The top of a table is rectangular and its dimensions are 6' × 10'. Two rectangular portions of the table top are painted in blue colour; both these portions have dimensions 2·5' × 8' and each of them has exactly two sides common with two edges of the table top. If the table is fixed to the ground and the remaining portion of the table top is painted in white, how many different patterns are possible when observed from above?
- (a) 2
- (b) 4 ✓ UPSC's answer
- (c) 6
- (d) 8
Why the answer is (b)
• Each blue portion is 2·5′ × 8′ and shares two sides with two edges of the table, so it sits in a corner.
• Its 8′ side cannot lie along the 6′ edge, so it must run along a 10′ edge. Each portion therefore fills one corner, 8′ along the long edge and 2·5′ into the width.
• Two portions on the same long edge would overlap, since 8′ + 8′ is more than 10′. Portions on opposite long edges never overlap, since 2·5′ + 2·5′ = 5′ is less than 6′.
• Of the 6 ways to choose two corners, the 2 pairs on the same long edge are ruled out. The remaining 4 (left pair, right pair and the two diagonal pairs) look different from above because the table is fixed: (b).
Why the other options are wrong
- (a) 2
- Only counting the diagonal pairs misses the left and right pairs.
- (c) 6
- 6 counts all corner pairs, including the two that would overlap.
- (d) 8
- 8 double-counts; there are only 4 valid pairs of corners.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.