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Intern  Joined: 04 Jan 2013
Posts: 2
If x is an integer, is x even?  [#permalink]

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8 00:00

Difficulty:   45% (medium)

Question Stats: 63% (01:39) correct 37% (01:47) wrong based on 366 sessions

### HideShow timer Statistics If x is an integer, is x even?

(1) x^2-y^2 = 0
(2) x^2+y^2 = 98

From: Economist GMAT

This is the kind of question that makes me anxious. I could have sworn the answer would be B. It took me several minutes to realize that Y doesn't have to be an integer.

P.S. - Question for the experts (not you, fellow rabble), is the level (600-700) appropriate? If not, please kindly change it as you see fit.

Regards,
Ian
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4487
Re: If x is an integer, is x even?  [#permalink]

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IanElliott wrote:
If x is an integer, is x even?

1.) x^2-y^2 = 0
2.) x^2+y^2 = 98

First of all, this strikes me as a little harder than 600-level, so I would estimate 700-level. I would be interested to hear other experts' estimations.

Statement #1
This tells us
x^2 = y^2
x = +/-y
So, x and y have the same absolute value, could be same signed or opposite signed, and could be anything. We have no idea whether x is even or odd. This statement, alone and by itself, is insufficient.

Statement #2
We know x is an integer, but y doesn't have to be an integer. Remember, never make restrictions for things that aren't there -- that's a huge trap on all GMAT math. We know x is an integer, but y can be absolutely anything from the continuous infinity of the number line. For example

x = 1 y = sqrt(97)
x = 2 y = sqrt(94)
x = 3 y = sqrt(89)
x = 4 y = sqrt(82)
etc. etc.
So, x could be even or odd. This statement, alone and by itself, is insufficient.

Combined statements
Now, we know that both x & y must be integers, either equal, or positive/negative versions of each other.
Since, from statement #1, we know x^2 = y^2, we can sub this into statement #2:
x^2 + y^2 = 98
x^2 + x^2 = 98
2(x^2) = 98
x^2 = 49
x = +/-7
So, x could be positive or negative 7, but either one is an odd integer, and therefore we can give a clear "no" to the prompt question. Since we are able to give a definitive answer to the prompt question, that means the combined statement are sufficient.

Does this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
##### General Discussion
SVP  Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
Re: If x is an integer, is x even?  [#permalink]

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This problem shouldn't be an issue at all. Let's see

Statement 1 Clearly insuff as O + O = E or E+E= E

Statement 2. Ditto. Same'o as O + O = E or E+E= E

Both together, well we can add em up and get 2x^2=98
x^2 = 49

Thus 'x' is indeed an odd integer. So the answer is NO

Sufficient

C
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4487
Re: If x is an integer, is x even?  [#permalink]

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2
jlgdr wrote:
This problem shouldn't be an issue at all. Let's see

Statement 1 Clearly insuff as O + O = E or E+E= E

Statement 2. Ditto. Same'o as O + O = E or E+E= E

Both together, well we can add em up and get 2x^2=98
x^2 = 49

Thus 'x' is indeed an odd integer. So the answer is NO

Sufficient

C

Dear jlgdr,
My friend, I'm very sorry to pick on you again, but there's no addition in statement #1, and in statement #2 we have absolutely no guarantee that y is an integer, so it may be neither even nor odd. One of the worst GMAT traps is to assume a variable has an integer value when, in fact, any real number is possible.
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
SVP  Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
Re: If x is an integer, is x even?  [#permalink]

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Thanks Mike! Glad to have someone picking on me when Im making these silly mistakes. Thats whats keeping me away from that Q51. Need to be more careful

Cheers!
J

Posted from my mobile device
Current Student D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154 If x is an integer, is x even?  [#permalink]

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Great Question.
This Question can be solved in easily if you look at it from point of view of Even/odd .
Key Rules Applicable here=>
Power/Exponent Does not affect the Even/odd nature of any integer.
Given x=> Integer (Very important Info)
Statement 1
Here x^2=y^2
so y and x must have the same even odd/nature
If y is odd=> x is odd
if y is even => x is even
Hence insufficient
Statement 2
Here x^2+y^2 is 98
not here we can use test cases
let y be √97
x=1/-1=> odd
let y be √94
x=>2/-2 => Even
hence insufficient

Combing them Together we get
x=7/-7
hence x is always odd
Hence C

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Re: If x is an integer, is x even?  [#permalink]

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_________________ Re: If x is an integer, is x even?   [#permalink] 14 Jul 2018, 14:34
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