mathewhe/aqua_rat huggingface dataset:
Question: In a rectangular coordinate system, points O (2,0), P (2,6), and Q (8,0) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
(A) (3,4)
(B) (5,3)
(C) (3,2)
(D) (3,3)
(E) (4,3)
Rationale: All points equidistant from O and Q lie on the line x = 5, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 3, so the fire station should lie on this line.
These two intersect at (5,3) and that will be the point equidistant from all 3 points.
The answer is B.
Answer: (B) (5,3)
Question: Whats the reminder when 879,548,521,456,258,759,653,258,778,455,658,985 is divided by 4
(A) 1
(B) 7.
(C) 2.
(D) 3
(E) 9
Rationale: A number ending in a 0 is divisible by 2. A number ending in 2 zeroes is divisible by 4.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
879,548,521,456,258,759,653,258,778,455,658,985 = 879,548,521,456,258,759,653,258,778,455,658,900+85
The first number is divisible by 16. You just have to find the remainder when you divide 5287 by 16. That will be the remainder when you divide the original number by 4.
85/4 gives remainder 1.
Answer (A)
Answer: (A) 1
Question: A car gets 28 miles to the gallon. If it is modified to use a solar panel, it will use only 80 percent as much fuel as it does now. If the fuel tank holds 15 gallons, how many more miles will the car be able to travel, per full tank of fuel, after it has been modified?
(A) 85
(B) 90
(C) 95
(D) 100
(E) 105
Rationale: Originally, the distance the car could go on a full tank was 15*28=420 miles.
After it has been modified, the car can go 28/0.8= 35 miles per gallon.
On a full tank, the car can go 15*35= 525 miles, thus 105 miles more.
The answer is E.
Answer: (E) 105
Question: If 4 2/3 is subtracted form 10 1/2 and the difference is multiplied by 450, then what is the final answer?
(A) 2725
(B) 2675
(C) 2875
(D) 2525
(E) None of these
Rationale: Final answer = (10 1/2 - 4 2/3) * 450
= 5 5/6 * 450 = 5 * 450 + 5/6 * 450
= 2250 + 375 = 2625.
ANSWER:E
Answer: (E) None of these
Question: What does the hexa number E78 in radix 7.
(A) 12455
(B) 14153
(C) 14256
(D) 13541
(E) 14541
Rationale: conversion of hexa decimal to decimal
(E78)=(8*16^0) + (7*16^1) + (14*16^2)=8 + 112 + 3584 =3704
conversion of decimal to Radix 7
3704/7:reminder:1 and dividend:529
529/7:reminder:4 and dividend:75
75/7:reminder:5 and dividend:10
10/7:reminder:3 and dividend:1
1/7:reminder 1
Then finally result is:13541
ANSWER:D
Answer: (D) 13541
Question: Rectangular tile each of size 70cm by 30cm must be laid horizontally on a rectangular floor of size 110cm by 130cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is:
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Area of tile = 70*30 = 2100
Area of floor = 130*110 = 14300
No of tiles = 14300/2100 = 6.8
So, the no of tile = 6
ANSWER:A
Answer: (A) 6
Question: Which of the following is closest to 10^170 – 10^30 ?
(A) 10^210
(B) 10^180
(C) 10^170
(D) 10^90
(E) 10^6
Rationale: 10^170 – 10^30
10^30 * (10^140 – 1)
as we know 10^2 - 1 means 100-1 and we get 99, which is approximately 100. hence (10^140 – 1) would remain as 10^140.
and 10^30 * 10^150 = 10^180. Answer is C.
Answer: (C) 10^170
Question: When average age of 25 members are 0, how many members greater than 0?
(A) 17
(B) 24
(C) 21
(D) 23
(E) 25
Rationale: Average of 25 numbers = 0.
Sum of 25 numbers (0 x 25) = 0.
It is quite possible that 24 of these numbers may be positive and if their sum is a then 25th number is (-a)
Answer is 24 (B)
Answer: (B) 24
Question: The average of the marks of 11 students in a class is 36. If the marks of each student are doubled, find the new average?
