Cheukting/mathqa huggingface dataset:
Question (geometry): a rectangular tiled patio is composed of 30 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 30 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 30 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 30 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 30 ( 2 r - 4 ) * r = 30 2 r ^ 2 - 4 r - 30 = 0 r can not be negative so r = 5 and c = 6 so , answer will be a"
Answer: a
Question (general): a row of ants comprised of 102 ants . a man walked upon it and all except 42 were crushed beneath his foot . how many ants are left alive ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: solution : all except 42 were crushed means that all the ants except 42 were crushed beneath the man ' s foot . hence , 42 ants are alive now answer b
Answer: b
Question (general): at a certain food stand , the price of each apple is 40 ¢ and the price of each orange is 60 ¢ . mary selects a total of 10 apples and oranges from the food stand , and the average ( arithmetic mean ) price of the 10 pieces of fruit is 54 ¢ . how many oranges must mary put back so that the average price of the pieces of fruit that she keeps is 45 ¢ ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "if the average price is 54 , then mary has 7 oranges and 3 apples ( a ratio of 7 : 3 ) . for the average price to be 45 , the ratio should be 1 : 3 . mary must put back 6 oranges . the answer is e ."
Answer: e
Question (gain): what percent is 50 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2 % , e ) 5 %
Rationale: "1 kg = 1000 gm 50 / 1000 × 100 = 5000 / 1000 = 5 % e )"
Answer: e
Question (geometry): the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17
b ) 2 : 5
c ) 5 : 16
d ) 10 : 19
e ) 32 : 25
Rationale: answer : d .
Answer: d
Question (general): john purchased some shirts and trousers for $ 1300 . he paid $ 500 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "given that the total purchase of two items cost 1300 so the average purchase of one item will cost 1300 / 2 = 650 . its given as total shirt cost 500 $ less . hence total shirt cost = 650 - 250 and total trouser cost = 650 + 250 5 shirts = 400 $ = = > one shirt = 80 $ one trouser = 80 + 20 = 100 $ total trousers = 900 / 100 = 9 . e"
Answer: e
Question (physics): a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 75 men , b ) 80 men , c ) 70 men , d ) 60 men , e ) 50 men
Rationale: "in 120 days , only 240 m of the tunnel is constructed by 50 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 50 = 70 men . answer : c"
Answer: c
Question (general): for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?
Options: a ) 60 , b ) 116 , c ) 210 , d ) 263 , e ) 360
Rationale: since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e
Answer: e
Question (geometry): two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?
Options: a ) 16 - 4 pi
b ) 4 - pi
c ) 2 pi - 4
d ) 8 pi - 16
e ) pi ^ 2 - 4
Rationale: drawing a diagram , we see that the radius of the circle equals the side of the square . the area of intersection is : pi * r ^ 2 / 4 - ( r ^ 2 - pi * r ^ 2 / 4 ) = pi * r ^ 2 / 2 - r ^ 2 = 8 pi - 16 the answer is d .
Answer: d
Question (general): pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 500 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 35 % of x = 150 + 25 = > 35 / 100 x = 175 x = ( 17500 / 35 ) x = 500 . answer : d"
Answer: d
Question (probability): if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 11 / 12
Rationale: "each couple can send only one ` ` representative ' ' to the committee . we can choose 4 couples ( as there should be 4 members ) to send only one ` ` representatives ' ' to the committee in c 46 c 64 # of ways . but these 4 chosen couples can send two persons ( either husband or wife ) : 2 ∗ 2 ∗ 2 ∗ 2 = 242 ∗ 2 ∗ 2 ∗ 2 = 24 . so # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is : c 46 ∗ 24 c 64 ∗ 24 . total # of ways to choose 4 people out of 12 is c 412 c 124 . p = c 46 ∗ 24 c 412 = 1633 p = c 64 ∗ 24 c 124 = 1633 answer : d ."
Answer: d
Question (geometry): if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?
