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If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest

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Bunuel
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If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   10 Apr 2019, 23:33
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If \(\frac{x + y}{x - y} = \frac{4}{3}\) and x ≠ 0, then what percentage (to the nearest integer) of x + 3y is x – 3y ?

(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%
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E
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If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   11 Apr 2019, 01:31
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Bunuel wrote:
If \(\frac{x + y}{x - y} = \frac{4}{3}\) and x ≠ 0, then what percentage (to the nearest integer) of x + 3y is x – 3y ?

(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%



Given,

\(\frac{x + y}{x - y} = \frac{4}{3}\)

3x + 3y = 4x - 4y

x = 7y.

Required % : (\(\frac{x - 3y}{x + 3y}\))*100

= (\(\frac{7y - 3y}{7y + 3y}\) )*100

=\(\frac{4y}{10y}\) * 100

= 40%

E is the correct answer.
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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   13 Apr 2019, 19:01
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Bunuel wrote:
If \(\frac{x + y}{x - y} = \frac{4}{3}\) and x ≠ 0, then what percentage (to the nearest integer) of x + 3y is x – 3y ?

(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%



Simplifying, we have:

3x + 3y = 4x - 4y

7y = x

Thus:

x + 3y = 10y

x - 3y = 4y

So 4y/(10y) * 100 = 40%.

Answer: E
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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   02 Jun 2020, 09:14
ScottTargetTestPrep why not 10y/4y. I didn't completely understand this question.
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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   02 Jun 2020, 09:30
Bunuel wrote:
If \(\frac{x + y}{x - y} = \frac{4}{3}\) and x ≠ 0, then what percentage (to the nearest integer) of x + 3y is x – 3y ?

(A) 20%
(B) 25%
(C) 30%
(D) 35%
(E) 40%

\(\frac{x + y}{x - y} = \frac{4}{3}\)

Or, \(3x + 3y = 4x - 4y\)

Or, x = 7y

Now plug in the values of x = 7 and y =1 and check

x + 3y = 7 + 3 => 10

x – 3y = 7 - 3 =>4

Or, 4/10 => 40% , Answer must be (E)
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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink] New post   16 Jun 2020, 17:37
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abhishek13916 wrote:
ScottTargetTestPrep why not 10y/4y. I didn't completely understand this question.


The question asks us to express x - 3y as a percentage of x + 3y. If we did (x + 3y)/(x - 3y) = 10y/4y, then we would have expressed x + 3y as a percentage of x - 3y. When in doubt, you can always replace expressions by numbers; for instance, if the same question asked “What percent of 100 is 25?”, then the answer is clearly 25%. Therefore, x - 3y will be in the numerator, and x + 3y will be in the denominator.

Finally, (x - 3y)/(x + 3y) = 4y/10y gives us the answer as a decimal, therefore we multiply it by 100 to express it as a percent.
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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest [#permalink]
16 Jun 2020, 17:37
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