Cheukting/mathqa huggingface dataset:
Question (other): a 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
Options: a ) 1 / 4 , b ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 2 / 3
Rationale: "the bar lost certain percentage of its weight . we do n ' t know how much tin was lost and how much silver was lost but in all 2 kg was lost with is 10 % of its overall weight . tin loses 1.375 kg in 10 kg so 13.75 % of its weight when it is put in water . silver loses . 375 kg in 5 kg so . 375 / 5 * 100 = 7.5 % of its weight in water . now , we just need to use weighted averages : wt / ws = ( 7.5 - 10 ) / ( 10 - 13.75 ) = 2.5 / 3.75 = 2 / 3 answer ( e )"
Answer: e
Question (geometry): the radius of a cylinder is 10 m , height 12 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 3771.4 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 10 ã — 10 ã — 12 = 3771.4 m ( power 3 ) answer is d ."
Answer: d
Question (gain): what amount does an investor receive if the investor invests $ 6000 at 10 % p . a . compound interest for two years , compounding done annually ?
Options: a ) $ 6980 , b ) $ 7070 , c ) $ 7120 , d ) $ 7260 , e ) $ 7340
Rationale: a = ( 1 + r / 100 ) ^ n * p ( 1.1 ) ^ 2 * 6000 = 1.21 * 6000 = 7260 the answer is d .
Answer: d
Question (physics): the racing magic takes 50 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 50 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 50 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 450 * 2 = 900 seconds = 15 mins answer e"
Answer: e
Question (physics): three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 2 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 6 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 360 min = 6 hours answer : e"
Answer: e
Question (physics): a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 340 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40 sec , e ) 56
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 340 = 700 meter time taken to cross the platform = 700 / ( 25 / 2 ) = 700 ã — 2 / 25 = 56 seconds answer : e"
Answer: e
Question (gain): in a certificate by mistake a candidate gave his height as 25 % more than actual height . in the interview panel , he clarified that his height was 5 feet 6 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 15 , b ) 20 , c ) 18 , d ) 16.5 , e ) 25
Rationale: his height was = 5 feet 6 inch = 6 + 60 = 66 inch . required % correction = 66 * ( 1.25 - 1 ) = 16.5 d
Answer: d
Question (other): there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability q that the both positions will be taken by members of just one party ?
Options: a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
Rationale: "q probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total candidates . since this result can happen for both parties , ( 12 / 49 ) + ( 12 / 49 ) = ( 24 / 49 ) answer : d"
Answer: d
Question (general): what is the smallest positive integer k such that the product of 3675 x k is a perfect square ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 3675 = 5 ^ 2 * 7 ^ 2 * 3 , so if k = 3 then 3675 k = ( 5 * 7 * 3 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 39 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 156 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 39 = > 4 / x = 1 / 39 x = 39 ∗ 4 = 156 mins option d"
Answer: d
Question (geometry): there are 7 non - collinear points . how many triangles can be drawn by joining these points ?
Options: a ) 22 , b ) 38 , c ) 35 , d ) 29 , e ) 18
Rationale: explanation : a triangle is formed by joining any three non - collinear points in pairs . there are 7 non - collinear points the number of triangles formed = \ inline { \ color { black } 7 c _ { 3 } } = 35 answer : c ) 35
Answer: c
Question (gain): a man buys 58 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 24.82 % , d ) 13.6 % , e ) 27.82 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 58 pens = rs . 46 s . p . of 58 pens = 99 % of rs . 58 = rs . 57.42 profit % = ( profit / c . p . ) x 100 profit % = ( 11.42 / 46 ) x 100 = 24.82 % answer : c"
Answer: c
Question (gain): the sale price sarees listed for rs . 200 after successive discount is 10 % and 5 % is ?
Options: a ) 187 , b ) 169 , c ) 172 , d ) 178 , e ) 171
Rationale: "200 * ( 90 / 100 ) * ( 95 / 100 ) = 171 answer : e"
Answer: e
Question (general): if josh , doug , and brad have a total of $ 68 between them , and josh has two times as much money as brad but only 3 - fourths as much as doug , how much money does doug have ?
