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If 5n/(4n - x) = (0.788), then x/n =

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New post 13 Feb 2018, 08:39
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If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25

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If 5n/(4n - x) = (0.788), then x/n =  [#permalink]

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New post 13 Feb 2018, 08:44
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GMATPrepNow wrote:
If 5n/(4n - x) = (0.788)^-1, then x/n =

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25


\(\frac{5n}{(4n-x)}=(0.788)^{-1}=\frac{1000}{788}\)....
\(3940n=4000n-1000x...........
60n=1000x\)
So\(\frac{x}{n}=\frac{60}{1000}=\frac{3}{50}\)
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If 5n/(4n - x) = (0.788), then x/n =  [#permalink]

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New post 13 Feb 2018, 19:50
1
GMATPrepNow wrote:
If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25



\(\frac{5n}{4n - x} = 0.788^{-1}\)=\(\frac{5n}{4n - x} = \frac{1000}{788}\)

\(\frac{5}{4 - (x/n)} = \frac{1000}{788}\)

On simplification

\(\frac{x}{n}=3/50\)

D
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If 5n/(4n - x) = (0.788), then x/n =  [#permalink]

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New post Updated on: 17 Feb 2018, 12:32
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GMATPrepNow wrote:
If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25


I created this question to test a certain fraction property that the GMAT 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: D

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Originally posted by GMATPrepNow on 14 Feb 2018, 08:19.
Last edited by GMATPrepNow on 17 Feb 2018, 12:32, edited 1 time in total.
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If 5n/(4n - x) = (0.788), then x/n =  [#permalink]

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New post 14 Feb 2018, 09:54
1
GMATPrepNow wrote:
If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25



\(\frac{5n}{4n - x} = 0.788^{-1}\) -> \(\frac{5n}{4n - x} = \frac{1}{0.788}\) -> \(\frac{5n}{4n - x} = \frac{1000}{788}\)

We can break the fraction to form the two simultaneous equation(s)

\(5n = 1000\) -> \(n = 200\)
\(4n - x = 788\) -> \(800 - x = 788\) -> \(x = 12\)

We have been asked to find the value of \(\frac{x}{n}\) which is \(\frac{12}{200} = \frac{3}{50}\)(Option D)
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If 5n/(4n - x) = (0.788), then x/n =  [#permalink]

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New post 15 Oct 2019, 02:22
GMATPrepNow wrote:
If \(\frac{5n}{4n - x} = 0.788^{-1}\), then \(\frac{x}{n} =\)

A) 3/500
B) 3/250
C) 3/125
D) 3/50
E) 3/25


This is how i solved
5n4n−x=0.788−15n4n−x=0.788−1=5n4n−x=10007885n4n−x=1000788

54−(x/n)=100078854−(x/n)=1000788

On simplification

Just follow the principals of Bodmas or Pemdas

788 * 5n = 1000* ( 4n- x)
3940 n = 4000n -1000 x
1000x = 60 n
X/n = 60 /1000 = 3/50

D
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If 5n/(4n - x) = (0.788), then x/n =   [#permalink] 15 Oct 2019, 02:22
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