GATE 2022 BM – Question 9

General Aptitude · Analytical Aptitude: Logical Reasoning, Deduction and Analogy · 2 marks · Multiple choice

The three corners and three side midpoints of a triangle are labelled P,Q,R,S,T,U in some order. PR is parallel to QS; P is on the side opposite corner T; S and U cannot lie on the same side. Which statement must hold?

P cannot be at a corner
S cannot be at a corner
U cannot be at a midpoint
R cannot be at a corner

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Show answer and explanation

Correct answer: (B) S cannot be at a corner

Explanation

Suppose S were a corner. Because S and U cannot share a side, U must be the midpoint of the opposite side; every other position shares a side with S. T is one of the other two corners. For either symmetric choice of T, placing P at either remaining position on the opposite side leaves no assignment of Q,R with PR parallel to QS. Hence S cannot be a corner, B. P may be a side endpoint; it is not restricted to a midpoint.

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