# CAT - Linear Quadratic Equations

Question:
3x + 4|y| = 33. How many integer values of (x, y) are possible?
A.  6
B.  3
C.  4
D.  More than 6

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 will 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.

Level of difficulty 1

IIM CAT Preparation Tips: CAT - Linear Quadratic Equations

## Aug 8, 2013

### CAT - Linear Quadratic Equations

Question:
3x + 4|y| = 33. How many integer values of (x, y) are possible?
A.  6
B.  3
C.  4
D.  More than 6

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 will 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.

Level of difficulty 1