Cheukting/mathqa huggingface dataset:
Question (general): a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 22 years , e ) 17 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 x = 22 . answer d"
Answer: d
Question (general): 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25073 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 9 , c ) 10 ^ 8 , d ) 10 ^ 10 , e ) 10 ^ 11
Rationale: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,073 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,073 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is c .
Answer: c
Question (other): the simple form of the ratio 5 / 3 : 2 / 5 is ?
Options: a ) 10 : 6 , b ) 10 : 3 , c ) 25 : 6 , d ) 25 : 3 , e ) 30 : 3
Rationale: "5 / 3 : 2 / 5 = 25 : 6 answer : c"
Answer: c
Question (general): pat , kate and mark charged a total of 180 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much times as mark , how many more hours did mark charge to the project than kate .
Options: a ) 18 , b ) 36 , c ) 72 , d ) 90 , e ) 100
Rationale: let kate charge for x hours , then pat charged for 2 x and mat - for 6 x . so , 2 x + 6 x + x = 180 - total hours charged for , x = 20 . mat charged 6 x - x or 5 x for more hours than kate , or for 100 hours . e is correct
Answer: e
Question (physics): one tap , working alone at its maximum constant rate , can fill a certain sink in 287 seconds . a second tap , working alone at its maximum constant rate , can fill the same sink in 283 seconds . if both taps work together at their respective maximum constant rates , the time it will take to fill the sink is closest to
Options: a ) 142 seconds , b ) 150 seconds , c ) 177 seconds , d ) 200 seconds , e ) 270 seconds
Rationale: tap 1 : 283 secs tap 2 : 287 secs considering the average of these 2 taps : 285 secs . so 1 tap can fill the tank in 285 secs , so 2 taps can fill the tank in 285 / 2 = 142.5 secs . closest answer is a .
Answer: a
Question (other): of the 85 house in a development , 50 have a two - car garage , 40 have an in - the - ground swimming pool , and 35 have both a two - car garage and an in - the - ground swimming pool . how many houses in the development have neither a two - car garage nor an in - the - ground swimming pool ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "neither car nor garage = total - garage - ( swim - common ) = 85 - 50 - ( 40 - 35 ) = 85 - 55 = 30 answer e"
Answer: e
Question (physics): a train running at the speed of 240 km / hr crosses a pole in 21 seconds . what is the length of the train ?
Options: a ) 1300 m , b ) 1350 m , c ) 1400 m , d ) 1450 m , e ) 1500 m
Rationale: "speed = ( 240 * 5 / 18 ) m / sec = ( 200 / 3 ) m / sec length of the train = ( speed x time ) = ( 200 / 3 * 21 ) m = 1400 m . answer : c"
Answer: c
Question (general): the difference between the squares of two consecutive odd integers is a square < 1000 whose root equals the combined sum of the digits of the two integers . what is the sum of the digits m of the larger integer ?
Options: a ) m = 2 , b ) m = 5 , c ) m = 8 , d ) 10 , e ) 11
Rationale: really hard . but let ' s start with few concepts : 1 . square of an odd integer will be odd . 2 . difference of odd and odd will be even . 3 . any odd integer can be expressed as difference of two squares . 4 . an even integer can be expressed as difference of two squares only if that even integer is a multiple of 4 . assume two odd integers to be ( 2 x - 1 ) and ( 2 x + 1 ) . difference of their squares = ( 2 x + 1 ) ^ 2 - ( 2 x - 1 ) ^ 2 = 4 x ^ 2 + 1 + 4 x - ( 4 x ^ 2 + 1 - 4 x ) = 4 x ^ 2 + 1 + 4 x - 4 x ^ 2 - 1 + 4 x = 8 x now root of 8 x needs to be an integer such that it is equal to the sum of the digits of the two odd integers . 8 = 2 ^ 3 , so x needs to be such that itcompletesa perfect square . if we find x , we can find the value of 2 x + 1 ( larger integer ) and then sum of its digits . let ' s check the options , starting with c . for sum to be 8 , few possibilities are : 17 , 35 , 53 , 71 if we take 17 , the pair is 15 and 17 , meaning x = 8 . 8 x = 64 root of 64 = 4 but 4 is not equal to 1 + 5 + 1 + 7 . reject . if we take 35 , the pair is 33 and 35 , meaning x = 17 . 8 x = 8 * 17 reject since perfect square is not possible . if we take 53 , the pair is 51 and 53 , meaning x = 26 . 8 x = 8 * 26 reject since perfect square is not possible . if we take 71 , the pair is 69 and 71 , meaning x = 35 . 8 x = 8 * 35 reject since perfect square is not possible . i tried each option and the possibilities and then got lost . then , it occurred to me that i was only checking 2 - digit integers . what about 3 - digits ? starting with option a , only 2 - digit odd integer whose sum is 2 is 101 . if we take 101 , the pair is 99 and 101 , meaning x = 50 . 8 x = 8 * 50 = 400 root of 400 = 20 which is indeed equal to 9 + 9 + 1 + 1 . answer ( a ) .