Options: a ) $ 8 , b ) $ 9 , c ) $ 27 , d ) $ 32 , e ) $ 36
Rationale: josh + doug + brad = 68 ; josh = 2 brad , josh = 3 / 4 doug josh + 1 / 2 josh + 4 / 3 josh = 68 ( substituted the given values ) josh = 24 . 24 = 3 / 4 doug = > doug = 32 answer is d .
Answer: d
Question (gain): the bankers discount of a certain sum of money is rs . 144 and the true discount on the same sum for the same time is rs . 120 . the sum due is :
Options: a ) 715 , b ) 716 , c ) 718 , d ) 720 , e ) 722
Rationale: sum = ( b . d * t . d ) / ( b . d - t . d ) ( 144 * 120 ) / 144 - 120 ; 720 answer : d
Answer: d
Question (physics): tammy climbed a mountain in two days . she spent a total of 14 hours climbing the mountain . on the second day , she walked at an average speed that was half a kilometer per hour faster , but 2 hours less than what she walked on the first day . if the total distance she climbed during the two days is 52 kilometers , how many t kilometers per hour did tammy walk on the second day ?
Options: a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 6
Rationale: "ans : c total time = 14 hrs let time traveled during 1 st day = x let time traveled during 2 nd day = x - 2 total time = 14 x + x - 2 = 14 x = 8 speed * time = distance s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 solving s = 4.5 now speed for 2 nd day is 0.5 less than the 1 st day which is 4.5 thus speed for 2 nd day = 4 its simple algebra for s * 8 + ( s + 0.5 ) ( 8 - 2 ) = 52 but for some reason im getting 3.5 and not 4.5 . 8 s + 6 s + 3 = 52 14 s = 49 s = 3.5"
Answer: c
Question (physics): two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 22 , b ) 12 , c ) 67 , d ) 20 , e ) 81
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 120 + 280 = 400 m . the time required = d / s = 400 / 20 = 20 sec . answer : d"
Answer: d
Question (physics): pipe a fills a tank of capacity 950 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 57 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: in one cycle they fill 40 + 30 - 20 = 50 liters 950 = 50 * n = > n = 19 here n = number of cycles . total time = 19 * 3 = 57 as in one cycle there are 3 minutes . thus 57 minutes answer : a
Answer: a
Question (gain): during a sale , the price of a pair of shoes is marked down 12 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
Options: a ) 9 % , b ) 10 % , c ) 11 % , d ) 14 % , e ) 90 %
Rationale: "assume the price = 100 price during sale = 88 price after sale = 100 percent increase = 12 / 88 * 100 = 14 % approx . correct option : d"
Answer: d
Question (general): if p / q = 5 / 4 , then 2 p + q = ?
Options: a ) 12 , b ) 14 , c ) 13 , d ) 15 , e ) 16
Rationale: "let p = 5 , q = 4 then 2 * 5 + 4 = 14 so 2 p + q = 14 . answer : b"
Answer: b
Question (gain): find the missing figures : 0.75 % of ? = 0.06
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: "let 0.75 % of x = 0.06 . then , 0.75 * x / 100 = 0.06 x = [ ( 0.06 * 100 ) / 0.75 ] = 8 . answer is c ."
Answer: c
Question (other): m is 30 % of q . q is 20 % of p . n is 50 % of p . find m : n ratio
Options: a ) 1 : 25 , b ) 2 : 25 , c ) 3 : 25 , d ) 4 : 25 , e ) 5 : 25
Rationale: let p be 100 n = 50 % of 100 ( p = 100 ) = 50 q = 20 % of 100 ( p = 100 ) = 20 m = 30 % of 20 ( q = 20 ) = 6 m : n = 6 : 50 m : n = 3 : 25 answer : c
Answer: c
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 5000 . with the help of c , they completed the work in 3 days . how much is to be paid to c ?
