Cheukting/mathqa huggingface dataset:
Question (physics): two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.10 km and 0.4 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
Options: a ) 65 sec , b ) 36 sec , c ) 48 sec , d ) 33 sec , e ) 12 sec
Rationale: "relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.10 + 0.4 = 1.5 km = 1500 m . required time = 1500 * 3 / 125 = 36 sec . answer : b"
Answer: b
Question (general): how much time does a train 225 metres long running at 90 km / hr take to pass a pole ?
Options: a ) 7.9 s , b ) 2.5 s , c ) 7.5 s , d ) 9 s , e ) 7.4 s
Rationale: "explanation : 90 km / hr = 90 * 5 / 18 = 25 m / s speed = distance / time ; v = d / t 25 = 225 / t t = 9 s answer : d"
Answer: d
Question (general): of the goose eggs laid at a certain pond , 1 / 3 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1000 , b ) 1200 , c ) 1400 , d ) 1600 , e ) 1800
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 3 ) x = 120 ( 6 / 60 ) x = 120 x = 1200 the answer is b ."
Answer: b
Question (general): the price of lunch for 20 people was $ 300 including a 20 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12.5 , c ) 13.8 , d ) 14 , e ) 15.87
Rationale: "clearly b is the answer i used poe here lets consider option ( b ) 20 * 12.5 = 250 now 250 ( 120 / 100 ) = 300 = > possible answer imo b"
Answer: b
Question (geometry): the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 28 - inch flat - screen television than a square 25 - inch flat - screen television ?
Options: a ) 79.5
b ) 89.3
c ) 85.5
d ) 75.4
e ) 72.5
Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 28 - inch flat - screen television the diagonal ( hypotenuse ) = 28 so , we can apply the pythagorean theorem to get x ² + x ² = 28 ² simplify : 2 x ² = 28 ² divide both sides by 2 to get : x ² = 28 ² / 2 since the area of the square = x ² , we can see that the area of this square is 28 ² / 2 square 25 - inch flat - screen television the diagonal ( hypotenuse ) = 25 so , we can apply the pythagorean theorem to get x ² + x ² = 25 ² simplify : 2 x ² = 25 ² divide both sides by 2 to get : x ² = 25 ² / 2 since the area of the square = x ² , we can see that the area of this square is 25 ² / 2 difference in areas = 28 ² / 2 - 25 ² / 2 = ( 28 ² - 25 ² ) / 2 = ( 784 - 625 ) / 2 = 159 / 2 = 79.5 a
Answer: a
Question (physics): the sector of a circle has radius of 14 cm and central angle 144 o . find its perimeter ?
Options: a ) 60 cm , b ) 63.2 cm , c ) 70 cm , d ) 80 cm , e ) 90 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 35.2 + 28 = 63.2 cm answer : b"
Answer: b
Question (general): a number is doubled and 4 is added . if the resultant is divided by 5 , it becomes 25 . what is that number ?
Options: a ) 73.5 , b ) 68 , c ) 60.5 , d ) none of these , e ) can not be determined
Rationale: "solution let the number be x . then , ( 2 x + 4 ) / 5 ‹ = › 25 ‹ = › 2 x + 4 = 125 ‹ = › 2 x = 121 x = 60.5 answer c"
Answer: c
Question (general): chris mixed 4 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 4 lbs of raisin = $ 4 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 4 = 16 fraction of the value of raisin = 4 / 16 = 1 / 4 ans : c"
Answer: c
Question (general): how many 3 digit numbers are divisible by 6 in all ?
Options: a ) 149 , b ) 150 , c ) 151 , d ) 166 , e ) 172
Rationale: "explanation : required numbers are 102 , 108 , 114 , . . . , 996 this is an a . p . in which a = 102 , d = 6 and l = 996 let the number of terms be n . then , a + ( n - 1 ) d = 996 102 + ( n - 1 ) x 6 = 996 6 x ( n - 1 ) = 894 ( n - 1 ) = 149 n = 150 . answer is b"
Answer: b
Question (general): 1907 x 1907 = ?
Options: a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3636649 , e ) e ) 3625216
Rationale: "1907 x 1907 = ( 1907 ) 2 = ( 1900 + 7 ) 2 = ( 1900 ) 2 + ( 7 ) 2 + ( 2 x 1900 x 7 ) = 3610000 + 49 + 26600 . = 3636649 . d )"
Answer: d
Question (general): an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of c ?
