regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 150 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40.8 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 150 = 510 meter time taken to cross the platform = 510 / ( 25 / 2 ) = 510 ã — 2 / 25 = 40.8 seconds answer : d"
Answer: d
Problem: the mean proportional between 4 and 16 is ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "root of ( 4 * 16 ) = 2 * 4 = 16 answer : e"
Answer: e
Problem: two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 7 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 21 , c ) 2 / 23 , d ) 2 / 29 , e ) 2 / 10
Rationale: explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 7 ) = 2 / 21 answer : b ) 2 / 21
Answer: b
Problem: if a speaks the truth 60 % of the times , b speaks the truth 50 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.8 , b ) 0.9 , c ) 1.0 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 6 / 10 ; false = 4 / 10 probability of b speaks truth p ( b ) = 5 / 10 ; false = 5 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 4 / 10 ) * ( 5 / 10 ) ] = 4 / 5 = 0.8 answer : a"
Answer: a
Problem: meena wrote all the numbers from 1 to 29,999 inclusive . how many digits did she write in total ?
Options: a ) 118,889 , b ) 138,889 , c ) 159,889 , d ) 188,789 , e ) 188,989
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 29999 = > 5 * 20,000 = 100,000 the answer is 138,889 the answer is b ."
Answer: b
Problem: a box contains 22 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 99 , e ) 26 / 77
Rationale: "solution p ( none is defective ) = 18 c 2 / 22 c 2 = 51 / 77 p ( at least one is defective ) = ( 1 - 51 / 77 ) = 26 / 77 . answer e"
Answer: e
Problem: the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 8 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 3 , e ) 2 / 3
Rationale: "let us say probability of a occurring is a . let us say probability of b occurring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 8 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 8 * 2 b * b 3 b - 2 b ^ 2 = 16 b ^ 2 3 b = 18 b ^ 2 b = 3 / 18 = 1 / 6 so , a = 2 b = 1 / 3 answer : d"
Answer: d
Problem: if - 2 and - 3 are negative integers , then - 2 * - 3 + 2 is
Options: a ) - 5 , b ) 8 , c ) - 6 , d ) - 3 , e ) - 8
Rationale: answer : b
Answer: b
Problem: a can give b 50 meters start and c 100 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 111.64 , d ) 52.63 , e ) 101.12
Rationale: "a runs 1000 m while b runs 950 m and c runs 900 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 900 ) / 950 = 947.37 m . b can give c = 1000 - 947.37 = 52.63 m . answer : d"
Answer: d
Problem: a train covers a distance of 100 km in 1 hour . if its speed is decreased by 10 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 6 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 10 = 90 km / hr time taken = 100 / 90 = 1 hr 6 min answer is b"
Answer: b
Problem: if s = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if s = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by b are ?
Options: a ) 24 , b ) 18 , c ) 13 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 100 = 24 answer : a"
Answer: a
Problem: a train 100 m long crosses a platform 125 m long in 1 sec ; find the speed of the train ?
Options: a ) 810 , b ) 700 , c ) 930 , d ) 100 , e ) 200
Rationale: "d = 100 + 125 = 225 t = 15 s = 225 / 1 * 18 / 5 = 810 kmph answer : a"
Answer: a
Problem: if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 2.6 ] + [ 1.4 ] + [ 2.7 ] ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 6 , e ) 7
Rationale: you are asked what the closest lesser integer value to [ x ] is . [ - 2.6 ] = - 3.0 [ 1.4 ] = 1.0 [ 2.7 ] = 2.0 therefore , answer is : - 3.0 + 1.0 + 2.0 = 0.0 option a .
Answer: a
Problem: if i equals the sum of the even integers from 2 to 200 , inclusive , and k equals the sum of the even integers from 20 to 200 , inclusive , what is the value of i - k ?
