Cheukting/mathqa huggingface dataset:
Question (general): the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum t of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just t = 900 : the answer is c ."
Answer: c
Question (general): in δ pqs above , if pq = 2 and ps = 3 , then
Options: a ) 3 / 2 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 20 / 3
Rationale: there are two ways to calculate area of pqs . area remains same , so both are equal . 2 * 3 / 2 = pr * 4 / 2 pr = 3 / 2 a
Answer: a
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 11000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 14 , b ) 21 , c ) 22 , d ) 23 , e ) none
Rationale: "sol . let the total number of workers be x . then , 8000 x = ( 10000 × 7 ) + 6000 ( x – 7 ) ‹ = › 2000 x = 28000 ‹ = › x = 14 . answer a"
Answer: a
Question (general): a man whose speed is 8 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 3 kmph , find his average speed for the total journey ?
Options: a ) 1 kmph , b ) 5 kmph , c ) 6 kmph , d ) 4 kmph , e ) 6.8 kmph
Rationale: "explanation : speed of man = 8 kmph speed of stream = 3 kmph speed in downstream = 11 kmph speed in upstream = 5 kmph average speed = ( 2 x 11 x 5 ) / 16 = 6.8 kmph . answer : e"
Answer: e
Question (general): of 30 applicants for a job , 9 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 10 , c ) 9 , d ) 7 , e ) 5
Rationale: "b . 10 30 - 3 = 27 27 - 9 - 18 = - 10 then 5 are in the intersection between 4 years experience and degree . answer b"
Answer: b
Question (gain): a fruit seller had some apples . he sells 50 % apples and still he has 5000 . originally he had how many apples ?
Options: a ) 10000 , b ) 15200 , c ) 11005 , d ) 12540 , e ) 12450
Rationale: "suppose originally he had x apples then ( 100 - 50 ) % of x = 5000 50 x / 100 = 5000 x = 10000 answer is a"
Answer: a
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 9 feet between each tree . how many trees can be planted if the road is 151 feet long ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 16
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 14 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 9 feet spaces will be t - 1 . then , the length of sidewalk required for 9 feet spaces will be 9 * ( t - 1 ) it is given that total lenght of sidewalk is 151 feet . or 9 ( t - 1 ) + t = 151 or 9 t - 9 + t = 151 or 10 t = 160 or t = 16 answer : - e"
Answer: e
Question (geometry): the slant height of a cone is 35 cm and radius of the base is 14 cm , find the curved surface of the cone .
Options: a ) 4150
b ) 1780
c ) 1540
d ) 1500
e ) 6100
Rationale: π * 14 * 35 = 1540 answer : c
Answer: c
Question (general): if a ã — b = 2 a - 3 b + ab , then 3 ã — 2 + 2 ã — 3 is equal to :
Options: a ) 7 , b ) 8 , c ) 9 , d ) 25 , e ) 26
Rationale: "explanation : 3 ã — 2 + 2 ã — 3 = ( 2 ã — 3 - 3 ã — 2 + 2 ã — 3 ) + ( 2 ã — 2 - 3 ã — 3 + 2 ã — 3 ) = ( 6 + 4 - 9 + 6 ) = 7 . answer : a"
Answer: a
Question (gain): a 20 % stock yielding 12 % is quoted at :
Options: a ) rs . 83.33 , b ) rs . 167 , c ) rs . 112 , d ) rs . 120 , e ) rs . 140
Rationale: "income of rs 12 on investment of rs 100 income of rs 20 on investment of ? = ( 20 * 100 ) / 12 = 167 answer : b"
Answer: b
Question (geometry): if the length of the sides of two cubes are in the ratio 6 : 1 , what is the ratio of their total surface area ?
Options: a ) 6 : 1 , b ) 12 : 1 , c ) 24 : 1 , d ) 36 : 1 , e ) 72 : 1
Rationale: "let x be the length of the small cube ' s side . the total surface area of the small cube is 6 x ^ 2 . the total surface area of the large cube is 6 ( 6 x ) ^ 2 = 216 x ^ 2 . the ratio of surface areas is 36 : 1 . the answer is d ."
Answer: d
Question (physics): two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 12 seconds . the length of the faster train is
Options: a ) 80 m , b ) 270 m , c ) 120 m , d ) 180 m , e ) none
Rationale: "solution relative speed = ( 36 + 45 ) km / hr = ( 81 x 5 / 18 ) m / sec = ( 45 / 2 ) m / sec length of the train = ( 45 / 2 x 12 ) m = 270 m . answer b"
Answer: b
Question (other): the ratio of number of boys and girls in a school is 2 : 5 . if there are 350 students in the school , find the number of girls in the school ?
