Direction: The following consists of a question and two statements numbered I…
2024
Direction: The following consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
There are seven letters W, M, V, N, Q, R, and J. What is the fifth letter from the left end?
Statement I. Q is placed fifth to the right of V. W and J are not placed immediately next to either Q or V. Q is placed to the immediate left of R.
Statement II. M is placed to the immediate left of W but is not an immediate neighbour of Q. N is placed second to the left of R.
- A.
Statement I alone is sufficient.
- B.
Statement II alone is sufficient.
- C.
Both statement I and II together are sufficient.
- D.
Either statement I or II alone is sufficient.
Show answer & explanation
Correct answer: C
Concept
In a linear seating/letter-arrangement data-sufficiency question, a statement (or a combination of statements) is "sufficient" only if applying its conditions leaves exactly one possible arrangement of every item. If more than one arrangement still fits the given conditions, that statement (or combination) is insufficient.
Application: Statement I alone
Q is fifth to the right of V, and Q is immediately to the left of R. Among 7 positions, the only placement that keeps Q at least 5 slots after V and still leaves room for R right after Q is V at position 1, Q at position 6, R at position 7:
V __ __ __ __ Q R
W and J are not placed immediately next to Q or V, so positions 2 and 5 (the neighbours of V and Q) cannot hold W or J — they must hold M and N in some order, leaving positions 3 and 4 for W and J in some order:
V (M/N) (W/J) (W/J) (M/N) Q R
This still leaves two independent swaps open (M with N, and W with J), so more than one full arrangement satisfies Statement I by itself — it does not pin down a single sequence.
Application: Statement II alone
Statement II only fixes relative facts: M sits immediately left of W, M is not next to Q, and N sits two places left of R. Without also knowing where V, Q and R actually sit — information only Statement I supplies — this M-W block and the N-to-R gap could be slotted into more than one set of absolute positions among the seven, so Statement II alone does not fix a single arrangement either.
Application: Statement I and II together
Start from Statement I's skeleton: V=1, Q=6, R=7, with {2,5} holding M and N, and {3,4} holding W and J.
Statement II adds: M is immediately left of W. Since W must be one of positions {3,4} and M must be one of positions {2,5}, the only pair satisfying "M position + 1 = W position" is M=2 and W=3.
That forces the remaining letters: N=5 (the other slot in {2,5}) and J=4 (the other slot in {3,4}).
Checking Statement II's remaining conditions against this: M (position 2) is not an immediate neighbour of Q (position 6) — holds. N (position 5) is two places left of R (position 7) — holds.
No other assignment satisfies both statements at once, so the full arrangement is fixed uniquely:
Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
Letter | V | M | W | J | N | Q | R |
Cross-check
Verify the finished arrangement against Statement I's own conditions too: W (position 3) and J (position 4) are not immediate neighbours of Q (position 6) or V (position 1) — holds. Every condition from both statements is satisfied by this arrangement and by no other, confirming it is unique.
Since neither statement alone fixes a single arrangement, but the two together do, the fifth letter from the left end is N, and the data in both statements together — but not either one alone — are sufficient to answer the question.