Cheukting/mathqa huggingface dataset:
Question (general): on a certain date , pat invested $ 8,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 32,000 , in how many years total will the total value of the investment plus interest increase to $ 64,000 ?
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24
Rationale: "32,000 = 8,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 64,000 = 8,000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."
Answer: a
Question (general): the average age of 10 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 99 , d ) 38 , e ) 32
Rationale: "total age increased = ( 10 * 2 ) years = 20 years . sum of ages of two new men = ( 21 + 23 + 20 ) years = 64 years average age of two new men = ( 64 / 2 ) years = 32 years . answer : e"
Answer: e
Question (general): if 64 ( 8 ^ x ) = 1 then x =
Options: a ) 2 , b ) – 1 , c ) 0 , d ) 1 , e ) - 2
Rationale: "8 ^ x = 1 / 64 8 ^ x = 1 / 8 ^ 2 8 ^ x = 8 ^ - 2 x = - 2 e"
Answer: e
Question (geometry): a rectangle having length 105 cm and width 40 cm . if the length of the rectangle is increased by twenty five percent then how much percent the breadth should be decreased so as to maintain the same area .
Options: a ) 25 % , b ) 19.23 % , c ) 40 % , d ) 75 % , e ) none of these
Rationale: "explanation : solution : ( 25 / ( 105 + 25 ) * 100 ) % = 19.23 % answer : b"
Answer: b
Question (geometry): a tailor trims 6 feet from opposite edges of a square piece of cloth , and 5 feet from the other two edges . if 80 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 32
Rationale: "let the original side of the square be x . ( x - 12 ) * ( x - 10 ) = 80 = 8 * 10 x = 20 the answer is c ."
Answer: c
Question (geometry): the base and height of a parallelogram are 12 m and 6 m respectively . then its area is = = = = = = ?
Options: a ) 27 sq . m
b ) 126 sq . m
c ) 84 sq . m
d ) 18 sq . m
e ) 72 sq . m
Rationale: a = b * h = > a = 12 * 6 = 72 sq . m . answer : ( e )
Answer: e
Question (general): how many prime numbers are between 76 / 8 and 124 / 5 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "76 / 8 = 38 / 4 = 19 / 2 = 10 - 124 / 5 = 25 - prime numbers between 10 and 29 are 11 , 13 , 17 , 19 , and 23 - sign signifies that the number is marginally less . answer e"
Answer: e
Question (general): evaluate : 40 - 12 * 3 * 2 = ?
Options: a ) 62 , b ) 52 , c ) 32 , d ) 12 , e ) 22
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 40 - 12 * 3 * 2 = 40 - 8 = 32 correct answer c"
Answer: c
Question (physics): pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 96 , d ) 27 , e ) 21
Rationale: "let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c"
Answer: c
Question (gain): what is the compound interest on rs : 40,000 for 4 months at the rate of 5 % per annum
Options: a ) 670.85 , b ) 671.85 , c ) 672.85 , d ) 673.85 , e ) 674.85
Rationale: "it is monthly compound rate = 5 / 12 % per month 40000 * ( 1 + 5 / 1200 ) ^ 4 - 40000 = 670.85 answer : a"
Answer: a
Question (general): mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 6 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "if n = 7 mark sold 1 box and ann sold 5 boxes total 6 < 7 answer : e"
Answer: e
Question (general): the number of diagonals of a polygon of n sides is given by the formula q = n ( n - 3 ) / 2 . if a polygon has twice as many diagonals as sides , how many sides does it have ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "q = n ( n - 3 ) q = 2 * n 2 n = n ( n - 3 ) = > 2 = n - 3 = > n = 5 answer b"
Answer: b
Question (gain): a fair price shopkeeper takes 10 % profit on his goods . he lost 70 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 32 % , d ) 67 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 30 . s . p . of each item = rs . 1.10 total sale = 1.10 * 30 = rs . 33 hence , loss % = 67 / 100 * 100 = 67 % answer : d"
Answer: d
Question (general): the age of somu is one - third his father ' s . 8 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 16 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 8 = 3 x - 8 / 5 = x = 16 answer : option d"
Answer: d
Question (physics): 13 buckets of water fill a tank when the capacity of each bucket is 42 litres . how many buckets will be needed to fill the same tank , if the capacity of each bucket is 6 litres ?
