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If w, x, and y are integers and 54^=2^w * 3^(x+y)

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If w, x, and y are integers and 54^=2^w * 3^(x+y)  [#permalink]

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New post 02 Oct 2018, 08:57
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Difficulty:

  55% (hard)

Question Stats:

61% (02:13) correct 39% (01:50) wrong based on 54 sessions

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If \(w, x\), and \(y\) are integers and \(54^6 = 2^w * 3^{x+y}\), what is the value of \(x*y\)?

(1) \(2w = \frac{y^2}{3}\)

(2) \(x = \frac{w^2}{3}\)

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Re: If w, x, and y are integers and 54^=2^w * 3^(x+y)  [#permalink]

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New post 02 Oct 2018, 09:39
54^6 = 2^6 * 3^18 = 2^w * 3^(x+y)
w = 6
x + y = 18

Statement 1:
2w = 1/3 * y^2
Substituting known values:
36 = y^2 = y = +6,-6
Two different values of x*y
Not sufficient

Statement 2:
We will get a single value of x.
Sufficient

Choose B

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Re: If w, x, and y are integers and 54^=2^w * 3^(x+y)  [#permalink]

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New post 02 Oct 2018, 19:42
XavierAlexander wrote:
If \(w, x\), and \(y\) are integers and \(54^6 = 2^w * 3^{x+y}\), what is the value of \(x*y\)?

(1) \(2w = \frac{y^2}{3}\)

(2) \(x = \frac{w^2}{3}\)



\(52^6\)=\(2^w*36(x+y)\)
2^6*3^18=2^w*3^(x+y)

so w=6 and x+y=18

statement 1:

2w=(y^2)/3
y^2=36
y=6,-6
x=12,24

not sufficient

statement 2:

x=(w^2)/3
x=12 so y=6

statement 2 is sufficient

answer is B
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Re: If w, x, and y are integers and 54^=2^w * 3^(x+y)   [#permalink] 02 Oct 2018, 19:42
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