Eight boys M, N, O, P, Q, R, S, and T are sitting in a row, facing towards the north (but not necessarily in the same order). R is fifth to the right of M. P is fifth to the right of Q. Q is to the immediate right of M. T is third to the left of P. N is third to the right of S. S is an immediate neighbor of M. Which of the following statements is/are NOT correct?
I. N is third to the left of R.
II. P is sixth to the right of M.
Show answer & explanation
Correct answer: C
Explanation
Answer: Neither I nor II — both statements are correct.
Setting up positions (1 = leftmost to 8 = rightmost, facing north):
- Q is immediate right of M → Q = M+1
- R is fifth to right of M → R = M+5
- P is fifth to right of Q → P = Q+5 = M+6
- T is third to left of P → T = P−3 = M+3
- S is immediate neighbor of M → since Q = M+1, S = M−1
- N is third to right of S → N = S+3 = M+2
For all positions to fit in 1–8: M+6 ≤ 8 → M ≤ 2, and M−1 ≥ 1 → M ≥ 2, so M = 2.
This gives:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Person | S | M | Q | N | T | O | R | P |
Checking the statements:
- I. N(4) is third to the left of R(7) → 7−4=3 ✓ Correct
- II. P(8) is sixth to the right of M(2) → 8−2=6 ✓ Correct
Since both statements hold true, none of the statements is incorrect.