UPSC Prelims 2026 · CSAT
Question 68: Basic Numeracy
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
AnswerUPSC’s answer is (a).
The 3′ width is fixed, so each tile lies lengthwise along the 100′ side and adds 3, 7 or 11 feet: 3a + 7b + 11c = 100. Most tiles: use as many 3′ tiles as possible, 31 × 3 + 1 × 7 = 100, so x = 32. Fewest tiles: use as many 11′ as possible, 8 × 11 + 4 × 3 = 100, so y = 12; ten or eleven tiles cannot make 100. Then x − y = 32 − 12 = 20.
Why each option is right or wrong
- (a) Right: 32 − 12 = 20.
- (b) Wrong: 12 is the minimum number of tiles, not the difference.
- (c) Wrong: 10 does not match 32 − 12.
- (d) Wrong: 7 does not match 32 − 12.
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.