Options: a ) 150 , b ) 250 , c ) 300 , d ) 370 , e ) 280
Rationale: "let the number of boys and girls be 2 x and 5 x total students = 350 number of girls in the school = 5 * 350 / 7 = 250 answer is b"
Answer: b
Question (physics): if the perimeter of a rectangular garden is 1800 m , its length when its breadth is 400 m is ?
Options: a ) 500 , b ) 600 , c ) 700 , d ) 800 , e ) 900
Rationale: 2 ( l + 400 ) = 1800 = > l = 500 m answer : a
Answer: a
Question (general): solve for x and check : - 3 x = 12
Options: a ) - 4 , b ) - 2 , c ) 1 , d ) 3 , e ) none of these
Rationale: "solution : dividing each side by - 3 , we obtain ( - 3 x / - 3 ) = ( 12 / - 3 ) therefore : x = - 4 check : - 3 x = 12 ( - 3 * - 4 ) = 12 12 = 12 answer : a"
Answer: a
Question (physics): sarah is driving to the airport . after driving at 15 miles per hour for one hour , she realizes that if she continues at that same average rate she will be an hour late for her flight . she then travels 60 miles per hour for the rest of the trip , and arrives 30 minutes before her flight departs . how many miles did she drive in all ?
Options: a ) 45 , b ) 175 , c ) 210 , d ) 245 , e ) 280
Rationale: after driving at 15 miles per hourfor one hour , this distance left to cover is d - 15 . say this distance is x miles . now , we know that the difference in time between covering this distance at 15 miles per hour and 60 miles per hour is 1 + 1 / 2 = 3 / 2 hours . so , we have that x / 15 - x / 60 = 3 / 2 - - > 4 x / 60 - x / 60 = 3 / 2 - - > 3 x / 60 = 3 / 2 - - > x = 30 . total distance = x + 15 = 45 miles . answer : a
Answer: a
Question (general): on dividing a number by 48 , we get 29 as remainder . on dividing the same number by 8 , what will be the remainder ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "number = 48 x + 29 ( ∵ since the number gives 29 as remainder on dividing by 48 ) = ( 6 × 8 × x ) + ( 3 × 8 ) + 5 hence , if the number is divided by 8 , we will get 5 as remainder . answer : d"
Answer: d
Question (gain): a shopkeeper sells 600 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 35 , e ) 21
Rationale: sp per metre = 18000 / 600 = rs . 40 loss per metre = rs . 5 cp per metre = 40 + 5 = rs . 45 . answer : d
Answer: d
Question (geometry): obra drove 140 π meters along a circular track . if the area enclosed by the circular track on which she drove is 57,600 π square meters , what percentage of the circular track did obra drive ?
Options: a ) 6.67 % , b ) 12.5 % , c ) 18.75 % , d ) 29.16 % , e ) 33.3 %
Rationale: "area enclosed by the circular track on which she drove is 57,600 π square meters so , π ( r ^ 2 ) = 57,600 π - - - > ( r ^ 2 ) = 57,600 - - - > r = 240 circumference of the circular track = 2 π r = 480 π therefore , part of circumference covered = 140 π / 480 π = 29.16 % hence , answer is d ."
Answer: d
Question (physics): a certain number of men can finish a piece of work in 100 days . if there were 10 men less , it would take 10 days more for the work to be finished . how many men were there originally ?
Options: a ) 120 , b ) 105 , c ) 115 , d ) 110 , e ) 140
Rationale: originally let there be x men . less men , more days ( indirect proportion ) therefore ( x - 10 ) : x : : 100 : 110 = ( x - 10 ) x 110 - x ( 100 ) = 10 x = 1100 x = 110 answer is d .
Answer: d
Question (physics): find the cost of fencing around a circular field of diameter 16 m at the rate of rs . 3 a meter ?
