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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If positive integers x and y are not both odd, which of the following Question banks Downloads My Bookmarks Reviews Important topics
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Intern  Joined: 26 Feb 2011
Posts: 29
If positive integers x and y are not both odd, which of the following  [#permalink]

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4 00:00

Difficulty:   5% (low)

Question Stats: 88% (00:48) correct 12% (01:04) wrong based on 152 sessions

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If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-positive-integers-x-and-y-are-not-both-odd-which-of-the-165827.html

Originally posted by Madelaine88 on 01 Mar 2011, 08:20.
Last edited by Bunuel on 15 May 2016, 04:01, edited 1 time in total.
Renamed the topic and edited the question.
Retired Moderator Joined: 20 Dec 2010
Posts: 1504
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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means either one of x and y is even or both x and y are even.

First case:
where one is even;
xy = even; even multiplied by odd is even.
where both are even;
xy = even; even multiplied by even is even.

so; "A" must be even.

$$\frac{x+y}{x-y}$$

These rules don't apply to division.

Say one of x and y is even.
x+y = odd
x-y = odd

odd/odd can be odd or non-integer but never even.

Say both x and y are even
x+y = even
x-y = even

even/even can be odd, even or non-integer.
(12+4)/(12-4) = 2 even
(8+4)/(8-4) = 3 odd
(12+2)/(12-2) = 1.4 non integer
GMAT Tutor P
Joined: 24 Jun 2008
Posts: 2015
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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1
If positive integers x and y are not both odd, which of the following must be even?
a/ xy
b/ x+y
c/ x-y
d/ x+y-1
e/ 2(x+y)-1

Why x+y/x-y cant be even?

fluke, I think Madelaine was asking why x+y or x-y is not the correct answer here (I don't think the question was about division, since (x+y)/(x-y) is not among the answer choices). It's vital here to note that the question asks "which of the following *must* be even". That's a very different question from "which of the following *could* be even". Certainly x+y *could* be even, if x and y are both even, but if, say, x is even and y is odd, then x+y will be odd. So x+y does not need to be even, and B is thus not the right answer here. But if at least one of x or y is even, then xy will always be even, so the answer is A.
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If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Retired Moderator Joined: 20 Dec 2010
Posts: 1504
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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IanStewart wrote:
If positive integers x and y are not both odd, which of the following must be even?
a/ xy
b/ x+y
c/ x-y
d/ x+y-1
e/ 2(x+y)-1

Why x+y/x-y cant be even?

fluke, I think Madelaine was asking why x+y or x-y is not the correct answer here (I don't think the question was about division, since (x+y)/(x-y) is not among the answer choices). It's vital here to note that the question asks "which of the following *must* be even". That's a very different question from "which of the following *could* be even". Certainly x+y *could* be even, if x and y are both even, but if, say, x is even and y is odd, then x+y will be odd. So x+y does not need to be even, and B is thus not the right answer here. But if at least one of x or y is even, then xy will always be even, so the answer is A.

I see!!! Now, that makes sense! I wondered that for a second and then carried on. thanks IanStewart.
Manager  Joined: 14 Dec 2010
Posts: 104
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 680 Q44 V39
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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thanks IanStewart. Nicely explained.
Intern  Joined: 26 Feb 2011
Posts: 29
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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Yeah, exactly ... I was asking for x+y and x-y separately ... my fault ... however both explanations are useful
Math Expert V
Joined: 02 Sep 2009
Posts: 62619
Re: If positive integers x and y are not both odd, which of the following  [#permalink]

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If positive integers x and y are not both odd, which of the following must be even?

(A) xy
(B) x + y
(C) x - y
(D) x + y -1
(E) 2(x + y) - 1

Positive integers x and y are NOT both odd, means that either both x and y are even or one is even and the other one is odd. In either case xy must be even.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-positive-integers-x-and-y-are-not-both-odd-which-of-the-165827.html
_________________ Re: If positive integers x and y are not both odd, which of the following   [#permalink] 15 May 2016, 04:03
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