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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If x is a positive integer and w is a negative integer, what is the va

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Math Expert V
Joined: 02 Sep 2009
Posts: 64318
If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 70% (01:09) correct 30% (01:14) wrong based on 383 sessions

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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

_________________
Manager  G
Status: In last prep stage
Joined: 11 Jun 2017
Posts: 161
GMAT 1: 630 Q44 V33
GMAT 2: 680 Q47 V37
GPA: 3.2
Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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Bunuel wrote:
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

Logically we cannot find xw by just knowing the value of w.We can conclude that xw=-x but do not have a singular value .
So insuff.

Now consider Stmt1:
x^w=1/2 ,this is possible for different values of x and w .Not a singular value
Insuff

Combining both:
We know that w=-1
So x^w=1/2...x^-1=1/2....1/x^1=1/2....1/x=1/2 ..x=2
So we know x and w ,Suff

AnsC
Intern  B
Joined: 23 Apr 2018
Posts: 1
GMAT 1: 760 Q50 V44 Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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3
My OA= A
Statement 2= clearly Insufficient.

Statement one means there is only one value each of x and that satisfy the equation, vis-
x=2
And W=-1

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Intern  B
Joined: 03 Sep 2018
Posts: 19
WE: Analyst (Consulting)
Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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Bunuel wrote:
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) Let's assume w to be the smallest negative integer i.e -1, so for this condition to be true, x must be equal to 2, hence xw =-2.
This condition is SUFFICIENT as other than the above values of x and w, no other integer values satisfy the condition.

2) This gives no information about x, so NOT SUFFICIENT.

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Manager  G
Joined: 19 Apr 2017
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Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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2
If x is a positive integer and w is a negative integer, what is the value of xw?

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

x is a positive integer means x is a whole number (not a fractional number) that is positive.
W is a negative integer means x is a whole number (not a fractional number) that is negative

so
x has to be 2
w has to be -1

so xw=2*-1 = -2 hence sufficient

2) $$w = -1$$

Does not talk about x, so not sufficient
Intern  B
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GMAT 1: 730 Q48 V42 GPA: 3.3
If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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(1) $$x^w = \frac{1}{2}= 2^-1, 4^\frac{-1}{2}, 8^\frac{-1}{3}...$$

However, w must be an integer. Therefore, w must be -1. Sufficient.

(2) $$w = -1$$

Tells us nothing about x. Insufficient. If x is a positive integer and w is a negative integer, what is the va   [#permalink] 27 Mar 2020, 11:12

# If x is a positive integer and w is a negative integer, what is the va  