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If x and y are integers, is 4x^2-y^2 an odd number?

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If x and y are integers, is 4x^2-y^2 an odd number?

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[GMAT math practice question]

If x and y are integers, is 4x^2-y^2 an odd number?

1) x is an odd number
2) y is an odd number

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

Modifying the question:
In order for 4x^2 - y^2 to be odd, y^2 must be odd since 4x^2 is always even. This is equivalent to y being odd. So, the question asks if y is odd. Thus, the answer is B.

Condition 1)
If y is an odd number, then both 2x + y and 2x - y are odd numbers and (2x+y)(2x-y) is an odd number.
If y is an even number, both 2x + y and 2x - y are even numbers and (2x+y)(2x-y) is an even number.
Since the question does not have a unique answer, condition 1) is not sufficient.


Therefore, the answer is B.

Answer: B

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Max@Math Revolution wrote:
[GMAT math practice question]

If x and y are integers, is 4x^2-y^2 an odd number?

1) x is an odd number
2) y is an odd number
Let’s recall some facts about odds and evens: (1) Even x even = even and even x odd = even. Thus, 4x^2 will always be an even number. (2) Odd x odd = odd. So if y is odd, then y^2 will be odd.

Thus, in order for 4x^2 - y^2 to be odd, y must be odd.

Statement One Alone:

x is an odd number

Since we know nothing regarding y, statement one alone is not sufficient to answer the question.

Statement Two Alone:

y is an odd number

Since y is odd, 4x^2 - y^2 must be odd since even - odd = odd. Statement two alone is sufficient to answer the question.

Answer: B

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jeff@targettestprep.com



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