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In a class there are seven students (including boys and girls) P, Q, R, S, T, U and V. They sit on three benches I, II and III such that at least two students on each bench and at least one girl on each bench. R who is a girl student, does not sit with P, T and S. U the boy student, sits with only Q. P sits on the bench I with his best friends. V sits on the bench III. T is the brother of R?
Q. On which bench there are three students?
  • a)
    I
  • b)
    II
  • c)
    III
  • d)
    I or II
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
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In a class there are seven students (including boys and girls) P, Q, R...
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In a class there are seven students (including boys and girls) P, Q, R...
Solution:

Given, there are 7 students: P, Q, R, S, T, U, and V.
They sit on 3 benches: I, II and III.

Let's analyze the given conditions:

1. At least two students on each bench and at least one girl on each bench.
- This means that we cannot have a bench with all boys.

2. R who is a girl student, does not sit with P, T, and S.
- This means that R cannot sit on bench I with P, and she cannot sit on bench II with T and S.

3. U the boy student, sits with only Q.
- This means that U and Q will sit together on one of the benches.

4. P sits on the bench I with his best friends.
- This means that P will sit on bench I with some of his friends.

5. V sits on the bench III.
- This means that V will sit on bench III.

6. T is the brother of R/Q.
- This means that T will sit on the same bench as R or Q.

Now, let's try to place the students on the benches based on the given conditions:

- Bench III will have V (as per condition 5).
- U and Q will sit together on one of the benches (as per condition 3). Let's assume they sit on bench II.

Now, we need to place the remaining students on benches I and II such that each bench has at least one girl and at least two students. Also, R cannot sit on bench I with P and cannot sit on bench II with T and S.

Let's consider the following cases:

Case 1: R sits on bench I with P's best friends.
- In this case, bench I will have P, R, and two of P's best friends. But then bench II will have only two students (T and S) which is not allowed. Hence, this case is not possible.

Case 2: R sits on bench II with T.
- In this case, bench II will have R, T, and one more student (either S or P's best friend). Bench I will have P and two more students (including at least one girl). This case satisfies all the given conditions.

Therefore, the answer is option 'A' - Bench I has three students.
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In a class there are seven students (including boys and girls) P, Q, R, S, T, U and V. They sit on three benches I, II and III such that at least two students on each bench and at least one girl on each bench. R who is a girl student, does not sit with P, T and S. U the boy student, sits with only Q. P sits on the bench I with his best friends. V sits on the bench III. T is the brother of R?Q.On which bench there are three students?a)Ib)IIc)IIId)I or IIe)None of theseCorrect answer is option 'A'. Can you explain this answer?
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