(A) 69
(B) 70
(C) 71
(D) 72
(E) 75
Rationale: Sum of the marks for the 11 students = 11 * 36 = 396. The marks of each student are doubled, the sum also will be doubled.
The new sum = 396 * 2 = 792. So, the new average = 792/11 = 72.
ANSWER:D
Answer: (D) 72
Question: David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 2,500 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 160,000. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
(A) 45,000
(B) 40,000
(C) 50,000
(D) 55,000
(E) 60,000
Rationale: let the rate be x, then population of the bacteria after each hour can be given as 2500, 2500x, 2500(x^2), 2500(x^3)
now population at 4pm =160,000
thus we have 2500(x^3) = 160,000 =64
thus x=4
therefore population at 3pm = 2500(16) = 40,000
Answer : B
Answer: (B) 40,000
Question: A car starts from X and moves towards Y. At the same time another car starts from Y and moves towards X. Both travel at a constant speed and meet after 6 hours. During that time, the faster car traveled 1/3 of the distance XY. How long would it take the slower car to travel the distance XY?
(A) 6 hours
(B) 9 hours
(C) 10 hours
(D) 12 hours
(E) 15 hours
Rationale: If one car travelled 1/3, then the other car must have travelled only 2/3, as they are meeting after 6 hours in a certain point. So:
(2/3)XY= 6*y --> It took the car 6 hours to travel 2/3 of the distance at a constant speed y.
So if we solve this last equation:
2XY= 3*6*y= 9*y --> It will take this car 9 hours in total to reach its final destination.
Answer: B
Answer: (B) 9 hours
Question: X can do a piece of work in 40 days; Y can do the same in 30 days. X started alone but left the work after 10 days, then Y worked at it for 10 days. Z finished the remaining work in 10 days. Z alone can do the whole work in?
(A) days
(B) days
(C) days
(D) 1/2 days
(E) days
Rationale: Explanation:
10/40 + 10/30 + 10/x = 1
x = 24 days
Answer: A
Answer: (A) days
Question: The average marks of 30 students in a class is 60. But a student mark is wrongly noted as 90 instead of 15 then find the correct average marks?
(A) 55.65
(B) 57.5
(C) 62.5
(D) 45.25
(E) 50
Rationale: correct avg marks = 60+(15-90)/30
avg = 60-2.5 = 57.5
Answer is B
Answer: (B) 57.5
Question: A man is 22 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is
(A) 8 years
(B) 2 years
(C) 7 years
(D) 8 years
(E) 5 years
Rationale: Let's Son age is x, then Father age is x+22.
=> 3(x+3) = (x+22+3)
=> 3x+9 = x+25
=> 2x = 16 years = 8 YEARS
Answer: D
Answer: (D) 8 years
Question: In how many ways can the letters of a word 'ENGINEERING' be arranged such that vowels DO NOT together?
(A) 253000
(B) 263000
(C) 273000
(D) 283000
(E) 293000
Rationale: ENGINEERING
total 11 letters
E=3,N=3,G=2,I=2,R=1,
Total no. of ways = 11!/3!3!2!2! = 277200
when vowels come together = (EEEII)NNNGGR => 7!/3!2! * 5!/3!2! = 4200
No. of ways when vowels DO NOT together = 277200 - 4200 = 273000
ANSWER:C
Answer: (C) 273000
Question: If 'Pink' is called 'Orange', 'Orange' is called 'Blue', 'Blue' is called 'Red', 'Red' is called 'Green', 'Green' is called 'Black' and 'Black' is called 'white', what would be the color of charcoal ?
(A) White
(B) BLUE
(C) PINK
(D) ORANCE
(E) BLACK
Rationale: Explanation:
Pink → Orange
Orange → Blue
Blue → Red
Red → Green
Green → Black
Black → White
The color of charcoal is 'Black' but in coding language, 'Black' is called 'White'.
