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GATE 2022 CS – Question 9

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

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order. Consider the following statements:
- The line joining P and R is parallel to the line joining Q and S.
- P is placed on the side opposite to the corner T.
- S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?

  1. P cannot be placed at a corner
  2. S cannot be placed at a corner
  3. U cannot be placed at a mid-point
  4. R cannot be placed at a corner

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Show answer and explanation

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

Explanation

Enumerating the valid placements (a midsegment parallel to a side) shows S is always a mid-point. P, U and R can each be at a corner or a mid-point in some valid arrangement.