 % is rs 3 . the ratio of two selling prices is
Options: a ) 51 : 53 , b ) 52 : 53 , c ) 53 : 54 , d ) 54 : 55 , e ) none of these
Rationale: "explanation : let the cost price of article is rs . x required ratio = ( 102 % of x ) / ( 106 % of x ) = 102 / 106 = 51 / 53 = 51 : 53 . answer : a"
Answer: a
Question (physics): two trains of equal length , running with the speeds of 60 and 60 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 1.0 , b ) 8.2 , c ) 7.7 , d ) 2.6 , e ) 8.3
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 60 = 120 * 5 / 18 t = 2500 / 9 * 18 / 600 = 8.3 sec . answer : e"
Answer: e
Question (gain): in a certain village , 200 litres of water are required per household per month . at this rate , if there are 10 households in the village , how long ( in months ) will 2000 litres of water last ?
Options: a ) 1 , b ) 20 , c ) 2 , d ) 200 , e ) 2.5
Rationale: "i find it much easier to understand with real numbers , so choose ( almost ) any numbers to replace m , n and p : in a certain village , m 200 litres of water are required per household per month . at this rate , if there aren 10 households in the village , how long ( in months ) willp 2000 litres of water last ? water required is 200 * 10 = 2000 ( m * n ) water available is 2000 ( p ) it will last 1 months ( p / m * n ) answer ( a )"
Answer: a
Question (gain): in a factory , there are 80 % technicians and 20 % non - technicians . if the 80 % of the technicians and 20 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 68 % , c ) 52 % , d ) 22 % , e ) 42 %
Rationale: "total = 100 t = 80 nt = 20 80 * ( 20 / 100 ) = 24 80 * ( 20 / 100 ) = 24 16 + 16 = 32 = > 100 - 32 = 68 % answer : b"
Answer: b
Question (general): what is the units digit of ( 147 ^ 21 ) ^ 48 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 21 has the form 4 n + 1 so the units digit is 7 inside the bracket . the number 48 has the form 4 n , so the units digit is 1 . the answer is a .
Answer: a
Question (gain): what percentage of numbers from 1 to 70 have 1 or 9 in the unit ' s digit ?
Options: a ) 10 % , b ) 30 % , c ) 20 % , d ) 70 % , e ) 45 %
Rationale: d 20 % clearly , the numbers which have 1 or 9 in the unit ' s digit , have squares that end in the digit 1 . such numbers from 1 to 70 are 1 , 9 , 11 , 19 , 21 , 29 , 31 , 39 , 41 , 49 , 51 , 59 , 61 , 69 . number of such number = 14 required percentage = ( 14 x 100 / 70 ) % = 20 % .
Answer: c
Question (geometry): what is the measure of the radius of the circle inscribed in a triangle whose sides measure 8 , 15 and 19 units ?
Options: a ) 2.8 units , b ) 6 units , c ) 3 units , d ) 5 units , e ) 12 units
Rationale: "sides are 8 , 15 and 19 . . . thus it is right angle triangle since 19 ^ 2 = 8 ^ 2 + 15 ^ 2 therefore , area = 1 / 2 * 15 * 8 = 60 we have to find in - radius therefore , area of triangle = s * r . . . . where s = semi - perimeter and r = in - radius now s = semi - perimeter = 19 + 15 + 8 / 2 = 21 thus , 60 = 21 * r and hence r = in - radius = 2.8 option a"
Answer: a
Question (gain): 12 is what % of 80 ?
Options: a ) 6 , b ) 6.67 , c ) 12 , d ) 13 , e ) 15
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x % = 12 therefore , 100 / x = 80 / 12 100 / x = 6.6667 x = 15 e"
Answer: e
Question (general): when greenville state university decided to move its fine arts collection to a new library , it had to package the collection in 20 - inch by 20 - inch by 15 - inch boxes . if the university pays $ 1.20 for every box , and if the university needs 3.06 million cubic inches to package the collection , what is the minimum amount the university must spend on boxes ?
