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.