In the sum ⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗ for which digit does the symbol ⊗ stand?
- (a) 2
- (b) 3 ✓ UPSC's answer
- (c) 4
- (d) 5
Why the answer is (b)
• Let ⊗ = x. Then ⊗ = x, 1⊗ = 10 + x, 5⊗ = 50 + x, ⊗⊗ = 11x, ⊗1 = 10x + 1 and 1⊗⊗ = 100 + 11x.
• Left side: x + (10 + x) + (50 + x) + 11x + (10x + 1) = 24x + 61.
• So 24x + 61 = 100 + 11x, giving 13x = 39 and x = 3.
• Check: 3 + 13 + 53 + 33 + 31 = 133 = 1⊗⊗.
• Hence option (b).
Why the other options are wrong
- (a) 2
- Substituting 2 gives 2 + 12 + 52 + 22 + 21 = 109, but the right side is 122.
- (c) 4
- Substituting 4 gives 4 + 14 + 54 + 44 + 41 = 157, but the right side is 144.
- (d) 5
- Substituting 5 gives 5 + 15 + 55 + 55 + 51 = 181, but the right side is 155.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.