mathewhe/aqua_rat huggingface dataset:
Question: Set F consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set F?
(A) 5
(B) 6
(C) 56
(D) 46
(E) 1
Rationale: Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
E
Answer: (E) 1
Question: Ravid has d books, which is 3 times as many as Jeff and 1/2 as many as Paula. How many books do the three of them have altogether, in terms of d?
(A)  5/6*d
(B)  7/3*d
(C)  10/3*d
(D)  7/2*d
(E)  9/2*d
Rationale: Ravid has d books;
Jeff has d/3 books;
Paula has 2d books;
Total = d+d/3+2d=10d/3.
Answer: C.
Answer: (C)  10/3*d
Question: One night 15 percent of the female officers on a police force were on duty. If 300 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 90
(B) 180
(C) 270
(D) 500
(E) 1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 300
Number of female officers on duty on that night = 300/2 = 150
(15/100)*F =150
=>F = 1000
Answer E
Answer: (E) 1,000
Question: Suresh and Ramesh started a business investing Rs. 24,000 and Rs. 40,000 respectively. Out of total profit of Rs. 18,000, what is Ramesh's share?
(A) s. 6500
(B) s. 7250
(C) s. 8250
(D) s. 9500
(E) s. 11250
Rationale: Explanation:
Ratio of Suresh and Ramesh's share = 24,000 : 40,000 = 3 : 5
Ramesh's share = Rs. (18000 x 5 / 8) = Rs. 11250
ANSWER: E
Answer: (E) s. 11250
Question: How many three-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: The possible number N can be written as follow:
N = Multiple of LCM(6,10) + 1st such number
N = 30x + 1
Possible values = 1, 31, 61, 91,121,151,181,211,241,271.....991
Answer : None:A
Answer: (A) None
Question: A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
(A) Rs. 650
(B) Rs. 690
(C) Rs. 698
(D) Rs. 700
(E) Rs. 710
Rationale: S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
Answer: (C) Rs. 698
Question: Solution for 2.01+.3+.34
(A) 2.91
(B) 2.65
(C) 2.938
(D) 2.986
(E) 2.999
Rationale: 2.01+.3+.34=0
0=0-2.01-0.3-0.34
0=-2.65
answer :B
Answer: (B) 2.65
Question: The ratio of investments of two partners A and B is 7:5 and the ratio of their profits is 7:10. If A invested the money for 5 months, find for how much time did B invest the money ?
(A) 11 months
(B) 9 months
(C) 7 months
(D) 10 months
(E) NONE OF THESE
Rationale: Explanation:
7x5: 5xk = 7:10
k = 10 months
ANSWER IS D
Answer: (D) 10 months
Question: 90 students represent x percent of the boys at Jones Elementary School. If the boys at Jones Elementary make up 60% of the total school population of x students, what is x?
(A) 122
(B) 150
(C) 225
(D) 250
(E) 500
Rationale: 90=x/100*60/100*x=>x^2 = 9*10000/6 = > x = 122
A
Answer: (A) 122
Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
(A) Rs. 18.20
(B) Rs. 70
(C) Rs. 72
(D) Rs. 88.25
(E) Rs. 80
Rationale: Explanation:
C.P. = Rs.(100/122.5 x 392)= Rs.(1000*1225 x 392)= Rs. 320
Profit = Rs. (392 - 320) = Rs. 72.
ANSWER IS C
Answer: (C) Rs. 72
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ?
(A) 13 m
(B) 14 m
(C) 15 m
(D) 16 m
(E) 17 m
Rationale: Explanation:
the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is=13mts.
ANSWER IS A
Answer: (A) 13 m
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 9:00 a.m. and drives north on the same highway at an average speed of 60 km per hour. Mr. Dinkle will
(A) overtake Mr. Smitherly at 10:30 a.m.
(B) overtake Mr. Smitherly at 11:30 a.m.
(C) overtake Mr. Smitherly at 2:00 p.m.
(D) be 30 miles behind at 9:35 a.m.
(E) never overtake Mr. Smitherly
Rationale: After one hour, Mr. Smitherly is ahead by 50 km.
Mr. Dinkle gains on Mr. Smitherly 10 km each hour.
Five hours after 9:00 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: (C) overtake Mr. Smitherly at 2:00 p.m.
