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 pos…

Question

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

1. A. 11
2. B. 12
3. C. 13 (Correct answer)
4. D. 14

Correct Answer

Option C — 13

Detailed Solution & Explanation

The correct answer is Option C (13).

Key Points

• x, y, z are distinct values from {2, 3, 4, 5} and we evaluate (x × y) + z.
• Maximum: take the two largest for the product, 4 × 5 = 20, plus the largest remaining distinct value z = 3 → 23.
• Minimum: take the two smallest, 2 × 3 = 6, plus the smallest remaining z = 4 → 10.

Additional Information

• M − N = 23 − 10 = 13, so Option C.