RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: When the integer n is divided by 17, the quotient is x and the remainder is 7. When n is divided by 23, the quotient is y and the remainder is 14. Which of the following is true?
A. 23x + 17y =19
B. 17x –23y = 7
C. 17x +23y =19
D. 14x + 5y = 6
Answer: B. 17x –23y = 7
Explanation: From the problem it follows:
n=17x+7
n=23y+14
So, 17x+7=23y+14
17x-23y=7
The answer is B
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
A.33
B.11
C.38
D.50
Answer: D.50
Explanation: Assume that the person would have covered x km if travelled at 10 km/hr
⇒Speed = DistanceTime=x10.....(Equation1)
Give that the person would have covered (x + 20) km if travelled at 14 km/hr
⇒Speed = DistanceTime=(x+20)14.....(Equation2)
From Equations 1 and 2,
x10=(x+20)1414x=10x+2004x=200x=2004=50
Answer : D
Question: R is the set of positive odd integers less than 40, and S is the set of the squares of the integers in R. How many elements does the intersection of R and S contain ?
A.None
B.Three
C.Four
D.Five
Answer: B.Three
Explanation: squares < 40 {1,4,9,16,25,36}
S = {1,9,25}
R = {1,3,.....40}
Hence B.
Question: A straight fence is to be constructed from posts 7 inches wide and separated by lengths of chain 5 feet long. If a certain fence begins and ends with a post, which of the following couldnotbe the length of the fence in feet? (12 inches = 1 foot)
A.17
B.28
C.35
D.39
Answer: D.39
Explanation: The fence begins and ends with a post: {post = 0.5 feet}{chains = 5 feet}{post = 0.5 feet}...{chains = 5 feet}{post = 0.5 feet}
The minimum length is with 2 posts = 0.5 + 5 + 0.5 = 6 feet. To increase the fence, each time we should add{post = 0.5 feet}{chains = 5 feet}, so 5.5 feet. Thus, the lengths could be:
6 feet;
7+ 5.5 = 12.5 feet;
11.5 + 5.5 = 18 feet;
17 + 5.5 = 23.5 feet;
22.5 + 5.5 = 29feet;
28 + 5.5 = 34.5 feet;
33.5 + 5.5 = 40 feet.
...
We skipped 39 feet.
Answer: D.
Question: Anu normally takes 4 hours more than the time taken by Sachin to walk D km. If Anu doubles her speed, she can make it in 2 hours less than that of Sachin. How much time does Sachin require for walking D km?
A.10 hours
B.4 hours
C.8 hours
D.9 hours
Answer: C.8 hours
Explanation: Explanation :
Let Sachin takes x hours to walk D km.
Then, Anu takes (x + 4) hours to walk D km.
With double of the speed, Anu will take (x + 4)/2 hours.
x – (x + 4)/2 = 2
=> 2x – (x + 4) = 4
=> 2x – x – 4 = 4
x = 4 + 4 = 8 hours
Answer – C
Question: Convert the following into a fraction: 0.5%
A.1/5
B.1/2
C.5/10
D.2/5
Answer: B.1/2
Explanation: 0.5 =5/10 (Simplify: both are divisible by 5)= 1/2
Answer is B.
Question: If 5 < x < 12 and y = x + 3, what is the greatest possible integer value of x + y?
A.23
B.24
C.25
D.26
Answer: D.26
Explanation: x+y = x+x+3 = 2x+3
We need to maximize this value and it needs to be an integer.
2x is an integer when the decimal of x is .0 or .5
The largest such value is 11.5
Then x+y = 11.5 + 14.5 = 26.
The answer is D.
Question: The average weight of 9 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
A.85.5
B.86.5
C.87.5
D.88.5
Answer: C.87.5
Explanation: Total increase in weight =9 × 2.5 = 22.5
If x is the weight of the new person, total increase in weight = x−65
=> 22.5 = x - 65
=> x = 22.5 + 65 = 87.5
ANSWER:C
Question: By selling an article at Rs.120, a profit of 25% is made. Find its cost price?
