UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 48 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 48

Question

There are three types of rectangular tiles : 3' × 3', 3' × 7' and 3' × 11'. An area of rectangular shape of dimensions 3' × 100' is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x − y is

(a)20
(b)12
(c)10
(d)7

UnlockIAS answer: (a)20

Solution

Each tile spans the 3' width, so we cover length 100 using pieces of 3, 7, 11. The maximum tile count is 32 (e.g. 31×3 + 1×7) and the minimum is 12 (e.g. 8×11 + 4×3). So x − y = 32 − 12 = 20.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Numeracy — Tiling / linear combinations

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

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Official Notification

PIB Release 2262441

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