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