Cheukting/mathqa huggingface dataset:
Question (physics): if a truck is traveling at a constant rate of 108 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 20 , b ) 24 , c ) 30 , d ) 36 , e ) 48
Rationale: speed = 108 km / hr = > 108,000 m / hr in one minute = > 108000 / 60 = 1800 meters in one sec = > 1800 / 60 = 30 meters time = total distance need to be covered / avg . speed = > 600 / 30 = 20 and hence the answer : a
Answer: a
Question (general): if x + y = 4 and x 2 y 3 + y 2 x 3 = 36 , what is the value of xy ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "xy = 3 as x + y = 4 x 2 y 3 + y 2 x 3 = 36 x 2 y 2 ( y + x ) = 36 substituting x + y x 2 y 2 = 4 xy = 4 answer : d"
Answer: d
Question (general): what is the least number that should be added to 1054 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1054 / 23 ) gives a remainder 19 so we need to add 4 . the answer is d ."
Answer: d
Question (physics): two bullet trains of equal lengths take 10 seconds and 12 seconds respectively to cross a telegraph post . if the length of each bullet train be 120 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 11 sec . , b ) 15 sec . , c ) 12 sec . , d ) 17 sec . , e ) 19 sec .
Rationale: "speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 12 m / sec = 10 m / sec . relative speed = ( 12 + 10 ) = 22 m / sec . required time = ( 120 + 120 ) / 22 sec = 11 sec . a"
Answer: a
Question (general): if d is the standard deviation a , b , and c , what is the standard deviation of a + 6 , b + 6 , c + 6 ?
Options: a ) d , b ) 6 d , c ) 6 d + 6 , d ) 6 d + 12 , e ) 6 d + 18
Rationale: "concept : standard deviation is defined as average deviation of terms in the set from the mean value of the set . i . e . 1 ) it depends on the separation between the successive terms of the set 2 ) if a constant value is added / subtracted in every terms of set then the separation between successive terms does not change hence s . d . remains constant e . g . { 1 , 2 , 3 , 4 , 5 } will have same standard deviation as { 1 + 10 , 2 + 10 , 3 + 10 , 4 + 10 , 5 + 10 } 3 ) if a constant value is multiplied in every terms then the separation between succesive terms gets multiplied by the constant hence s . d . remains gets multiplied by same number e . g . { 0.7 , 1.4 , 2.1 , 2.8 , 3.5 } will have standard deviation = 0.7 * standard deviation of set { 1 , 2 , 3 , 4 , 5 } when 6 is added in each term of set { a , b , c } then the new set { a + 6 , b + 6 , c + 6 } will remain same as the previous standard deviation i . e . d answer : a"
Answer: a
Question (general): 70 % of x is greater than 1 / 3 rd of x by 110 . what is x ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 350 , e ) 400
Rationale: "7 x / 10 - x / 3 = 110 11 x / 30 = 110 x = 300 answer : c"
Answer: c
Question (physics): eight machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 16 days ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 2
Rationale: "rate of one machine = 1 job / ( 20 * 8 ) days let x = number of machines needed to complete the job in 16 days 1 / ( 8 * 20 ) * 16 * x = 1 job x = 10 10 - 8 = 2 answer : e"
Answer: e
Question (general): in a competitive examination in state a , 6 % candidates got selected from the total appeared candidates . state b had an equal number of candidates appeared and 7 % candidates got selected with 80 more candidates got selected than a . what was the number of candidates appeared from each state ?
Options: a ) 7000 , b ) 8000 , c ) 8800 , d ) 8900 , e ) 9000
Rationale: "state a and state b had an equal number of candidates appeared . in state a , 6 % candidates got selected from the total appeared candidates in state b , 7 % candidates got selected from the total appeared candidates but in state b , 80 more candidates got selected than state a from these , it is clear that 1 % of the total appeared candidates in state b = 80 = > total appeared candidates in state b = 80 x 100 = 8000 = > total appeared candidates in state a = total appeared candidates in state b = 8000"
Answer: b
Question (physics): the sector of a circle has perimeter of 144 cm and central angle 180 o . find its radius ?
