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# If x and y are integers, and (-x)^x = ...

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CEO
Joined: 12 Sep 2015
Posts: 2900
If x and y are integers, and (-x)^x = ...  [#permalink]

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Updated on: 21 May 2018, 14:58
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Difficulty:

85% (hard)

Question Stats:

49% (02:18) correct 51% (02:34) wrong based on 59 sessions

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If x and y are non-zero integers, and $$(-x)^x = y^y$$, then what is the value of x?

(1) x + y = 0
(2) x is odd

*kudos for all correct solutions

_________________

Brent Hanneson – GMATPrepNow.com

Originally posted by GMATPrepNow on 21 May 2018, 07:04.
Last edited by GMATPrepNow on 21 May 2018, 14:58, edited 2 times in total.
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Joined: 03 Oct 2016
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Re: If x and y are integers, and (-x)^x = ...  [#permalink]

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21 May 2018, 08:07
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1
GMATPrepNow wrote:
If x and y are integers, and $$(-x)^x = y^y$$, then what is the value of x?

(1) x + y = 0

$$x=-y$$
$$(-x)^x = y^y$$
$$y^-^y$$= $$y^y$$
$$y^2^y$$ =1 which can be written as:

$$y^2^y$$ = $$1^2=0^0$$=$$(-1)^-^2$$

y=0 x=0
y =1 x =-1
y=-1 x=1

Not sufficient.

(2) x is odd

x can be any odd number. 1,3,5 .... Not Sufficient.

1)+2) We have to pick odd values of x .i.e 1 and -1.

y =1 x =-1
y=-1 x=1

Two values of x, so 1)+2) is also not sufficient.

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Joined: 12 Dec 2016
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GMAT 1: 660 Q49 V31
GPA: 3
Re: If x and y are integers, and (-x)^x = ...  [#permalink]

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21 May 2018, 12:56
1
GMATPrepNow wrote:
If x and y are non-negative integers, and $$(-x)^x = y^y$$, then what is the value of x?

(1) x + y = 0
(2) x is odd

Quite a strange question. I thing the condition that both are non-negative should be deleted, otherwise E can't be the right answer.

x,y are non-negative means that x,y >=0, so $$(y)^y$$ >= 0
at the same time $$(-x)^x$$ >= 0 only if x is even (inlc. 0)

1) x+y = 0 is true only if both are 0, since x,y are non-negative

2) x is odd, just can't be true, because the equation in the condition will never be true for x,y >=0
CEO
Joined: 12 Sep 2015
Posts: 2900
Re: If x and y are integers, and (-x)^x = ...  [#permalink]

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21 May 2018, 15:01
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Yeesh I read my question several times before posting and each time I read it as NON-ZERO. My bad. I have edited the original question accordingly.
Sorry for the confusion I've caused.

Cheers
Brent

Posted from my mobile device
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Brent Hanneson – GMATPrepNow.com

CEO
Joined: 12 Sep 2015
Posts: 2900
Re: If x and y are integers, and (-x)^x = ...  [#permalink]

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22 May 2018, 08:06
Top Contributor
GMATPrepNow wrote:
If x and y are non-zero integers, and $$(-x)^x = y^y$$, then what is the value of x?

(1) x + y = 0
(2) x is odd

Target question: What is the value of x?

Given: x and y are non-zero integers, and $$(-x)^x = y^y$$
When we see this given information, we should be thinking of a few different ways for the equation to hold true.
For example, if x = 1, then (-x)^x = (-1)^1 = -1. What value of y is necessary for y^y to equal -1? Well, if y = -1, then y^y = (-1)^(-1) = 1/(-1) = -1
So, one possible solution to the given equation is x = 1 and y = -1
Using very similar logic, we can see that x = -1 and y = 1 is another possible solution to the given equation

Now let's check the statements....

Statement 1: x + y = 0
As we can see from our earlier work, there are at least two possible solutions that satisfy statement 1:
Case a: x = 1 and y = -1. In this case, the answer to the target question is x = 1
Case b: x = -1 and y = 1. In this case, the answer to the target question is x = -1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x is odd
We should recognize that we can RE-USE the same values we used to show that statement 1 is not sufficient (since 1 and -1 are both ODD)
That is....
Case a: x = 1 and y = -1. In this case, the answer to the target question is x = 1
Case b: x = -1 and y = 1. In this case, the answer to the target question is x = -1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words:
Case a: x = 1 and y = -1. In this case, the answer to the target question is x = 1
Case b: x = -1 and y = 1. In this case, the answer to the target question is x = -1
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com

Re: If x and y are integers, and (-x)^x = ... &nbs [#permalink] 22 May 2018, 08:06
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