If 4/(5 - a/b) = 1, which of the following must be true?

Question

If  \frac{4}{5 - \frac{a}{b}} = 1  which of the following must be true?

(A) a = 0
(B) b = 0
(C) a = 1
(D) b = 1
(E) a = b

Silviax · Answer

I just figured out the answer to my problem.
if x = y then no matter what these numbers of this second fraction are it will be 1. A number divided by itself = 1.
So 5-1 = 4 and that's exactly what I need as the denominator by which to divide the numerator in order to get 1.

:idea:

chetan2u · Answer

\frac{4}{5-a/b}=1  .....
fraction can be 1 when numerator and denominator are equal, so  4 = 5- \frac{a}{b} .......... \frac{a}{b} = 5-4 = 1........a=b 
E

BrentGMATPrepNow · Answer

Chetan2u has done a great job applying what I call the Something Method.

Given:  \frac{4}{5-a/b}=1 
So, we have: 4/ something  = 1
This means that  something  = 4
In other words,  5 - a/b  = 4

Now we have 5 -  a/b  = 4
If 5 -  something  = 4, then  something  = 1
In other words,  a/b  = 1
If  a/b  = 1, then we can be certain that a = b

Answer:  E

Here's a video on the Something Method:
  Something Method  
 https://www.youtube.com/watch?v=mmTisgtNfTI

Abhishek009 · Answer

\frac{4}{5-a/b}=1

Or,  4 = 5 - \frac{a}{b}

So,  \frac{a}{b} = 1

Thus,  a = b  , Answer must be (E)

BrushMyQuant · Answer

\frac{4}{5 - \frac{a}{b}} = 1

=> 4 = 5 -  \frac{a}{b} 
=>  \frac{a}{b}  = 5 - 4 = 1

Since b is in the denominator
=> b ≠ 0

\frac{a}{b}  = 1
=> a = b will always be true

So,  Answer will be E 
Hope it helps!

uCS2020 · Answer

To solve this question,
4/5-a/b I first found out what 5-a/b is
It’s is = to 5b-a/b
Let’s substitute it 
4/5b-a/b = 4b/5b-a = 1
Now,what we need to know is that if a fraction is = 1 then both the numerator and denominator are the same
Let’s make an equation

4b = 5b-a
Add a from both sides
4b+a = 5b
Subtract 4b from each side
a=b

Answer = E

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If 4/(5 - a/b) = 1, which of the following must be true?

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If 4/(5 - a/b) = 1, which of the following must be true?

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