Options: a ) 720 , b ) 360 , c ) 250 , d ) 280 , e ) 290
Rationale: "let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of c = 3 / 13 * 3120 = rs . 720 answer : a"
Answer: a
Question (gain): a certain company ’ s profit in 1996 was 10 percent greater than its profit in 1995 , and its profit in 1997 was 20 percent greater than its profit in 1996 . the company ’ s profit in 1997 was what percent greater than its profit in 1995 ?
Options: a ) 5 % , b ) 18 % , c ) 32 % , d ) 35 % , e ) 38 %
Rationale: profit in 1995 - 100 profit in 1996 - 110 % increae profit in 1997 in comparison to 1995 = 10 + 110 * 20 % = 32 correct option : c
Answer: c
Question (general): if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 11 .
Options: a ) 8 , b ) 5 , c ) 1 , d ) 3 , e ) 4
Rationale: "6 * 15 * 11 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 11 + 1 ) = ( √ 8 * 18 ) / 12 = ( √ 144 ) / 12 = 12 / 124 = 1 . answer is c"
Answer: c
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 8 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 1700
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 8 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 2400 . hence , ( r - p ) = ( 2400 - 900 ) = 1500 answer : b"
Answer: b
Question (general): in a caravan , in addition to 50 hens , there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads in the caravan , the number of keepers is
Options: a ) 5 , b ) 8 , c ) 10 , d ) 15 , e ) 20
Rationale: explanation : let number of keepers be x . then , total number of feet = 2 x 50 + 4 x 45 + 4 x 8 + 2 x = 2 x + 312 . total number of heads = 50 + 45 + 8 + x = 103 + x . therefore ( 2 x + 312 ) = ( 103 + x ) + 224 or x = 15 . answer : d
Answer: d
Question (physics): a 1500 m long train crosses a tree in 120 sec , how much time will it take to pass a platform 500 m long ?
Options: a ) 288 , b ) 160 , c ) 188 , d ) 188 , e ) 12
Rationale: "l = s * t s = 1500 / 120 s = 12.5 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 12.5 t = 160 sec answer : b"
Answer: b
Question (general): n is a positive integer . when n + 1 is divided by 6 , the remainder is 4 . what is the remainder when n is divided by 2 ?
Options: a ) 6 , b ) 5 , c ) 1 , d ) 3 , e ) 2
Rationale: n + 1 = 6 a + 4 i . e . n + 1 = 10 , 16 , 22 , 28 , . . . etc . i . e . n = 9 , 15 , 21 , 27 , . . . etc . when n is divided by 2 remainder is always 1 answer : c
Answer: c
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 2999 , b ) 1350 , c ) 2677 , d ) 2898 , e ) 2787
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 2 = rs . 1350 answerb"
Answer: b
Question (general): if 9 / ( 5 + 3 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 3 / 4 , d ) - 1 / 3 , e ) - 3
Rationale: the expression 9 / ( 5 + 3 / x ) = 1 should have been equal to something . if 9 / ( 5 + 3 / x ) = 1 = > 9 x / ( 5 x + 3 ) = 1 = > 9 x = 5 x + 3 = > 4 x = 3 = > x = 3 / 4 correct option : c
Answer: c
Question (gain): if price of t . v set is reduced by 25 % , then its sale increases by 75 % , find net effect on sale value
Options: a ) 31 , b ) 32 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 25 + 75 + ( - 25 * 75 ) / 100 = - 25 + 75 - 19 = 31 answer : a"
Answer: a
Question (general): 25 , 50 , 100 , 175 , 275 , ( . . . . )
Options: a ) 400 , b ) 300 , c ) 425 , d ) 450 , e ) 325
Rationale: "explanation : the pattern is 25 , 50 , 75 , 100 , etc . hence 125 = 400 answer : a"
Answer: a
Question (physics): 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 9 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 19 , d ) 29 , e ) 39
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 9 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 9 * ( 2 / 3 ) ) days = > 20 days answer : b"
Answer: b
Question (physics): kathleen can paint a room in 3 hours , and anthony can paint an identical room in 4 hours . how many hours would it take kathleen and anthony to paint both rooms if they work together at their respective rates ?
