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. The official UPSC provisional key has been released.

Section

Mathematics

Topic Reference

Numeracy — Two-digit numbers

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