Options: a ) $ 255 , b ) $ 275 , c ) $ 510 , d ) $ 612 , e ) $ 2,550
Rationale: total no . of boxes = 3060000 / ( 20 × 20 × 15 ) = 510 total cost = 510 × $ 1.20 = $ 612 answer d
Answer: d
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 40 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 297 , e ) 400
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 140 = rs . 400 answer : e"
Answer: e
Question (physics): find l . c . m of 852 and 1491
Options: a ) 5964 , b ) 5664 , c ) 4964 , d ) 4664 , e ) 5555
Rationale: 852 ) 1491 ( 1 852 639 ) 852 ( 1 639 213 ) 639 ( 3 639 0 h . c . f of 852 and 1491 is 213 : . l . c . m = 852 * 1491 / 213 = 5964 answer is a .
Answer: a
Question (general): how many positive integers less than 300 are there such that they are multiples of 17 or multiples of 16 ?
Options: a ) 31 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: "300 / 17 = 17 ( plus remainder ) so there are 17 multiples of 17 300 / 16 = 18 ( plus remainder ) so there are 18 multiples of 16 we need to subtract 1 because 17 * 16 is a multiple of both so it was counted twice . the total is 17 + 18 - 1 = 34 the answer is d ."
Answer: d
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 25 hours respectively . the ratio of their speeds is :
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none of these
Rationale: "let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 9 = 5 : 3 . answer b"
Answer: b
Question (physics): convert 700 miles into meters ?
Options: a ) 784596 , b ) 1126538 , c ) 804670 , d ) 784596 , e ) 864520
Rationale: "1 mile = 1609.34 meters 700 mile = 700 * 1609.34 = 1126538 meters answer is b"
Answer: b
Question (general): what is the remainder when 1274 * 1275 * 1277 * 1285 is divided by 12 ?
Options: a ) 0 , b ) 6 , c ) 11 , d ) 9 , e ) 7
Rationale: "1271 * 1275 * 1277 * 1285 = ( 1272 - 2 ) ( 1272 + 3 ) ( 1284 - 7 ) ( 1284 + 1 ) = ( multiple of 12 - 1 ) ( multiple of 12 + 3 ) ( multiple of 12 - 7 ) ( multiple of 12 + 1 ) now , if we expand this expression all terms but the last one will have a multiple of 12 in them , thus will leave no remainder upon division by 12 , the last term will be ( - 2 ) ( 3 ) ( - 7 ) ( 1 ) = 42 . thus the question becomes : what is the remainder upon division of 42 by 12 ? the answer to this question is 6 . answer : b"
Answer: b
Question (geometry): how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 17 inches than that of a rectangular sheet of paper measuring 8.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "area of sheet a = 11 * 17 area of sheet b = 11 * 8.5 difference in area = 11 * 8.5 required % = ( 11 * 8.5 ) * 100 / ( 11 * 8.5 ) % = 100 % answer : c"
Answer: c
Question (general): when the positive integer a is divided by 11 , the quotient is b and the remainder 3 . when a is divided by 19 , the remainder is also 3 . what is the remainder when b is divided by 19 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: any number which when divided by divisor d 1 , d 2 , etc . leaving same remainderrtakes the form ofk + r where k = lcm ( d 1 , d 2 ) in this case the divisors are 1119 and remainder is 3 . so lcm ( 11,19 ) = 209 so n = 209 + 3 = 212 also a = d 1 q + 3 ; which means d 1 q = 209 d 1 = 11 therefore q = 19 and ( b divided by 19 ) 19 / 19 leaves remainder 0 . answer is e
Answer: e
Question (general): yearly subscription to professional magazines cost a company $ 940.00 . to make a 35 % cut in the magazine budget , how much less must be spent ?
