ExplanationTranslate the question and answer choices into algebra.

You are given that \(x - y = 4\).

Choice (A) tells you that \(x + y = 4\), and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.

Choice (A) is sufficient and correct.

Choice (B) tells you that \(x^2 - y^2 = 16\), and can be factored: \(x^2 - y^2 = (x + y)(x - y) = 16\). You are given that \((x - y) = 4\), so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.

Choice (B) is also sufficient and correct.

Choice (C) states \((x - y)^2 = 16\). This is simply the result of squaring what you were already given and you have no way to determine what the values of x

and y are, making this choice incorrect.

Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.

Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.

Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.

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Sandy

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