Question

Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights?
I) V is taller than Q but shorter than M.
II) T is taller than Q and M but shorter than P.

• A. Statement I alone is sufficient to answer the question
• B. Statement II alone is sufficient to answer the question.
• C. Statement I and II together are sufficient to answer the question but neither statement alone is sufficient.
• D. Statement I and II together are not sufficient to answer the question and additional data is required.

Hint:

In ordering questions, combine inequalities carefully and try to form a complete chain. The middle element in 5 items is always the 3rd after arranging.

Answer 1

The Correct Option is C

Concept: In ordering problems, we arrange elements based on given comparisons. For five elements, the one in the middle is the third position in ascending order.
Step 1: Analyze Statement I alone.
Given: \[ Q<V<M \] No information about P and T. Hence, full order cannot be determined.
Statement I alone is NOT sufficient.
Step 2: Analyze Statement II alone.
Given: \[ Q<M<T<P \] No information about V. Hence, complete arrangement is not possible.
Statement II alone is NOT sufficient.
Step 3: Combine both statements.
From Statement I: \[ Q<V<M \] From Statement II: \[ Q<M<T<P \] Combining: \[ Q<V<M<T<P \] Thus, the middle (3rd position) is M.
Hence, both statements together are sufficient, but neither alone is sufficient.