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Modulus of a number cannot be negative. A simple idea that somehow escapes our mind every now and then.

## Counting - Linear Equations

3x + 4|y| = 33. How many integer values of (x, y) are possible?
1. 6
2. 3
3. 4
4. More than 6

Choice D. More than 6

## Detailed Solution

Let us rearrange the equation:
3x = 33 – 4|y|

Since x and y are integers, and since |y| is always positive regardless of the sign of y, this means that when you subtract a multiple of 4 from 33, you need to get a multiple of 3.

Since 33 is already a multiple of 3, in order to obtain another multiple of 3, you will have to subtract a multiple of 3 from it. So, y has to be a positive or a negative multiple of 3.

y = 3, -3, 6, -6, 9, -9, 12, -12...etc.
For every value of y, x will have a corresponding integer value.
So there are infinite integer values possible for x and y.

Correct Answer: More than 6 values are possible.

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