Options: a ) s . 375 , b ) s . 425 , c ) s . 625 , d ) s . 800 , e ) s . 850
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 1 / 3 - 7 / 24 = 1 / 24 a ' s wages : b ' s wages : c ' s wages = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ' s share ( for 3 days ) = rs . ( 3 * 1 / 24 * 5000 ) = rs . 625 answer = c"
Answer: c
Question (general): a box contains 9 pairs of shoes ( 18 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 17 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 18 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 17 ( as after taking one at random there are 17 shoes left and only one is the pair of the first one ) = 1 / 17 answer : b ."
Answer: b
Question (general): a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations x are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) x = 8
Rationale: the combinations could be { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e
Answer: e
Question (general): what is the lowest positive integer that is divisible by each of the integers 1 through 7 , inclusive ?
Options: a ) 420 , b ) 840 , c ) 1,260 , d ) 2,520 , e ) 5,040
Rationale: "the integer should be divisible by : 2 , 3 , 4 ( = 2 ^ 2 ) , 5 , 6 ( = 2 * 3 ) , and 7 . the least common multiple of these integers is lcm = 2 ^ 2 * 3 * 5 * 7 = 420 . answer : a ."
Answer: a
Question (gain): the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 5225 . what was his original salary ?
Options: a ) 2277 , b ) 5000 , c ) 1000 , d ) 2651 , e ) 1971
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 5225 x * ( 11 / 10 ) * ( 1 / 100 ) = 55 x = 5000 answer : b"
Answer: b
Question (gain): the regular price per can of a certain brand of soda is $ 0.15 . if the regular price per can is discounted 10 percent when the soda is purchased in 24 - can cases , what is the price of 75 cans of this brand of soda purchased in 24 - can cases ?
Options: a ) $ 16.32 , b ) $ 18.00 , c ) $ 10.125 , d ) $ 24.48 , e ) $ 28.80
Rationale: the discounted price of one can of soda is ( 0.9 ) ( $ 0.15 ) , or $ 0.135 therefore , the price of 75 cans of soda at the discounted price would be ( 75 ) ( $ 0.135 ) = 10.125 answer : c .
Answer: c
Question (general): solve : - 666 x 666 x 666 + 555 x 555 x 555 = ? ( 666 x 666 - 666 x 555 + 555 x 555 )
Options: a ) 888 , b ) 333 , c ) 555 , d ) 1221 , e ) 889
Rationale: given exp . = ( a 3 + b 3 ) = ( a + b ) = ( 666 + 555 ) = 1221 ( a 2 - ab + b 2 ) answer d
Answer: d
Question (general): when positive integer x is divided by positive integer y , the remainder is 11.52 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 11.52 - - > x = qy + 11.52 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 11.52 - - > y = 96 . answer : a ."
Answer: a
Question (general): if 213 × 16 = 3408 , then 0.016 × 2.13 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) 0.03408
Rationale: "solution 0.016 × 2.13 = ( 16 / 1000 x 213 / 100 ) = ( 16 / 1000 x 213 / 100 ) = 3408 / 100000 = 0.03408 . answer e"
Answer: e
Question (general): in a certain accounting class of 90 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 65 % , and the students on the make - up date had an average score of 85 % , what was the average score for the entire class ?
Options: a ) 68 % , b ) 71 % , c ) 73 % , d ) 75 % , e ) 79 %
Rationale: "70 % of the students took the final exam on the assigned day - - > 0.7 * 90 = 63 students took the final exam on the assigned day , with an average score of 65 . the rest of the students took the exam on a make - up date - - > 90 - 63 = 27 students took the exam on a make - up date , with an average score of 85 . ( average score ) = ( sum of the scores ) / ( total students ) = ( 63 * 65 + 27 * 85 ) / 90 = 71 . answer : b ."