Options: a ) 4 % increase
b ) 6 % increase
c ) 5 % decrease
d ) 4 % decrease
e ) none of these
Rationale: percentage change = x - y - xy ⁄ 100 = 20 – 20 – 20 × 20 / 100 = − 4 % = 4 % decrease answer d
Answer: d
Question (gain): each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 75 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 6.7 % , b ) 10.3 % , c ) 14.5 % , d ) 18.2 % , e ) 23.6 %
Rationale: "let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.75 ( i + f ) 0.05 f = 0.35 i f = 7 i this means that for every 1 incandescent bulb , there are 7 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 7 i ) = 0.4 i / 6 i = 1 / 15 which is about 6.7 % . the answer is a ."
Answer: a
Question (physics): a and b can do a piece of work in 2 days and 6 days respectively . both work for 1 days and then a goes away . find how long will b take to complete the remaining work ?
Options: a ) 1 days , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 1 / 2 + ( 1 + x ) / 6 = 1 x = 2 days answer : b
Answer: b
Question (physics): karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many h miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him h : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Question (general): rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount .
Options: a ) rs . 300 , b ) rs . 400 , c ) rs . 480 , d ) rs . 490 , e ) rs . 500
Rationale: "p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b"
Answer: b
Question (other): in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 14.50 per kg to obtain a mixture costing rs . 9.75 per kg ?
Options: a ) 19 : 10 , b ) 19 : 11 , c ) 11 : 19 , d ) 12 : 18 , e ) 11 : 20
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 14.50 - 9.75 ) / ( 9.75 - 7 ) = 31 / 15 answer : b"
Answer: b
Question (general): if 10 is added to thrice a number and this sum is multiplied by 5 , the result is the same as if the number is multiplied by 5 and 13 is added to the product . what is the number ?
Options: a ) - 3.5 , b ) - 3.7 , c ) - 5 , d ) - 9 , e ) 11
Rationale: "let the number be x ; 5 ( 10 + 3 x ) = 5 x + 13 ; x = - 3.7 answer : b"
Answer: b
Question (general): if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is
Options: a ) 19 , b ) 20 , c ) 25 , d ) 30 , e ) 64
Rationale: by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 390 and ab + bc + ca = 5 , ( a + b + c ) ^ 2 = 390 + 2 ( 5 ) = 400 = 20 ^ 2 therefore : a + b + c = 20 answer : b
Answer: b
Question (gain): in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1500 employees , then the no . of female employees who are computer literate ?
Options: a ) 630 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1500 female employees , 60 % of 1500 . = ( 60 * 1500 ) / 100 = 900 . then male employees , = 600 50 % of male are computer literate , = 300 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1500 ) / 100 = 930 computer literate . thus , female computer literate = 930 - 300 = 630 answer : option a"
Answer: a
Question (general): what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28
Rationale: "x ^ n + 1 will be divisible by x + 1 only when n is odd 27 ^ 27 + 1 will be divisible by 27 + 1 ( 27 ^ 27 + 1 ) + 26 , when divided by 28 will give 26 as remainder answer is d"
Answer: d
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 18
Rationale: let number of hens = h number of cows = c number of heads = 48 ⇒ h + c = 48 ⋯ ( 1 ) number of feet = 140 ⇒ 2 h + 4 c = 140 ⇒ h + 2 c = 70 ⋯ ( 2 ) ( 2 ) − ( 1 ) gives 2 c − c = 70 − 48 ⇒ c = 22 substituting the value of c in ( 1 ) , we get h + 22 = 48 ⇒ h = 48 − 22 = 26 h + 22 = 48 ⇒ h = 48 − 22 = 26 i . e . , number of hens = 26 answer : c
Answer: c
Question (general): the cash realised on selling a 14 % stock is rs . 120.50 , brokerage being 1 / 4 % is
Options: a ) 120.25 , b ) 120.35 , c ) 106.5 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 120.50 - 0.25 ) = rs . 120.25 . answer : a"
Answer: a
Question (general): a and b are two partially filled buckets of water . if 7 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 7 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 ) 77 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 7 = 1 / 3 ( b + 7 ) - - - - > 3 a - 21 = b + 7 scenario 2 b - 7 = 1 / 2 ( a + 7 ) - - - - - > 2 b - 14 = a + 7 from scenario 1 , b = 3 a - 28 substitute b with this information in stmt 2 2 ( 3 a - 28 ) - 14 = a + 7 - - - - - - > 6 a - 56 - 14 = a + 7 - - - - - - > 6 a - a = 70 + 7 - - - > 5 a = 77 a = 77 / 5 , answer choice a"
Answer: a
Question (gain): how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 35
Rationale: "let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.05 ( 50 - x ) 0.05 x = 2.5 - 1 x = 1.5 / 0.05 = 30 liters the answer is c ."