Options: a ) 91 , b ) 80 , c ) 96 , d ) 98 , e ) 90
Rationale: "capacity of the tank = ( 13 ã — 42 ) litre number of buckets required of capacity of each bucket is 17 litre = 13 ã — 42 / 6 = 13 ã — 7 = 91 answer is a"
Answer: a
Question (general): a car ferry can hold up to 70 tons of cargo . what is the greatest number of vehicles that the ferry can carry if half the vehicles are cars with an average ( arithmetic mean ) weight of 0.75 tons and half of the vehicles are trucks with an average ( arithmetic mean ) weight of 4 tons ?
Options: a ) 14 , b ) 20 , c ) 28 , d ) 32 , e ) 36
Rationale: "the weight of one car and one truck is 4.75 tons . 70 / 4.75 = 14 plus a remainder the ferry could carry 14 cars and 14 trucks for a total of 28 vehicles . the answer is c ."
Answer: c
Question (physics): two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 22 seconds . the ratio of their speeds is ?
Options: a ) 3 / 1 , b ) 3 / 1 , c ) 1 / 1 , d ) 3 / 5 , e ) 5 / 2
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 27 x meters , and length of the second train = 17 y meters . ( 27 x + 17 y ) / ( x + y ) = 22 = = > 27 x + 17 y = 22 x + 22 y = = > 5 x = 5 y = = > x / y = 1 / 1 . answer : c"
Answer: c
Question (general): exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 9 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 27 , b ) 35 , c ) 39 , d ) 60 , e ) 65
Rationale: "the total number of the people in the room must be a multiple of both 7 and 9 ( in order 3 / 7 and 5 / 9 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 9 , which is 63 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 91 people in the room . therefore there are 3 / 7 * 63 = 27 people in the room under the age of 21 . answer : a ."
Answer: a
Question (general): 4 , 12 , 48 , 240 , 1440 , 10080 , ( . . . )
Options: a ) 80640 , b ) 10080 , c ) 6200 , d ) 10020 , e ) 12500
Rationale: "explanation : go on multiplying the given numbers by 3 , 4 , 5 , 6 , 7,8 answer : option a"
Answer: a
Question (general): the product of two successive numbers is 7832 . which is the smaller of the two numbers ?
Options: a ) 78 , b ) 68 , c ) 88 , d ) 97 , e ) 37
Rationale: "c 88 from the given alternatives , 88 × 89 = 7832 ∴ smaller number = 88"
Answer: c
Question (general): the value of 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 is
Options: a ) 80 , b ) 800 , c ) 8000 , d ) 80000 , e ) none of these
Rationale: "solution therefore = 3.6 x 0.48 x 2.50 / 0.12 x 0.09 x 0.5 = 36 x 48 x 250 / 12 x 9 x 5 = 800 answer b"
Answer: b
Question (physics): two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 30 hr . if all pipes are opened simultaneously , then the cistern will be filled in
Options: a ) 6.67 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
Rationale: "solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 − 1 / 30 = 3 / 20 hence , tank will be filled in 20 / 3 = 6.67 hour option ( a )"
Answer: a
Question (general): if 1 / 8 of a pencil is black 1 / 2 of the remaining is white and the remaining 7 / 2 is blue find the total length of the pencil ?
Options: a ) 7.33 cm , b ) 6.33 cm , c ) 5.33 cm , d ) 9.33 cm , e ) 8.33 cm
Rationale: ( 1 / 8 ) p + ( 1 / 2 ) p + ( 7 / 2 ) = p on solving the above for p we get 9.333 now checking for the answer : 9.333 / 8 = 1.166 cm 9.333 / 2 = 4.665 cm now 1.166 + 4.665 + ( 7 / 2 ) = 9.33 cm answer : d
Answer: d
Question (general): the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 42 degrees . find the temperature on friday ?
