Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M - N is
- (a) 11
- (b) 12
- (c) 13 ✓ UPSC's answer
- (d) 14
Why the answer is (c)
• x, y, z are three different values from 2, 3, 4, 5.
• Largest (x × y) + z: multiply the two biggest and add the next: 5 × 4 + 3 = 23 = M.
• Smallest: multiply the two smallest and add the next: 2 × 3 + 4 = 10 = N (the alternatives 2 × 4 + 3 = 11 and 3 × 4 + 2 = 14 are larger).
• M − N = 23 − 10 = 13: (c).
Why the other options are wrong
- (a) 11
- 11 uses a wrong minimum or maximum; M = 23 and N = 10.
- (b) 12
- 12 would need N = 11, but 2 × 3 + 4 = 10 is smaller.
- (d) 14
- 14 would need M = 24, which is not possible with distinct values.
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.