# CAT 2006 | Question: 58

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The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x \leq y$ is:

1. $7$
2. $13$
3. $14$
4. $18$
5. $20$

13 solutions.

For x = y, there are no integer solutions as there is no positive integer x for which 3x = 40.

For x < y, we have 13 integer solutions for each x from 1 to 13 as

(x, y) = (1,38), (2,36), (3,34)...... (13,14)

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