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18 Nov 2021, 06:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
72% (01:43) correct
28%
(01:43)
wrong
based on 85
sessions
History
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If xy = 1 and x is not equal to y, then what is the value of \((7 ^{(\frac{1}{x-y})})^{(\frac{1}{x}- \frac{1}{y})}\)?
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
A. \(\frac{1}{49}\)
B. \(\frac{1}{7}\)
C. 1
D. 7
E. 49
Updated on: 21 Nov 2021, 08:04
Originally posted by BrentGMATPrepNow on 18 Nov 2021, 07:12.
Last edited by BrentGMATPrepNow on 21 Nov 2021, 08:04, edited 1 time in total.
Last edited by BrentGMATPrepNow on 21 Nov 2021, 08:04, edited 1 time in total.
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Bunuel
Let's first simplify the exponent \(\frac{1}{x}- \frac{1}{y}\)
\(\frac{1}{x}- \frac{1}{y}=\frac{y}{xy}- \frac{x}{xy}=\frac{y-x}{xy}\)
So we get: \((7 ^{(\frac{1}{x-y})})^{(\frac{1}{x}- \frac{1}{y})}=(7 ^{(\frac{1}{x-y})})^{(\frac{y-x}{xy})}\)
Apply the power of a power law: \(=7 ^{(\frac{1}{x-y})(\frac{y-x}{xy})}\)
Simplify: \(=7 ^{(\frac{-1}{xy})}\)
Substitute \(1\) for \(xy\) to get: \(=7 ^{(\frac{-1}{1})} = 7^{-1}=\frac{1}{7}\)
Answer: B
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21 Nov 2021, 00:37
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BrentGMATPrepNow
Hey BrentGMATPrepNow,
Not that it changes the answer but I'm sure you meant:
Simplify: \(=7 ^{(\frac{-1}{xy})}\)
Substitute \(1\) for \(xy\) to get: \(=7 ^{(\frac{-1}{1})} = 7^{-1}=\frac{1}{7}\)