Answer: a
Question (general): if f ( x ) = 2 x + 3 , & g ( x ) = ( x - 3 ) / 2 , then what is the value of , fo ( fo ( go ( go ( fo ( fo ( go ( go . . . . . . . . . . . . . . . . ( fo ( fo ( go ( gof ( x ) ) ) ) ) . . . . . ) ) ) ) ) ) ?
Options: a ) 3 , b ) 2 , c ) 9 , d ) 7 , e ) 1
Rationale: f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 − 32 = x 2 x + 3 − 32 = x gogof ( x ) = x − 32 x − 32 fogogof ( x ) = 2 ( x − 32 ) + 32 ( x − 32 ) + 3 = 2 x − 6 + 622 x − 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) .
Answer: d
Question (physics): the length of the bridge , which a train 150 metres long and travelling at 45 km / hr can cross in 30 seconds , is ?
Options: a ) 76 m , b ) 178 m , c ) 225 m , d ) 187 m , e ) 176 m
Rationale: "speed = [ 45 x 5 / 18 ] m / sec = [ 25 / 2 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 150 + x ) / 30 = 25 / 2 = > 2 ( 150 + x ) = 750 = > x = 225 m . answer : c"
Answer: c
Question (general): find the number which is nearest to 3105 and is exactly divisible by 21
Options: a ) 1208 , b ) 3108 , c ) 241 , d ) 217 , e ) 3147
Rationale: "on dividing 3105 by 21 , we get 18 as remainder .  number to be added to 3105 = ( 21 - 18 ) - 3 . hence , required number = 3105 + 3 = 3108 . answer b 3108"
Answer: b
Question (other): the ratio of pens to pencils is 5 to 6 . there are 5 more pencils than pens . how many pencils are there ?
Options: a ) 24 , b ) 30 , c ) 36 , d ) 42 , e ) 48
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 5 x = 5 the number of pencils is 30 . the answer is b ."
Answer: b
Question (physics): if length of a room is three times of its breadth and its area is 12 sq . m . what is perimeter of room ?
Options: a ) 14 m
b ) 18 m
c ) 24 m
d ) 16 m
e ) none of the above
Rationale: let breadth = x m . and length = 3 x m . x * 3 x = 12 , x ^ 2 = 4 , x = 2 . length = 6 m , breadth = 2 m . perimeter = 2 * ( 6 + 2 ) = 16 m answer d
Answer: d
Question (general): p is 3 times as old as q . in 11 years , p will be twice as old as q . how old was p 3 years ago ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 30 , e ) 33
Rationale: p = 3 q so q = p / 3 p + 11 = 2 ( q + 11 ) = 2 ( p / 3 + 11 ) p / 3 = 11 p = 33 three years ago , p was 30 . the answer is d .
Answer: d
Question (physics): a person can row at 9 kmph and still water . he takes 8 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 32 , b ) 38 , c ) 29 , d ) 54 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 8.5 = > x / 10 + x / 8 = 17 / 2 = > ( 4 x + 5 x ) / 40 = 17 / 2 = > x = 38 km . answer : b"
Answer: b
Question (physics): a walks at 30 kmph and 30 hours after his start , b cycles after him at 50 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2250 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 50 = 30 x = 2250 km answer is d"
Answer: d
Question (probability): a box contains 1 red balls and 5 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2 / 3
Rationale: "my complicated version of your simple approach let the 5 black balls be bbbbb and 1 red balls be r they can be arranged in 6 slots _ _ _ _ _ _ _ _ in ( 6 ! ) / ( 5 ! x 1 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 5 slots and 4 black ( bbbb ) and 1 red ( r ) they can be arranged in ( 5 ! ) / ( 4 ! x 1 ! ) hence required probability = [ ( 6 ! ) / ( 5 ! x 1 ! ) ] / [ ( 5 ! ) / ( 4 ! x 1 ! ) ] = 6 / 5 c"
Answer: c
Question (general): in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 13 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 27 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 13 * 2 = 38 . to maximize the number of books borrowed by 1 student , let ' s assume that 12 students borrowed 3 books and 1 student borrowed the rest . 80 - 38 - 3 * 12 = 6 the maximum number of books borrowed by any student is 6 . the answer is d ."
Answer: d
Question (general): if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 4 m + n ?