A.s.96
B.s.45
C.s.120
D.s.180
Answer: A.s.96
Explanation: SP = 120
CP = (SP)*[100/(100+P)]
= 120* [100/(100+25)]
= 120* [100/125]
= Rs.96
Answer: A
Question: Mudit's age 16 years hence will be thrice his age four years ago. Find Mudit's present age?
A.14
B.19
C.27
D.18
Answer: A.14
Explanation: Explanation:
Let Mudit's present age be 'm' years.
m + 16 = 3(m - 4)
=> 2m = 28 => m = 14 years.
Answer:A
Question: Anna left for city A from city B at 5.20 a.m. She travelled at the speed of 80 km/hr for 2 hrs 15 min. After that the speed was reduced to 60 km/hr. If the distance between two cities is 350 kms, at what time did Anna reach city A?
A.10.25 a.m
B.9.25 a.m
C.11.25 a.m
D.12.25 a.m
Answer: A.10.25 a.m
Explanation: A
10.25 a.m
Distance covered in 2 hrs 15 min i.e., 2 1/4 hrs = 80 * 9/4 = 180 hrs.
Time taken to cover remaining distance = (350 - 180)/60 = 17/6 hrs
= 2 5/6 = 2 hrs 50 min
Total time taken = (2 hrs 15 min + 2 hrs 50 min) = 5 hrs 5 min.
So, Anna reached city A at 10.25 a.m.
Question: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance q before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
A.25%
B.50%
C.75%
D.100%
Answer: A.25%
Explanation: John and Karen begin running at opposite ends of a trail until they meet somewhere in between their starting points. They each run at their respective constant rates until John gets a cramp and stops. If Karen runs 50% faster than John, who is only able to cover 25% of the distance q before he stops, what percent longer would Karen have run than she would have had John been able to maintain his constant rate until they met.
Lets say the distance of the trail is 100 miles. Lets also say that J rate = 10 miles/hour and K rate = 15 miles/hour.
If John stops at the 25% mark that means he travels 25 miles in 2.5 hours. It would take Karen t=d/r t=75/15 = 5 hours to reach john. If John had not stopped, their combined rate would 10+15 = 25 miles/hour meaning they would have met in 4 hours. Therefore, she ran one hour longer (25%) longer than she would have needed to if John ran for the entire time.
ANSWER: A) 25%
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
A.5
B.6
C.7
D.9
Answer: C.7
Explanation: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7
Answer:C
Question: The equal amounts of money are deposited in two banks each at 15% per annum for 3.5 years and 10 years respectively. If the difference between their interests is Rs.144, find the each sum?
A.Rs.117.69
B.Rs.147.69
C.Rs.137.69
D.Rs.157.69
Answer: B.Rs.147.69
Explanation: (P*10*15)/100 - (P*3.5*15)/100 = 144
=> P = Rs.147.69
ANSWER:B
Question: A person's present age is two-fifth of the age of his mother. After 8years, he will be one - half of the age of his mother. How old is the mother at present ?
A.25
B.40
C.32
D.45
Answer: B.40
Explanation: Let the mother's present age be x years
Then the person's present age = 2x/5
(2x/5)+8 = 1/2(x+8)
2(2x+40) = 5 (x+8)
x = 40
Answer is B
Question: A group of men decided to do a work in 20days, but 2 of them became absent. If the rest of the group did the work in 22days, Find the original number of men?
A.15
B.22
C.27
D.29
Answer: B.22
Explanation: Original number of men = 2*22 / (22-20) = 22
Answer is B
Question: If the weight of 13 meters long rod is 23.4 kg. What is the weight of 6 meters long rod ?
A.7.2 kg.
B.10.8 kg.
C.12.4 kg.
D.18.0 kg
Answer: B.10.8 kg.
Explanation: Answer
∵Weight of 13 m long rod = 23.4 kg
∴ Weight of 1 m long rod = 23.4 / 13 kg
∴ Weight of 6 m long rod = 23.4 x 6 / 13
= 10.8 kg
Option: B
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
A.1520 m2
B.2420 m2
C.2480 m2
D.2520 m2
Answer: D.2520 m2
Explanation: EXPLANATION
We have: (l – b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m2.
