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If 5n/4n - x = 0.788^-1

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If 5n/4n - x = 0.788^-1 [#permalink] New post 14 Feb 2018, 09:54
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If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

[Reveal] Spoiler:
3/50

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Re: If 5n/4n - x = 0.788^-1 [#permalink] New post 15 Feb 2018, 01:13
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\(0.788^-^1\) can be expressed as \(\frac{1}{0.788}\)

we have,

\(\frac{5n}{4n - x} = \frac{1}{0.788}\)

we can equate the two numerators to get,
\(5n = 1\) or \(n = \frac{1}{5}\)

similarly we can also equate the denominator,
\(4n - x = 0.788\)

Replace the value of n in the eqn to get,
\(4*\frac{1}{5} - x = 0.788\)
solve for x, x = \(\frac{4}{5} - \frac{788}{1000}\) = 3/250
Now, \(X/N = \frac{3}{250} * 5 = \frac{3}{50}\)

If nothing is mentioned on input type can the ans be an equivalent decimal 0.06?
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: If 5n/4n - x = 0.788^-1 [#permalink] New post 17 Feb 2018, 11:31
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GreenlightTestPrep wrote:
If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

[Reveal] Spoiler:
3/50


I created this question to test a certain fraction property that the GRE likes to test: (a - b)/c = a/c - b/c
There's also (a + b)/c = a/c + b/c

Given: 5n/(4n - x) = (0.788)^(-1)
Rewrite as: 5n/(4n - x) = 1/0.788
Flip each fraction: (4n-x)/5n = 0.788
Apply above property: 4n/5n - x/5n = 0.788
Simplify: 4/5 - x/5n = 0.788
Simplify: 0.8 - x/5n = 0.788
So: x/5n = 0.012
Multiply both sides by 5 to get: x/n = 0.06
Rewrite as fraction: x/n = 6/100 = 3/50

Answer: 3/50

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Re: If 5n/4n - x = 0.788^-1   [#permalink] 17 Feb 2018, 11:31
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