NIMCET 2015 — Reasoning PYQ

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Question

NIMCET 2015 — Reasoning PYQ

NIMCET | Reasoning | 2015

P,Q,R,S,T,U and V are sitting in a row facing North. In order determine, who is sitting exactly in the middle of the row, which of the following information is needed?
I. T and U are sitting at extreme ends of the row.
II. S is third to the right of T
III. Q is four places to the left of R and P is two places of the left of V

Choose the correct answer:

Explanation

1. Analyzing the statements:

There are $7$ positions: $\underline{1} \text{ } \underline{2} \text{ } \underline{3} \text{ } \underline{4} \text{ } \underline{5} \text{ } \underline{6} \text{ } \underline{7}$
Statement I: T and U are at the ends. This gives two possibilities:
- Case 1: $T$ is at 1, $U$ is at 7.
- Case 2: $U$ is at 1, $T$ is at 7.
Statement II: S is third to the right of T.
- If we use Case 1 ( $T$ at 1), then $S$ is at position $1 + 3 = 4$ .
- If we use Case 2 ( $T$ at 7), $S$ cannot be to the right of $T$ .
- So, combining I and II, we fix $T$ at 1, $S$ at 4, and $U$ at 7. Position 4 (Middle) is S. Thus, I and II together are sufficient.
Statement III: $Q$ is four places to the left of $R$ ( $Q \text{ _ _ _ } R$ ) and $P$ is two places to the left of $V$ ( $P \text{ _ } V$ ).
- Let's check I and III together. If $T$ and $U$ are at ends:
- If $T=1, U=7$ , we need to fit $Q \text{ _ _ _ } R$ in the remaining spots ( $2, 3, 4, 5, 6$ ).
- The only way $Q$ (4 places left of $R$ ) fits is $Q=2, R=6$ .
- Then we fit $P \text{ _ } V$ in the remaining spots ( $3, 4, 5$ ). The only way is $P=3, V=5$ .
- This leaves position $4$ for the only remaining person, S.
- If $U=1, T=7$ , the same logic applies, and S still ends up at position $4$ .
- Thus, I and III together are also sufficient.

Conclusion:

Since both pairs (I & II) and (I & III) independently lead us to the answer, the required information is I and either II or III.

Correct Option: (c) I and either II or III are sufficient