Options: a ) 654 , b ) 655 , c ) 611 , d ) 657 , e ) 658
Rationale: "total cost 940 940 * 35 / 100 = 329 so the cut in amount is 329 the less amount to be spend is 940 - 329 = 611 answer : c"
Answer: c
Question (gain): a certain article of clothing was discounted during a special sale to 2 / 3 of its original retail price . when the clothing did n ' t sell , it was discounted even further to 1 / 2 of its original retail price during a second sale . by what percent did the price of this article of clothing decrease from the first sale to the second sale ?
Options: a ) 50 % , b ) 22.22 % , c ) 25 % , d ) 16.66 % , e ) 12.5 %
Rationale: "say the original retail price of the item was $ 200 . the price after the first sale = 2 / 3 * $ 200 = $ 400 / 3 . the price after the second sale = 1 / 2 * $ 200 = $ 100 . the percent change from the first sale to the second = ( 400 / 3 - 100 ) / 150 = 1 / 3 = 22.22 % . answer : b ."
Answer: b
Question (general): rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 5 per page each time a page is revised . if a certain manuscript has 100 pages , of which 20 were revised only once , 30 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 1200 , b ) $ 1500 , c ) $ 1400 , d ) $ 1250 , e ) $ 1350
Rationale: "50 pages typed 1 x 20 pages typed 2 x ( original + one revision ) 30 pages typed 3 x ( original + two revisions ) 50 ( 10 ) + 20 ( 10 + 5 ) + 30 ( 10 + 5 + 5 ) = 500 + 300 + 600 = 1400 answer - c"
Answer: c
Question (general): the average ( arithmetic mean ) of 20 , 40 , and 60 is 7 more than the average of 10 , 70 , and what number ?
Options: a ) 19 , b ) 25 , c ) 35 , d ) 45 , e ) 55
Rationale: "a 1 = 120 / 3 = 40 a 2 = a 1 - 7 = 33 sum of second list = 33 * 3 = 99 therefore the number = 99 - 80 = 19 answer : a"
Answer: a
Question (general): there are 2 sections a and b in a class , consisting of 50 and 40 students respectively . if the average weight of section a is 50 kg and that of section b is 70 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 58.88 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 40 students = 50 * 50 + 40 * 70 = 2500 + 2800 average weight of the class is = 5300 / 90 = 58.88 kg answer is d"
Answer: d
Question (general): dan ' s age after 20 years will be 7 times his age 4 years ago . what is the present age of dan ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let dan ' s present age be x . x + 20 = 7 ( x - 4 ) 6 x = 48 x = 8 the answer is b ."
Answer: b
Question (physics): a work as fast as b . if b can complete a work in 12 days independently , the number of days in which a and b can together finish the work in ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 6 days
Rationale: ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 6 b ' s 1 day work = 1 / 12 a + b 1 day work = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 a and b can finish the work in 4 days answer is c
Answer: c
Question (other): in a group of 6 boys & 4 girls a committee of 4 persons is to be formed . in how many different ways can it be done so that the committee has at least 1 girl ?
Options: a ) 187 , b ) 190 , c ) 192 , d ) 195 , e ) 213
Rationale: the committee of 4 persons is to be so formed that it has at least 1 woman the different ways that we can choose to form such a committee are : ( i ) lw . 3 m in t 6 x 5 x 4 ' x 6 c 3 = 4 x — — 80 3 x 2 x 1 x 6 c 2 = 42 : : x 26 : : = 90 ( ii ) 2 w . 2 m in ° c 2 ( iii ) 3 w . 1 m in 4 c 3 x 6 c 1 = 4 x 6 = 24 ( iv ) 4 w in 6 c 4 = 1 total no . of different ways in which a committee of 4 persons can be formed so that it has at least one woman . = 80 + 90 + 24 + 1 = 195 d
Answer: d
Question (geometry): three circles of radius 3.5 cm are placed in such a way that each circle touches the other two . the area of the portion enclosed by the circles is
Options: a ) 1.967
b ) 1.963
c ) 2.388
d ) 3.388
e ) 2.382
Rationale: explanation : required area = ( area of an equilateral triangle of side 7 cm ) - ( 3 * area of sector with ã = 60 degrees and r = 3.5 cm ) \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 7 \ times 7 ) - ( 3 \ times \ frac { 22 } { 7 } \ times 3.5 \ times 3.5 \ times \ frac { 60 } { 360 } ) } sq cm = \ inline { \ color { black } ( \ frac { \ sqrt { 3 } } { 4 } \ times 49 ) - ( 11 \ times 0.5 \ times 3.5 ) } sq cm = 1.967 sq cm answer : a ) 1.967
Answer: a
Question (physics): 2 a 33 + b 9 ____ 99 if a and b represent positive single digits in the correctly worked computation above , what is the value of a + 3 b ?
