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

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Bunuel
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If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   11 Oct 2018, 21:50
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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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TanayLohia
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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   11 Oct 2018, 22:08
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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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StudiosTom
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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   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


Since Stmt 2 looks simple,i will start with it.
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] If x is a positive integer and w is a negative integer, what is the va   12 Oct 2018, 10:24
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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


Answer.
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.

Hence answer is A.

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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   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
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If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   27 Mar 2020, 12:12
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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.

Answer is (A)
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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   03 Jun 2022, 04:54
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TanayLohia wrote:
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

Posted from my mobile device

NO
we can put X=1/4 and W=-1/2 as well .........no unique value
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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   03 Apr 2023, 19:37
NarayanaGupta007 wrote:
TanayLohia wrote:
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

Posted from my mobile device

NO
we can put X=1/4 and W=-1/2 as well .........no unique value



EXACTLY. IF WE TAKE X=4 AND W = -2 ; WE GET 1/2; AND XY= -8; THEREFORE NOT UNIQUE SOLUTION. ONLY IF WE CONSIDER THE STATEMENT 2 TOGETHER WILL WE GET A UNIQUE SOLUTION.
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Re: If x is a positive integer and w is a negative integer, what is the va [#permalink] If x is a positive integer and w is a negative integer, what is the va   12 Apr 2023, 10:17
adityavishnu wrote:
NarayanaGupta007 wrote:
TanayLohia wrote:
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

Posted from my mobile device

NO
we can put X=1/4 and W=-1/2 as well .........no unique value



EXACTLY. IF WE TAKE X=4 AND W = -2 ; WE GET 1/2; AND XY= -8; THEREFORE NOT UNIQUE SOLUTION. ONLY IF WE CONSIDER THE STATEMENT 2 TOGETHER WILL WE GET A UNIQUE SOLUTION.


adityavishnu

You made a mistake while calculating the value
If x=4 and w=-2
then x^w=1/16, not 1/2.
These 2 value don't satisfy the equation.
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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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Bunuel
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