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What is the value of positive integer x?

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What is the value of positive integer x? [#permalink]

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New post 12 Feb 2015, 07:01
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Re: What is the value of positive integer x? [#permalink]

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New post 12 Feb 2015, 08:37
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The properties of exponents state that the value of any number raised to the power of zero is one.

(1) x^w=1 [Insufficient] w could be 1 or 0, so x could be any integer.

(2) w is even [Insufficient] By itself, this tells us nothing about x.

Both statements together reveal that w must be zero, but x could still be any integer.
The correct answer is E.

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Re: What is the value of positive integer x? [#permalink]

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New post 12 Feb 2015, 08:55
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Okay lets start with

1) Statement 1 : If X = 1 , W = 0 or 10 it suffices the equation .
If X = 2 , W = 0 it also suffices the equation.
As such X can be 1 or 2 .

2) Statement 2 : W can be 0 or 10 or any even number , nothing is known about X .

When we combine Statements also

If X = 1 , W = 0 or 10 it suffices the equation .
If X = 2 , W = 0 it also suffices the equation.
As such X can be 1 or 2 .
Hence the answer is E

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Re: What is the value of positive integer x? [#permalink]

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New post 12 Feb 2015, 12:37
Hi sterling19,

While you've selected the correct answer, your logic is incomplete/incorrect.

We're told that X is a POSITIVE INTEGER.

Fact 1: X^W = 1

You correctly deduced that W could be 0 or 1, but W can actually be ANY VALUE (if X = 1, 1^(any) = 1). In that same way, X can be ANY positive integer (if X = 0, (any)^0 = 1).
Fact 1 is INSUFFICIENT

Fact 2: W is even

This tells us nothing about the value of X.
Fact 2 is INSUFFICIENT

Combined, we know....
X^W = 1
W is EVEN

IF....
W = 0, then X = ANY positive integer (1^0 = 2^0 = 3^0, = 1 etc.)
W = 2, 4, 6, 8, etc. then X = 1 (1^2 = 1^4 = 1^6 = 1^8 = 1 etc.)
W = -2, then X = 1 since (1^(-2) = 1)
So, W can be ANY EVEN INTEGER and X can be ANY positive integer.
Combined, INSUFFICIENT

Final Answer:
[Reveal] Spoiler:
E


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Re: What is the value of positive integer x? [#permalink]

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New post 13 Feb 2015, 07:46
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Bunuel wrote:
What is the value of positive integer x?

(1) x^w=1

(2) w is even


Kudos for a correct solution.


e
x^w=1: x can be any value with w as 0 and x 1 can take w any value not sufficient
w even nothng from it
combined w =0 can give different values for x so not sufficient

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Re: What is the value of positive integer x? [#permalink]

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New post 16 Feb 2015, 06:12
Bunuel wrote:
What is the value of positive integer x?

(1) x^w=1

(2) w is even


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VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

Any number raised to the zero power results in 1, so statement (1) tells us that w = 0 (in which case x could be anything) or that x = 1 (in which case w can be anything); not sufficient. Statement (2) tells us nothing about x; not sufficient. Combining the two statements, we learn that w still could be 0, since zero is an even integer, or x could be 1. But in the case that w = 0, x could still be any number, so both statements together are not sufficient.
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Re: What is the value of positive integer x? [#permalink]

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New post 17 Feb 2015, 03:21
from stmt 2 we cant say anything hence not sufficient. From satemet 1 a could be any number ...combining also we get w as event number may be 0 then staemnt 1 x can be any number from 1 to infinity hence E.

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Re: What is the value of positive integer x? [#permalink]

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Re: What is the value of positive integer x?   [#permalink] 24 Aug 2017, 05:49
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