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Senior Manager  Joined: 25 Oct 2008
Posts: 492
Location: Kolkata,India
If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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4 00:00

Difficulty:   45% (medium)

Question Stats: 61% (01:07) correct 39% (01:04) wrong based on 218 sessions

### HideShow timer Statistics If x ≠ 0, what is the value of $$(x^w/x^y)^4$$?

(1) w = y

(2) x^2 = 1

Just wanted to get a clarification.
Stmt 1 is suff.
Stmt 2 i marked as insuff. cos x can have two values +1,-1..'cos in GMAT:
root16= 4
but x^2=16 means x=+4,-4 right?
So ans here should be A.

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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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hi tejal, u r right that x has 2 values +1 and -1.... but you have to take 4th power of whats in bracket .. so +1 or -1 will not make any diff... ans wud b always 1.... ans - D
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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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tejal777 wrote:
If x ≠ 0, what is the value of $$(x^w/x^y)^4$$?

(1) w = y

(2) x^2 = 1

Just wanted to get a clarification.
Stmt 1 is suff.
Stmt 2 i marked as insuff. cos x can have two values +1,-1..'cos in GMAT:
root16= 4
but x^2=16 means x=+4,-4 right?
So ans here should be A.

1) is suff as you already noted.
2) regardless of if they are -1 or +1 once it is ^4 it will be positive. so also suff.

Hence D. What's OA?
Manager  Joined: 23 Sep 2009
Posts: 105
Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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Ans: d)
As long as it is the powers of even number the answer is going to be 1.
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Posts: 443
Schools: Fuqua
Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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My take is D.

Here is my explanation.

The equation in question stem can be simplfied as X^(4*(w-y)).

Clue 1: w = y ==> X ^ 0 = 1 We know the value of the expression in the question stem. Hence sufficient.

Clue 2: x^2 = 1 ==> X = +/-1 ==> 1 ^ even number = 1. ==> 1 ^ 2*2*(w-y) = 1. Again we know the value of the expression in the question stem. Hence sufficient.
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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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Dear Bunuel, I want to ask what will be the value of (a/b)^- m/n equal to? Does it will be equal to (b/a)^n/m?
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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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23a2012 wrote:
Dear Bunuel, I want to ask what will be the value of (a/b)^- m/n equal to? Does it will be equal to (b/a)^n/m?

$$(\frac{a}{b})^{-\frac{m}{n}}=\frac{1}{(\frac{a}{b})^{\frac{m}{n}}}=$$

$$=(\frac{1}{\frac{a}{b}})^{\frac{m}{n}}=(\frac{b}{a})^{\frac{m}{n}}$$.
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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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tejal777 wrote:
If x ≠ 0, what is the value of $$(x^w/x^y)^4$$?

(1) w = y

(2) x^2 = 1

Just wanted to get a clarification.
Stmt 1 is suff.
Stmt 2 i marked as insuff. cos x can have two values +1,-1..'cos in GMAT:
root16= 4
but x^2=16 means x=+4,-4 right?
So ans here should be A.

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if-x-0-what-is-the-value-of-sq-root-x-u-x-v-95674.html
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Math Expert V
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Posts: 7764
If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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tejal777 wrote:
If x ≠ 0, what is the value of $$(x^w/x^y)^4$$?

(1) w = y

(2) x^2 = 1

Just wanted to get a clarification.
Stmt 1 is suff.
Stmt 2 i marked as insuff. cos x can have two values +1,-1..'cos in GMAT:
root16= 4
but x^2=16 means x=+4,-4 right?
So ans here should be A.

hi ... irrespective of the value of x as 1 or -1... the value will be 1 since the entire has the power of an even number,4..
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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Hi All,

This DS question can be solved with a mix of Number Property Rules and TESTing VALUES:

We're told that X cannot = 0. We're asked for the value of [(X^W)/(X^Y)]^4

While this may look "scary", it's actually based on some basic math rules/patterns. Notice how the "base" of both the numerator AND the denominator are the SAME....that matters....

Fact 1: W = Y

Let's TEST VALUES:

IF...
X = 1
W = 1
Y = 1

[(1^1)/(1^1)]^4 = (1/1)^4 = 1

IF....
X = 2
W = 3
Y = 3

[(2^3)/(2^3)]^4 = (8/8)^4 = (1/1)^4 = 1

From this work, you should notice that the fraction ALWAYS equals 1, so the answer will ALWAYS be 1^4 = 1. That will always occur regardless of what you TEST for the 3 variables (in Fact 1).
Fact 1 is SUFFICIENT

Fact 2: X^2 = 1

This tells us that X = 1 OR X = -1

Here's where some Number Property knowledge comes in handy.

+1 raised to ANY power = 1, so (1^W) and (1^Y) BOTH always = 1......and 1/1 = 1.....so 1^4 = 1

-1 raised to an EVEN power = 1
-1 raised to an ODD power = -1

While this might appear to yield different answer, you must remember what the specific question asks for....

With these two restrictions on the numerator and denominator, we have 4 possible calculations (and 2 possible outcomes):

(+1)/(-1) = -1
(-1)/(+1) = -1
(+1)/(+1) = 1
(-1)/(-1) = 1

(-1)^4 = 1
(+1)^4 = 1

So the answer is the SAME regardless.
Fact 2 is SUFFICIENT.

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Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y  [#permalink]

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_________________ Re: If x 0, what is the value of (x^w/x^y)^4 ? (1) w = y   [#permalink] 25 Sep 2018, 07:41
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