Options: a ) 34 , b ) 55 , c ) 66 , d ) 81 , e ) 21
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 42 tu + w + th = 192 - 42 = 150 f = 184 – 150 = 34 . answer : a"
Answer: a
Question (general): a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 17.7 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 2.10 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.10 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.1 + $ 15.6 = $ 17.7 . answer : c ."
Answer: c
Question (physics): two cyclist start from the same places in opposite directions . one is going towards north at 30 kmph and the other is going towards south 40 kmph . what time will they take to be 50 km apart ?
Options: a ) 1.32 hr , b ) 0.714 hrs , c ) 3.231 hrs , d ) 0.515 hrs , e ) 6.214 hrs
Rationale: "to be ( 30 + 40 ) km apart , they take 1 hour to be 50 km apart , they take 1 / 70 * 50 = 0.714 hrs answer is b"
Answer: b
Question (general): in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 25 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 20 , e ) 40
Rationale: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 25 ^ 2 16 x ^ 2 + 9 x ^ 2 = 625 25 x ^ 2 = 625 x ^ 2 = 25 x = 5 therefore ab = 5 * 4 = 20 answer : d"
Answer: d
Question (general): the average of 5 consecutive odd numbers a , b , c , d and e is 13 . what percent of b is c ?
Options: a ) 98.2 , b ) 102.8 , c ) 108.2 , d ) 118.2 , e ) 122.8
Rationale: explanation : in such a case the middle number ( c ) is the average ∴ c = 13 and b = 11 required percentage = 13 / 11 x 100 = 118.2 answer : option d
Answer: d
Question (general): a palindrome is a number that reads the same forward and backward , such as 343 . how many odd , 8 - digit numbers are palindromes ?
Options: a ) 4000 , b ) 4500 , c ) 5055 , d ) 5000 , e ) 2500
Rationale: "first recognize you only need to consider the first four digits ( because the second four are just the first four flipped ) there are 9000 possibilities for the first four digits of a 8 digit number , 1000 - 9999 inclusive . everything starting with a 1 , 3,5 , 7,9 will be odd , which is 5 / 9 ths of the combinations . 5 / 9 * 9000 = 5000 answer : d"
Answer: d
Question (gain): a person borrows rs . 7000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 6 p . a for 2 years . find his gain in the transaction per year .
Options: a ) 100 rs , b ) 150 rs , c ) 140 rs , d ) 180 rs , e ) 200 rs
Rationale: "gain in 2 years = [ ( 7000 * 6 * 2 ) / 100 ] - [ ( 7000 * 4 * 2 ) / 100 ] 840 - 560 = 280 gain in 1 year = ( 280 / 2 ) = 140 rs answer : c"
Answer: c
Question (gain): two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 240 marks in the second test and failed by 57 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 264 , e ) 224
Rationale: "let the maximum mark in each test be m . the candidate failed by 57 marks in the second test . pass mark in the second test = 240 + 57 = 297 45 / 100 m = 297 pass mark in the first test = 40 / 100 m = 40 / 45 * 297 = 264 . answer : d"
Answer: d
Question (geometry): if the side of the regular hexagon above is 2 , what is the circumference of the inscribed circle ?
Options: a ) 2 ∏ √ 3
b ) 3 ∏
c ) 4 ∏ / √ 3
d ) 2 ∏ / √ 3
e ) ∏ √ 3
Rationale: now ac will be 1 because circle is touching the midpoints of the circle . then we get kite acbo . we have ac = 1 and cb = 1 , now we need to find bo which is radius from triplets we get 30 : 60 : 90 = 1 : √ 3 : 2 now cbo is right angled triangle , then we get bo as √ 3 . r = √ 3 . . . circumference is 2 ∏ r is 2 ∏ √ 3 . answer : option a .
Answer: a
Question (general): what is the difference between the local value of 1 and 2 in the number 2124 ?
