Consider the following matrix : | 3 | 8 | 10 | 2 | ? | 1 | | 6 | 56 | 90 | 2 | 20 | 0 | What is the missing number at ‘?’ in the matrix ?
- (a) 5 ✓ UPSC's answer
- (b) 0
- (c) 7
- (d) 3
Why the answer is (a)
• In each column, the lower number equals the upper number multiplied by one less than itself: n × (n − 1).
• Check: 3 × 2 = 6; 8 × 7 = 56; 10 × 9 = 90; 2 × 1 = 2; 1 × 0 = 0.
• For the fifth column, let the missing upper number be x; then x × (x − 1) = 20.
• Solving x² − x − 20 = 0 gives (x − 5)(x + 4) = 0, so x = 5.
• Therefore the missing number is 5, which is option (a).
Why the other options are wrong
- (b) 0
- 0 would give 0 × (0 − 1) = 0, not the lower number 20.
- (c) 7
- 7 would give 7 × 6 = 42, not 20.
- (d) 3
- 3 would give 3 × 2 = 6, not 20.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.