CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

The question is about Possible pairs of Solutions of a Linear Equation. We need to find out the possible pairs that satisfy the given linear equation which contains modulus. Framing and solving equations is an integral part of this topic. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 1: 3x + 4|y| = 33. How many integer values of (x, y) are possible?

1. 6
2. 3
3. 4
4. More than 6

Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Linear Equations: Modulus of a number cannot be negative. A simple idea that somehow escapes our mind every now and then

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.

The question is "3x + 4|y| = 33. How many integer values of (x, y) are possible?"

Hence the answer is "More than 6"

Choice D is the correct answer.