ANSWER: A
Answer: (A) White
Question: An art gallery owner is hanging paintings for a new show. Of the five paintings she has to choose from, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
(A) 18
(B) 30
(C) 64
(D) 20
(E) 216
Rationale: Arrangement means permutations questions..
5P3 = 5!/3! = 20
.
ANS option D is correct answer..
Answer: (D) 20
Question: What is the area G of the square with the following coordinates: (x, y), (20, 20), (20, 5), (x, 5)?
(A) 60.
(B) 85.
(C) 125.
(D) 225.
(E) It cannot be determined from the information given
Rationale: Length of one side= 15 (20-5)
Since, its a square, the area will be G= 15^2= 225
D is the answer
Answer: (D) 225.
Question: The average weight of 8 persons is increased by 2.5 kg when one of them who weighs 56 kg is replaced by a new man. The weight of the new man is
(A) 76 years
(B) 78 years
(C) 86 years
(D) 16 years
(E) 46 years
Rationale: ANSWER: A
Answer: (A) 76 years
Question: If a farmer sells 15 of his goats, his stock of feed will last for 4 more days than planned, but if he buys 20 more goats, he will run out of feed 3 days earlier than planned. If no goats are sold or bought, the farmer will be exactly on schedule. How many goats does the farmer have?
(A) 12
(B) 24
(C) 48
(D) 60
(E) 55
Rationale: Say farmer has n goat and he is good for d days.:-
We have 3 equations given in question:-
(n-15) * d+4 =(n+20) *(d-3) = n * d
Solving these: (You can solve 1st and 3rd and 2nd and 3rd together)
We get:
20d-3n=60
4n-15d =60
=> n=60
Ans D it is!
Answer: (D) 60
Question: As a bicycle salesperson, John earns a fixed salary of $10 per week plus $6 per bicycle for the first 6 bicycles he sells, $12 per bicycle for the next 6 bicycles he sells, and $18 per bicycle for every bicycle sold after first 12. This week, he earned more than twice as much as he did last week. If he sold x bicycles last week and y bicycles this week, which of the following statements must be true? I. y<2x II. y>x III. y>3
(A) II,III only
(B) I,III only
(C) I,II only
(D) II only
(E) I only
Rationale: II. y>x --> since this week, John earned more than he did last week and the total salary is in direct relationship with the # of bicycle sold, then y (# of bicycle sold this week) must be more than x (# of bicycle sold last week);
III. y>3 --> if John sold 3 bicycles this week then this week he earned 10+3*6=$28, which cannot be more than twice as much as he earned the last week, since the minimum salary is fixed to $10. So y must be more than 3;
I. y<2x --> is not always true.
Answer: A
Answer: (A) II,III only
Question: I have an amazing bath tub having both hot and cold water taps.
The cold water tap can fill my tub in 6 hours while cold water tap can fill the tub in approx 4 hours.
I turned them on simultaneously but forgot to close the lid which remove water out of tub.
The lid can empty the tub in exact 13 hours.
Since both taps are open along with the lib , can you estimate the time needed to fill the bath tub ?
(A) 6 hours
(B) 5 hours
(C) 2 hours
(D) 4 hours
(E) 3 hours
Rationale: C
3 hours
Explanation :
(1/4 + 1/6 - 1/12) ^ (-1)
= (1/3)^(-1) = 3
Answer: (E) 3 hours
Question: The Sum of the average (arithmetic mean) of the even integers from 0 to 100 inclusive and the average (arithmetic mean) of the even integers from 0 to 50 inclusive?
(A) 15
(B) 125
(C) 25
(D) 75
(E) 50
Rationale: So, according to A mean of a set of even numbers from 0 to 100 =(0+100)/2=50 and mean of a set of even numbers from 0 to 50 =(0+50)/2=25
Sum=50+25=75
Answer: D.
Answer: (D) 75
Question: The forth proportional to 15,30,45 is?
