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655-705 (Hard)|   Exponents|      
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BrentGMATPrepNow
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If x and y are integers, and (-x)^x = ... Updated on: 21 May 2018, 14:58
Originally posted by BrentGMATPrepNow on 21 May 2018, 07:04.
Last edited by BrentGMATPrepNow on 21 May 2018, 14:58, edited 2 times in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

65% (hard)

Question Stats:

60% (02:07) correct 40% (02:28) wrong based on 262 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

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

Answer: (E).
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If x and y are integers, and (-x)^x = ... 21 May 2018, 12:56
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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

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

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If x and y are integers, and (-x)^x = ... 22 May 2018, 08:06
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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
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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

Answer: E

Cheers,
Brent
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If x and y are integers, and (-x)^x = ... 09 May 2024, 21:16
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