Options: a ) 8 / 15 , b ) 4 / 3 , c ) 15 / 8 , d ) 24 / 7 , e ) 15 / 4
Rationale: "( 1 / 3 + 1 / 4 ) t = 2 t = 24 / 7 answer : d"
Answer: d
Question (general): how many prime numbers are between 25 / 8 and 213 / 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "25 / 8 = 4 - 213 / 6 = 36 - prime numbers between 4 and 36 are 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , and 31 - sign signifies that the number is marginally less . answer d"
Answer: d
Question (general): on the number line , the number p is twice as many units from - 2 as - 2 is from 4 . if p is less than – 2 , what is the value of p ?
Options: a ) – 14 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
Rationale: "distance between - 2 and 4 = 6 since number p is twice as many units from - 2 as - 2 is from 4 , therefore p can be - 14 since , p is less than - 2 , the value of p = - 14 answer a"
Answer: a
Question (other): two vessels having volumes in the ratio 3 : 5 are filled with water and milk solutions . the ratio of milk and water in the two vessels are 1 : 2 and 3 : 1 respectively . if the contents of both the vessel are empties into a larger vessel , find the ratio of milk and water in the larger vessel .
Options: a ) 18 : 13 , b ) 16 : 13 , c ) 19 : 13 , d ) 14 : 11 , e ) 13 : 11
Rationale: "vessel a = 300 gallons - - > milk = 100 , water = 200 ; vessel b = 500 gallons - - > milk = 375 , water = 125 ; vessel a + b = 800 gallons - - > milk = 475 , water 325 . the ratio = 475 / 325 - - > 19 / 13 answer : c"
Answer: c
Question (physics): a bus travels first half distance between two places with a speed of 40 kmph and the rest half distance with a speed of 60 kmph . the average speed of the bus is ?
Options: a ) 48 kmph , b ) 78 kmph , c ) 28 kmph , d ) 18 kmph , e ) 98 kmph
Rationale: explanation : we know that speed = distance traveled / time taken let the total distance traveled by the car is 2 x km . then time taken by it to cover first half is hour . and for second half is hour . then average speed = total distance travelled / total time taken . i . e . = > = 48 kmph . answer : a
Answer: a
Question (general): in a hostel there were 100 students . to accommodate 20 more students the average is decreased by rupees 5 . but total expenditure increased by rs . 400 . find the total expenditure of the hostel now ?
Options: a ) 54888 , b ) 2777 , c ) 5400 , d ) 1278 , e ) 2881
Rationale: "100 x + 400 = 12 ( x – 5 ) x = 50 100 * 50 + 400 = 5400 answer : c"
Answer: c
Question (other): the ratio between the number of passengers travelling by i and ii class between the two railway stations is 1 : 50 , whereas the ratio of i and ii class fares between the same stations is 3 : 1 . if on a particular day rs . 1,325 were collected from the passengers travelling between these stations , then what was the amount collected from the ii class passengers ?
Options: a ) rs . 750 , b ) rs . 1000 , c ) rs . 850 , d ) rs . 1250 , e ) none of these
Rationale: let x be the number of passengers and y be the fare taken from passengers . 3 xy + 50 xy = 1325 = > xy = 25 amount collected from ii class passengers = 25 × 50 = rs . 1250 . answer : d
Answer: d
Question (general): a , b , c subscribe rs . 50,000 for a business . if a subscribes rs . 4000 more than b and b rs . 5000 more than c , out of a total profit of rs . 38,000 , what will be the amount a receives ?
Options: a ) 14700 , b ) 15960 , c ) 14900 , d ) 14300 , e ) 14000
Rationale: "total amount invested = 50000 assume that investment of c = x . then investment of b = 5000 + x , investment of a = 4000 + 5000 + x = 9000 + x x + 5000 + x + 9000 + x = 50000 ⇒ 3 x + 14000 = 50000 ⇒ 3 x = 50000 – 14000 = 36000 ⇒ x = 36000 / 3 = 12000 investment of c = x = 12000 investment of b = 5000 + x = 17000 investment of a = 9000 + x = 21000 ratio of the investment of a , b and c = 21000 : 17000 : 12000 = 21 : 17 : 12 share of a = total profit × 21 / 50 = 38000 × 21 / 50 = 15960 answer is b"
Answer: b
Question (general): ( ( - 1.9 ) ( 0.6 ) – ( 2.6 ) ( 1.2 ) ) / 4.0 = ?