Options: a ) 10 , b ) 99 , c ) 9 , d ) 88 , e ) 90
Rationale: "use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 200 - 2 ) / 2 ] + 1 = 100 and [ ( 200 - 20 ) / 2 ] + 1 = 91 mean of integers = ( 200 + 2 ) / 2 = 101 and ( 200 + 20 ) / 2 = 110 sum of integers = ( 100 * 101 ) = 10100 and ( 91 * 110 ) = 10010 thus their difference i - k = 10100 - 10010 = 90 answer : e"
Answer: e
Problem: by selling 32 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "40 % - - - 40 160 % - - - ? 40 / 160 * 40 = 10 answer : a"
Answer: a
Problem: how many seconds will a 800 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 52 , c ) 38 , d ) 42 , e ) 45
Rationale: "explanation : here distance d = 800 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = 800 x 18 / 60 x 5 = 48 sec . answer is a"
Answer: a
Problem: if a - b = 8 and a ^ 2 + b ^ 2 = 164 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 50 , d ) 18 , e ) 19
Rationale: 2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 164 - 64 = 100 = > ab = 50 answer : c
Answer: c
Problem: a sum fetched a total simple interest of rs . 929.20 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 2323 , b ) 1223 , c ) 2563 , d ) 1853 , e ) 2353
Rationale: "explanation : si = rs . 929.20 p = ? t = 5 years r = 8 % p = 100 × si / rt = 100 × 929.20 / 8 × 5 = rs . 2323 answer : option a"
Answer: a
Problem: ? % of 360 = 151.2
Options: a ) 42 , b ) 36 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 151.2 or , ? = 151.2 × 100 / 360 = 42 answer a"
Answer: a
Problem: the radius of a wheel is 22.5 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 707.14 m , c ) 774 m , d ) 714 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 22.5 = 70714 cm = 707.14 m answer : b"
Answer: b
Problem: jane makes toy bears . when she works with an assistant , she makes 89 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 110 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 75.6 bears per 36 hours a week or 2.1 bears / hr ( [ 40 bears * 1.89 ] / [ 40 hrs * . 90 ] ) . [ ( 2.1 - 1 ) / 1 ] * 100 % = 110 % answer : c"
Answer: c
Problem: how many cubes of 10 cm edge can be put in a cubical box of 1 m edge ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) none
Rationale: "sol . number of cubes = [ 100 * 100 * 100 / 10 * 10 * 10 ] = 1000 . answer d"
Answer: d
Problem: 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?
Options: a ) 8 days , b ) 9 days , c ) 11 days , d ) 13 days , e ) 15 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a )"
Answer: a
Problem: if a man lost 10 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 6.5 , b ) 7.5 , c ) 7 , d ) 8 , e ) 2
Rationale: 90 % - - - - 12 144 % - - - - ? 90 / 144 * 12 = 7.50 answer : b
Answer: b
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 10 : 5 , b ) 15 : 2 , c ) 20 : 2 , d ) 25 : 2 , e ) none of these
Rationale: "explanation : indian stamps are common to both ratios . multiply both ratios by factors such that the indian stamps are represented by the same number . us : indian = 5 : 2 , and indian : british = 5 : 1 . multiply the first by 5 , and the second by 2 . hence the two ratios can be combined and us : british = 25 : 2 now us : indian = 25 : 10 , and indian : british = 10 : 2 answer : d"
Answer: d
Problem: a canteen requires 13 dozen bananas per day . how many bananas will it require for 9 weeks ?
Options: a ) 728 , b ) 9828 , c ) 1404 , d ) 9882 , e ) none
Rationale: requirement of bananas for 1 day in the canteen = 13 dozens ∴ requirement of bananas for 9 weeks i . e . 63 days = 63 × 13 dozens = 63 × 13 × 12 = 9828 . answer d
Answer: d
Problem: an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 11 . 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 2400
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 11 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 3300 . hence , ( r - p ) = ( 3300 - 900 ) = 2400 answer : e"
Answer: e
Problem: the perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters . what is the length of the yard if the area of the yard is 40 meters squared ?
