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If 5n/(4n - x) = (0.788)^(-1) , then x/n =

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by EconomistGMATTutor » Tue Feb 13, 2018 12:54 pm
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
Source: www.gmatprepnow.com

Answer: D
Difficulty level: 650 - 700
Hi Brent@GMATPrepNow,
Let's take a look at your question.

$$\frac{5n}{\left(4n-x\right)}=\left(0.788\right)^{-1}$$
$$\frac{5n}{\left(4n-x\right)}=\frac{1}{0.788}$$
$$\frac{5n}{\left(4n-x\right)}=\frac{1000}{788}$$
$$\frac{5n}{\left(4n-x\right)}=\frac{250}{197}$$
$$197\left(5n\right)=250\left(4n-x\right)$$
$$197\left(n\right)=50\left(4n-x\right)$$
$$197n=200n-50x$$
$$50x=200n-197n$$
$$50x=3n$$
$$\frac{x}{n}=\frac{3}{50}$$

Therefore, Option D is correct.

Hope it helps.
I am available if you'd like any follow up.
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by Brent@GMATPrepNow » Wed Feb 14, 2018 7:17 am
Brent@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
Source: www.gmatprepnow.com

Answer: D
Difficulty level: 650 - 700
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

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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