How many three-digit numbers can be expressed as an integral power of 2?
- (a) 1
- (b) 2
- (c) 3 ✓ UPSC's answer
- (d) 4
Why the answer is (c)
• 2⁶ = 64 has two digits and 2¹⁰ = 1024 has four.
• The three-digit powers are 2⁷ = 128, 2⁸ = 256 and 2⁹ = 512.
• So there are 3: (c).
Why the other options are wrong
- (a) 1
- 128, 256 and 512 all have three digits.
- (b) 2
- 128, 256 and 512 all have three digits.
- (d) 4
- 1024 has four digits, so there are only three.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2026, held on 24 May 2026. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.