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# If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?

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If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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26 Apr 2017, 05:45
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63% (02:28) correct 37% (02:31) wrong based on 154 sessions

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If x and y are integers, and N = (x² – y + 3x)(2y + x), is N odd?

1) x+y is even
2) 3xy is odd

*kudos for all correct solutions

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Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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26 Apr 2017, 06:13
1
If x and y are integers, and N = (x² – y + 3x)(2y + x), is N odd?

1) x+y is even
2) 3xy is odd

for x+y to be even, we can have x,y as either even or odd
for xy to be odd, both x and y should be odd

So for 3xy is odd
(x² – y + 3x)=> odd^2-odd+odd is always an odd number
(2y + x) => 2*odd + odd=> even+odd= odd number
product of two odd numbers is odd.

Now x+y = even
consider x, y as even
(x² – y + 3x)=> even^2-even+even is always an even number
(2y + x) => 2*even+ even=> even+even= even number
product of two even numbers is even.

consider x,y as odd, so as per above discussion for 3xy
(x² – y + 3x)=> odd^2-odd+odd is always an odd number
(2y + x) => 2*odd + odd=> even+odd= odd number
product of two odd numbers is odd.

Hence for x+y, depending upon the the odd/even value, the result changes

So together
Hence B alone is sufficient
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If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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26 Apr 2017, 08:41
1
GMATPrepNow wrote:
If x and y are integers, and N = (x² – y + 3x)(2y + x), is N odd?

1) x+y is even
2) 3xy is odd

*kudos for all correct solutions

From 2)3xy is odd,x and y are integers ------->x and y should be odd
(x^2+3x -y) & (2y+x)----> cannot be zero---->clear cut answer will be obtained
hence sufficient

from 1)x+Y is even----> Both can be even or Both can be odd
----> N can be even or odd
hence insufficient

--->B
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Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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27 Apr 2017, 06:02
Top Contributor
GMATPrepNow wrote:
If x and y are integers, and N = (x² – y + 3x)(2y + x), is N odd?

1) x+y is even
2) 3xy is odd

Target question: Is N odd?

Given: N = (x² – y + 3x)(2y + x)
Before we examine the statements, it might be useful SYSTEMATICALLY examine all of the possible cases we need to consider:
case a: x is even, and y is even
case b: x is even, and y is odd
case c: x is odd, and y is even
case d: x is odd, and y is odd

There are two ways to analyze each case.
- We can take each case and apply the rules for evens and odd (e.g., even + odd = odd, even x even = even, etc)
- We can take each case and plug in even and odd numbers for x and y. The easiest values are 1 for odd numbers and 0 for even numbers.

When we do apply either of these strategies we get:
case a: x is even, and y is even. N is EVEN
case b: x is even, and y is odd. N is EVEN
case c: x is odd, and y is even. N is EVEN
case d: x is odd, and y is odd. N is ODD

The target question ask whether N is odd. Since N is odd only when x is odd and y is odd, we can rephrase our target question...
REPHRASED target question: Are x and y BOTH odd?

Okay, now onto the statements!!!

Statement 1: x+y is even
If x+y is even, then there are two possible cases:
- x and y are both odd, in which case, x and y ARE both odd
- x and y are both even, in which case, x and y are NOT both odd
Since we can answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3xy is odd
If 3xy is odd, then xy is odd, which means x and y ARE both odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

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If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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17 Nov 2017, 12:39
GMATPrepNow wrote:
GMATPrepNow wrote:
If x and y are integers, and N = (x² – y + 3x)(2y + x), is N odd?

1) x+y is even
2) 3xy is odd

Target question: Is N odd?

Given: N = (x² – y + 3x)(2y + x)
Before we examine the statements, it might be useful SYSTEMATICALLY examine all of the possible cases we need to consider:
case a: x is even, and y is even
case b: x is even, and y is odd
case c: x is odd, and y is even
case d: x is odd, and y is odd

There are two ways to analyze each case.
- We can take each case and apply the rules for evens and odd (e.g., even + odd = odd, even x even = even, etc)
- We can take each case and plug in even and odd numbers for x and y. The easiest values are 1 for odd numbers and 0 for even numbers.

When we do apply either of these strategies we get:
case a: x is even, and y is even. N is EVEN
case b: x is even, and y is odd. N is EVEN
case c: x is odd, and y is even. N is EVEN
case d: x is odd, and y is odd. N is ODD

The target question ask whether N is odd. Since N is odd only when x is odd and y is odd, we can rephrase our target question...
REPHRASED target question: Are x and y BOTH odd?

Okay, now onto the statements!!!

Statement 1: x+y is even
If x+y is even, then there are two possible cases:
- x and y are both odd, in which case, x and y ARE both odd
- x and y are both even, in which case, x and y are NOT both odd
Since we can answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 3xy is odd
If 3xy is odd, then xy is odd, which means x and y ARE both odd
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Hi GMATPrepNow

I have a question

the Solution assumes N as integer, but what if N is not an integer? no info about that in the question.

Thanks
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Joined: 11 Sep 2015
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Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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17 Nov 2017, 13:12
1
Top Contributor
hellosanthosh2k2 wrote:
Hi GMATPrepNow

I have a question

the Solution assumes N as integer, but what if N is not an integer? no info about that in the question.

Thanks

If x and y are integers, and N = (x² – y + 3x)(2y + x), then N must be an integer.
Here's why:

If x is an integer, then x², and 3x must also be integers.
If y is an integer, then 2y must also be an integer.
Also, the sums and differences of integers are also integers.

So, N = (x² – y + 3x)(2y + x)
= (some integer - some integer + some integer)(some integer + some integer)
= (an integer)(an integer)
= integer

Does that help?

Cheers,
Brent
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If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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17 Nov 2017, 13:18
Hi GMATPrepNow,

Thanks for reply. Actually I misread the question as N = (x² – y + 3x)/(2y + x) instead of N = (x² – y + 3x)(2y + x).

Sorry for confusion. I must have been asleep while solving

Posted from my mobile device
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Joined: 11 Sep 2015
Posts: 4318
Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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01 May 2018, 07:55
Top Contributor
hellosanthosh2k2 wrote:
Hi GMATPrepNow,

Thanks for reply. Actually I misread the question as N = (x² – y + 3x)/(2y + x) instead of N = (x² – y + 3x)(2y + x).

Sorry for confusion. I must have been asleep while solving

Posted from my mobile device

I'll take some responsibility on that too. I could have formatted the question better.

Cheers,
Brent
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Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?  [#permalink]

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24 Sep 2019, 21:58
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Re: If x and y are integers, and N = (x^2 – y + 3x)(2y + x), is N odd?   [#permalink] 24 Sep 2019, 21:58
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