Consider the following sum : • + 1• + 2• + • 3 + • 1 = 21• In the above sum, • stands for
- (a) 4
- (b) 5
- (c) 6
- (d) 8 ✓ UPSC's answer
Why the answer is (d)
• Let • = x, a single digit.
• Rewrite the terms: • = x, 1• = 10 + x, 2• = 20 + x, •3 = 10x + 3, •1 = 10x + 1, and 21• = 210 + x.
• Add the left side: x + (10 + x) + (20 + x) + (10x + 3) + (10x + 1) = 23x + 34.
• Set it equal to the right side: 23x + 34 = 210 + x.
• Solve: 22x = 176, so x = 8.
• Therefore • stands for 8, which is option (d).
Why the other options are wrong
- (a) 4
- If • = 4, the left side is 4 + 14 + 24 + 43 + 41 = 126, which does not equal 214.
- (b) 5
- If • = 5, the left side is 5 + 15 + 25 + 53 + 51 = 149, which does not equal 215.
- (c) 6
- If • = 6, the left side is 6 + 16 + 26 + 63 + 61 = 172, which does not equal 216.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.