Options: a ) 25 cm , b ) 32 cm , c ) 14 cm , d ) 28 cm , e ) 21 cm
Rationale: "let the radius is x cm perimeter of the sector = length of the arc + 2 ( radius ) 144 = ( 180 / 360 * 2 * 22 / 7 * x ) + 2 ( x ) 144 = 22 x / 7 + 2 x 144 = 36 x / 7 36 x = 1008 x = 28 answer : d"
Answer: d
Question (physics): the dimensions of a room are 10 m x 7 m x 5 m . there are 2 doors and 3 windows in the room . the dimensions of the doors are 1 m x 3 m . one window is of size 2 m x 1.5 m and the other 2 windows are of size 1 m x 1.5 m . the cost of painting the walls at rs . 3 per sq m is ?
Options: a ) rs . 229 , b ) rs . 429 , c ) rs . 129 , d ) rs . 474 , e ) rs . 111
Rationale: "area of 4 walls = 2 ( l + b ) h = 2 ( 10 + 7 ) x 5 = 170 sq m area of 2 doors and 3 windows = 2 ( 1 x 3 ) + ( 2 x 1.5 ) + 2 ( 1 x 1.5 ) = 12 sq m area to be planted = 170 - 12 = 158 sq m cost of painting = rs . 158 x 3 = rs . 474 answer : d"
Answer: d
Question (gain): ravi and kavi start a business by investing â ‚ ¹ 2000 and â ‚ ¹ 72000 , respectively . find the ratio of their profits at the end of year .
Options: a ) 2 : 36 , b ) 5 : 36 , c ) 7 : 36 , d ) 1 : 36 , e ) 3 : 36
Rationale: "ratio of profit = ratio of investments = 2000 : 72000 = 1 : 36 answer : d"
Answer: d
Question (gain): the owner of a furniture shop charges his customer 25 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 620 , b ) 400 , c ) 45 , d ) 500 , e ) 800
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 125 ) = rs . 800 . answer : e"
Answer: e
Question (physics): a worker earns $ 20 on the first day and spends $ 15 on the second day . the worker earns $ 20 on the third day and spends $ 15 on the fourth day . if this pattern continues , on which day will the worker first reach a net total of $ 100 ?
Options: a ) 30 , b ) 33 , c ) 35 , d ) 38 , e ) 40
Rationale: "every two days , the net total is $ 5 . after 32 days , the worker will have $ 80 . on day 33 , the worker will receive $ 20 for a net total of $ 100 . the answer is b ."
Answer: b
Question (gain): john makes $ 60 a week from his job . he earns a raise and now makes $ 100 a week . what is the % increase ?
Options: a ) 16 % , b ) 66.67 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
Rationale: "increase = ( 40 / 60 ) * 100 = ( 4 / 6 ) * 100 = 66.67 % . b"
Answer: b
Question (physics): 6 men and 8 women can complete a work in 10 days . 26 men and 48 women can finish the same work in 2 days . 15 men and 20 women can do the same work in - days .
Options: a ) 4 days , b ) 6 days , c ) 2 days , d ) 8 days , e ) 10 days
Rationale: "explanation : let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b work done by 6 men and 8 women in 1 day = 1 / 10 = > 6 m + 8 b = 1 / 10 = > 60 m + 80 b = 1 - - - ( 1 ) work done by 26 men and 48 women in 1 day = 1 / 2 = > 26 m + 48 b = ½ = > 52 m + 96 b = 1 - - - ( 2 ) solving equation 1 and equation 2 . we get m = 1 / 100 and b = 1 / 200 work done by 15 men and 20 women in 1 day = 15 / 100 + 20 / 200 = 1 / 4 = > time taken by 15 men and 20 women in doing the work = 4 days answer : option a"
Answer: a
Question (general): a farmer has an apple orchard consisting of fuji and gala apple trees . due to high winds this year 10 % of his trees cross pollinated . the number of his trees that are pure fuji plus the cross - pollinated ones totals 153 , while 3 / 4 of all his trees are pure fuji . how many of his trees are pure gala ?
