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If (x+5) (1/x+1/5)=5, then x=
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05 Apr 2019, 00:41
05 Apr 2019, 00:41
Expert Reply
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Question Stats:
93% (00:34) correct
6% (02:10) wrong based on 16 sessions
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If \(\frac{(x+5)}{(\frac{1}{x}+\frac{1}{5})}=5\), then x=
A. -5
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
A. -5
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (x+5) (1/x+1/5)=5, then x=
[#permalink]
19 Apr 2020, 06:43
19 Apr 2020, 06:43
1
Carcass wrote:
If \(\frac{(x+5)}{(\frac{1}{x}+\frac{1}{5})}=5\), then x=
A. -5
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
A. -5
B. \(\frac{1}{2}\)
C. 1
D. 5
E. 10
\(\frac{1}{x} + \frac{1}{5} = \frac{5}{5x}+\frac{x}{5x}= \frac{5+x}{5x}\)
Take: \(\frac{(x+5)}{(\frac{1}{x}+\frac{1}{5})}=5\)
Rewrite as follows: \(\frac{(x+5)}{(\frac{5+x}{5x})}=5\)
This becomes: \((x+5)(\frac{5x}{5+x})=5\)
In other words: \(\frac{(5x)(x+5)}{5+x}=5\)
Simplify: \(5x = 5\)
Solve: \(x = 1\)
Answer: C
Cheers,
Brent
gmatclubot
Re: If (x+5) (1/x+1/5)=5, then x= [#permalink]
19 Apr 2020, 06:43
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