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When x/y = 2.6, (x-y)/(x+y)=?

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by Max@Math Revolution » Wed Feb 28, 2018 12:23 am
[GMAT math practice question]

$$When\ \frac{x}{y}=2.6,\ \frac{\left(x-y\right)}{\left(x+y\right)}=?$$

$$A.\ \frac{2}{7}$$
$$B.\ \frac{3}{8}$$
$$C.\ \frac{4}{9}$$
$$D.\ \frac{5}{9}$$
$$E.\ \frac{7}{10}$$
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by Brent@GMATPrepNow » Wed Feb 28, 2018 7:10 am
Max@Math Revolution wrote:[GMAT math practice question]

$$When\ \frac{x}{y}=2.6,\ \frac{\left(x-y\right)}{\left(x+y\right)}=?$$

$$A.\ \frac{2}{7}$$
$$B.\ \frac{3}{8}$$
$$C.\ \frac{4}{9}$$
$$D.\ \frac{5}{9}$$
$$E.\ \frac{7}{10}$$
GIVEN: x/y = 2.6
Scan the answer choices....
All of them are in fraction form. So....

Rewrite 2.6 as a fraction: x/y = 2 3/5
Or...: x/y = 13/5

So, let's let x = 13 and y = 5, since these values satisfy the condition that x/y = 13/5
Our goal is to find the value of (x - y)/(x + y)
Plug in x = 13 and y = 5
We get: (x - y)/(x + y) = (13 - 5)/(13 + 5)
= 8/18
= 4/9

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by regor60 » Wed Feb 28, 2018 10:21 am
Brent@GMATPrepNow wrote:
Max@Math Revolution wrote:[GMAT math practice question]

$$When\ \frac{x}{y}=2.6,\ \frac{\left(x-y\right)}{\left(x+y\right)}=?$$

$$A.\ \frac{2}{7}$$
$$B.\ \frac{3}{8}$$
$$C.\ \frac{4}{9}$$
$$D.\ \frac{5}{9}$$
$$E.\ \frac{7}{10}$$
GIVEN: x/y = 2.6
Scan the answer choices....
All of them are in fraction form. So....

Rewrite 2.6 as a fraction: x/y = 2 3/5
Or...: x/y = 13/5

So, let's let x = 13 and y = 5, since these values satisfy the condition that x/y = 13/5
Our goal is to find the value of (x - y)/(x + y)
Plug in x = 13 and y = 5
We get: (x - y)/(x + y) = (13 - 5)/(13 + 5)
= 8/18
= 4/9

Answer: C

Cheers,
Brent
Yes, that's the way I did it, then there's this way also:

Given that X/Y has been specified, can (X-Y)/(X+Y) make direct use of it ?

Divide top and bottom by Y:
= (X/Y-1)/(X/Y+1)

Plug in X/Y=2.6:

(2.6-1)/(2.6+1) = 1.6/3.6 = 16/36 = 4/9
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by Max@Math Revolution » Fri Mar 02, 2018 12:12 am
$$\frac{\left(x-y\right)}{\left(x+y\right)}=\frac{\frac{x}{y}-1}{\frac{x}{y}+1}=\frac{\left(2.6-1\right)}{\left(2.6+1\right)}=\frac{1.6}{3.6}=\frac{16}{36}=\frac{4}{9}$$

Therefore, the answer is C.

Answer: C
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