Options: a ) 22 , b ) 33 , c ) 55 , d ) 27 , e ) 88
Rationale: "let f = pure fuji , g = pure gala and c - cross pollinated . c = 10 % of x where x is total trees . c = . 1 x also 3 x / 4 = f and c + f = 153 = > . 1 x + 3 / 4 x = 153 = > x = 180 180 - 153 = pure gala = 27 . d"
Answer: d
Question (physics): how long does a bus 100 m long traveling at 50 kmph takes to cross a bridge of 150 m in length ?
Options: a ) 18 , b ) 16 , c ) 15 , d ) 11 , e ) 12
Rationale: d = 100 + 150 = 250 m s = 50 * 5 / 18 = 125 / 9 t = 250 * 9 / 125 = 18 sec answer : a
Answer: a
Question (physics): a cistern 5 m long and 4 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 49 m 2 , b ) 42.5 m 2 , c ) 53.5 m 2 , d ) 55 m 2 , e ) 57 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 4 x 1.25 + 5 x 1.25 ) + 5 x 4 ] m 2 = 42.5 m 2 . answer : option b"
Answer: b
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 50 paisa . if the share of y is rs . 63 , what is the total amount ?
Options: a ) 115 , b ) 273 , c ) 117 , d ) 118 , e ) 119
Rationale: "x : y : z = 100 : 45 : 50 20 : 9 : 10 9 - - - 63 39 - - - ? = > 273 answer : b"
Answer: b
Question (general): find the value of 1 / ( 3 + 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) )
Options: a ) 21 / 29 , b ) 27 / 89 , c ) 89 / 21 , d ) 29 / 21 , e ) none
Rationale: 1 / [ 3 + ( 1 / ( 3 + 1 / ( 3 - 1 / 3 ) ) ) ] = > 1 / [ 3 + 1 / ( 3 + 1 / ( 8 / 3 ) ) ] = > 1 / [ 3 + 1 / ( 3 + 3 / 8 ) ] = > 1 / [ 3 + 8 / 27 ] = > 1 / ( 89 / 27 ) = > 27 / 89 b
Answer: b
Question (general): if a - b = 5 and a 2 + b 2 = 31 , find the value of ab .
Options: a ) 9 , b ) 2 , c ) 3 , d ) 7 , e ) 12
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 31 - 25 = 6 ab = 3 . answer : c"
Answer: c
Question (geometry): if circles x and y have the same area and circle x has a circumference of 18 π , half of the radius of circle y is :
Options: a ) 16 , b ) 4.5 , c ) 4 , d ) 2 , e ) 1
Rationale: "x be radius of circle x y be radius of circle y given : pi * x ^ 2 = pi * y ^ 2 also , 2 * pi * x = 18 * pi x = 9 thus y = 9 y / 2 = 4.5 ans : b"
Answer: b
Question (gain): the present population of a town is 2000 . population increase rate is 20 % p . a . find the population of town after 1 years ?
Options: a ) 1000 , b ) 2400 , c ) 1500 , d ) 1600 , e ) 1250
Rationale: "p = 2000 r = 20 % required population of town = p ( 1 + r / 100 ) ^ t = 2000 ( 1 + 20 / 100 ) = 2000 ( 6 / 5 ) = 2400 answer is b"
Answer: b
Question (other): the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 490 , krishan has ?
Options: a ) rs . 2890 , b ) rs . 2330 , c ) rs . 1190 , d ) rs . 1620 , e ) rs . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 490 : n & there n = 289 x 490 / 49 = rs . 2890 answer : a"
Answer: a
Question (gain): by selling an article for $ 195 , a person gains $ 45 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: s . p . = $ 195 gain = $ 45 c . p . = 195 - 45 = 150 gain % = 45 / 150 * 100 % = 30 % answer is b
Answer: b
Question (gain): by selling an article at rs . 600 , a profit of 60 % is made . find its cost price ?
Options: a ) 228 , b ) 267 , c ) 375 , d ) 480 , e ) 811
Rationale: "sp = 600 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 600 * [ 100 / ( 100 + 60 ) ] = 600 * [ 100 / 160 ] = rs . 375 answer : c"
Answer: c
Question (general): ray writes a two digit number . he sees that the number exceeds 4 times the sum of its digits by 3 . if the number is increased by 18 , the result is the same as the number formed by reversing the digits . find the number .
