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# If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6625
GMAT 1: 760 Q51 V42
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If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu  [#permalink]

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06 Feb 2016, 18:00
00:00

Difficulty:

25% (medium)

Question Stats:

77% (02:06) correct 23% (02:07) wrong based on 85 sessions

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If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can deduce that y is

A. not an even
B. an even
C. not an odd
D. an odd
E. a prime

* A solution will be posted in two days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" SC Moderator Joined: 13 Apr 2015 Posts: 1687 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu [#permalink] ### Show Tags 06 Feb 2016, 23:45 x^2 + 2x + 2y + 4 = 2x^2 + 3x + y - 2 2(x + y + 2) = x^2 + 3x + y - 2 even = x^2 + 3x + y - 2 If x = even --> even + even + y - even = even --> y has to be even If x = odd --> odd + odd + y - even = even --> y has to be even Answer: B Intern Joined: 14 Jul 2015 Posts: 22 GMAT 1: 680 Q44 V40 GMAT 2: 710 Q49 V37 If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu [#permalink] ### Show Tags 07 Feb 2016, 01:11 1. Given: $$x^2 + 2x + 2y + 4 = 2x^2 + 3x + y - 2$$ 2. $$y + 4 = x^2 - x - 2$$ 3. $$y = x^2 - x - 6$$ 4. We know that even - even = even, and that odd - odd = even 5. We see $$x^2 - x$$ in (3). This will always translate to one of the two statements: even - even or odd - odd. The result of either statement will be even. 6. We plug in (5) into our simplified formula: $$y = even - 6$$. Since even - even = even, we know that y = even. Therefore B, y must be even. Intern Joined: 07 Oct 2014 Posts: 9 Re: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu [#permalink] ### Show Tags 07 Feb 2016, 04:20 1 MathRevolution wrote: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can deduce that y is A. not an even B. an even C. not an odd D. an odd E. a prime * A solution will be posted in two days. $$2x^2-x^2+3x-2x+y-2y-2-4=0$$ $$x^2+x-y-6=0$$ Let's assume x is even Then even+even-y-even=even even - y=even, y is even Let's assume x is odd Then odd-odd-y-even=even even-y-even=even y is even Y is even in any case Answer: B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6625 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu [#permalink] ### Show Tags 08 Feb 2016, 17:37 If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can deduce that y is A. not an even B. an even C. not an odd D. an odd E. a prime --> In x^2+2x+2y+4=2x^2+3x+y-2, y=x^2+x-6=x(x+1)-6 is derived. Since x(x+1) is multiplication of consecutive integers, it is always an even number. Then, y=even number-6=even number. Therefore, the answer is B. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu  [#permalink]

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24 Jun 2018, 20:52
MathRevolution wrote:
If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can deduce that y is

A. not an even
B. an even
C. not an odd
D. an odd
E. a prime

* A solution will be posted in two days.

Don't B and C mean the same thing. Given x and y are integers and if Y is not an odd integer then it must be an even integer! If an integer is not odd then it must be even , must it not ?

Unlike positive and negative where an integer need not be positive if it not negative ( e.g. zero ), even and odd have no intermediate category unless I am missing something .

according to wikipedia " An integer that is not an odd number is an even number."

https://simple.wikipedia.org/wiki/Odd_number.

If I am correct then the answer choices in this question are ambiguous . Kindly share your views too.
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Re: If x and y are integers such that x^2+2x+2y+4=2x^2+3x+y-2, we can dedu &nbs [#permalink] 24 Jun 2018, 20:52
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