Options: a ) 150.84 , b ) 160.6 , c ) 150.45 , d ) 160.99 , e ) 180.4
Rationale: "2 * 22 / 7 * 8 = 50.28 50.28 * 3 = rs . 150.84 answer : a"
Answer: a
Question (physics): a alone can do a piece of work in 6 days and b alone in 8 days . a and b undertook to do it for rs . 3200 . with the help of c , they completed the work in 3 days . how much is to be paid to c
Options: a ) rs . 300 , b ) rs . 400 , c ) rs . 500 , d ) rs . 600 , e ) none of these
Rationale: "explanation : c ' s 1 day ' s work = 1 / 3 − ( 1 / 6 + 1 / 8 ) = ( 1 / 3 − 7 / 24 ) = 1 / 24 a : b : c = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 c ′ sshare = 1 / 8 ∗ 3200 = 400 option b"
Answer: b
Question (probability): find the probability that a number selected from numbers 1 , 2 , 3 , . . . , 30 is a prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 30 , b ) 1 / 30 , c ) 8 / 30 , d ) 3 / 30 , e ) 7 / 30
Rationale: "let x be the event of selecting a prime number . x = { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23,29 } n ( x ) = 10 , n ( s ) = 30 hence , the required probability is 10 / 30 . answer : c"
Answer: c
Question (physics): a worker can load one truck in 6 hours . a second worker can load the same truck in 4 hours . if both workers load one truck simultaneously while maintaining their constant rates , how long , in hours , will it take them to fill one truck ?
Options: a ) 2.1 , b ) 2.4 , c ) 2.7 , d ) 3.0 , e ) 3.3
Rationale: the workers fill the truck at a rate of 1 / 6 + 1 / 4 = 10 / 24 = 5 / 12 of the truck per hour . then the time to fill one truck is 12 / 5 which is 2.4 hours . the answer is b .
Answer: b
Question (general): 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 3 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 3 40 + 10 + 3 - 7 = 46 like apple answer : b
Answer: b
Question (general): in a group of cows and hens , the number of legs are 16 more than twice the number of heads . the number of cows is :
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: "let no of cows be x , no of hens be y . so heads = x + y legs = 4 x + 2 y now , 4 x + 2 y = 2 ( x + y ) + 16 2 x = 16 x = 8 . answer : d"
Answer: d
Question (physics): the distance between 2 cities a and b is 1000 km . a train starts from a at 10 a . m . and travels towards b at 100 km / hr . another starts from b at 11 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 10 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 10 + 5 = 3 p . m . answer is c"
Answer: c
Question (gain): 3 candidates in an election and received 1256 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate gotin that election ?
Options: a ) 56.7 % , b ) 55 % , c ) 57 % , d ) 60 % , e ) 62 %
Rationale: "total number of votes polled = ( 1256 + 7636 + 11628 ) = 20520 so , required percentage = 11628 / 20520 * 100 = 56.7 % a"
Answer: a
Question (geometry): the sum of two numbers is 16 and the sum of their squares is 113 . find the numbers .
Options: a ) 1 and 2 , b ) 4 and 5 , c ) 7 and 8 , d ) 2 and 3 , e ) 6 and 7
Rationale: let the numbers be x and ( 15 - x ) . then , x 2 + ( 15 - x ) 2 = 113 = > x 2 + 225 + x 2 - 30 x = 113 = > 2 x 2 - 30 x + 112 = 0 = > x 2 - 15 x + 56 = 0 = > ( x - 7 ) ( x - 8 ) = 0 = > x = 7 or x = 8 . so , the numbers are 7 and 8 . answer is c
Answer: c
Question (geometry): the ratio of the radius of two circles is 1 : 3 , and then the ratio of their areas is ?
Options: a ) 1 : 5 , b ) 1 : 6 , c ) 1 : 9 , d ) 1 : 3 , e ) 1 : 2
Rationale: "r 1 : r 2 = 1 : 3 π r 12 : π r 22 r 12 : r 22 = 1 : 9 answer : c"
Answer: c
Question (physics): if the population of a certain country increases at the rate of one person every 45 seconds , by how many persons does the population increase in 1 hour ?
Options: a ) 80 , b ) 120 , c ) 150 , d ) 180 , e ) 160
Rationale: "answer = 1.33 * 60 = 80 answer is a"
Answer: a
Question (geometry): a cube has one of its faces painted half red and half white . the other faces are completely painted white . what is the ratio between the red painted areas and the white painted areas of the cube ?
Options: a ) 1 : 6 , b ) 1 : 11 , c ) 2 : 5 , d ) 1 : 8 , e ) 3 : 11
Rationale: "let x be the area of each face of the cube . the area painted red is x / 2 the area painted white is x / 2 + 5 x = 11 x / 2 the ratio of red to white is ( x / 2 ) : ( 11 x / 2 ) which is 1 : 11 . the answer is b ."
Answer: b
Question (general): what is the units digit of ( 3 ^ 13 ) ( 4 ^ 13 ) ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: "- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 13 = 3 ^ 4 * 3 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 13 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
Answer: a
Question (general): bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 63 more . what was his original selling price ?
