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Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
Correct
Incorrect
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Question 2 of 5
2. Question
Two pipes P and Q can fill a tank in 8 hours and 12 hours respectively. They are opened together, and due to leakage in the tank, the tank gets filled in 5 hours.
Quantity I: Time taken to fill the tank by both pipes together in the presence of leakage
Quantity II: Time taken by the leakage to empty 40% of the completely filled tankSelect the correct answer using the codes given below:
Correct
Answer: (b)
Explanation
Pipe P fills 1/8 of the tank per hour
Pipe Q fills 1/12 of the tank per hourTogether, their rate = 1/8 + 1/12 = 5/24
With leakage, tank fills in 5 hours
So net rate = 1/5Leakage rate = 5/24 − 1/5
Taking LCM 120:
= 25/120 − 24/120 = 1/120So leakage alone empties full tank in 120 hours
Time to empty 40% tank = 120 × 40/100 = 48 hours
Now compare:
Quantity I = 5 hours
Quantity II = 48 hoursSo, Quantity I < Quantity II
Hence, option (b) is correct.
Incorrect
Answer: (b)
Explanation
Pipe P fills 1/8 of the tank per hour
Pipe Q fills 1/12 of the tank per hourTogether, their rate = 1/8 + 1/12 = 5/24
With leakage, tank fills in 5 hours
So net rate = 1/5Leakage rate = 5/24 − 1/5
Taking LCM 120:
= 25/120 − 24/120 = 1/120So leakage alone empties full tank in 120 hours
Time to empty 40% tank = 120 × 40/100 = 48 hours
Now compare:
Quantity I = 5 hours
Quantity II = 48 hoursSo, Quantity I < Quantity II
Hence, option (b) is correct.
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Question 3 of 5
3. Question
Consider the following statements and a question:
Statement I: The sum of two numbers is 91.
Statement II: The larger number is 7 more than twice the smaller number.Question: What is the larger number?
Which one of the following is correct in respect of the Statements and the Question?
Correct
Answer: (c)
Explanation:
From Statement I alone, only the sum is known.
Many pairs are possible.From Statement II alone, if smaller number is x, then larger number is 2x + 7.
Again many pairs are possible.Using both together:
x + (2x + 7) = 91
3x = 84
x = 28
Larger number = 2 × 28 + 7 = 63
So both statements together are required.
Incorrect
Answer: (c)
Explanation:
From Statement I alone, only the sum is known.
Many pairs are possible.From Statement II alone, if smaller number is x, then larger number is 2x + 7.
Again many pairs are possible.Using both together:
x + (2x + 7) = 91
3x = 84
x = 28
Larger number = 2 × 28 + 7 = 63
So both statements together are required.
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Question 4 of 5
4. Question
The class size is 32 students. A student who had chosen to work on a Computer Science project also decided to work on English. A student who does the project on Computer Science does not do project on Hindi. The English and Hindi projects together are completed by 10 students, that is, 10 students do both English and Hindi. Every student completes a project on at least one of the three subjects. The number of students who do project on exactly one of the three subjects is at least 6 more than the number of students who do project on more than one of the three.
What are the maximum and minimum number of students who could have done project on Hindi only?
Correct
Answer: (a)
Explanation:
Let the number of students who did:
English only = x
Computer Science and English = y
English and Hindi = 10
Hindi only = zSo,
x + y + 10 + z = 32
That gives,
x + y + z = 22
Students doing exactly one subject are:
x + z
Students doing more than one subject are:
y + 10
Given,
x + z is at least 6 more than y + 10
So,
x + z ≥ y + 16
Now for maximum Hindi only, keep x and y as small as possible.
Take x = 0 and y = 0
Then z = 22
So maximum is 22.
For minimum Hindi only, try z = 0
Then x + y = 22
Condition becomes:
x ≥ y + 16
This is possible, for example, if y = 3 and x = 19.
So minimum is 0.
Hence, the answer is 22, 0.
Incorrect
Answer: (a)
Explanation:
Let the number of students who did:
English only = x
Computer Science and English = y
English and Hindi = 10
Hindi only = zSo,
x + y + 10 + z = 32
That gives,
x + y + z = 22
Students doing exactly one subject are:
x + z
Students doing more than one subject are:
y + 10
Given,
x + z is at least 6 more than y + 10
So,
x + z ≥ y + 16
Now for maximum Hindi only, keep x and y as small as possible.
Take x = 0 and y = 0
Then z = 22
So maximum is 22.
For minimum Hindi only, try z = 0
Then x + y = 22
Condition becomes:
x ≥ y + 16
This is possible, for example, if y = 3 and x = 19.
So minimum is 0.
Hence, the answer is 22, 0.
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Question 5 of 5
5. Question
A Statement is given below followed by two Conclusions numbered I and II.
Statement:
P < Q ≤ R, R = S > T ≥ UConclusions:
I. P < S
II. U < QWhich one of the following is correct in respect of the above Statement and the Conclusions?
Correct
Answer: (a)
Explanation
From the statement:
P < Q ≤ R and R = SThis implies:
P < Q ≤ R = S
Therefore, P < SSo, Conclusion I is correct.
Now consider the second part:
R = S > T ≥ UThis gives:
S > T ≥ U, hence S > UHowever, we only know that Q ≤ R and R = S, so Q ≤ S.
There is no definite relation between Q and U.Possible cases:
- Q > U
- Q = U
- Q < U
Since all possibilities exist, Conclusion II (U < Q) does not necessarily follow.
Incorrect
Answer: (a)
Explanation
From the statement:
P < Q ≤ R and R = SThis implies:
P < Q ≤ R = S
Therefore, P < SSo, Conclusion I is correct.
Now consider the second part:
R = S > T ≥ UThis gives:
S > T ≥ U, hence S > UHowever, we only know that Q ≤ R and R = S, so Q ≤ S.
There is no definite relation between Q and U.Possible cases:
- Q > U
- Q = U
- Q < U
Since all possibilities exist, Conclusion II (U < Q) does not necessarily follow.
