The digit in the unit place of the number 6^129 × 7^307 is (a) 2 (b) 4 (c) 8 (d) 6

Join @UPSCneil — Free Guidance

UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 22 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 22

Question

The digit in the unit place of the number 6^129 × 7^307 is

(a)2
(b)4
(c)8
(d)6

UnlockIAS answer: (c)8

Solution

6 raised to any power ends in 6. For 7, the unit-digit cycle is 7, 9, 3, 1 (period 4); 307 mod 4 = 3 → unit digit 3. Then 6 × 3 = 18, so the unit digit is 8.

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 — Unit digit / cyclicity

Official UPSC Provisional Key Released

The official provisional answer key for CSE Prelims 2026 has been released. Compare your answers with the official key using our CSAT score calculator, and file objections via the QPRep portal before 6:00 PM on 31 May 2026.

CSAT Score Calculator

Check your 33% qualifying status

Official Notification

PIB Release 2262441

Back to all 80 CSAT questions