Question: A 6-liter solution is 40% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?
(A) 1.2
(B) 1.5
(C) 1.8
(D) 2.1
(E) 2.4
Rationale: Let x be the amount of pure alcohol required.
0.4(6) + x = 0.5(x+6)
0.5x = 3 - 2.4
x = 1.2 liters
The answer is A.
Answer: (A) 1.2
Question: The list price of an article is Rs.65. A customer pays Rs.56.16 for it. He was given two successive discounts, one of them being 10%. The other discount is?
(A) 9%
(B) 4%
(C) 3%
(D) 6%
(E) 7%
Rationale: 65*(90/100)*((100-x)/100) = 56.16
x = 4%
Answer: B
Answer: (B) 4%
Question: Which of the following is equal to x!/(x-1)!?
(A) x-1
(B) 1+(1/x)
(C) 1
(D) x+1
(E) x
Rationale: x! = (x -1)! * x
x!/(x-1)! = x
Answer: E
Answer: (E) x
Question: For the set { 4, 4, 5, 5, x}, which of the following values of x will most increase the standard deviation?
(A) 1
(B) (-3.5)^2
(C) 3
(D) 4
(E) 5
Rationale: Standard Deviation Step 1, as pointed out by others, is to find out the mean = 4.5
Step 2, For each number: subtract the Mean and square the result =
(1-4.5)^2=(-3.5)^2
(2-4.5)^2=(-2.5)^2
(3-4.5)^2 =(-1.5)^2
(4-4.5)^2=(.5)^2
(5-4.5)^2=(.5)^2
Clearly (1-4.5)^2=(-3.5)^2 will give you the greatest value among all the other options.
Hence B
Answer: (B) (-3.5)^2
Question: N and M are each 3-digit integers. Each of the numbers 1, 2, 3,4,5 and 6 is a digit of either N or M. What is the smallest possible positive difference between N and M?
(A) 59
(B) 49
(C) 58
(D) 113
(E) 131
Rationale: You have 6 digits: 1,2, 3, 4, 5, 6
Each digit needs to be used to make two 3 digit numbers. This means that we will use each of the digits only once and in only one of the numbers. The numbers need to be as close to each other as possible. The numbers cannot be equal so the greater number needs to be as small as possible and the smaller number needs to be as large as possible to be close to each other.
The first digit (hundreds digit) of both numbers should be consecutive integers
Now let's think about the next digit (the tens digit). To minimize the difference between the numbers, the tens digit of the greater number should be as small as possible and the tens digit of the smaller number should be as large as possible . So let's not use 1 and 6 in the hundreds places and reserve them for the tens places Now what are the options?
Try and make a pair with (2** and 3**). Make the 2** number as large as possible and make the 3** number as small as possible.
265 and 314 (difference is 49) or
Try and make a pair with (4** and 5**). Make the 4** number as large as possible and make the 5** number as small as possible. We get 463 and 512 (difference is 49)
B
Answer: (B) 49
Question: All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 148 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quantity of water in container A?
(A) 648
(B) 888
(C) 928
(D) 1184
(E) None of these
Rationale: B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 148 liters was transferred from container C to container B, then both the containers would have equal quantities of water.
5k - 148 = 3k + 148 => 2k = 296 => k = 148
The initial quantity of water in A = 8k = 8 * 148 = 1184 liters.
ANSWER:D
Answer: (D) 1184
Question: What is the average of four tenths and five thousandths
(A) 0.2022
(B) 0.3325
(C) 0.2025
(D) 0.2012
(E) 0.2114
Rationale: Explanation:
Four tenths = 0.4
Five thousandths = 0.005
The average is (0.4 + 0.005)/2 = 0.2025
Answer: C
Answer: (C) 0.2025
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
(A) 16 min
(B) 26 min
(C) 34 min
(D) 20 min
(E) 12 min
Rationale: Speed Ratio = 1:4/5 = 5:4Time Ratio
= 4:51 -------- 5 4 --------- ? è 20
Answer: D
Answer: (D) 20 min
Question: If u and v are two different prime numbers, which of the following cannot be true?
(A) uv is odd.
(B) u + v is even.
(C) u + v is odd.
(D) uv is even.
(E) u/v is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (u/v=integer means that u is a multiple of v).
Answer: E.