(A) 100
(B) 45
(C) 90
(D) 75
(E) 100
Rationale: Let the fourth proportional to 15,30,45 be x
then 15:30::45:x
15x = 30*45
x = 90
Answer is C
Answer: (C) 90
Question: (4 x 10^4) + (2 x 10^2) + (4 x 10) =
(A) 302400
(B) 32400
(C) 40240
(D) 3240
(E) 324
Rationale: When you multiply a number by 10 you just add a zero
=> 4 x 10^4 => add 4 zeros => 4 x 10^4 = 40000
=>2 x 10^2 = 200
=> 4 x 10 = 40
=>4 x 10^4 + 2 x 10^2 + 4 x 10 = 40000 + 200 + 40 = 40240
=> answer is C ( 40240)
Answer: (C) 40240
Question: Souju's age is 150% of what it was 10 years ago, but 75% of what it will be after 10 years. What is her present age?
(A) 25 years
(B) 27years
(C) 30 years
(D) 42 years
(E) 66 years
Rationale: Let the age before 10 years =x. Then,
150x/100=x+10
â‡’150x=100x+1000
â‡’x=1000/50=20
Present age =x+10=20+10=30
ANSWER:C
Answer: (C) 30 years
Question: A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
(A) 22
(B) 28
(C) 120
(D) 287
(E) 278
Rationale: Let speed of the car = x kmphThen speed of the train = (100+50)100x=150100x=32x kmphTime taken by the car to travel from A to B=75x hoursTime taken by the train to travel from A to B=75(32x)+12.560 hoursSince Both start from A at the same time and reach point B at the same time75x=75(32x)+12.56025x=12.560x=25×6012.5=2×60=120
Answer : C
Answer: (C) 120
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 874 in 4 years. The sum is:
(A) s. 650
(B) s. 638
(C) s. 698
(D) s. 700
(E) s. 760
Rationale: S.I. for 1 year = Rs. (874 - 815) = Rs. 59.
S.I. for 3 years = Rs.(59 x 3) = Rs. 177.
Principal = Rs. (815 - 177) = Rs. 638.
Answer: Option B
Answer: (B) s. 638
Question: Sandy had $140 left after spending 30% of the money she took for shopping. How much money did Sandy take along with her?
(A) $180
(B) $200
(C) $220
(D) $240
(E) $260
Rationale: Let the money Sandy took for shopping be x.
0.7x = 140
x = 200
The answer is B.
Answer: (B) $200
Question: A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 6 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour?
(A) 2:33 pm
(B) 2:45 pm
(C) 2:54 pm
(D) 3:06 pm
(E) 3:12 pm
Rationale: The question is asking when the first clock will have chirped 18 times (3*6 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 18th chirp is at 54 minutes after 2:00.
The answer is C.
Answer: (C) 2:54 pm
Question: Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is:
(A) 55 %
(B) 26 %
(C) 44%
(D) 32 %
(E) 16 %
Rationale: Explanation:
Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.(5/6*30)=Rs.25
S.P. of 30 articles = Rs.(6/5*30)=Rs.36
Gain %=(11/25*100)%=44%
ANSWER:C
Answer: (C) 44%
Question: The average salary/head of all the workers ina workshop is Rs.850, if the average salary/head of 7technician is Rs.1000 and the average salary/head of the rest is Rs.780, the total no. of workers in the work-shop is ?
(A) 18
(B) 20
(C) 22
(D) 23
(E) 25
Rationale: Let the total number of workers be y.
So sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y -7 workers.
7 x 1000 + 780(y -7) = 850 y
⇒ 7000 + 780y - 5460 = 850y
⇒ 70y = 1540
∴ y = 22
So total number of workers = 22
C
Answer: (C) 22
Question: A certain box has 11 cards and each card has one of the integers from 1 to 11 inclusive. Each card has a different number. If 2 different cards are selected at random, what is the probability that the sum of the numbers written on the 2 cards is less than the average (arithmetic mean) of all the numbers written on the 11 cards?