Options: a ) 11 , b ) 18 , c ) 55 , d ) 25 , e ) 33
Rationale: "k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 4 * 10 + 15 = 55 answer : c"
Answer: c
Question (general): on rainy mornings , mo drinks exactly n cups of hot chocolate ( assume that n is an integer ) . on mornings that are not rainy , mo drinks exactly 3 cups of tea . last week mo drank a total of 26 cups of tea and hot chocolate together . if during that week mo drank 10 more tea cups than hot chocolate cups , then how many rainy days were there last week ?
Options: a ) 0 , b ) 1 , c ) 4 , d ) 5 , e ) 6
Rationale: "t = the number of cups of tea c = the number of cups of hot chocolate t + c = 26 t - c = 10 - > t = 18 . c = 8 . mo drinks 3 cups of tea a day then number of days that are not rainy = 18 / 3 = 6 so number of rainy days = 7 - 6 = 1 b is the answer ."
Answer: b
Question (general): the mean of 50 observations was 36 . it was found later that an observation 45 was wrongly taken as 23 . the corrected new mean is ?
Options: a ) 36.7 , b ) 36.4 , c ) 36.5 , d ) 36.9 , e ) 36.3
Rationale: "correct sum = ( 36 * 50 + 45 - 23 ) = 1822 . correct mean = 1822 / 50 = 36.4 answer : b"
Answer: b
Question (general): a and b are two partially filled buckets of water . if 4 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 4 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 44 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 4 = 1 / 3 ( b + 4 ) - - - - > 3 a - 12 = b + 4 scenario 2 b - 4 = 1 / 2 ( a + 4 ) - - - - - > 2 b - 8 = a + 4 from scenario 1 , b = 3 a - 16 substitute b with this information in stmt 2 2 ( 3 a - 16 ) - 8 = a + 4 - - - - - - > 6 a - 32 - 8 = a + 4 - - - - - - > 6 a - a = 40 + 4 - - - > 5 a = 44 a = 44 / 5 , answer choice a"
Answer: a
Question (physics): pipe a can fill a tank in 4 hours . due to a leak at the bottom , it takes 6 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 12 , b ) 67 , c ) 95 , d ) 36 , e ) 66
Rationale: "let the leak can empty the full tank in x hours 1 / 4 - 1 / x = 1 / 6 = > 1 / x = 1 / 4 - 1 / 6 = ( 3 - 2 ) / 12 = 1 / 12 = > x = 12 . answer : a"
Answer: a
Question (general): an individual deposited 20 % of 25 % of 30 % of what he had into his account with a bank . if he deposited rs . 750 , how much was he having initially with him before depositing ?
Options: a ) rs . 500000 , b ) rs . 50000 , c ) rs . 5000 , d ) rs . 15000 , e ) rs . 6000
Rationale: let x amount he has then 20 % of 25 % of 30 % of x = 750 so x = 50000 answer : b
Answer: b
Question (general): in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many r cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer r = 44 . d"
Answer: d
Question (general): dacid obtained 96 , 98 , 99 , 100 and 98 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 88 , d ) 88 , e ) 98
Rationale: "average = ( 96 + 98 + 99 + 100 + 98 ) / 5 = 491 / 5 = 98 . answer : e"
Answer: e
Question (general): if 4 x + 3 y = 8 and y − 3 x = 2 , then what is the value of x + 4 y ?
Options: a ) 10 , b ) 3 , c ) 15 , d ) 52 / 7 , e ) 60 / 7
Rationale: "4 x + 3 y = 8 − 3 x + y = 2 adding both the equations - - > x + 4 y = 10 answer : a"
Answer: a
Question (general): a lemonade stand sold only small and large cups of lemonade on tuesday . 3 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 1 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
Options: a ) 7 / 16 , b ) 7 / 15 , c ) 10 / 21 , d ) 17 / 35 , e ) 1 / 10
Rationale: "let the total # of cups be 10 . # of small cups sold 3 / 5 * 10 = 6 ; # of large cups sold 10 - 6 = 4 ; let the price of small cup be $ 6 , then the price of larges cup would be 1 / 6 * 6 = $ 1 ; revenue from small cups : 6 * $ 6 = $ 36 ; revenue from large cups cups : 4 * $ 1 = $ 4 ; fraction of total revenue from large cups : 4 / ( 36 + 4 ) = 1 / 10 . answer : e ."
Answer: e
Question (general): there are 10 baskets numbered from 1 to 10 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 330 , b ) 390 , c ) 450 , d ) 510 , e ) 570
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 10 * 11 / 2 = 55 apples . the total number of apples taken by 10 children is 10 * 55 = 550 the number of apples left in the end is 1000 - 550 = 450 apples . the answer is c ."