All other options are possible:
A. uv is odd -->u=3 and v=5;
B. u + v is even -->u=3 and v=5;
C. u + v is odd -->u=2 and v=3;
D. uv is even --> u=2 and v=3;
E
Answer: (E) u/v is an integer
Question: A train sets off at 2 p.m. at the speed of 70 kmph. Another train starts at 3:30 p.m. in the same direction at the rate of 85 kmph. At what time the trains will meet?
(A) 10.37 p.m
(B) 10.20 p.m
(C) 10.30 p.m
(D) 10.38 p.m
(E) 10.10 p.m
Rationale: D = 70 * 1 ½ = 105 km
RS = 85 – 70 = 15
T = 105/15 = 7 h
3.30 + 7 h = 10.30 p.m.
Answer: C
Answer: (C) 10.30 p.m
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
(A) Sunday
(B) Friday
(C) Saturday
(D) Monday
(E) None of these
Rationale: Explanation :
Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366
(Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday
Answer : Option A
Answer: (A) Sunday
Question: The difference between simple interest and compound interest of a certain sum of money at 20% per annum for 2 years is $48. Then the sum is
(A) $600
(B) $1000
(C) $1200
(D) $1500
(E) $2000
Rationale: 20% of (Year 1 Interest) = 20% of (20% of Principal) = 48
Principal = $1200
Answer (C)
Answer: (C) $1200
Question: What is the height of the triangle?
I.	The area of the triangle is 20 times its base.
II.	The perimeter of the triangle is equal to the perimeter of a square of side 10 cm.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
I. A = 20 x B ⇒1-div-1by2 x B x H = 20 x B⇒H = 40.
I alone gives the answer.
II gives, perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
answer is (A).
Answer: (A) I alone sufficient while II alone not sufficient to answer
Question: If jeya rows 21 km upstream and 56 km down steam taking 3 hours each, then the speed of the stream
(A) 1.5 kmph
(B) 0.2 kmph
(C) 0.3 kmph
(D) 0.4 kmph
(E) 0.5 kmph
Rationale: Speed upstream = 21/3 = 7 kmph
Speed down stream = 56/7 = 8 kmph
Speed of stream = ½ (8-7) = 0.5 kmph
ANSWER:E
Answer: (E) 0.5 kmph
Question: Dacid obtained 51, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 29
(B) 38
(C) 39
(D) 70
(E) 75
Rationale: Average = (51 + 65 + 82 + 67 + 85)/5
= 70
Answer: D
Answer: (D) 70
Question: The population of a town is 7800. It decreases annually at the rate of 10% p.a. What was its population 2 years ago?
(A) 9600
(B) 8000
(C) 8500
(D) 9500
(E) 10000
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
7800 Ã— 100/90 Ã— 100/90 = 9629
A)
Answer: (A) 9600
Question: In a certain lottery, the probability that a number between 12 and 20, inclusive, is drawn is 1/4 . If the probability that a number 12 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn?
(A)  1/18
(B)  1/6
(C)  1/3
(D)  1/2
(E)  7/12
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 12 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or lessOR both)
2/3 + P(Set 2) - 1/4 = 1
P(Set 2) = 7/12
Answer (E)
Answer: (E)  7/12
Question: The largest 4 digit number exactly divisible by 90 is?
(A) 9935
(B) 9939
(C) 9944
(D) 9954
(E) 9990
Rationale: Largest 4-digit number = 9999
90) 9999 (111
9990
------------ Largest number divisible by 90 is 9990
Answer : E
Answer: (E) 9990
Question: A man swims downstream 120 km and upstream 50 km taking 5 hours each time; what is the speed of the current?
(A) 3 kmph
(B) 7 kmph
(C) 13 kmph
(D) 6.5 kmph
(E) 7:3kmph
Rationale: Explanation:
120 --- 5 DS = 24
? ---- 1
50 ---- 5 US = 10
? ---- 1 S = ?
S = (24 - 10)/2 = 7
Answer: Option B
Answer: (B) 7 kmph
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should A pay?
(A) 270
(B) 279
(C) 226
(D) 231
(E) 232
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
8/29 * 841 = 232
Answer: E
Answer: (E) 232
Question: Find the number of different prime factors of 1250
(A) 4
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: Explanation:
L.C.M of 1250 = 2 x 5 x 5 x 5 x 5
2, 5
Number of different prime factors is 2.