Options: a ) 12 , b ) 10 , c ) 8 , d ) 14 , e ) 16
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 36 - - > l + b = 18 area = l * b = 40 b = 18 - l l ( 18 - l ) = 40 18 l - l ^ 2 = 40 l ^ 2 - 18 l + 40 = 0 upon simplifying we get l = 5 or 8 . only 8 is there in the answer choice . answer : c"
Answer: c
Problem: a shipment of 230 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 9 / 68 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = ( 84 / 230 ) probability of chosing one defective phone from a lot of 229 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 229 ) combined probability of series of events = product of the probabilities = ( 84 / 230 ) * ( 83 / 229 ) 84 / 230 is close to ( 23 / 63 ) and ( 83 / 229 ) = ( 29 / 80 ) so answer is ( 23 / 63 ) * ( 29 / 80 ) = ( 9 / 68 ) so , answer will be d"
Answer: d
Problem: a large box contains 20 small boxes and each small box contains 32 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 640
Rationale: "the only thing you have to do is a simple multiply we have : 20 * 32 = 640 correct answer is : e ) 640"
Answer: e
Problem: how many digits are in ( 8 × 10 ^ 12 ) ( 10 × 10 ^ 9 ) ?
Options: a ) 20 , b ) 23 , c ) 26 , d ) 27 , e ) 28
Rationale: "the question simplfies to ( 8 × 10 ^ 12 ) ( 10 ^ 10 ) = > 8 * 10 ^ 22 = > will contain 22 zeros + 1 digit 8 = > 23 ans b"
Answer: b
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 6 : 00 am and pipe b at 7 : 00 am , at what time will the pool be full ?
Options: a ) 14 : 00 , b ) 15 : 00 , c ) 13 : 00 , d ) 16 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 6 : 00 a . m and pipe b at 7 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 7 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 6 : 00 a . m , pool is full at 16 : 00 hrs answer : d"
Answer: d
Problem: in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .
Answer: b
Problem: a train 800 m long can cross a pole in 10 sec and then find the speed of the train ?
Options: a ) 280 , b ) 282 , c ) 284 , d ) 286 , e ) 288
Rationale: "length = speed * time speed = l / t s = 800 / 10 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 288 kmph answer : e"
Answer: e
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is two times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 18 : 8
Rationale: water : soap = 3 : 2 soap : salt = 6 : 2 = > for 6 soap , salt = 2 = > for 2 soap , salt = ( 2 / 6 ) * 2 = 2 / 3 so , water : soap : salt = 3 : 2 : 2 / 3 = 18 : 12 : 4 after open container , water : soap : salt = 9 : 18 : 4 so , water : salt = 9 : 4 = 18 : 8 e
Answer: e
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 150 cookies , what percent of the cookies did nell bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 12.6 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 150 cookies x = 150 / 16.4 = 9.1 ( approx ) so , nell baked 9.1 * 2.05 cookies or 19 cookies ( approx ) % share = 19 / 150 = 12.6 approx hence , answer is c ."
Answer: c
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c − a ?
Options: a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 90 ) b + c = 160 c - a = 60 b . 60"
Answer: b
Problem: a string of 30 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.1 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.1 , b ) ( 0.1 ) ^ 30 , c ) 1 - ( 0.1 ) ^ 30 , d ) ( 0.93 ) ^ 30 , e ) 1 - ( 0.90 ) ^ 30
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 30 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.1 = 0.90 the the probability that none of the 30 light bulbs fails is 0.90 ^ 30 . hence , the probability that at least one light bulb fails is 1 - 0.90 ^ 30 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 30 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.1 = 10 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: e
Problem: the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 800 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 9 = 512 < 800 , then the greatest possible length of integer z is 9 . the answer is c ."
Answer: c
Problem: an association of mathematics teachers has 1,260 members . only 560 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 26.67 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 560 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 560 = 336 percent of total membership that voted for winning candidate = ( 336 / 1260 ) * 100 = 26.67 % answer b"
Answer: b
Problem: the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 750 ft , d ) 900 ft , e ) 2400 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 32 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 75 . sub x = 75 either in ( x + 5 ) * 30 or in x * 32 to get the distance , which is 2400 . so the correct choice is e ."
Answer: e
Problem: for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160
Rationale: from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive there are 8 * 12 = 96 five - minute intervals , thus total of 96 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 96 * 30 - - > x = 24 * 30 and 3 x = 3 * ( 24 * 30 ) = 24 * 90 . therefore , the total revenue from ticket sales that day was 24 * 30 * 6 + 24 * 90 * 10 = $ 25,920 . answer : b .
