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# Official Guide Quantitative Problem

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Intern
Joined: 03 Jul 2007
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Official Guide Quantitative Problem [#permalink]  12 Jul 2007, 22:15
This is Question 111 (pg 157) from OG Quantitative Review, a DS problem.

If x is a positive integer and w is a negative integer, what is the value of xw?

1) x^w = 1/2
2) w = -1

1) Since value of w is not known, this eq is INSUFFICIENT.
2) Since x is unknown, this eq is INSUFFICIENT.

However, when you plug in w = -1 in eq (1), the answer is obtained. I felt that both statements together are sufficient.

The official answer: statement 1) alone is sufficient, but 2) is insufficient.

Where am I doing wrong??
GMAT Instructor
Joined: 04 Jul 2006
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Re: Official Guide Quantitative Problem [#permalink]  12 Jul 2007, 22:39
tmani136 wrote:
This is Question 111 (pg 157) from OG Quantitative Review, a DS problem.

If x is a positive integer and w is a negative integer, what is the value of xw?

1) x^w = 1/2
2) w = -1

1) Since value of w is not known, this eq is INSUFFICIENT.
2) Since x is unknown, this eq is INSUFFICIENT.

However, when you plug in w = -1 in eq (1), the answer is obtained. I felt that both statements together are sufficient.

The official answer: statement 1) alone is sufficient, but 2) is insufficient.

Where am I doing wrong??

If you think that (1) is insufficient, show that it is so by finding two different answers to the question that are consistent with (1)
Senior Manager
Joined: 04 Jun 2007
Posts: 350
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Re: Official Guide Quantitative Problem [#permalink]  12 Jul 2007, 22:47
tmani136 wrote:
This is Question 111 (pg 157) from OG Quantitative Review, a DS problem.

If x is a positive integer and w is a negative integer, what is the value of xw?

1) x^w = 1/2
2) w = -1

1) Since value of w is not known, this eq is INSUFFICIENT.
2) Since x is unknown, this eq is INSUFFICIENT.

However, when you plug in w = -1 in eq (1), the answer is obtained. I felt that both statements together are sufficient.

The official answer: statement 1) alone is sufficient, but 2) is insufficient.

Where am I doing wrong??

We know x>0 and w<0.
From stmt 1: x^w = 1/2 = 2^(-1)
x=2, w=-1. Sufficient.

Stmt 2: Insufficient. x can be any value.
Director
Joined: 16 May 2007
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only 2^-1 satisfies stmt 1. Sometimes it is preferred to plug in some kind of numbers to test the statement. This helps in most of the cases, specially with DS number properties. Make sure, to consider all types of numbers unless specified
Director
Joined: 30 Nov 2006
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If x is a positive integer and w is a negative integer, what is the value of xw?

1) x^w = 1/2
2) w = -1

It's either A, C, or E

Obviously once we know w=-1, then x^-1 = 1/x = 1/2 and thus x = 2 and xw = -2

So, it's either A or C

Last step,

x^w = 1/2 , since both x and y are integers, I believe there is only one solution for this equation
it really comes to 1/x^w , where w becomes a positive integer here

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