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

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

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10 Apr 2019, 22:33
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25% (medium)

Question Stats:

78% (01:53) correct 23% (02:08) wrong based on 80 sessions

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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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Posts: 1491
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest  [#permalink]

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11 Apr 2019, 00:31
2
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%

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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest  [#permalink]

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13 Apr 2019, 18:01
1
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%.

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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest  [#permalink]

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02 Jun 2020, 08:14
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]

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02 Jun 2020, 08:30
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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Abhishek....

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Re: If (x + y)/x - y = 4/3 and x 0, then what percentage (to the nearest  [#permalink]

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16 Jun 2020, 16:37
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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# Scott Woodbury-Stewart

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Scott@TargetTestPrep.com
225 Reviews

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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, 16:37