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: solution : let the two digit number be xy . 4 ( x + y ) + 3 = 10 x + y . . . . . . . ( 1 ) 10 x + y + 18 = 10 y + x . . . . ( 2 ) solving 1 st equation we get 2 x - y = 1 . . . . . ( 3 ) solving 2 nd equation we get y - x = 2 . . . . . ( 4 ) solving 3 and 4 , we get x = 3 and y = 5 answer : b
Answer: b
Question (general): how many 3 - digit integers between 311 and 401 , exclusive , are divisible by 3 when the tens digit and the hundered digit are switched ?
Options: a ) 30 , b ) 19 , c ) 22 , d ) 3 , e ) 90
Rationale: answer is 30 no of digits between 311 and 401 ( exclusive ) = 401 - 311 - 1 = 89 no intergers divisble by 3 = ~ 89 / 3 ~ 30 divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . e . g 372 is divisble by 3 ( becae 3 + 7 + 2 = 12 ( divisble by 3 ) ) switch digits 732 also divisble by 3 ( becae 7 + 3 + 2 = 12 ( divisble by 3 ) ) divsiblivity rule for 3 is sum of all digits must be divisble by 3 . it does n ' t matter if hundred digit and tens digits are switched . you have right . so it is enough to proceed like usual to find the numbers in a given range that are divisible by 3 . so 399 - 312 / 3 + 1 = 30 . answer : a
Answer: a
Question (geometry): the length of a rectangle is reduced by 22 % . by what % would the width have to be increased to maintain the original area ?
Options: a ) 14 % , b ) 15 % , c ) 28 % , d ) 30 % , e ) 35 %
Rationale: "sol . required change = ( 22 * 100 ) / ( 100 - 22 ) = 28.2 % c"
Answer: c
Question (physics): a can do a piece of work in 28 days and b alone can do it in 10 days . b works at it for 5 days and then leaves . a alone can finish the remaining work in
Options: a ) 5 days , b ) 6 days , c ) 7.5 days , d ) 14 days , e ) 9 days
Rationale: "explanation : b ' s 5 days work = 1 / 10 ∗ 5 = 1 / 2 remaining work = 1 − 1 / 2 = 1 / 2 a can finish work = 28 ∗ 1 / 2 = 14 days option d"
Answer: d
Question (general): if ( x + 3 ) ^ 2 / ( 3 x + 5 ) = 2 , then the difference between the two possible values of x is :
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "( x + 3 ) ^ 2 / ( 3 x + 5 ) = 2 ( x + 3 ) ^ 2 = 2 ( 3 x + 5 ) x ^ 2 + 6 x + 9 = 6 x + 10 x ^ 2 - 1 = 0 ( x - 1 ) ( x + 1 ) = 0 x = 1 or x = - 1 the answer is a ."
Answer: a
Question (physics): a train 110 m long is running with a speed of 90 km / h . in how many seconds will the train pass a man who is running at 9 km / h in the direction opposite to that in which the train is going ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: the speed of the train relative to the man = 90 + 9 = 99 km / h . 99000 m / h * 1 h / 3600 s = ( 990 / 36 ) m / s ( 110 m ) / ( 990 / 36 m / s ) = ( 110 * 36 ) / 990 = 36 / 9 = 4 seconds the answer is b .
Answer: b
Question (physics): the ratio between the length and the breadth of a rectangular park is 2 : 3 if a man cycling along the boundary of the park at the speed of 10 km / hr completes one round in 18 min , then the area of the park ( in sq . m ) is ?
Options: a ) 3000 m , b ) 9000 m , c ) 540000 m , d ) 10000 m , e ) 54000 m
Rationale: "perimeter = distance covered in 8 min . = ( 10000 x 18 ) / 60 m = 3000 m . let length = 2 x metres and breadth = 3 x metres . then , 2 ( 2 x + 3 x ) = 3000 or x = 300 . length = 600 m and breadth = 900 m . area = ( 600 x 900 ) m 2 = 540000 m c"
Answer: c
Question (physics): a car drives 60 miles on local roads at 20 mph , and 195 miles on the highway at 65 mph , what is the average speed of the entire trip ?
