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If x, y, and z are integers, and x and y are both even, which of the f
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05 Jan 2023, 02:13
05 Jan 2023, 02:13
Expert Reply
00:00
Question Stats:
50% (00:58) correct
50% (00:34) wrong based on 2 sessions
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If x, y, and z are integers, and x and y are both even, which of the following could be an odd integer?
(A) y + x
(B) xy + y
(C) y − xz
(D) x + yz
(E) xy + z
(A) y + x
(B) xy + y
(C) y − xz
(D) x + yz
(E) xy + z
Re: If x, y, and z are integers, and x and y are both even, which of the f
[#permalink]
05 Feb 2023, 09:56
05 Feb 2023, 09:56
Expert Reply
OE
The product of two even numbers, such as xy, will always be even. However, z could be odd, and an even plus an odd is always odd. Therefore, the expression in choice (E) could be odd. In choices (A) and (B), an even plus an even must be even. In choice (C), an even minus an even must be even. In choice (D), yz (an even number, because y is even) plus x, which is even, will be even. Note that this problem could be easily solved by either applying these odd/even principles as demonstrated, or by picking numbers for x, y, and z.
The product of two even numbers, such as xy, will always be even. However, z could be odd, and an even plus an odd is always odd. Therefore, the expression in choice (E) could be odd. In choices (A) and (B), an even plus an even must be even. In choice (C), an even minus an even must be even. In choice (D), yz (an even number, because y is even) plus x, which is even, will be even. Note that this problem could be easily solved by either applying these odd/even principles as demonstrated, or by picking numbers for x, y, and z.
gmatclubot
Re: If x, y, and z are integers, and x and y are both even, which of the f [#permalink]
05 Feb 2023, 09:56
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