Answer D
Question: A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?
A.40 minutes
B.1 hour
C.1 hr 15 min
D.1 hr 30 min
Answer: C.1 hr 15 min
Explanation: 2km in 1hr=2km/hr
1 km in 10 minutes means [1/10]*60=6km/hr
speed in still water is=1/2(6+2)=4km/hr
Required time=[5/4]hrs means 1hr 15 minutes
ANSWER:C
Question: John walked to the bus stop at a speed of 3 kph, but walked home at a speed of 6 kph. What was his average speed walking to and from the bus stop?
A.9 kph
B.3 kph
C.4.5 kph
D.6 kph
Answer: C.4.5 kph
Explanation: (3 kph + 6 kph)/2= 4.5 kph
Correct answer is C
Question: A word is defined as a sequence of four dots arranged in a row. Each dot is colored either yellow or blue. How many distinct words can be formed?
A.4
B.8
C.12
D.16
Answer: D.16
Explanation: 2^4 = 16
The answer is D.
Question: Find the probability if a two digit number multiplied by 3 but not 5
A.2/15
B.3/15
C.4/15
D.5/15
Answer: C.4/15
Explanation: sample space of 2 digit number = (99-10)+1 = 90
probability of number multiplied by 3 but not 5 = total no. multiplied by 3 - total no. multiplied by 5
= 30 - 6=24
so, probability= 24/90 = 4/15
ANSWER:C
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 5 out of 8 consecutive days in Rwanda?
A.4/7
B.3/7
C.7/32
D.4/28
Answer: C.7/32
Explanation: using Binomial. theorem
nCr (p)^r (q)^n-r
8C5 (1/2)^5 (1/2)^r
which is 7/32
Answer is C.
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 10 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
A.2
B.4
C.12
D.40
Answer: A.2
Explanation: Actual miles/gallon is = 480/40 = 12 miles/gallon.
Current engine miles/gallon is 10 miles/gallon.
Additional 2 miles/gallon is required to match the actual mileage.
IMO option A.
Question: Average of 5 numbers is zero. At most how many numbers may be greater than zero
A.0
B.4
C.5
D.9
Answer: B.4
Explanation: Answer: Option B
Question: A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage
A.25% gain
B.20% gain
C.20% loss
D.15% gain
Answer: A.25% gain
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
A
Question: A train is moving at a speed of 132 km/hr. If the length of the train is 150 meters, how long will it take to cross a railway platform 235 meters long
A.6 ½ sec
B.7 ½ sec
C.8 sec
D.10 ½ sec
Answer: D.10 ½ sec
Explanation: Explanation:
Speed of train = 132 ×(5/18) m/sec = 110/3 m/sec.
Distance covered in passing the platform = (150 + 235) m = 385 m.
Time taken =385 ×(3/110) sec =21/2 sec = 710½ sec
Answer: Option D
Question: If x is a sum of all even integers on the interval 13...65 and y is their number, what is the GCD (x, y)?
A.1
B.13
C.26
D.52
Answer: C.26
Explanation: x = 14 + 16 + ... + 64 = (largest + smallest)/2 *(# of terms) = (14 + 64)/2*26 = 39*26.
GCD of 26 and 39*26 is 26.
Answer: C.
Question: How many pages the book have, if total 300 digits are used to form the page numbers?
A.135 pages
B.136 pages
C.137 pages
D.138 pages
Answer: B.136 pages
Explanation: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 37 pages ... 111 digits
----------------------
Total ...136 pages ...300 digits
ANSWER:B
Question: The sum of two numbers is 16. The difference is 4. What are the two numbers?
A.10-6
B.8-8
C.9-7
D.11-5
Answer: A.10-6
Explanation: Let x be the first number. Ley y be the second number
x + y = 16
x - y = 4
Solve the system of equations by elimination
Adding the left sides and the right sides gives:
x + x + y + -y = 16 + 4
2x = 20
x = 10
Since x + y = 16, 10 + y = 16
10 + y = 16
10 - 10 + y = 16 - 10
y = 6
The numbers are 10 and 6
correct answer is A)10-6
Question: For the sequence a1, a2, a3. ..an, an is defined by an=1/2n−1−1/2n for each integer n≥1. What is the sum of the first 8 terms of the sequence?