Answer: b
Question (general): 3 - 5 * 6 + 2 =
Options: a ) a ) 2 , b ) b ) - 13 , c ) c ) - 18 , d ) d ) - 17 , e ) e ) - 25
Rationale: 3 - 5 * 6 + 2 = 5 - 30 = - 25 . . . so the answer is - 25 . . . e
Answer: e
Question (physics): 75 boys can complete a work in 36 days . how many men need to complete twice the work in 20 days
Options: a ) 160 , b ) 170 , c ) 270 , d ) 190 , e ) 200
Rationale: one man can complete the work in 36 * 75 = 2700 days = one time work to complete the work twice it will be completed in let m be the no . of worker assign for this therefore the eqn becomes m * 20 = 2 * 2700 m = 270 workers answer : c
Answer: c
Question (general): ratio of the earnings of a and b is 4 : 7 . if the earnings of a increases by 50 % and those of b decreased by 25 % , the new ratio of their earnings becomes 8 : 7 . what are a ' s earnings ?
Options: a ) 8 : 6 , b ) 8 : 9 , c ) 8 : 3 , d ) 8 : 7 , e ) 8 : 1
Rationale: let the original earnings of a and b be rs . 4 x and rs . 7 x . new earnings of a = 150 % 0 f rs . 4 x = ( 150 / 100 * 4 x ) = rs . 6 x new earnings of b = 75 % of rs . 7 x = ( 75 / 100 * 7 x ) = rs . 21 x / 4 6 x : 21 x / 4 = 8 : 7 this does not give x . so , the given data is inadequate . answer : d
Answer: d
Question (general): the expression x # y denotes the product of the consecutive multiples of 3 between x and y , inclusive . what is the sum of the exponents in the prime factorization of 21 # 30 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "first , let ' s translate the expression 21 # 30 , using the definition given : 21 # 30 = 21 × 24 × 27 × 30 we need the prime factorization of this product . let ' s factor out 3 from each multiple . 21 # 30 = 3 ^ 4 ( 7 × 8 × 9 × 10 ) now let ' s replace each consecutive integer with its prime factorization : 21 # 30 = 3 ^ 4 ( 7 × 2 ^ 3 × 3 ^ 2 × ( 2 × 5 ) ) let ' s group the prime bases : 21 # 30 = 2 ^ 4 × 3 ^ 6 × 5 × 7 the sum of the exponents is 4 + 6 + 1 + 1 = 12 the answer is c ."
Answer: c
Question (other): what is the square root of 144 , divided by 6 ?
Options: a ) 9 , b ) 36 , c ) 2 , d ) 6 , e ) 1
Rationale: "square root is a number times itself square root of 144 = 12 , 12 / 6 = 2 ( c ) 2"
Answer: c
Question (physics): the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 20 kmph ?
Options: a ) 21.21 , b ) 20.25 , c ) 32.25 , d ) 75.75 , e ) 62.61
Rationale: distance covered in 1 min = ( 20 * 1000 ) / 60 = 333.33 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 333.33 / 4.4 = 75.75 answer : d
Answer: d
Question (gain): a grocer has 400 pounds of coffee in stock , 30 percent of which is decaffeinated . if the grocer buys another 100 pounds of coffee of which 60 percent is decaffeinated , what percent , by weight , of the grocer ’ s stock of coffee is decaffeinated ?
Options: a ) 28 % , b ) 30 % , c ) 36 % , d ) 36 % , e ) 40 %
Rationale: "1 . 30 % of 400 = 120 pounds of decaffeinated coffee 2 . 60 % of 100 = 60 pounds of decaffeinated coffee 3 . wt have 180 pounds of decaffeinated out of 500 pounds , that means 180 / 500 * 100 % = 36 % . the correct answer is d ."
Answer: d
Question (physics): a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets into it . the mass of the man is ?