(A) 1/11
(B) 2/11
(C) 2/33
(D) 4/55
(E) 5/66
Rationale: The average of the numbers is 6
The total number of ways to choose 2 cards from 11 cards is 11C2 = 55.
The ways to choose 2 cards with a sum less than the average are:
{1,2},{1,3},{1,4},{2,3}
The probability is 4/55
The answer is D.
Answer: (D) 4/55
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
(A) 2/15
(B) 3/17
(C) 5/26
(D) 4/19
(E) 5/21
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: (C) 5/26
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 453
(B) 568
(C) 155
(D) 150
(E) 171
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time)
= (50/3 * 9) m
= 150 m.
Answer: D
Answer: (D) 150
Question: Before leaving for his business trip, Chad asks his assistant to choose and pack four shirts from his closet, which currently contains seven shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the shirts packed but the blue shirt will not?
(A) 3/7
(B) 3/14
(C) 10/35
(D) 5/28
(E) 4/21
Rationale: The total number of ways to choose 4 shirts from 7 is 7C4 = 35
The number of ways to choose a pink shirt plus 3 shirts from 5 is 5C3 = 10
P(a pink shirt but not a blue shirt) = 10/35 = 2/7
The answer is C.
Answer: (C) 10/35
Question: A bakery currently has 8 pies and 3 cakes in its inventory. The bakery’s owner has decided to display 5 of these items in the bakery’s front window. If the items are randomly selected, what is the probability that the display will have exactly 3 pies?
(A) 3/7
(B) 5/7
(C) 4/11
(D) 7/11
(E) 23/33
Rationale: The total number of ways to choose 5 from 11 is 11C5 = 462.
The number of ways that include 3 pies is 8C3*3C2 = 56*3 = 168
P(exactly 3 pies) = 168/462 = 4/11
The answer is C.
Answer: (C) 4/11
Question: x% of y is y% of ?
(A) x/y
(B) 2y
(C) x
(D) 1
(E) can’t be determined
Rationale: x/100*y = y/100*(?)
So, x is the answer.
ANSWER:C
Answer: (C) x
Question: A invested some money in 10% stock at 96.If B wants to invest in an equally good 12% stock ,he must purchase a stock worth of :
(A) Rs. 80
(B) Rs. 115.20
(C) Rs. 120
(D) Rs. 125.40
(E) None of these
Rationale: Solution
For an income of Rs. 10, investment = Rs. 96.
For an income of Rs. 12, investment = Rs.(96/12x12) = Rs. 115.20.
Answer B
Answer: (B) Rs. 115.20
Question: In how many Q ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places? Assume that the pieces are distinct.
(A) 288
(B) Q=144
(C) Q=12
(D) Q=48
(E) 96
Rationale: 4 white chess pieces can be arranged in 4! ways and 4 black pieces can be arranged in 3 ! ways.
W_W_W_W
Number of ways = 4!*3! = 24 * 6 = 144
Answer B
Answer: (B) Q=144
Question: 4, 10, (?), 82, 244, 730
(A) 26
(B) 28
(C) 40
(D) 48
(E) 50
Rationale: Explanation :
4 × 3 - 2 = 10
10 × 3 - 2 = 28
28 × 3 - 2 = 82
82 × 3 - 2 = 244
244 × 3 - 2 = 730
Answer : Option B
Answer: (B) 28
Question: A motor car starts with a speed of 50km/hr with its speed increasing every 2hours by 20kmph. In how many hours will it cover 510kms?