Options: a ) 1.07 , b ) 1.0 , c ) - 1.065 , d ) 1.71 , e ) 2.71
Rationale: "dove straight into calculation but quickly realized that the sum of two negatives is a negative so there is only one option . - 1.065 answer c"
Answer: c
Question (general): if â € œ * â €  is called â € œ + â €  , â € œ / â €  is called â € œ * â €  , â € œ - â €  is called â € œ / â €  , â € œ + â €  is called â € œ - â €  . 120 / 40 â € “ 30 * 20 - 5 = ?
Options: a ) 178.5 , b ) 156.6 , c ) 160.4 , d ) 163.6 , e ) 164.1
Rationale: "explanation : given : 120 / 40 â € “ 30 * 20 - 5 = ? substituting the coded symbols for mathematical operations , we get , 120 * 40 / 30 + 20 / 5 = ? 120 * 1.33 + 4 = ? 159.6 + 4 = 163.6 answer : d"
Answer: d
Question (geometry): the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle . the shorter side of the triangle is 7 centimeters less than the longer side . find the length of the hypotenuse .
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21
Rationale: let a and b be the two sides of the triangle such that a is longer than b . the statement ` ` the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle ' ' may be fomulated by h = a + 2 or a = h - 2 the statement ` ` the shorter side of the triangle is 7 centimeters less than the longer side ' ' may be formulated . b = a - 7 or b = ( h - 2 ) - 7 = h - 9 we now use pythagora ' s theorem to write a third equation h 2 = a 2 + b 2 substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only . h 2 = ( h - 2 ) 2 + ( h - 9 ) 2 simplify and rewrite the above equation in standard form . h 2 - 22 h + 85 = 0 solve for h . h = 5 and h = 17 . only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle . answer a
Answer: a
Question (physics): how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 145 m length ?
Options: a ) 13.9 sec , b ) 12.1 sec , c ) 17.9 sec , d ) 13.9 sec , e ) 47.98 sec
Rationale: "speed = 70 * 5 / 18 = 19 m / sec total distance covered = 120 + 145 = 265 m . required time = 265 / 19 = 13.9 sec . answer : d"
Answer: d
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 650 , what is the least possible value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "650 = 2 * 5 * 5 * 13 so the least value forncan be 13 . d"
Answer: d
Question (geometry): a rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered . if the area of the field is 600 sq . ft , how many feet of fencing will be required ?
Options: a ) 70 feet , b ) 52 feet , c ) 32 feet , d ) 12 feet , e ) 55 feet
Rationale: "explanation : we are given with length and area , so we can find the breadth . as length * breadth = area = > 30 * breadth = 600 = > breadth = 20 feet area to be fenced = 2 b + l = 2 * 20 + 30 = 70 feet answer : option a"
Answer: a
Question (general): two employees x and y are paid a total of rs . 560 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 254 , b ) s . 284 , c ) s . 290 , d ) s . 304 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 560 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 560 ⇒ y [ 12 / 10 + 1 ] = 560 ⇒ 22 y / 10 = 560 ⇒ 22 y = 5600 ⇒ y = 5600 / 22 = rs . 254 ( approx ) a )"
Answer: a
Question (general): calculate the sum of first 28 natural numbers .
Options: a ) 426 , b ) 406 , c ) 401 , d ) 409 , e ) 405
Rationale: "solution we know that ( 1 + 2 + 3 + . . . . . + 28 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 28 ) = ( 28 × 29 / 2 ) = 406 . answer b"
Answer: b
Question (probability): when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 4 times , what is the probability that it will land on the same side each time ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 16 , d ) 1 / 2 , e ) 1 / 32
Rationale: "must be either 4 tails or 4 heads 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 1 / 16 + 1 / 16 = 1 / 8 answer : a"
Answer: a
Question (physics): trapezoid jklm in the x - y plane has coordinates j = ( – 2 , – 3 ) , k = ( – 2 , 1 ) , l = ( 6 , 7 ) , and m = ( 6 , – 3 ) . what is its perimeter ?
Options: a ) 32 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
Rationale: "jk = 4 lm = 10 kl = using distance formula 10 jm = using distance formula 8 sum of all is 32 a"
Answer: a
Question (gain): the c . p of 8 books is equal to the s . p of 16 books . find his gain % or loss % ?
