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

• The variables x, y, and z must be distinct values chosen from the set {2, 3, 4, 5}.

• To find M (the maximum value of (x × y) + z), we need to maximize the product x × y. The largest distinct pair is 5 and 4, giving a product of 20.

• The remaining value for z is 3 (since 2 is unused and we want to maximize the sum, but z is just added; actually, to maximize the total, we should check if using 5 and 4 for x,y and 3 for z is better than other combos. Let's list max products: 5*4=20 (z=3 or 2), 5*3=15 (z=4 or 2), 4*3=12. Max product is 20. If x=5, y=4, z can be 3 or 2. Max sum is 20+3=23. So M = 23.

• To find N (the minimum value of (x × y) + z), we need to minimize the product x × y. The smallest distinct pair is 2 and 3, giving a product of 6.

• The remaining values for z are 4 and 5. To minimize the sum, we choose the smallest available z, which is 4. So N = 6 + 4 = 10.

• The difference M - N is 23 - 10 = 13.