A.63/64
B.127/128
C.255/256
D.511/512
Answer: C.255/256
Explanation: a1=1/2^0−1/2^1
a2=1/2^1−1/2^2....
a8=1/2^7−1/2^8
a1+a2+...+a8=1/2^0−1/2^8=255/256
The answer is C.
Question: A can do a piece of work in 15 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
A.5 days
B.6 days
C.7.5 days
D.8.5 days
Answer: C.7.5 days
Explanation: Explanation:
B's 5 days work = 1/10*5=1/2
Remaining work =1âˆ’1/2=1/2
A can finish work =15âˆ—1/2=7.5days
ANSWER IS C
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
A.No profit, no loss
B.5%
C.8%
D.10%
Answer: B.5%
Explanation: Explanation:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =(80/1600 x 100\ )% = 5%. Answer: B
Question: I have only 1$ and 2$ note. I want to give 95$ to John. How many maximum number of 1$ note I need?
A.53
B.35
C.47
D.95
Answer: D.95
Explanation: To give 95$ we need of 95 1$ notes
so ans is D
Question: There are 100 students in a certain geometry class. If one half of the students are boys and one fifth of the boys are under six feet tall, how many boys in the class are under six feet tall?
A.6
B.10
C.18
D.24
Answer: B.10
Explanation: Total Students = 100
One half of the students are boys = 1/2*100 = 50
One fifth of the boys are under six feet tall = 1/5*50 = 10 ...
Therefore Number of boys in the class under six feet tall = 10 ... Answer B....
Alternatively... Number of boys in the class under six feet tall = 1/5 of 1/2 of Total Students = 1/5*1/2*100 = 10...
Answer B
Question: A company has 600 employees, 40% of whom are employed full time. If it hires 80 new employees, 15% of whom are employed part time, what will be the percent increase in part time employees?
A.1 2/3 %
B.2 2/3 %
C.4 %
D.3.33 %
Answer: D.3.33 %
Explanation: Total employee = 600
Full time Empl = 600 * 40/100 =240
Part time Emp = 600 - 240 = 360
New part time empl = 80 * (15/100)
=12
Total new part time Emp = 12+360= 372
Old part time Emp = 360
% increase = (new - old)*100/old
=12*100/360
= 3.33 %
Ans-D
Question: Four friends are pooling their money for pizza. Emma has 8 dollars. Daya has 25% more money than Emma, Jeff has 2/5 of the money Daya has, and Brenda has 4 more dollars than Jeff. How much money does Brenda have?
A.14
B.6
C.7
D.8
Answer: D.8
Explanation: D
8
Emma has 8 dollars.
Daya has 25% more dollars than Emma.
Daya= 8 + 8 x 25%
= 8 + 8 x .25
=8 + 2
=10
Jeff has 2/5 of what Daya has.
= 10 x 2/5
= 4
Brenda has 4 more dollars than Jeff.
= 4 + 4
=8
Brenda has 8 dollars.
The correct answer is D.
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.7 SDs from the mean?
A.12.5
B.13
C.14
D.11.8
Answer: D.11.8
Explanation: 2.7 SD's mean is equal to: +/- 2.7*3 = +/- 8.1
ie. 11.9 to 28.1
Answer is: D
Question: In a flower shop there were 8 flowers in each bouquet. If the seller has doubled the number of flowers in each bouquet then the new average of flowers in each bouque is
A.12
B.16
C.8
D.9
Answer: B.16
Explanation: Answer
Now required average
= old average x Multiplicand
= 8 x 2 = 16
Correct Option: B
Question: If n is the greatest positive integer for which 2^n is a factor of 6!, then n =?
A.2
B.4
C.6
D.8
Answer: B.4
Explanation: 6! = 720
E. 2^10 = 512 (720/512) - this is not a factor of 6!
D. 2^8 = 256 (720/256) - this is not a factor of 6!
C. 2^6 = 64 (720/64) - this is not a factor of 6!
B. 2^4 = 16 (720/16) - this is a factor of 6!
B is answer
Question: Fresh fruit contains 55% water and dry fruit contains 10% water. How much dry fruit can be obtained from 100kg of fresh fruit?