Answer: b
Problem: during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 105 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: "easy 280 is the answer . 3 / 4 ( x / 2 ) = 105 x = 105 * 8 / 3 = 280 . answer a"
Answer: a
Problem: a can do a job in 20 days and b can do it in 30 days . a and b working together will finish thrice the amount of work in - - - - - - - days ?
Options: a ) 22 days , b ) 22 days , c ) 36 days , d ) 72 days , e ) 24 days
Rationale: "1 / 20 + 1 / 30 = 5 / 60 = 1 / 12 12 / 1 = 12 * 3 = 36 days answer : c"
Answer: c
Problem: if 2 / 3 rd of the contents of a container evaporated on the 1 st day . and 1 / 4 th of the remaining evaporated on the second day . what part of the contents of the container is left at the end of the second day ?
Options: a ) 1 / 4 , b ) 1 / 12 , c ) 1 / 18 , d ) 1 / 6 , e ) 1 / 2
Rationale: after first day , 1 / 3 of the contents remain . after second day , ( 1 / 3 ) - ( 1 / 4 ( 2 / 3 ) ) = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 of the contents remain answer : d
Answer: d
Problem: the average of first 7 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 8.29 , d ) 13.11 , e ) 14.11
Rationale: "sum of 7 prime no . = 58 average = 58 / 7 = 8.29 answer : c"
Answer: c
Problem: in a group of 28 junior high school students , 5 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 13 , c ) 9 , d ) 12 , e ) 10
Rationale: b 13 add 1 + 10 + 4 to get 15 . then subtract 21 from the total students ⇒ 28 – 15 = 13 . answer is b
Answer: b
Problem: if pintu is coded as 79523 in a certain code language , how would you code dumbo in the same language ?
Options: a ) 43426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . dumbo is 43426 . . . answer : a"
Answer: a
Problem: a , b , c can complete a piece of work in 3,9 and 15 days respectively . working together , they will complete the same work in how many days ?
Options: a ) 45 / 23 , b ) 55 / 23 , c ) 61 / 57 , d ) 12 / 13 , e ) 22 / 23
Rationale: ( a + b + c ) ' s 1 day work = ( 1 / 3 ) + ( 1 / 9 ) + ( 1 / 115 ) = 23 / 45 a , b , c together will complete the work in 45 / 23 days answer is a
Answer: a
Problem: in a group of cows and chickens , the number of legs was 12 more than twice the number of heads . the number of cows was :
Options: a ) 6 , b ) 7 , c ) 10 , d ) 12 , e ) 14
Rationale: "let the number of cows be x and their legs be 4 x . let the number of chicken be y and their legs be 2 x . total number of legs = 4 x + 2 y . total number of heads = x + y . the number of legs was 12 more than twice the number of heads . therefore , 2 × ( x + y ) + 14 = 4 x + 2 y . or , 2 x + 2 y + 12 = 4 x + 2 y . or , 2 x + 12 = 4 x [ subtracting 2 y from both sides ] . or , 12 = 4 x – 2 x [ subtracting 2 x from both sides ] . or , 12 = 2 x . or , x = 6 [ dividing by 2 on both sides ] . therefore , the number of cows = 6 . correct answer : a ) 6"
Answer: a
Problem: a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 320 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 320 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 320 ) / 320 ] x 100 65 / 320 x 100 13 / 64 x 100 ≈ 13 / 65 x 100 ≈ 1 / 5 x 100 ≈ 20 % . the answer is c ."
Answer: c
Problem: if a - b = 3 and a ^ 2 + b ^ 2 = 29 , find the value of ab .
Options: a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 29 - 9 = 20 ab = 10 . b )"
Answer: b
Problem: a man is 24 years older than his son . in six years , his age will be twice the age of his son . the present age of the son is
Options: a ) 14 years , b ) 28 years , c ) 20 years , d ) 22 years , e ) none
Rationale: "solution let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . then â € ¹ = â € º ( x + 24 ) + 6 = 2 ( x + 6 ) â € ¹ = â € º x + 30 = 2 x + 12 x = 18 . answer e"
Answer: e
Problem: for what value of x between − 7 and 7 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 7 , b ) − 2 , c ) 0 , d ) 2 , e ) 7
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 7 will give the greatest value . . ans a"
Answer: a