Options: a ) 60 % , b ) 50 % , c ) 70 % , d ) 90 % , e ) 55 %
Rationale: "explanation : 8 cp = 16 sp 16 - - - 8 cp loss 100 - - - ? = > 50 % loss answer : b"
Answer: b
Question (general): a & b started a partnership business . a ' s investment was thrice the investment of b and the period of his investment was two times the period of investments of b . if b received rs 5000 as profit , what is their total profit ?
Options: a ) 28000 , b ) 30000 , c ) 32000 , d ) 35000 , e ) none of these
Rationale: "explanation : suppose b ' s investment = x . then a ' s investment = 3 x suppose bs period of investment = y , then a ' s period of investment = 2 y a : b = 3 x * 2 y : xy = 6 : 1 total profit * 1 / 7 = 5000 = > total profit = 5000 * 7 = 35000 . answer : option d"
Answer: d
Question (physics): a can do a work in 6 days , b can do a work in 8 days and c can do it in 12 days . b left work after 1 day . for how many number of days should a and c should work together to complete the remaining work ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 7
Rationale: b work 1 / 8 * 1 = 1 / 8 remaining work = 1 - 1 / 8 = 7 / 8 a and c work together = 1 / 6 + 1 / 12 = 3 / 12 = 1 / 4 take reciprocal 7 / 8 * remaining work = 8 / 7 * 1 / 4 = 2 / 7 answer : b
Answer: b
Question (other): the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 6 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 6 pounds of clothes doubles the ratio of books to clothes , then 6 pounds represents half the weight of the clothes . 2 k = 6 pounds and then k = 3 pounds . the electronics weigh 3 ( 3 ) = 9 pounds . the answer is e ."
Answer: e
Question (probability): a bag consists of 50 marbles , of which 5 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 3 / 4 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 9 / 10
Rationale: "bag consists of 50 marbles , of which 5 are blue , 9 are red remainder are white . so , white = 50 - 5 - 9 = 36 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 50 + 36 / 50 = 45 / 50 = 9 / 10 hence , answer will be e ."
Answer: e
Question (general): how many integers between 100 and 200 , inclusive , can not be evenly divided by 3 nor 5 ?
Options: a ) 46 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the total numbers between 100 and 200 , inclusive , is 101 . 3 * 34 = 102 and 3 * 66 = 198 so the number of multiples of 3 is 33 . 5 * 20 = 100 and 5 * 40 = 200 so the number of multiples of 5 is 21 . however , the multiples of 15 have been counted twice . 15 * 7 = 105 and 15 * 13 = 195 so the number of multiples of 15 is 7 . thus the total number is 101 - 33 - 21 + 7 = 54 . the answer is e ."
Answer: e
Question (general): for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 22 , the mean is how much greater than the median ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 7
Rationale: mean = ( x + x + 2 + x + 4 + x + 7 + x + 22 ) / 5 = ( 5 x + 35 ) / 5 = x + 7 median = x + 4 thus mean - median = x + 7 - ( x + 4 ) = 3 answer = d
Answer: d
Question (physics): pavan travelled for 11 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan ?
Options: a ) 398 km , b ) 892 km , c ) 387 km , d ) 300 km , e ) 230 km
Rationale: "let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 11 = > x / 60 + x / 50 = 11 = > ( 5 x + 6 x ) / 300 = 11 = > x = 300 km answer : d"
Answer: d
Question (general): 3 / 4 of 1 / 2 of 2 / 5 of 5100 = ?
Options: a ) 392 , b ) 229 , c ) 765 , d ) 493 , e ) 540
Rationale: "c 765 ? = 5100 * ( 2 / 5 ) * ( 1 / 2 ) * ( 3 / 4 ) = 765"
Answer: c
Question (gain): in order to obtain an income of rs . 900 from 20 % stock at rs . 102 , one must make an investment of
Options: a ) rs . 6000 , b ) rs . 4590 , c ) rs . 4560 , d ) rs . 4500 , e ) rs . 4570
Rationale: "explanation : market value = rs . 102 . required income = rs . 900 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 20 ( ie , 20 % of the face value 100 ) , investment = rs . 102 to obtain rs . 900 , investment = 102 / 20 ã — 900 = rs . 4590 answer : option b"
Answer: b
Question (general): what is the value of ( p + q ) / ( p - q ) if p / q is 10 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 11 / 9 , e ) 8 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 10 + 1 ) / ( 10 - 1 ) = 11 / 9 = 11 / 9 answer : d"
Answer: d