Answer: Option B
Answer: (B) 2
Question: A speed of 24 metres per second is the same as :
(A) 60.4 km/hr
(B) 86.4 km/hr
(C) 65 km/hr
(D) 68.5 km/hr
(E) None
Rationale: Sol.
24 m/sec = [24 * 18/5] km/hr = 86.4 km/hr.
Answer B
Answer: (B) 86.4 km/hr
Question: The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
(A) 3 and 5
(B) 3 and 6
(C) 3 and 7
(D) 3 and 8
(E) 3 and 9
Rationale: Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
As an exercise, check that the perimeter of this rectangle is 16 and its area is 15.
Answer A
Answer: (A) 3 and 5
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 26 sec. What is the length of the goods train?
(A) 230
(B) 240
(C) 250
(D) 270
(E) 280
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 250)/26 = 20
x = 270 m.
Answer: Option D
Answer: (D) 270
Question: A number increased by 20% gives 1080. The number is?
(A) 800
(B) 700
(C) 500
(D) 900
(E) 600
Rationale: Formula = TOTAL=100% ,INCREASE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 1080 (120 Ã— 9 = 1080)
100 % -------> 900 (100 Ã— 9 = 900)
Option 'D'
Answer: (D) 900
Question: A thief goes away with a SANTRO car at a speed of 40 kmph. The theft has been discovered after half an hour and the owner sets off in a bike at 50 kmph when will the owner over take the thief from the start?
(A) 2 Hrs
(B) 3 Hrs
(C) 1 Hr
(D) 4 Hrs
(E) 5 Hrs
Rationale: |-----------20--------------------|
50 40
D = 20
RS = 50 â€“ 40 = 10
T = 20/10 = 2 hours
ANSWER A
Answer: (A) 2 Hrs
Question: John has taken four (4) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 86. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 90
(C) 92
(D) 94
(E) 97
Rationale: Traditional Method:
Total scored till now 82*4=328
Total score to avg 86 in 6 tests = 86*6=516
Total to be scored on 2 tests = 516-328=188
Avg on 2 tests = 188/2 = 94
Answer: D
Answer: (D) 94
Question: If 6<x<10<y<17, then what is the greatest possible positive integer difference of x and y?
(A) 3
(B) 4
(C) 10
(D) 6
(E) 7
Rationale: Let x=6.1 and y=16.1
Greatest possible difference=16.1-6.1=10
Answer C
Answer: (C) 10
Question: Joshua is fifth from the bottom in a queue of 100 boys.
What is the position of Joshua from the top of the queue?
(A) 51
(B) 52
(C) 53
(D) 54
(E) 55
Rationale: Solution:
51
Explanation:
The position of boys higher than Joshua in the queue is 100 - 50 = 50.
Therefore, the position of Joshua from the top is 50 + 1 = 51.
Answer A
Answer: (A) 51
Question: Robert's salary was decreased by 30% and subsequently increased by 30%. how much percentage does he lose?
(A) 10%
(B) 9%
(C) 25%
(D) 30%
(E) 50%
Rationale: let original salary be $100
Salary after decreasing 30% = 100 - 100 x 30/100 = $70
Salary after increasing 30% on $70 = 70 + 70 x 30/100 = $91
Percentage of loss = 100 - 91 = 9%
Answer : B
Answer: (B) 9%
Question: The average of temperatures at noontime from Monday to Friday is 45; the lowest one is 42, what is the possible maximum range of the temperatures?
(A) 15
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: there are 5 days so the sum of temperature can be 45*5=225
lowest is 42. to find the maximum range we can say the temperature was the lowest for 4 of the 5 days
so 4*42=168.
on the fifth day it is 225-168=57
range is therefore 57-42=15
answer A
Answer: (A) 15
Question: A certain taxi company charges $2.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
(A) 15.6
(B) 18.1
(C) 17.5
(D) 18.7
(E) 19.1
Rationale: A certain taxi company charges $2.50 for the first 1/5 of a mile plus $0.40 for each additional 1/5 of a mile. What would this company charge for a taxi ride that was 8 miles long?
A. 15.60
B. 16.00
C. 17.50
D. 18.70
E. 19.10
1/5 miles = 0.2 miles.