Options: a ) 2 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: adding the digits in unit ' s place , a + 3 + 9 = 19 ( since a and b are positive single digits ) = > a = 7 now adding the digits in ten ' s place , 2 + 3 + b + 1 = 9 ( 1 has been carried over from nit ' s place addition ) = > b = 3 a + 3 b = 2 + 2 * 3 = 11 answer d
Answer: d
Question (general): if ( 5 - x ) / ( 7 + x ) = x , what is the value of x ^ 2 + 8 x - 5 ?
Options: a ) - 4 , b ) - 3 , c ) - 2 , d ) - 1 , e ) 0
Rationale: "( 5 - x ) = x * ( 7 + x ) ( 5 - x ) = 7 x + x ^ 2 0 = x ^ 2 + 8 x - 5 the answer is e ."
Answer: e
Question (gain): what percent is 300 gm of 1 kg ?
Options: a ) 25 % , b ) 40 % , c ) 30 % , d ) 8 % , e ) 12 %
Rationale: "1 kg = 1000 gm 300 / 1000 ã — 100 = 30000 / 1000 = 30 % answer is c"
Answer: c
Question (gain): a man two flats for $ 675958 each . on one he gains 11 % while on the other he loses 11 % . how much does he gain or lose in the whole transaction ?
Options: a ) 1.21 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
Rationale: "in such a case there is always a loss loss % = ( 11 / 10 ) ^ 2 = 23 / 19 = 1.21 % answer is a"
Answer: a
Question (geometry): what is the ratio between perimeters of two squares one having 2 times the diagonal then the other ?
Options: a ) 3 : 8 , b ) 3 : 6 , c ) 3 : 7 , d ) 2 : 1 , e ) 3 : 3
Rationale: "d = 2 d d = d a √ 2 = 2 d a √ 2 = d a = 2 d / √ 2 a = d / √ 2 = > 2 : 1 answer : d"
Answer: d
Question (physics): richard traveled the entire 60 miles trip . if he did the first 2 miles of at a constant rate 24 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 32 mph , e ) 55 mph
Rationale: average speed = sum of distance / sum of time . if he travelled the first 2 miles at 24 miles / hr , it would take 0.083 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.083 + 1 ) hrs = 55 miles / 1 hr . therefore , the answer is e .
Answer: e
Question (general): a man ’ s current age is ( 2 / 5 ) of the age of his father . after 8 years , he will be ( 1 / 2 ) of the age of his father . what is the age of father at now ?
Options: a ) 40 , b ) 45 , c ) 38 , d ) 50 , e ) 39
Rationale: a 40 let , father ’ s current age is a years . then , man ’ s current age = [ ( 2 / 5 ) a ] years . therefore , [ ( 2 / 5 ) a + 8 ] = ( 1 / 2 ) ( a + 8 ) 2 ( 2 a + 40 ) = 5 ( a + 8 ) a = 40
Answer: a
Question (gain): a feed store sells two varieties of birdseed : brand a , which is 60 % millet and 40 % sunflower , and brand b , which is 65 % millet and 35 % safflower . if a customer purchases a mix of the two types of birdseed that is 50 % millet , what percent of the mix is brand a ?