Options: a ) 36 mph , b ) 40 mph , c ) 44 mph , d ) 43 mph , e ) 58 mph
Rationale: "so the answer is plainly d . . . . we have a general relation for speed , time and distance : v ( velocity ) * t ( time ) = d ( distance ) for first part we have d = 60 miles , and v = 20 mph so we can obtain time : 20 * t = 60 or t = 60 / 20 = 3 hours the needed time to cover 60 miles in the same way we should divide 195 to 65 to find the needed time to cover 195 miles , so t = 3 hours so the total time for covering total distance would be 3 + 3 = 6 hours and total distance is 60 + 195 = 255 miles final stage : average speed is total distance divide to total time : 255 / 6 = 42.5 miles per hour rounded up to 43 mph . . . ."
Answer: d
Question (general): a number x is mistakenly divided by 10 instead of being multiplied by 10 . what is the percentage error in the result ?
Options: a ) - 99 % , b ) - 100 % , c ) + 99 % , d ) + 100 % , e ) none
Rationale: solution : actual result = 10 x by mistake it has been divided by 10 = x / 10 % change = [ 10 x - ( 10 / x ) / 10 x ] * 100 = 99 = - 99 % . since , actual value is greater than the wrong value . alternatively , let , x = 10 actual result = 10 * 10 = 100 wrong result = 10 / 10 = 1 . change = ( 1 - 100 ) = - 99 % change = - 99 % . answer : option a
Answer: a
Question (general): if x > 3000 , then the value of ( 1.2 x ) / ( 0.5 x - 406 ) is closest to ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 10 / 21 , d ) 1 / 2 , e ) 3 / 1
Rationale: assume x = 3002 ( 1.2 x ) / ( 0.5 x - 406 ) = 3602.4 / ( 3002 * 0.5 - 406 ) = 3602.4 / 1095 = = 3 / 1 e
Answer: e
Question (physics): a room 5 m 55 cm long and 3 m 74 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor ?
Options: a ) 122 , b ) 123 , c ) 828 , d ) 122 , e ) 176
Rationale: "area of the room = ( 544 * 374 ) size of largest square tile = h . c . f of 544 & 374 = 34 cm area of 1 tile = ( 34 x 34 ) number of tiles required = = [ ( 544 x 374 ) / ( 34 x 34 ) ] = 176 answer : e"
Answer: e
Question (physics): a train passes a platform in 32 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 180 meter , b ) 240 meter , c ) 200 meter , d ) 260 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 32 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 32 = > 300 + l = 15 × 32 = 480 = > l = 480 - 300 = 180 meter answer : option a"
Answer: a
Question (gain): the cost price of an book is 64 % of the marked price . calculate the gain percent after allowing a discount of 12 % ?
Options: a ) 33 % , b ) 28.02 % , c ) 37.5 % , d ) 30.5 % , e ) 22 %
Rationale: c 37.5 % let marked price = $ 100 . then , c . p . = $ 64 , s . p . = $ 88 gain % = 24 / 64 * 100 = 37.5 % .
Answer: c
Question (general): how much water must be added to 64 litres of milk at 1 1 ⁄ 2 litres for 20 so as to have a mixture worth 10 2 ⁄ 3 a litre ?
Options: a ) 16 litres , b ) 12 litres , c ) 15 litres , d ) 18 litres , e ) none of these
Rationale: "c . p . of 1 litre of milk = ( 20 × 2 ⁄ 3 ) = 40 ⁄ 3 ∴ ratio of water and milk = 8 ⁄ 3 : 32 ⁄ 3 = 8 : 32 = 1 : 4 ∴ quantity of water to be added to 64 litres of milk = ( 1 ⁄ 4 × 64 ) litres = 16 litres . answer a"
Answer: a
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along theoundary of the park at the speed of 12 km / hr completes one round in 8 min , then thearea of the park ( in sq . m ) is ?
Options: a ) 124545 m , b ) 134561 m , c ) 156787 m , d ) 15450 m , e ) 153600 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m e"
Answer: e
Question (other): 3 numbers are in the ratio 3 : 5 : 7 . the largest number value is 70 . find difference between smallest & largest number is ?
