P is 8 ranks ahead of Q who ranks twenty–sixth in a group of 42. What is the…
2022
P is 8 ranks ahead of Q who ranks twenty–sixth in a group of 42. What is the rank of P from the last?
Answer: D. 25th — Concept: For a group of N people ranked without ties, a person's rank counted from the front (r_front) and rank counted from the last (r_last) always satisfy…
- A.
18th
- B.
19th
- C.
24th
- D.
25th
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Show answer & explanation
Correct answer: D
Concept: For a group of N people ranked without ties, a person's rank counted from the front (r_front) and rank counted from the last (r_last) always satisfy r_front + r_last - 1 = N — equivalently, r_last = N - r_front + 1. Being "k ranks ahead" of another person means having a front-rank that is exactly k less than theirs.
Application:
Q's rank from the front is given as 26th, out of a group of N = 42.
P is 8 ranks ahead of Q, so P's rank from the front = 26 - 8 = 18.
Convert P's front rank to a rank from the last using r_last = N - r_front + 1: r_last = 42 - 18 + 1 = 25.
Cross-check: Compute Q's own rank from the last first: 42 - 26 + 1 = 17. Since P is 8 ranks ahead of Q, P has exactly 8 more people trailing behind (including Q), so P's rank from the last = 17 + 8 = 25 — the same value obtained independently, confirming the answer.
Answer: P's rank from the last is 25th.