A.A)32kg
B.B)40kg
C.C)52kg
D.D)50kg
Answer: D.D)50kg
Explanation: Quantity of pulp in 100kg of fresh fruits = (100-55)% of 100kg = 45kg
Let the quantity of dry fruit obtained be x kg
then, (100-10)% of x = 45
(90/100)*x = 45
x = 50
correct option is D
Question: Two trains 111 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
A.4.85
B.7.85
C.6.85
D.5.85
Answer: C.6.85
Explanation: T = (111 + 165)/ (80 + 65) * 18/5
T = 6.85
ANSWER:C
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
A.288
B.266
C.120
D.287
Answer: C.120
Explanation: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Question: How many real roots does the equation x^2y+16xy+60y=0 have if y < 0?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: x^2y+16xy+60y=0
=> y ( x^2 + 16x + 60) = 0
=> y (x+8)^2 = 0
if y<0 , then x=-9
So although there are 2 factors , they are the same x=-9 .
The equations has 3 distinct real root .
Answer D
Question: A container contains a dry mixture of sand and stones. Mass of sand and stones in the container is in the ratio 1:3. If 12 kg sand is added to the container, the ratio of masses of sand and stones becomes 5:3. Originally, how much more was the mass of stones than sand in the container?
A.12
B.9
C.6
D.3
Answer: C.6
Explanation: Suppose originally the mass of sand in the container was x. So the mass of stones, originally, would be 3x because mass of sand and stones in the container is in the ratio 1:3.
If 12 kg sand is added, mass of sand becomes x + 12, and the mass of stones remains unchanged. But now the ratio of the mass of sand and stones is 5:3.
This means,
(x + 12)/3x = 5/3, which gives x = 3.
So originally, there was 3 kg sand and 9 kg stones.
So, the mass of stones was 6 kg more than the mass of sand.
Ans C
Question: A person borrows Rs.5000 for 2 years at 5% p.a. simple interest. He immediately lends it to another person at 61⁄4% p.a for 2 years. Find his gain in the transaction per year.
A.62.5
B.150
C.225
D.112.5
Answer: A.62.5
Explanation: Explanation :
The person borrows Rs. 5000 for 2 years at 5% p.a. simple interest
Simple interest that he needs to pay = PRT/100=5000×5×2/100=500
He also lends it at 6 1⁄4% p.a for 2 years
Simple interest that he gets = PRT/100=5000×25/4×2/100=625
His overall gain in 2 years = Rs.625 - Rs.500 = Rs.125
His overall gain in 1 year = 125/2 = Rs.62.5
Answer : Option A
Question: A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If four, rather than five people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?
A.x/4
B.x/5
C.x/9
D.x/20
Answer: D.x/20
Explanation: If 5 people share the rent, each person would pay x/5.
If 4 people share the rent, each person will pay x/4.
The extra amount each person pays is x/4 - x/5 = 5x/20 - 4x/20 = x/20
The answer is D.
Question: The bankerâ€™s discount on Rs. 1600 at 8% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is :
A.2 months
B.4.5 months
C.6.5 months
D.7.5 months
Answer: D.7.5 months
Explanation: Sol.
S.I. on Rs. 1600 = R.D. on Rs. 1680.
âˆ´ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is S.I. on Rs. 1600 at 8%.
âˆ´ Time = [100 * 80 / 1600 * 8] year = 5/8 year = 7.5 months.
Answer D
Question: A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
A.Rs.3600
B.Rs.3607
C.Rs.3627
D.Rs.3661
Answer: A.Rs.3600
Explanation: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
Answer:A
Question: At what time between 5.30 and 6 will the hands of a clock be at right angles?
A.43*8/11 min past 5
B.42*7/11 min past 5
C.43*7/11 min past 5
D.43*7/11 min past 7
Answer: C.43*7/11 min past 5
Explanation: Explanation:
At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min.
