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10 May 2017, 11:41
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A
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Difficulty:
35%
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Question Stats:
73% (01:55) correct
27%
(02:21)
wrong
based on 1080
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If \(5*\sqrt[x]{125}=\frac{1}{5^{^{\frac{1}{x}}}}\), then x = ?
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
A. -4
B. \(\frac{-1}{\sqrt{2}}\)
C. 0
D. \(\frac{1}{\sqrt{2}}\)
E. 1
ydmuley
Retired Moderator
Joined: 19 Mar 2014
Last visit: 01 Dec 2019
Posts: 807
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
Schools: Haas '20 HBS '20 CBS '20 Wharton '20 Stanford '20 Kellogg '20
GPA: 3.5
17 Jul 2017, 06:27
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If \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\), then x = ?
\(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)
\(5 * (125)^{\frac{1}{x}} = 5^{\frac{-1}{x}}\)
\(5^1 * (5)^{\frac{3}{x}} = 5^{\frac{-1}{x}}\)
\((5)^{{1} + \frac{3}{x}} = 5^{\frac{-1}{x}}\)
\({{1} + \frac{3}{x}} = {\frac{-1}{x}}\)
\(\frac{(x + 3)}{x} = \frac{-1}{x}\)
\(x + 3 = -1\)
\(x = -4\)
Hence, Answer is A
\(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)
\(5 * (125)^{\frac{1}{x}} = 5^{\frac{-1}{x}}\)
\(5^1 * (5)^{\frac{3}{x}} = 5^{\frac{-1}{x}}\)
\((5)^{{1} + \frac{3}{x}} = 5^{\frac{-1}{x}}\)
\({{1} + \frac{3}{x}} = {\frac{-1}{x}}\)
\(\frac{(x + 3)}{x} = \frac{-1}{x}\)
\(x + 3 = -1\)
\(x = -4\)
Hence, Answer is A
Updated on: 08 Mar 2021, 14:34
Originally posted by BrentGMATPrepNow on 11 May 2017, 10:06.
Last edited by BrentGMATPrepNow on 08 Mar 2021, 14:34, edited 2 times in total.
Last edited by BrentGMATPrepNow on 08 Mar 2021, 14:34, edited 2 times in total.
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Bunuel
\(\sqrt[x]{125}\) = 125^(1/x)
= (5^3)^(1/x)
= 5^(3/x)
So, \(5*\sqrt[x]{125}\) = (5^1)[5^(3/x)] = 5^(3/x + 1)
RULE: b^(-x) = 1/(b^x)
So, \(\frac{1}{5^{\frac{1}{x}}}\) = 5^(-1/x)
Given: \(5*\sqrt[x]{125}=\frac{1}{5^{\frac{1}{x}}}\)
We get: 5^(3/x + 1) = 5^(-1/x)
Since the bases are equal, we can conclude: 3/x + 1 = -1/x
Multiply both sides by x to get: 3 + x = -1
Solve: x = -4
Answer: A