Options: a ) $ 850 , b ) $ 990 , c ) $ 1050 , d ) $ 1180 , e ) $ 1340
Rationale: "let p be the original purchase price of the product . bill originally sold the product for 1.1 * p . in the second scenario , the purchase price is 0.9 * p . a 30 % profit means the selling price would be 1.3 * 0.9 * p = 1.17 * p thus , according to the information in the question , 1.17 p - 1.1 p = 63 0.07 = 63 p = 900 the original selling price was 900 * 1.1 = 990 . the correct answer is b ."
Answer: b
Question (gain): one - third of 1206 is what percent of 162 ?
Options: a ) 324.11 , b ) 300.12 , c ) 248.14 , d ) none of these , e ) can not be determined
Rationale: "answer let one - third of 1206 is n % of 162 . ∵ 1206 / 3 = ( n x 162 ) / 100 ∴ n = ( 402 x 100 ) / 162 = 248.14 correct option : c"
Answer: c
Question (general): 1399 x 1399
Options: a ) 1957201 , b ) 1981709 , c ) 18362619 , d ) 2031719 , e ) none of these
Rationale: "1399 x 1399 = ( 1399 ) 2 = ( 1400 - 1 ) 2 = ( 1400 ) 2 + ( 1 ) 2 - ( 1 x 1400 x 1 ) = 1957201 . answer : option a"
Answer: a
Question (gain): on a certain road 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 50 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on the road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 20 %
Rationale: 0.1 m = 0.50 e = > e / m = 1 / 5 * 100 = 20 % so answer is e . m - # of motorists e - # of motorists exceeding speed
Answer: e
Question (other): in a group of 7 boys and 8 girls , 5 members are to be selected . in how many different ways can they be selected such that at least 3 boys should be there ?
Options: a ) 1200 , b ) 1500 , c ) 1281 , d ) 1339 , e ) 1296
Rationale: no of boys = 7 no of girls = 8 therefore , no of ways at least 3 boy can be selected = 7 c 5 * 8 c 0 + 7 c 4 * 8 c 1 + 7 c 3 * 8 c 2 = 1281 ans - c
Answer: c
Question (general): the average marks of a class of 40 students is 44 and that of another class of 45 students is 70 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 69.5 , e ) 52.9
Rationale: "sum of the marks for the class of 40 students = 40 * 44 = 1760 sum of the marks for the class of 45 students = 45 * 70 = 3150 sum of the marks for the class of 85 students = 2760 + 3150 = 5910 average marks of all the students = 5910 / 85 = 69.5 . answer : d"
Answer: d
Question (general): { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x + 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = - 5 , x = - 10 andx = 5 / 2 = 2.5 . so , three solutions present in our set of 12 distinct numbers , therefore p = 3 / 12 = 1 / 4 . answer : c .
Answer: c
Question (gain): a towel , when bleached , was found to have lost 20 % of its length and 10 % of its breadth . the percentage of decrease in area is
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 38 % , e ) 40 %
Rationale: "let original length = x and original breadth = y . decrease in area = xy - 80 x x 90 y 100 100 = xy - 18 xy 25 = 7 xy . 25 decrease % = 7 xy x 1 x 100 % = 28 % . 25 xy a )"
Answer: a
Question (general): 5 / 8 of 3 / 10 of a number is greater than 4 / 9 of 1 / 4 of the same number by 55 . what is half of that number ?
Options: a ) 310 , b ) 312 , c ) 320 , d ) 314 , e ) 360
Rationale: "let no . be x 5 / 8 * 3 / 10 * x - 4 / 9 * 1 / 4 * x = 55 by further solving 15 x / 80 - 4 x / 36 = 55 11 x / 144 = 55 x = 720 we have to find x / 2 = 720 / 2 = 360 answer : e"
Answer: e
Question (general): the average of 10 numbers is calculated as 18 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 16 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 18 + 36 – 26 = 190 = > 190 / 10 = 19 c )"
Answer: c
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 34.5 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 5 ) = 47 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 47 = 34.5 km answer : c"
Answer: c
Question (general): what is the remainder when 1024 * 1047 * 1050 * 1053 is divided by 33 ?
Options: a ) 3 , b ) 27 , c ) 30 , d ) 21 , e ) 18
Rationale: "take the remainder from each of 1024 / 33 , 1047 / 33 and so on . . 1024 / 33 gives remainder = 1 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 1 * 24 * 27 * 30 break them into pairs 1 * 24 / 33 gives remainder 24 and 27 * 30 / 33 gives remainder 18 so 24 * 18 / 33 gives remainder 3 . a"
Answer: a
Question (general): the average of first 20 natural numbers is ?