Options: a ) 40 % , b ) 60 % , c ) 50 % , d ) 45 % , e ) 55 %
Rationale: yes there is a simple method : consider the following method brand a : 60 % millet and 40 % sunflower brand b : 65 % millet and 35 % safflower mix : 50 % millet here the weighted average is 50 % , now brand a has 60 % millet , which is 10 % more than the weighted average of mix = + 0.10 a - - - - - - - - - - - - - - - i similarly , brand b has 65 % millet , which is 15 % more than the weighted average of mix = + 0.15 b - - - - - - - - - - - - ii now , both brand a and brand b are combined to give a 50 % mix containing millet , so equate i and ii implies , 0.10 a = 0.15 b therefore a / b = 0.15 / 0.10 = 3 / 2 a : b : ( a + b ) = 3 : 2 : ( 3 + 2 ) = 3 : 2 : 5 we have to find , percent of the mix is brand a i . e . a : ( a + b ) = 3 : 5 = ( 3 / 5 ) * 100 = 60 % here is a pictorial representation : brand a = 60 % - - - - - - - - - - - - - - - - - - - - - - - - 10 % or 0.10 above average , a times - - - - - - - - - - - - - - - - - total above = + 0.10 a - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - average = 50 % or 0.50 brand b = 65 % - - - - - - - - - - - - - - - - - - - - - - - - - - 15 % or 0.15 above average , b times - - - - - - - - - - - - - - - - - total above = + 0.15 b since the amount below the average has to equal the average above the average ; therefore , 0.10 a = 0.15 b a / b = 3 / 2 a : b : total = 3 : 2 : 5 therefore a / total = 3 : 5 = 60 % answer : b
Answer: b
Question (gain): if the cost price of 30 articles is equal to the selling price of 45 articles , what is the % profit or loss made by the merchant ?
Options: a ) 33.33 % loss , b ) 25 % profit , c ) 20 % loss , d ) 20 % profit , e ) 5 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 30 articles = 30 * 1 = $ 30 the selling price of 45 articles = cost price of 30 articles = $ 30 . now , we know the selling price of 45 articles . let us find the cost price of 45 articles . cost price of 45 articles = 45 * 1 = $ 45 . therefore , profit made on sale of 45 articles = selling price of 45 articles - cost price of 45 articles = 30 - 45 = - $ 15 . as the profit is in the negative , the merchant has made a loss of $ 15 . therefore , % loss = loss / cp * 100 % loss = - 15 / 45 * 100 = 33.33 % loss . a"
Answer: a
Question (general): the average age of 21 students of a class is 21 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years , the age of the 21 th student is
Options: a ) 164 , b ) 152 , c ) 100 , d ) 182 , e ) 195
Rationale: "explanation : age of the 21 th student = [ 21 * 21 - ( 14 * 5 + 16 * 9 ) ] = ( 378 - 214 ) = 164 years . answer : a"
Answer: a
Question (physics): the length of the bridge , which a train 180 meters long and travelling at 48 km / hr can cross in 70 seconds , is :
Options: a ) 245 , b ) 276 , c ) 987 , d ) 168 , e ) 1981
Rationale: "speed = ( 45 * 5 / 18 ) m / sec = ( 25 / 2 ) m / sec . time = 30 sec . let the length of bridge be x meters . then , ( 130 + x ) / 30 = 25 / 2 = = > 2 ( 130 + x ) = 750 = = > x = 245 m . answer : a"
Answer: a
Question (general): the average age of a group of 10 persons was decreased by 3 years when one person , whose age was 40 years , was replaced by a new person . find the age of the new person ?
Options: a ) 18 , b ) 56 , c ) 12 , d ) 17 , e ) 10
Rationale: "initial average age of the 10 persons be p . age of the new person q . sum of the ages of the initial 10 persons = 10 p new average = ( p - 3 ) 10 ( p - 3 ) = 10 p - 40 + q = > q = 10 answer : e"
Answer: e
Question (gain): an error 12 % in excess is made while measuring the side of a square . now what is the percentage of error in the calculated area of the square ?
