UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 46 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 46

Question

A is a 2-digit number with different digits. B is also a 2-digit number, which is obtained by reversing the digits of A. If A − B is a multiple of 27, where A > B, how many such different A's are possible?

(a)6
(b)9
(c)12
(d)18

UnlockIAS answer: (c)12

Solution

A − B = 9(t − u). For this to be a multiple of 27, t − u must be a multiple of 3, i.e. 3, 6 or 9. Counting (t > u): 7 + 4 + 1 = 12 such numbers A.

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 — Two-digit numbers

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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