Question

If p, q, r and s are four positive integers such that pqrs = 1, what is the minimum value of (2 + p)(3 + q)(4 + r)(5 + s)?

• A. 1
• B. 12
• C. 120
• D. 240
• E. 360

Answer 1

Answer: (E)

The correct answer is option (E):

360

Let's analyze the problem. We are given four positive integers p, q, r, and s, such that their product pqrs = 1. Since p, q, r, and s are positive integers, and their product is 1, the only possible value for each of p, q, r, and s is 1.

Therefore, p = q = r = s = 1.

We are asked to find the minimum value of the expression (2 + p)(3 + q)(4 + r)(5 + s). Substituting the values p=1, q=1, r=1, and s=1, we get:

(2 + 1)(3 + 1)(4 + 1)(5 + 1) = (3)(4)(5)(6) = 360

Thus, the minimum value of (2 + p)(3 + q)(4 + r)(5 + s) is 360.