Options: a ) 6.64 % , b ) 16.64 % , c ) 15.64 % , d ) 25.44 % , e ) 10.64 %
Rationale: "percentage error in calculated area = ( 12 + 12 + ( 12 ã — 12 ) / 100 ) % = 25.44 % answer : d"
Answer: d
Question (general): the difference between a number and its two - fifth is 510 . what is 30 % of that number ?
Options: a ) 158 , b ) 200 , c ) 255 , d ) 400 , e ) 280
Rationale: "let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 10 % of 850 = 255 . answer : c"
Answer: c
Question (physics): john and jacob set out together on bicycle traveling at 18 and 15 miles per hour , respectively . after 40 minutes , john stops to fix a flat tire . if it takes john one hour to fix the flat tire and jacob continues to ride during this time , how many hours will it take john to catch up to jacob assuming he resumes his ride at 18 miles per hour ? ( consider john ' s deceleration / acceleration before / after the flat to be negligible )
Options: a ) 3 , b ) 3 1 / 3 , c ) 3 1 / 2 , d ) 4 , e ) 4 1 / 3
Rationale: "john ' s speed - 18 miles / hr jacob ' s speed - 15 miles / hr after 40 min ( i . e 2 / 3 hr ) , distance covered by john = 18 x 2 / 3 = 12 miles . jacob continues to ride for a total of 1 hour and 40 min ( until john ' s bike is repaired ) . distance covered in 1 hour 40 min ( i . e 5 / 3 hr ) = 15 x 5 / 3 = 25 miles . now , when john starts riding back , the distance between them is 13 miles . jacob and john are moving in the same direction . for john to catch jacob , the effective relative speed will be 18 - 15 = 3 miles / hr . thus , to cover 13 miles at 3 miles / hr , john will take 13 / 3 = 4 1 / 3 hours answer e"
Answer: e
Question (geometry): the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 56 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 24 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 56 ounces of a substance has a volume of ( 48 / 112 ) * 56 = 24 cubic inches answer d"
Answer: d
Question (gain): 800 is increased by 110 % . find the final number .
Options: a ) 1200 , b ) 1210 , c ) 1180 , d ) 1190 , e ) 1680
Rationale: explanation final number = initial number + 110 % ( original number ) = 800 + 110 % ( 800 ) = 800 + 880 = 1680 . answer e
Answer: e
Question (gain): company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 40 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 82 % , d ) 116 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 40 % more than company a ' s assets which is 140 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 70 a + b = 170 kw = 140 kw / ( a + b ) * 100 = 140 / 170 * 100 = 82.35 % or 82 % c"
Answer: c
Question (general): if a : b = 2 : 3 , b : c = 4 : 5 and c : d = 5 : 9 then a : d is equal to :
Options: a ) 11 : 17 , b ) 8 : 27 , c ) 5 : 9 , d ) 2 : 9 , e ) none
Rationale: "solution : a / d = ( a / b ) * ( b * c ) * ( c / d ) = ( 2 / 3 ) * ( 4 / 5 ) * ( 5 / 9 ) = ( 2 * 4 * 5 ) / ( 3 * 5 * 9 ) = 8 / 27 . answer : option b"
Answer: b
Question (general): if an integer n is to be selected at random from 1 to 105 , inclusive , what is probability n ( n + 1 ) will be divisible by 7 ?
Options: a ) 1 / 7 , b ) 3 / 14 , c ) 1 / 2 , d ) 2 / 7 , e ) 3 / 4
Rationale: "for n ( n + 1 ) to be a multiple of 7 , either n or n + 1 has to be a multiple of 7 . thus n must be of the form 7 k or 7 k - 1 . the probability is 2 / 7 . the answer is d ."
Answer: d
Question (other): two numbers are respectively 20 % and 50 % more than a third number . the ratio of the two numbers is
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 5 , d ) 6 : 5 , e ) 7 : 5
Rationale: "explanation : let the third number be x . first number ( 120 / 100 ) * x = 6 x / 5 second number ( 150 / 100 ) * x = 3 x / 2 ratio = 6 x / 5 : 3 x / 2 = > 4 : 5 option c"
Answer: c