Options: a ) 70 , b ) 75 , c ) 20 , d ) 80 , e ) 60
Rationale: explanation : 100 â € “ 20 = 80 answer : d
Answer: d
Question (general): in 10 years , a will be twice as old as b was 10 years ago . if a is now 7 years older than b the present age of b is
Options: a ) 37 , b ) 38 , c ) 39 , d ) 40 , e ) 41
Rationale: "let present age of a be a and b be b a + 10 = 2 * ( b - 10 ) = > 2 b - a = 30 . . . . . . ( i ) a = b + 7 = > 2 b - b - 7 = 30 b = 37 so the present age of b is 37 years answer : a"
Answer: a
Question (other): the ratio of the present age of sandy to that of molly is 9 : 2 . eight years from now , the ratio of the ages of sandy to molly will be 5 : 2 . what was sandy ' s age 6 years ago ?
Options: a ) 18 , b ) 21 , c ) 24 , d ) 27 , e ) 30
Rationale: "let the present age of sandy be 9 x years and that of molly be 2 x years . ( 9 x + 8 ) / ( 2 x + 8 ) = 5 / 2 8 x = 24 x = 3 six years ago , sandy ' s age was 9 ( 3 ) - 6 = 21 the answer is b ."
Answer: b
Question (general): rebecca ' s annual income is $ 15 , and jimmy ' s annual income is $ 18 . by how much must rebecca ' s annual income increase so that it constitutes 50 % of rebecca and jimmy ' s combined income ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 10
Rationale: "total rebecca = x + 15 ; total = x + 20 + 18 x + 15 / x + 33 = 50 / 100 therefore x = 3 d"
Answer: d
Question (geometry): you buy a piece of land with an area of â ˆ š 1600 , how long is one side of the land plot ?
Options: a ) 28 , b ) 40 , c ) 30 , d ) 31 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 900 . answer b"
Answer: b
Question (physics): a can do a work in 15 days b in 14 days and c in 16 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 3360 / 210 , b ) 3360 / 21 , c ) 3360 / 674 , d ) 3360 / 240 , e ) 3360 / 224
Rationale: person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 15 ) ( 14 ) ( 16 ) rate - ( 224 ) ( 240 ) ( 210 ) ( 674 ) work - ( 3360 ) ( 3360 ) ( 3360 ) ( 3360 ) therefore a + b + c requires ( 3360 / 674 ) days to complete entire work = 3360 / 674 answer is c
Answer: c
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 10 meters and a circumference of 9 meters , and the interior of tank b has a height of 9 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 75 % , b ) 90 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "the radius of tank a is 9 / ( 2 * pi ) . the capacity of tank a is 10 * pi * 81 / ( 4 * pi ^ 2 ) = 405 / ( 2 * pi ) the radius of tank b is 10 / ( 2 * pi ) . the capacity of tank b is 9 * pi * 100 / ( 4 * pi ^ 2 ) = 450 / ( 2 * pi ) tank a / tank b = 405 / 450 = 9 / 10 = 90 % the answer is b ."
Answer: b
Question (general): what is the smallest positive integer x such that 66 - x is the cube of a positive integer
Options: a ) 5 , b ) 7 , c ) 47 , d ) 9 , e ) 2
Rationale: "given 66 - x is a perfect cube so we will take 64 = 4 * 4 * 4 66 - x = 64 x = 66 - 64 = 2 correct option is e"
Answer: e
Question (physics): a cistern can be filled by a tap in 6 hours while it can be emptied by another tap in 12 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 5.2 hrs , b ) 2.9 hrs , c ) 12 hrs , d ) 7.2 hrs , e ) 1.4 hrs
Rationale: "net part filled in 1 hour = ( 1 / 6 - 1 / 12 ) = 1 / 12 the cistern will be filled in 12 / 1 hrs i . e . , 12 hrs . answer : c"
Answer: c
Question (gain): seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 40 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 100 % , b ) 33.33 % , c ) 40 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 40 % 0.4 x + ( m - x ) 0.25 = 0.4 m 0.15 x = 0.15 m x = 1 m x = 100 % of m a"
Answer: a
Question (general): a survey of n people in the town of eros found that 50 % of them preferred brand a . another survey of 125 people in the town of angie found that 60 % preferred brand a . in total , 55 % of all the people surveyed together preferred brand a . what is the total number of people surveyed ?