Answer: c
Question (geometry): an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 50 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues . so we have 50,25 , 12.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 50 / 1 - ( 1 / 2 ) = 100 equilateral triangle perimeter is 3 a = 3 * 100 = 300 . so option e ."
Answer: e
Question (geometry): three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 36 square meters , c ) 40 square meters , d ) 83.3 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 40 = 80 sq m of the wallpaper overlaps in three layers . 80 sq m makes two extra layers hence the area over which it makes two extra layers is 40 sq m . answer ( c ) ."
Answer: c
Question (general): a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 4 x km .
Options: a ) 16 , b ) 18 , c ) 32 , d ) 19 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 4 x / ( x / 8 ) = 32 kmph answer : c"
Answer: c
Question (general): if n = 2.0254 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0046 , e ) 0.0153
Rationale: "n * = 2.03 n * - n = 2.03 - 2.0254 0.0046 answer : d"
Answer: d
Question (general): find the sum lend at c . i . at 5 p . c per annum will amount to rs . 240 in 2 years ?
Options: a ) 217 , b ) 287 , c ) 400 , d ) 288 , e ) 171
Rationale: "explanation : 240 = p ( 21 / 20 ) 2 p = 217 answer : a"
Answer: a
Question (other): a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 4 / 13 , b ) 6 / 13 , c ) 8 / 21 , d ) 11 / 21 , e ) 17 / 42
Rationale: "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 7 c 2 = 21 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 42 / 91 = 6 / 13 the answer is b ."
Answer: b
Question (gain): a vendor sells 60 percent of apples he had and throws away 15 percent of the remainder . next day he sells 50 percent of the remainder and throws away the rest . what percent of his apples does the vendor throw ?
Options: a ) 17 , b ) 23 , c ) 77 , d ) 26 , e ) 30
Rationale: explanation : let , the number of apples be 100 . on the first day he sells 60 % apples i . e . , 60 apples . remaining apples = 40 . he throws 15 % of the remaining i . e . , 15 % of 40 = 6 . now he has 40 − 6 = 34 apples the next day he throws 50 % of the remaining 34 apples i . e . , 17 . therefore , in total he throws 6 + 17 = 23 apples . answer : b
Answer: b
Question (geometry): the radius of a cylinder is 8 m , height 14 m . the volume of the cylinder is :
Options: a ) 2816 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 8 ã — 8 ã — 14 = 2816 m ( power 3 ) answer is a ."
Answer: a
Question (general): average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 880 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1600 , d ) 1100 , e ) 1200
Rationale: 0.2 x = 4 ( 880 - 800 ) 0.2 x = 320 x = 1600 answer c
Answer: c
Question (general): when a student joe , weighing 43 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 6.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 43 + 30 = 73 so , the average the two persons = 36.5 that gives the answer 43 - 36.5 = 6.5 answer d"
Answer: d
Question (physics): while working alone at their respective constant rates , server p uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ?
Options: a ) 2 hr , b ) 2 hr 20 min , c ) 2 hr 40 min , d ) 5 hr 40 min , e ) 6 hr
Rationale: server p processes 480 / 4 files per hour = 120 per hour server y processes 180 / 8 files per hour = 60 per hour total files processed per hour when p and y work together = 120 + 60 per hour = 180 files per hour 480 / 180 = 2 2 / 3 hours = c
Answer: c
Question (general): 0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = ?
Options: a ) 0.7 , b ) 0 , c ) 0.8 , d ) 8 , e ) 7
Rationale: "= 0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = 203 x 292 / 73 x 145 x 7 = 4 / 5 = 0.8 answer is c ."
