Question: Who among P, Q, T, V and M is exactly in the middle when they are…
2024
Question: Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights ?
Statements:
V is taller than Q but shorter than M.
T is taller than Q and M but shorter than P.
- A.
I alone is sufficient while II alone is not sufficient
- B.
II alone is sufficient while I alone is not sufficient
- C.
Either I or II is sufficient
- D.
Both I and II are sufficient
Show answer & explanation
Correct answer: D
Concept: In a Data Sufficiency ranking question, a statement is sufficient only when it lets you fix the position asked for — here, who is exactly in the middle once all five people are ordered by height. Two partial statements can be combined into one complete order only if their chains share a common person linking them together.
Applying it here:
Statement I says V is taller than Q but shorter than M, giving the chain M > V > Q.
Statement II says T is taller than Q and M but shorter than P, giving the chain P > T > M (and T > Q).
Statement I alone never places P or T, so it cannot fix the middle position among all five people by itself.
Statement II alone never places V, so it cannot fix the middle position among all five people by itself either.
Combining both: Statement I's chain (M > V > Q) and Statement II's chain (P > T > M) share M as the common link, merging into one complete order: P > T > M > V > Q.
Cross-check: Re-reading the merged order P > T > M > V > Q against both statements confirms V sits between M and Q (Statement I), and T sits between P and M, both above Q (Statement II) — so the merged order is consistent with everything given.
Both statements together are needed and sufficient — combining them places M exactly in the middle of the five.