Options: a ) 50 , b ) 100 , c ) 150 , d ) 200 , e ) 250
Rationale: it is simply a weighted average question . since the given average of 50 % and 60 % is 55 % ( right in the middle ) , it means the number of people surveyed in eros ( n ) is same as the number of people surveyed in angie . so n = 125 total = 125 + 125 = 250 answer ( e )
Answer: e
Question (general): the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if y 12 = 110 , what is the value of y ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: ab = ( a - 1 ) ( b - 1 ) y 12 = ( y - 1 ) ( 12 - 1 ) = 110 - - > y - 1 = 10 - - > y = 11 answer : a
Answer: a
Question (gain): each month a retailer sells 100 identical items . on each item he makes a profit of $ 60 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 60 sell price = $ 600 + $ 60 thus , the sell price is $ 660 for each item . selling all 100 items gives the retailer . . . 100 ( $ 60 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 660 ) = $ 33 discount $ 627 = $ 600 + $ 27 now , the retailer makes a profit of just $ 27 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 27 ( x ) = $ 2,000 x = 2,000 / 27 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Question (physics): a and b go around a circular track of length 200 m on a cycle at speeds of 36 kmph and 72 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 198 sec , c ) 178 sec , d ) 20 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 200 / ( 36 * 5 / 18 ) , 200 / ( 72 * 5 / 18 ) } = lcm ( 20 , 10 ) = 20 sec . answer : d"
Answer: d
Question (other): if x and y are both odd prime numbers and x < y , how many distinct positive r integer factors does 2 xy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 xy prime r factors are x ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer .
Answer: d
Question (physics): a man can row 8 kmph in still water . when the river is running at 3 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.75 , b ) 5.7 , c ) 5.76 , d ) 5.74 , e ) 6.8
Rationale: "m = 8 s = 3 ds = 11 us = 5 x / 11 + x / 5 = 1 x = 3.4 d = 3.4 * 2 = 6.8 answer : e"
Answer: e
Question (physics): the length of a train and that of a platform are equal . if with a speed of 36 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 752 , b ) 799 , c ) 300 , d ) 750 , e ) 712
Rationale: "speed = [ 36 * 5 / 18 ] m / sec = 10 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 10 ã ¨ x = 10 * 60 / 2 = 300 answer : c"
Answer: c
Question (general): the overall age of x and y is 19 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 15 , c ) 12 , d ) 19 , e ) 20
Rationale: "d 19 ( x + y ) â € “ ( y + z ) = 19 x â € “ z = 19"
Answer: d
Question (general): for all real numbers v , an operation is defined by the equation v * = v - v / 3 . if ( v * ) * = 16 , then v =
Options: a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42
Rationale: "( v * ) * = ( v - v / 3 ) - ( v - v / 3 ) / 3 16 = 2 v / 3 - 2 v / 9 = 4 v / 9 v = 36 the answer is c ."
Answer: c
Question (geometry): find the perimeter and area of the rectangle of length 11 cm and breadth 9 cm .
Options: a ) 71 cm 2 , b ) 99 cm 2 , c ) 141 cm 2 , d ) 171 cm 2 , e ) 221 cm 2
Rationale: "length = 11 cm , breadth = 9 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 11 + 9 ) cm = 2 × 20 cm = 40 cm we know that the area of rectangle = length × breadth = ( 11 × 9 ) cm 22 = 99 cm 2 answer : b"
Answer: b
Question (physics): a group of men decided to do a work in 55 days , but 15 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 180 , b ) 150 , c ) 140 , d ) 100 , e ) 25
Rationale: "original number of men = 15 * 60 / ( 60 - 55 ) = 180 answer is a"
Answer: a
Question (physics): two trains are moving in the same direction at 108 kmph and 54 kmph . the faster train crosses a man in the slower train in 24 seconds . find the length of the faster train ?
Options: a ) 320 , b ) 330 , c ) 340 , d ) 350 , e ) 360
Rationale: "relative speed = ( 108 - 54 ) * 5 / 18 = 3 * 5 = 15 mps . distance covered in 27 sec = 24 * 15 = 360 m . the length of the faster train = 360 m . answer : e"
Answer: e