Answer: c
Question (physics): the speed of a train is 90 kmph . what is the distance covered by it in 30 minutes ?
Options: a ) 15 , b ) 66 , c ) 77 , d ) 52 , e ) 45
Rationale: "90 * 30 / 60 = 45 kmph answer : e"
Answer: e
Question (general): what is the smallest positive integer x such that 280 - x is the cube of a positive integer
Options: a ) 5 , b ) 64 , c ) 62 , d ) 60 , e ) 12
Rationale: "given 280 - x is a perfect cube so we will take 216 = 6 * 6 * 6 280 - x = 216 x = 280 - 216 = 64 correct option is b"
Answer: b
Question (physics): in a kilometer race , a beats b by 60 meters or 15 seconds . what time does a take to complete the race ?
Options: a ) 221 , b ) 235 , c ) 245 , d ) 289 , e ) 260
Rationale: "time taken by b run 1000 meters = ( 1000 * 15 ) / 60 = 250 sec . time taken by a = 250 - 15 = 235 sec . answer : b"
Answer: b
Question (general): in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.3 , 9.0 , 6.0 , and 8.6 , what was the point value of the dive ?
Options: a ) 78.08 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 81.6
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.3 + 8.6 ) = 24 point of value of the dive = 24.4 * 3.2 = 78.08 answer a"
Answer: a
Question (physics): train starts from amritsar to bombay at 9 am . it reaches destination after 3 days at 9 : 30 am . every day a train starts . how many trains does it come across on the way ?
Options: a ) 5 th , b ) 4 th , c ) 6 th , d ) 7 th , e ) 8 th
Rationale: because one train taking 3 days so 1 train first day another at second day and 3 rd one at third day but as given train reaches at 9.30 am insted of 9 . oo am so d same day train already left that train will be 4 th train . answer : b
Answer: b
Question (general): if a ( a - 9 ) = 10 and b ( b - 9 ) = 10 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 10 or if a = 10 then b = - 1 but in each case a + b = - 1 + 10 = 9 answer : option d"
Answer: d
Question (general): there are 12 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 132
Rationale: "every team plays with 11 teams . . . so total no of matches = 12 x 11 = 132 . now , each match is played twice = > 132 x 2 but 2 teams play a match = > 132 x 2 / 2 = 132 . answer : e"
Answer: e
Question (gain): at what rate percent per annum will the simple interest on a sum of money be 1 / 5 of the amount in 10 years ?
Options: a ) 2 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = x / 5 , time = 10 years . rate = ( 100 * x ) / ( x * 5 * 10 ) = 2 % answer : a"
Answer: a
Question (physics): a man can do a job in 15 days . his father takes 10 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 15 + 1 / 10 + 1 / 25 ) = 21 / 150 so , all three together will complete the work in 150 / 21 = 7.1 days . answer : c"
Answer: c
Question (other): in a neighborhood having 90 households , 11 did not have either a car or a bike . if 22 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: { total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 22 + 11 - - > { bike } = 57 - - > # those who have bike only is { bike } - { both } = 57 - 22 = 35 . answer : b .
Answer: b
Question (general): the 3 digits of a number add up to 11 . the number is divisible by 5 . the leftmost digit is double the middle digit . what is the product of the 3 digits ?
Options: a ) 38 , b ) 40 , c ) 78 , d ) 88 , e ) 125
Rationale: xyz is a 3 digit integer divisible by 5 . so z can take only 0 or 5 . we are also given that x = 2 y this means x + y ( 2 y + y ) must be a multiple of 3 xy 5 or xy 0 case 1 x + y + 0 = 11 x + y = 11 this ca n ' t be the case because 11 is not a multiple of 3 case 2 x + y + 5 = 11 x + y = 6 solving we get , x = 4 y = 2 so the 3 digit number is 425 thus the product of the digits will be = 4 x 2 x 5 = 40 answer b
Answer: b
Question (general): if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability t that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability t = 1 / 24 . answer c ."
Answer: c