Options: a ) 40 , b ) 45 , c ) 35 , d ) 30 , e ) 50
Rationale: = = 3 : 5 : 7 total parts = 15 = the largest number value is 70 = the largest number is = 7 = then 7 parts - - - - - > 70 ( 7 * 10 = 70 ) = smallest number = 3 & largest number = 7 = difference between smallest number & largest number is = 7 - 3 = 4 = then 4 parts - - - - - > 40 ( 4 * 10 = 40 ) a
Answer: a
Question (physics): in a 80 meters race a beats b by 56 m or 7 seconds . a ' s time over the course is :
Options: a ) 3 seconds , b ) 12 seconds , c ) 10 seconds , d ) 18 seconds , e ) 28 seconds
Rationale: "b runs 56 m in 7 sec . = > b runs 80 m in 7 / 56 * 80 = 10 seconds since a beats b by 7 seconds , a runs 80 m in ( 10 - 7 ) = 3 seconds hence , a ' s time over the course = 3 seconds answer : a"
Answer: a
Question (physics): there are 5 people who can build 5 houses in just 5 days . increase the amount of people to 100 . how long would it take these 100 people to build 100 houses ?
Options: a ) 2 days , b ) 3 days , c ) 4 days , d ) 5 days , e ) 1 days
Rationale: it will take 5 days for 100 people to build 100 houses . 1 person can build 1 house in 5 days . so , 100 people can build 100 houses in 5 days . answer d
Answer: d
Question (general): the smallest number which when diminished by 2 , is divisible by 12 , 16 , 18 , 21 and 28 is
Options: a ) 1008 , b ) 1010 , c ) 1022 , d ) 1032 , e ) 1043
Rationale: required number = ( l . c . m of 12 , 16 , 18 , 21,28 ) + 2 = 1008 + 2 = 1010 answer : b
Answer: b
Question (physics): 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 55 meters deep by working for 6 hours ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: "45 workers * 8 hours / 30 meters = x * 6 / 55 x = 110 total workers 110 - 45 = 65 new workers the answer is d ."
Answer: d
Question (physics): the length of the bridge , which a train 150 metres long and travelling at 54 km / hr can cross in 30 seconds , is ?
Options: a ) 340 m . , b ) 350 m . , c ) 320 m . , d ) 330 m . , e ) 360 m .
Rationale: "speed = [ 54 x 5 / 18 ] m / sec = [ 15 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) / 30 = 320 = > x = 320 m . answer : c"
Answer: c
Question (physics): a train 700 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 288 m , b ) 256 m , c ) 600 m , d ) 278 m , e ) 287 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 700 + x ) / 60 = 65 / 3 x = 600 m . answer : c"
Answer: c
Question (geometry): in a new housing development , trees are to be planted along the sidewalk of a certain street . each tree takes up one square foot of sidewalk space , and there are to be 12 feet between each tree . how many trees can be planted if the road is 157 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 13
Rationale: "let t be the number of trees . then the length required for trees on the sidewalk will be 1 * t = t to maximize the number of trees , the number of 12 feet spaces between trees should be 1 less than total number of trees . for example , if there are 3 trees , then there should be 2 spaces between them . so the number of 12 feet spaces will be t - 1 . then , the length of sidewalk required for 12 feet spaces will be 12 * ( t - 1 ) it is given that total lenght of sidewalk is 157 feet . or 12 ( t - 1 ) + t = 157 or 12 t - 12 + t = 157 or 13 t = 169 or t = 13 answer : - e"
Answer: e
Question (general): how many integers from 0 to 56 , inclusive , have a remainder of 1 when divided by 3 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "my ans is also c . 17 . explanation : 1 also gives 1 remainder when divided by 3 , another number is 4 , then 7 and so on . hence we have an arithmetic progression : 1 , 4 , 7 , 10 , . . . . . 55 , which are in the form 3 n + 1 . now we have to find out number of terms . tn = a + ( n - 1 ) d , where tn is the nth term of an ap , a is the first term and d is the common difference . so , 55 = 1 + ( n - 1 ) 3 or , ( n - 1 ) 3 = 54 or , n - 1 = 18 or , n = 19 e"
Answer: e