UPSC Prelims 2026 · CSAT
Question 15: Basic Numeracy
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?
AnswerUPSC’s answer is (b).
The 8′ side cannot fit along the 6′ edge, so it lies along a 10′ edge and the 2.5′ side along a 6′ edge. Each blue rectangle therefore sits in a corner of the table. Two corners on the same long edge would overlap (8 + 8 is more than 10), so they are not two separate portions. The allowed pairs are the two corners at one short end (top or bottom, 2 ways) and the two diagonal pairs (2 ways): 4 patterns.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows UPSC’s provisional key; the final key could change it.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: there are more than two distinct corner placements.
- (b) Right: 2 short-end pairs plus 2 diagonal pairs.
- (c) Wrong: 6 would count the two long-edge pairs, whose rectangles overlap.
- (d) Wrong: eight overcounts; the corner placements are limited to 4 non-overlapping pairs.
Worth knowing: The key's 4 assumes the two blue portions cannot overlap; if overlapping placements were allowed there would be 6 patterns.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.