Options: a ) 77 kg , b ) 60 kg , c ) 77 kg , d ) 55 kg , e ) 47 kg
Rationale: "in this type of question , first we will calculate the volume of water displaces then will multiply with the density of water . volume of water displaced = 3 * 2 * 0.01 = 0.06 m cube mass of man = volume of water displaced * density of water = 0.06 * 1000 = 60 kg answer : b"
Answer: b
Question (physics): a cyclist covers a distance of 500 m in 4 min 30 sec . what is the speed in km / hr of the cyclist ?
Options: a ) 2 , b ) 2.5 , c ) 3.2 , d ) 4.6 , e ) 2.8
Rationale: distance = 500 m time = 4 min 10 sec = 250 sec speed = ( 500 / 250 ) m / s = 2 m / s speed in km / hr = 2 * 18 / 5 = 3.2 km / hr correct option is c
Answer: c
Question (general): the number n is 76 h 4 , where h represents the 10 ' s digit . if n is divisible by 9 , what is the value of h ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: integer is divisible by 9 - sum of digits is divisible by 9 answer : a
Answer: a
Question (physics): if a boat is rowed downstream for 96 km in 3 hours and upstream for 88 km in 11 hours , what is the speed of the boat and the river ?
Options: a ) 12 , 20 , b ) 20 , 20 , c ) 20 , 11 , d ) 20 , 12 , e ) 12 , 12
Rationale: explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 32 ; us = 8 x = ( 32 + 8 ) / 2 = 40 / 2 = 20 km / hr y = ( 32 - 8 ) / 2 = 24 / 2 = 12 km / hr answer : d
Answer: d
Question (general): 117 x 217 + 83 x 83 = ?
Options: a ) 79698 , b ) 20578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 117 ) ^ 2 + ( 83 ) ^ 2 = ( 100 + 17 ) ^ 2 + ( 100 - 17 ) ^ 2 = 2 [ ( 100 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 10000 + 289 ] = 2 x 10289 = 20578 answer is b"
Answer: b
Question (physics): a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be
Options: a ) 12.5 m , b ) 10 m , c ) 17.5 m , d ) 21.25 m , e ) 9.8 m
Rationale: "let the height of the building x metres . less lengthy shadow , less in the height ( direct proportion ) 40.25 : 28.75 : : 17.5 : x 40.25 * x = 28.75 * 17.5 x = ( 28.75 x 17.5 ) / 40.25 x = 12.5 answer is a ."
Answer: a
Question (geometry): three rugs have a combined area of 196 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 24 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 15 square meters , b ) 20 square meters , c ) 24 square meters , d ) 28 square meters , e ) 30 square meters
Rationale: "total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 194 - 24 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 15 . answer : a ."
Answer: a
Question (general): a line has a slope of 3 / 4 and intersects the point r ( - 12 , - 39 ) . at which point does this line intersect the x - axis ?
Options: a ) ( 40,0 ) , b ) ( 30,0 ) , c ) ( 0,40 ) , d ) ( 40,30 ) , e ) ( 0,30 )
Rationale: "assume that the equation of the line is y = mx + c , where m and c are the slope and y - intercept . you are also given that the line crosses the point ( - 12 , - 39 ) , this means that this point will also lie on the line above . thus you get - 39 = m * ( - 12 ) + c , with m = 3 / 4 as the slope is given to be 3 / 4 . after substituting the above values , you get c = - 30 . thus the equation of the line is y = 0.75 * x - 30 and the point where it will intersect the x - axis will be with y coordinate = 0 . put y = 0 in the above equation of the line and you will get , x = 40 . thus , the point r of intersection is ( 40,0 ) . a is the correct answer ."
Answer: a
Question (other): 180 college students were asked in a survey if they preferred windows or mac brand computers . 50 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 60 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 70 , c ) 50 , d ) 60 , e ) 75
Rationale: "180 = 50 ( mac ) + x ( window ) + 60 ( both ) = > x = 70 answer : b"
Answer: b
Question (physics): a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 15 , b ) 44 , c ) 40 , d ) 27 , e ) 12
Rationale: "speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 2 / 25 ) = 40 seconds answer : c"
Answer: c