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

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

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11 Oct 2018, 21:50
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25% (medium)

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73% (01:07) correct 27% (01:10) wrong based on 207 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

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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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11 Oct 2018, 21:59
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

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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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11 Oct 2018, 22:08
1
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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Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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12 Oct 2018, 10:24
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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Re: If x is a positive integer and w is a negative integer, what is the va  [#permalink]

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13 Oct 2018, 11:58
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If x is a positive integer and w is a negative integer, what is the value of xw?

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

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
Re: If x is a positive integer and w is a negative integer, what is the va   [#permalink] 13 Oct 2018, 11:58
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