(A) 12 hr
(B) 10hr
(C) 9hr
(D) 11hr
(E) 8hr
Rationale: Distance covered in first 2hours = 50*2 = 100km
Distance covered in next 2hours = 70*2 = 140km
remaining distance = 510- (100+140) = 270km
speed in the fifth hour = 90km/hr
total time to cover 270km = 270/90 = 3 hr
total time taken = 4+(3) = 12hours
correct option is A
Answer: (A) 12 hr
Question: Three numbers are such that the Second is as much lesser than thr third as the first is lesser than the second.If the product of the two smaller numbers is 85 and product of two larger number is 115 then find the middle number
(A) 8
(B) 9
(C) 10
(D) 12
(E) 15
Rationale: Explanation :
its a bit funny sum.if you see the first sentence actually it saying that the numbers are in A.P.now as the first two numbers product is 85 so if you take factor 85 you get 5 and 17..now as per option 17 can not be the middle number so from intuition and seeing the option only 10 could be the middle number where 8.5 is the first number and 11.5 is the last
Answer : C
Answer: (C) 10
Question: A book seller had some books. He sells 50% and still has 540 books. Originally, he had ?
(A) 500 books
(B) 540 books
(C) 108 books
(D) 1080 books
(E) None
Rationale: Answer
âˆµ 50% of N =540
âˆ´ N = (540 x 100)/50 = 1080
Correct Option: D
Answer: (D) 1080 books
Question: The average of 11 observations is 60. If the average of first five observations is 58 and that of the last five is 56, then the sixth observation is.
(A) 85
(B) 90
(C) 100
(D) 110
(E) None of these
Rationale: Explanation :
Sixth observation=[60*11 - (58*5 + 56*5)] = 90.
Answer : B
Answer: (B) 90
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 9:17. The first number ?
(A) 36
(B) 86
(C) 27
(D) 86
(E) 27
Rationale: (3x-9):(5x-9) = 9:17
x = 12 => 3x
=36
Answer:A
Answer: (A) 36
Question: John went to a shop and bought things worth Rs. 25, out of which 30 Paisa went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 17
(B) 18
(C) 19.7
(D) 21
(E) 24
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C)
Answer: (C) 19.7
Question: s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits W are in s(99)?
(A) W=350
(B) W=353
(C) W=354
(D) 356
(E) 357
Rationale: Focus on the points where the number of digits in squares change:
1, 2, 3 - Single digit squares. First 2 digit number is 10.
4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square.
10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square.
32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2.
So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272 = 353.B
Answer: (B) W=353
Question: A train 150 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:
(A) 22
(B) 50
(C) 99
(D) 288
(E) 59
Rationale: Speed of the train relative to man = (150/10) m/sec = (15) m/sec. [(15) * (18/5)] km/hr = 54 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 54 ==> x = 59 km/hr.Answer: E
Answer: (E) 59
Question: A family with 1 mother, 1 father, and 3 children sit in a car with 2 front seats and 3 back seats. If the mother drives with a child in the front, and the father sits in the back center seat with the other two children on either side of him, how many seating arrangements are possible
(A)  3
(B)  6
(C)  4
(D)  8
(E)  10
Rationale: Mother has a fixed place and father, so there are 3! ways to arrange the children, hence B
Answer: (B)  6
Question: Which of the following points falls outside of the region defined by 2y≤6x−10?
(A) (5, 1)
(B) (3, -8)
(C) (2, 0)
(D) (0, -2)
(E) (0, -14)
Rationale: Equation given is 2y<=6x-10
Simplifying this; y<=3x-5
Plug in the values provided in the options,
A. 1<=10
B. -8<=4
C. 0<=1
D.-2<=-5
E. -14<=-12
Option C is the answer.
Answer: (C) (2, 0)
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
(A) 6.25
(B) 6.5
(C) 6.75
(D) 7
(E) None
Rationale: Sol.
Required run rate = 282 - (3.2 x 10) / 40 = 250/40 = 6.25.
Answer A
Answer: (A) 6.25
Question: The arithmetic mean of the set S = {6, K, 5, 11, M, 6} is 7. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
(A) 5
(B) 5.5
(C) 6
(D) 6.5
(E) 7
Rationale: The sum of the numbers is 6*7 = 42
K+M = 42 - 11 - 6 - 6 - 5 = 14
Since K ≠ M, K and M do not equal 7.
Thus one of the two numbers is 6 or less and one is 8 or more.
Then middle two numbers in the set are 6 and 6.
The median is 6.
The answer is C.
Answer: (C) 6