Answer: c
Question (general): the positive numbers w , x , y , and z are such that x is 30 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Question (general): an exam consists of 7 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 70 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 219 / 256 , e ) 15 / 16
Rationale: if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 219 / 256 . d
Answer: d
Question (general): what is difference between biggest and smallest fraction among 2 / 3 , 3 / 4 , 4 / 5 and 5 / 7
Options: a ) 2 / 15 , b ) 3 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) none of these
Rationale: explanation : 2 / 3 = . 66 , 3 / 4 = . 75 , 4 / 5 = . 8 and 5 / 7 = . 71 so biggest is 4 / 5 and smallest is 2 / 3 their difference is 4 / 5 - 2 / 3 = 2 / 15 option a
Answer: a
Question (general): last year department store x had a sales total for december that was 5 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 1 / 4 , b ) 4 / 15 , c ) 1 / 3 , d ) 5 / 16 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 50 year total = 11 * 10 + 50 = 160 answer = 50 / 160 = 5 / 16 = d"
Answer: d
Question (general): if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 6.2 ] + [ - 3.4 ] + [ 12.7 ] ?
Options: a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: "you are asked what the closest lesser integer value to [ x ] is . [ - 6.2 ] = - 7.0 [ - 3.4 ] = - 4.0 [ 12.7 ] = 12.0 therefore , answer is : - 7.0 - 4.0 + 12.0 = - 1.0 option a ."
Answer: a
Question (gain): a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is :
Options: a ) 13 % , b ) 14 % , c ) 18 % , d ) 20 % , e ) 28 %
Rationale: let original length = x and original breadth = y . decrease in area = xy - ( 80 / 100 * x * 90 / 100 * y ) = ( xy - 18 / 25 * xy ) = 7 / 25 * xy . decrease % = ( 7 / 25 * xy * 1 / xy * 100 ) % = 28 % . answer is e
Answer: e
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 2 / 5 of the amount in 10 years ?
Options: a ) 4 % , b ) 74 % , c ) 64 % , d ) 74 % , e ) 94 %
Rationale: let sum = x . then , s . i . = 2 x / 5 , time = 10 years . rate = ( 100 * 2 x ) / ( x * 5 * 10 ) = 4 % answer : a
Answer: a
Question (gain): a cycle is bought for rs . 900 and sold for rs . 1125 , find the gain percent ?
Options: a ) 27 % , b ) 20 % , c ) 80 % , d ) 30 % , e ) 25 %
Rationale: "900 - - - - 225 100 - - - - ? = > 25 % answer : e"
Answer: e
Question (general): the vertex of a rectangle are ( 1 , 0 ) , ( 5 , 0 ) , ( 1 , 2 ) and ( 5 , 2 ) respectively . if line l passes through the origin and divided the rectangle into two identical quadrilaterals , what is the slope of line l ?
Options: a ) 3 , b ) 6 , c ) 1 / 3 , d ) 1 / 2 , e ) 1 / 6
Rationale: "if line l divides the rectangle into two identical quadrilaterals , then it must pass through the center ( 3 , 1 ) . the slope of a line passing through ( 0,0 ) and ( 3 , 1 ) is 1 / 3 . the answer is c ."
Answer: c
Question (physics): a 140 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 43.2 sec , e ) none of the above
Rationale: speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 140 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 660 m time = distance / speed = 660 x 18 / ( 5 x 55 ) = 43.2 sec ans is : d
Answer: d
Question (gain): how long will a boy take to run round a square field of side 50 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 80 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 50 * 4 = 200 m time taken = 200 * 2 / 5 = 80 sec answer is a"
Answer: a
Question (other): if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 28 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 9 , e ) 1 / 9
Rationale: "28 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 28 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 28 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 27 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 27 = r ^ 3 r = 3 a"
Answer: a
Question (physics): 19 men take 21 days of 8 hours each to do a piece of work . how many days of 6 hours each would 21 women take to do the same . if 3 women do as much work as 2 men ?
Options: a ) 32 , b ) 87 , c ) 38 , d ) 99 , e ) 77
Rationale: "3 w = 2 m 19 m - - - - - - 21 * 8 hours 21 w - - - - - - x * 6 hours 14 m - - - - - - x * 6 19 * 21 * 8 = 14 * x * 6 x = 38 answer : c"
Answer: c
Question (gain): a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,056 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 400 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1056 / 1000 ) - 1 = 0.053 = 5.3 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.056 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.056 - 0.01 x = - 0.004 x = - 0.004 / - 0.01 = 4 / 10 = 40 % so x = 40 % of the 1000 which is 400 answer : b"
Answer: b
Question (physics): the length of the bridge , which a train 135 m long and traveling at 45 km / hr can cross in 30 sec is ?
Options: a ) 235 , b ) 240 , c ) 245 , d ) 250 , e ) 255
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec . time = 30 sec let the length of bridge be x meters . then , ( 135 + x ) / 30 = 25 / 2 x = 240 m . answer : option b"
Answer: b