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If x/(x+y)=6 then . . .

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by VJesus12 » Tue Oct 31, 2017 10:55 am
$$If\ \frac{x}{x+y}=6\ then\ \frac{y}{y+x}=$$

A -5
B 5/11
C 1
D 11/5
E 5

The OA is A.

How can I find this value without knowing x and y values? Experts, please give me some explanation here.
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by DavidG@VeritasPrep » Tue Oct 31, 2017 11:17 am
VJesus12 wrote:$$If\ \frac{x}{x+y}=6\ then\ \frac{y}{y+x}=$$

A -5
B 5/11
C 1
D 11/5
E 5

The OA is A.

How can I find this value without knowing x and y values? Experts, please give me some explanation here.
You could pick some easy numbers. Say x = 6. Well, if x/(x+y) = 6, and x, the numerator, is 6, then the denominator will have to be 1, so y would have to be - 5, as 6 + (-5) = 1.

Now take our values: x = 6 and y = -5 and plug them into y/(x+y) = -5/(6 + -5) = -5/1 = -5. The answer is A
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If x/(x+y)=6 then . . .

by GMATGuruNY » Tue Oct 31, 2017 11:38 am
VJesus12 wrote:$$If\ \frac{x}{x+y}=6\ then\ \frac{y}{y+x}=$$

A -5
B 5/11
C 1
D 11/5
E 5

The OA is A.

How can I find this value without knowing x and y values? Experts, please give me some explanation here.
x(x+y) = 6
x = 6(x+y)
x = 6x + 6y
-5x = 6y
x = -(6/5)y.

Let y=5, implying that x = -(6/5)(5) = -6.
In this case:
y/(y+x) = 5/(5 + (-6)) = 5/(-1) = -5.

The correct answer is A.
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by barksdale » Tue Oct 31, 2017 1:51 pm
David and Mitch. Can you guys please use the math input method? It makes it a lot easier for me to follow along with your math steps. I and I'm sure others in the forum would greatly appreciate it. Thanks!!!
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by GMATGuruNY » Wed Nov 01, 2017 3:27 am
barksdale wrote:David and Mitch. Can you guys please use the math input method? It makes it a lot easier for me to follow along with your math steps. I and I'm sure others in the forum would greatly appreciate it. Thanks!!!
I'm not quite sure what you mean by the math input method.
Here's an approach similar to David's:

Let x=6.
Plugging x=6 into the numerator of x/(x+y) = 6, we get:
6/(x+y) = 6.
The equation above is valid only if x+y = 1.
Plugging x=6 into x+y = 1, we get:
6+y = 1
y = 1-6 = -5.

Question: then y/(y+x)?
Plugging x=6 and y=-5 into y/(y+x), we get:
y/(y+x) = -5/(-5+6) = -5/1 = -5.

The correct answer is A.
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by Scott@TargetTestPrep » Thu Nov 02, 2017 4:06 pm
VJesus12 wrote:$$If\ \frac{x}{x+y}=6\ then\ \frac{y}{y+x}=$$

A -5
B 5/11
C 1
D 11/5
E 5
Since x/(x + y) = 6, (x + y)/x = 1/6. That is:

x/x + y/x = 1/6

1 + y/x = 1/6

y/x = -5/6

x/y = -6/5

Instead of calculating y/(y + x) directly, let's reciprocate y/(y + x) like we did for x/(x + y). Notice that the reciprocal of y/(y + x) is (y + x)/y.

(y + x)/y = y/y + x/y = 1 + (-6/5) = -1/5

Since (y + x)/y = -1/5, y/(y + x) = 1/(-1/5) = -5.

Answer: A

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by barksdale » Fri Nov 03, 2017 1:40 pm
Mitch, I mean typing your responses in proper math writing:

$$\frac{x}{\left(x+y\right)}=6$$

Instead of x/(x+y)=6

Just a suggestion. It's so much easier to read.
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