MathRevolution wrote:
[GMAT math practice question]
\(x\) and \(y\) are integers such that \(4x^2 – y^2 +4x + 4y – 3 = 0.\) Which of following is true?
A. \(y\) is an even number.
B. \(y\) is an odd number.
C. \(y\) is positive.
D. \(y\) is negative.
E. \(y\) is a prime number
Nice - several different solutions!!
Here's one more approach.
I'll start at the point where Payal (above) got to:
(
2x + 1)² – (
y – 2)² = 0
Since this is a difference of squares, we can factor the left side to get: [
(2x + 1) + (
y – 2)][
(2x + 1) - (
y – 2)] = 0
Simplify: (2x + y - 1)(2x - y + 3) = 0
So, EITHER 2x + y - 1 = 0 OR 2x - y + 3 = 0
If 2x + y - 1 = 0, then y = -2x + 1. Since -2x is always even, we know that -2x + 1 (aka y) is ODD
If 2x - y + 3 = 0, then y = 2x - 3. Since 2x is always even, we know that 2x - 3 (aka y) is ODD
So, it must be the case that y is ODD
Answer: B
Cheers,
Brent
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