Options: a ) 10.5 , b ) 11.4 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 20 natural no . = 420 / 2 = 210 average = 210 / 20 = 10.5 answer : a"
Answer: a
Question (gain): by investing in 1623 % stock at 64 , one earns rs . 1500 . the investment made is
Options: a ) rs . 9600 , b ) rs . 7500 , c ) rs . 5640 , d ) rs . 5760 , e ) rs . 6760
Rationale: "explanation : market value = rs . 64 face value is not given and hence take it as rs . 100 16 2 / 3 % of the face value = 50 / 3 ie , to earn 50 / 3 , investment = rs . 64 hence , to earn rs . 1500 , investment needed = 64 × 3 × 1500 / 50 = 5760 answer : option d"
Answer: d
Question (general): the sum of the squares of the first 15 positive integers ( 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + . . . + 15 ^ 2 ) is equal to 1240 . what is the sum of the squares of the second 15 positive integers ( 16 ^ 2 + 17 ^ 2 + 18 ^ 2 + . . . + 30 ^ 2 ) ?
Options: a ) 2480 , b ) 3490 , c ) 6785 , d ) 8215 , e ) 9255
Rationale: "sum of square of n numbers is found using the formula [ n ( n + 1 ) ( 2 n + 1 ) ] / 6 we have sum of 1 st 15 numbers = 1240 we need to find sum of squares from 16 to 30 which is = sum of squares of 1 st 30 + ve integers - sum of squares of 1 st 15 + ve integers . we will get d - 8215 ; answer : d"
Answer: d
Question (probability): in a department store prize box , 40 % of the notes give the winner a dreamy vacation ; the other notes are blank . what is the approximate probability that 3 out of 5 people that draw the notes one after the other , and immediately return their note into the box get a dreamy vacation ?
Options: a ) 0.12 , b ) 0.23 , c ) 0.35 , d ) 0.45 , e ) 0.65
Rationale: the probability of winning is 40 % = 40 / 100 = 2 / 5 . the probability of not winning is 60 % = 3 / 5 . p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 p ( wwwnn ) = 5 ! 3 ! 2 ! ∗ ( 25 ) 3 ∗ ( 35 ) 2 = 144625 ≈ 23 ( we multiply by 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! , because wwwnn scenario can occur in several ways : wwwnn , wwnwn , wnwwn , nwwwn , . . . the # of such cases basically equals to the # of permutations of 5 letters wwwnn , which is 5 ! 3 ! 2 ! 5 ! 3 ! 2 ! ) . answer : b .
Answer: b
Question (geometry): if the volume of the cube is 729 cm 3 , then the surface area of the cube will be
Options: a ) 486 sq . cm
b ) 456 sq . cm
c ) 446 sq . cm
d ) 476 sq . cm
e ) none of these
Rationale: explanation : a 3 = 729 ; a = 9 surface area = ( 6 x 9 x 9 ) = 486 cm 2 answer : a
Answer: a
Question (gain): what is the rate percent when the simple interest on rs . 1600 amount to rs . 200 in 4 years ?
Options: a ) 4 % , b ) 3.125 % , c ) 5 % , d ) 6 % , e ) 7 %
Rationale: "interest for 1 year = 200 / 4 = 50 interest on rs 1600 p / a = 50 interest rate = 50 / 1600 * 100 = 3.125 % answer : b"
Answer: b
Question (gain): if the simple interest on a certain sum of money for 2 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 14 % , b ) 7 % , c ) 10 % , d ) 15 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 2 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 2 ) = 20 / 2 = 10 % answer : option c"
Answer: c
Question (probability): a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , c sitting together ?
Options: a ) 3 / 14 , b ) 5 / 28 , c ) 3 / 28 , d ) 1 / 7 , e ) 9 / 28
Rationale: total number of arrangement is = 8 ! = 40320 favorable event i . e ) a , b and c can be arranged in 3 ! and the remaining can be arranged in 6 ! since ab can be in any of the four positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : c
Answer: c
Question (general): there are 2 sections a and b in a class , consisting of 50 and 50 students respectively . if the average weight of section a is 60 kg and that of section b is 80 kg , find the average of the whole class ?
Options: a ) 50.78 kg , b ) 49.32 kg , c ) 61.67 kg , d ) 70 kg , e ) 70.89 kg
Rationale: "total weight of 50 + 50 students = 50 * 60 + 50 * 80 = 3000 + 4000 average weight of the class is = 7000 / 100 = 70 kg answer is d"
Answer: d