Let p and q be positive integers satisfying p

1. A. 3
2. B. 4
3. C. 5
4. D. 6

Answer: C

Explanation

We are looking for the smallest positive integer k such that the equation p+q=k, with the conditions p and q are positive integers and p<q, yields more than one distinct pair for (p, q).

Let's test values of k:
– If k = 3: The only pair (p,q) satisfying p+q=3 and p<q (with p,q positive integers) is (1, 2). This is unique.
– If k = 4: The only pair (p,q) satisfying p+q=4 and p<q (with p,q positive integers) is (1, 3). This is unique.
– If k = 5: The possible pairs (p,q) satisfying p+q=5 and p<q (with p,q positive integers) are:
– (1, 4)
– (2, 3)
Since there are two distinct pairs for k=5, the values of p and q are not uniquely determined.

Therefore, the smallest value of k that does not determine p and q uniquely is 5. This question tests basic number theory and logical enumeration.