# 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

### Related posts

• June 7, 2013 CAT Linear Equations Another question from the book Quantitative Aptitude for CAT .  Question 1.       x + |y| = 8, |x| + y = 6.How many pairs of x, y satisfy these two equations? A.      2 B.      […] Posted in Linear & Quadratic Equations
• June 17, 2013 CAT Linear Equations Question (|x| -3) (|y| + 4) = 12. How many pairs of integers (x, y) satisfy this equation? 4 10 6 8 Answer: Choice (B) Explanatory Answer Product of two integers is […] Posted in Linear & Quadratic Equations
• August 13, 2014 CAT Coordinate Geometry Question and Solution Question   What is the area enclosed by the region defined by y = |x -1| + 2, the line x = 1; X-axis and Y-axis?   Explanation   Solution is available on […] Posted in Coordinate Geometry
• February 6, 2014 Algebra Question and Solution Question |x| + |2y| + |3z| = 13, x * y * z is non-zero; x, y, z are all integers. How many sets of values are possible? Answer 64 sets of values Explanation Posted in Functions