If x ≠0, what is the value of (x^w/x^y)^4?
(1) w = y
(2) x^2 = 1
The OA is D.
Experts, may you help me here? I need some help. I don't know how to prove that each statement alone is sufficient. <i class="em em-confused"></i>
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If x ≠0, what is the value of (x^w/x^y)^4?
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Vincen
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Hello.VJesus12 wrote:If x ≠0, what is the value of (x^w/x^y)^4?
(1) w = y
(2) x^2 = 1
The OA is D.
Experts, may you help me here? I need some help. I don't know how to prove that each statement alone is sufficient. <i class="em em-confused"></i>
I think I can help you. We need to find the value of $$\left(\frac{x^w}{x^y}\right)^4$$ but this expression is equal to $$\left(x^{w-y}\right)^4=x^{4w-4y}$$ Now:
If w=y then 4w-4y=0 and then $$x^{4w-4y}=x^0=1.$$ (1) is sufficient.
On the other hand, if $$x^2=1\ \leftrightarrow\ \ \ x=\pm1$$ Now, no matter the sign of x, we have that $$\frac{x^w}{x^y}=\pm1\ \leftrightarrow\ \ \ \left(\pm1\right)^4=1$$ and therefore (2) is sufficient.
The correct answer is D .
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Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
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Given: x ≠0VJesus12 wrote:If x ≠0, what is the value of (x^w/x^y)^4?
(1) w = y
(2) x^2 = 1
The OA is D.
Experts, may you help me here? I need some help. I don't know how to prove that each statement alone is sufficient. <i class="em em-confused"></i>
We have to get the value of (x^w/x^y)^4.
Let's take each statement one by one.
(1) w = y
(x^w/x^y)^4 => (x^w/x^w)^4; replacing the value of w as y.
(x^w/x^w)^4 = (1/1)^4 = 1. Sufficient.
(2) x^2 = 1
=> x = ±1
Case 1: Say x = 1, then (x^w/x^y)^4 = (1^w/1^y)^4 = 1/1)^4 = 1.
Case 2: Say x = -1, then (x^w/x^y)^4 = ((-1)^w/(-1)^y)^4 = [±(1/1)]^4 = ±1^4 = 1. Sufficient.
Note that -1 raised to even integer is positive.
The correct answer: D
Hope this helps!
-Jay
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