40 min. spaces are gained in 60/55 * 40 min= 43*7/11 min
Required time 43*7/11 min past 5
Answer is C
Question: there are 30 students in a classroom. The ratio of the # of girls to boys was 1:2, how many boys are there?
A.10
B.15
C.20
D.25
Answer: C.20
Explanation: # OF GIRLS = X
# OF BOYS =2X
X + 2X = 30
3X = 30
X = 30/3 = 10
BOYS = 2X = 2 * 10 =20
ANSWER: C
Question: The length of a room is 5.5 m and width is 3.75 m. What is the cost of paying the floor by slabs at the rate of Rs.800 per sq. metre.
A.Rs. 12000
B.Rs. 19500
C.Rs. 18000
D.Rs. 16500
Answer: D.Rs. 16500
Explanation: Area =5.5×3.75 sq. metre.
Cost for 1 sq. metre. = Rs.800
Hence, total cost=5.5×3.75×800=5.5×3000
= Rs.16500 Answer: Option D
Question: When ticket sales began, Pat was the nth customer in line for a ticket, and customers purchased their tickets at the rate of r customers per minute. Of the following, which best approximates the time, in minutes, that Pat had to wait in line from the moment ticket sales began?
A.(n - 1) r
B.(n-1)/r
C.n + r –1
D.r/(n-1)
Answer: B.(n-1)/r
Explanation: B. (n - 1) / r
Question: Set P is composed of nine numbers, labeled P1 through P9. Set Q is also composed of nine numbers, labeled Q1 through Q9. Set Q is defined as follows: Q1 = 1 + P1; Q2 = 2 + P2; and so on, including Q9 = 9 + P9. How much larger is the sum of set Q's mean and range than the sum of set P's mean and range?
A.3
B.6
C.9
D.cannot be determined
Answer: D.cannot be determined
Explanation: Yes, the correct answer is D
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
A.39
B.27
C.30
D.26
Answer: C.30
Explanation: 20 + 24 + 8 * 2 = 60/2 = 30
Answer: C
Question: A polygon has 135 diagonals. How many sides does it have?
Self made
A. 12
B. 13
C. 18
D. 15
Answer: C. 18
Explanation: The best way to solve this problem is to use the formula: An n sided polygon can have n*(n - 3)/2 diagonals
n*(n - 3)/2 = 135
n*(n - 3) = 270
Substitute n from the answer choices. n = 18
Answer: C
Question: The average age of a group of 10 students was 25. The average age increased by 3 years when two new students joined the group. What is the average age of the two new students who joined the group?
A.22 years
B.30 years
C.32 years
D.43 years
Answer: D.43 years
Explanation: The total age of 10 students with average 25 = 250
The total age of 12 students with average 28 = 336
The total age of 2 new students = 86
Their average =43
Correct Option D
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
A.23
B.46
C.47
D.76
Answer: B.46
Explanation: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on.
B
Question: If m and n are negative integers, which of the following statements must be true?
I. (-m)^n is positive.
II. (-m)^(-n) is positive.
III. m^(-n) is positive.
A.None
B.II only
C.I and II
D.I and III
Answer: C.I and II
Explanation: Let's m = -2 and n = -3
I. (-m)^n = (2)^(-3) = 1/(2^3) --> Positive
II. (-m)^(-n) is positive. = 2^3 --> Positive
III. m^(-n) is positive. = -2^3 --> Negative
Answer: C
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^2 + s^2?
A.0
B.1
C.2
D.8
Answer: C.2
Explanation: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^2+s^2 will have 1+1 = 2 as a units digit.
The answer is C.
Question: What is the greatest possible length which can be used to measure exactly the lengths 180 m, 500 m and 15m 20 cm?
A.80 cm
B.50 cm
C.40 cm
D.10 cm
Answer: A.80 cm
Explanation: Required length = HCF of 18000 cm, 50000 cm, 1520 cm = 80 cm
Answer is A
Question: If the simple interest on a certain amount in at 4% rate 5 years amounted to Rs.2080 less than the principal. What was the principal?
A.1500
B.2600
C.2507
D.3200
Answer: B.2600
Explanation: P - 2080 = (P*5*4)/100
P = 2600
Answer: B