CAT 2006 — QA Question 8
2 Variable EquationsEasy
The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:
Answer & solution
- A
7
13
- C
14
- D
18
- E
20
Solution
2x + y = 40
∴ y = 40 – 2x
x and y are positive integers and x ≤ y
If x = 1, y = 38
x = 2, y = 36
x = 3, y = 34
.
.
.
x = 12, y =16
x = 13, y = 14
x = 14, y = 12
∴ For x > 13, y ≤ x
∴ There are 13 solutions to the given equation.
Hence, option (b).