The cost of 8 miles long ride would be $2.50 for the first 0.2 miles plus (8-0.2)/0.2*0.4 = $2.50 + $15.6 = $18.1.
Answer: B.
Answer: (B) 18.1
Question: A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time?
(A) 43 kmph
(B) 45 kmph
(C) 47 kmph
(D) 49 kmph
(E) 42 kmph
Rationale: B
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
Answer: (B) 45 kmph
Question: What will be the product of (25-1)*(25-2)*(25-3)*..............*(25-49)*(25-50)?
(A) 0
(B) 1
(C) 625
(D) less than -100,000
(E) more than 100,000
Rationale: One of the terms is (25-25) so the product is 0.
The answer is A.
Answer: (A) 0
Question: 0.9999+0.1111=?
(A) 1
(B) 1.0001
(C) 1.0021
(D) 1.111
(E) 1.1111
Rationale: 0.9999 + 0.1111
= 0.9999 + 0.111 + 0.0001
= (0.9999 + 0.0001) + 0.111
= 1 + 0.111
= 1.111
D
Answer: (D) 1.111
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 3. What could be the ratio of Cats to dogs in the pet store?
(A) 12:15
(B) 1:4
(C) 1:5
(D) 2:5
(E) 1:3
Rationale: Say theratio of cats to dogs is a/b. Then the numberof cats would be ax and the number of dogs bx, for some positive integer x.
We are told that ax - bx = 3 --> x(a - b) = 3. Since 3 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*13.
The above implies that either x = 1 and (a - b) = 3 or x = 3 and (a - b )= 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.
For the original question only option which fits is E, 4:5. Cats = 3*4 = 12 and dogs = 3*5 = 15.
Answer: A.
Answer: (A) 12:15
Question: How many ways could five people sit at a table with eight seats in which three of the eight seats will remain empty?
(A) 6720
(B) 6520
(C) 56
(D) 120
(E) 40
Rationale: ways in which 5 seats out 8 can be selected = 8C5
ways in which 5 people can be arranged in 5 seats = 5!
Total ways of arrangement = 8C5*5!
=(8!/(5!*3!))*5!
=56*120
=6720
Ans = A
Answer: (A) 6720
Question: What is the difference between local value & face value of 7 in the numeral 65793?
(A) 693
(B) 656
(C) 691
(D) 9890
(E) 10000
Rationale: (Local value of 7) - (Face value of 7)
= (700 - 7) = 693
A
Answer: (A) 693
Question: A cube of volume 1000 cm 3 is divided into small cubes of 1 cm 3 ..& all the outer surfaces are painted how many cubes will be there with (at least one side painted or no side painted)
(A) 477
(B) 488
(C) 456
(D) 425
(E) 495
Rationale: Number of cubes with No side painted = 8*8*8 = 512
Number of cubes with atleast one side painted = 1000-512= 488
ANSWER:B
Answer: (B) 488
Question: From a theatre troupe of eight members, including Lou, one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine. What is the probability that Lou will NOT be chosen to play either Abel or Caine?
(A) 1/168
(B) 1/8
(C) 1/4
(D) 1/3
(E) 3/4
Rationale: "one person will be randomly chosen to play Abel, another person will be randomly chosen to play Barry, and a third person will be randomly chosen to play Caine"
The above statement is NOT clear
Still a solution:
For 8 students we have 3 posts
one post can be occupied by only one member
no two posts can be occupied by the same member
probability(P) for a member getting selected for particular 2 of the 3 posts=
probable outcomes=1(Caine)+1(Abel)=2
total outcomes=1(Caine)+1(Abel)+1(Barry)+5(non post positions)=8
=2/8=1/4
Probability required for the given case= 1-P=1-1/4=3/4
Answer: E
Answer: (E) 3/4
Question: 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
(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) 0.8
Question: The distance that light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100000 years is:
(A) 111 × 1827 miles
(B) 999× 1238 miles
(C) 346 × 1012 miles
(D) 587 x 10^15 miles
(E) 587 × 1012 miles
Rationale: The distance of the light travels in one years is:
5,870,000,000,000 = 587 * 10 ^10
The distance of the light travels in 100000 years is:
= 587 * 10^10 x 10 ^5 = 587 x 10^15 miles
Answer :D
Answer: (D) 587 x 10^15 miles