# Q. Let p and q be positive integers satisfying p<q and p+q=k.

What is the smallest value of k that does not determine p and q uniquely?

a) 3

b) 4

c) 5

d) 6

Correct answer: c) 5

##### Question from UPSC Prelims 2024 CSAT Paper

**Explanation:**

## p<q and p+q=k

Let’s approach this step-by-step:

1) First, let’s consider what it means for p and q to be determined uniquely. It means that for a given k, there’s only one possible pair of positive integers p and q that satisfy the conditions.

2) Now, let’s start with small values of k and see how many pairs of p and q we can find:

For k = 3:

p = 1, q = 2 (only possibility)

For k = 4:

p = 1, q = 3 (only possibility)

For k = 5:

p = 1, q = 4

p = 2, q = 3

3) We see that k = 5 is the first value where we have more than one possible pair of p and q.

The correct answer is c) 5.