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# If the ratio of x to y is 2 to 5, then (y-x)/(x+y)?

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Intern
Joined: 21 Nov 2013
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If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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18 Dec 2013, 15:16
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If the ratio of x to y is 2 to 5, then (y-x)/(x+y)?

A. -7/3
B. -3/7
C. 3/7
D. 1
E. 7/3

Can any one solve this using algebra and not plugging in?
[Reveal] Spoiler: OA

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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19 Dec 2013, 08:57
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Expert's post
MrWallSt wrote:
If the ratio of x to y is 2 to 5, then (y-x)/(x+y)?

A. -7/3
B. -3/7
C. 3/7
D. 1
E. 7/3

Can any one solve this using algebra and not plugging in?

Dear MrWallSt,
I'm happy to respond.

With all due respect, I believe the short answer to your question is simply "no." This is a very straightforward question, very easy, designed as a simple plug-in question by the test author. Plugging in is the ideal way to approach this problem. I know lots of algebra, through multivariable calculus, and it's really somewhat beyond me what algebra one would use to approach this. I honestly think that no one skilled in mathematics would want to bring the machinery of algebra anywhere near this problem.

Your very question makes me suspicious. Yes, algebra is awfully useful in a large number of problems, but it is unreasonable to think that algebra can be used in every single problem. It is highly unfruitful to see the letter x and immediately leap to algebra: that is precisely the kind of trap that GMAT writers design to ensnare students! If you routinely think this way, that mindset is an addiction to algebra and this addiction definitely will drag down your GMAT Quant score if you don't manage it.

The GMAT Quant section will always keep you on your toes. There's nothing you can memorize, no fixed set of rules, that will give you success every day. As soon as the GMAT writers realize that a large number of test-takers are using one fixed approach, they start writing problems designed to frustrate folks who are too attached to their rigid method. If you can't maintain mental agility, the GMAT will punish you. Here's an article about the type of thinking the GMAT demands:
http://magoosh.com/gmat/2013/mathematic ... -the-gmat/

I hope this wasn't too emphatic a response. You may not be an "algebra addict" at all, but I have met many of them preparing for the GMAT, and I like to warn students of this danger.

I hope all this helps.
Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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Intern
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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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19 Dec 2013, 11:24
Thank you very much for your response. I am huge fan of your math and sentence correction blogs. I will say that my tendency to revert to algebra is something that I most certainly need to work on. In this case, I was able to solve the problem using plugging in numbers. However, since ratios (along with coordinate geometry, divisibility, inequalities and odds/evens) is something that I need to develop, I thought that being able to follow an algebraic solution would help my understanding of ratios in general. If this is something that can not be solved / is too difficult to solve algebraically, it makes feel a little bit better. I have been working on having a better understanding of how to solve ratios conceptually and then saw this and thought “I have no idea how to solve this and guess it’s back to the basics”.
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Intern
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Concentration: Nonprofit, Entrepreneurship
Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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19 Dec 2013, 18:47
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I believe this problem can be solved using algebra.

The ratio of x to y is 2 to 5 means
(x/y)=(2/5)

Cross-multiply

2x = 5y
x = (2/5)*y

Then, substitute x in the original equation in the problem with the value we just found.

(y - (2/5)*y) / ((2/5)*y + y)
= ((3/5)*y) / ((7/5)*y)

Simplify by canceling the y in the numerator with the y in the denominator.
(3/5) / (7/5)
= (3/5) * (5/7)

The 5s cancel each other out, and you are left with 3/7.

I would love an expert to double check me on this, but this should be a sufficient way to complete the problem using algebra. However, plugging in numbers, in this case, is a more efficient way to complete the problem and is also less prone to error because you are eliminating variables.

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Manager
Joined: 19 Apr 2013
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Concentration: Entrepreneurship, Finance
GMAT Date: 06-05-2015
GPA: 3.88
WE: Programming (Computer Software)
Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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19 Dec 2013, 19:21
1
KUDOS
MrWallSt wrote:
If the ratio of x to y is 2 to 5, then (y-x)/(x+y)?

A. -7/3
B. -3/7
C. 3/7
D. 1
E. 7/3

Can any one solve this using algebra and not plugging in?

In my point of view this is very easy question. You can use Componendo and dividendo method to reach the answer.

x/y= 2/5
x+y/x-y = 2+5/2-5
x+y/x-y = 7/-3
Can be written as -3/7 = x-y/x+y
also 3/7 = y-x/x+y

Thanks,
AB

+1 Kudos if you like and understand

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Thanks,
AB

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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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20 Dec 2013, 10:44
@sjmarinov and @bhatiamanu05, both of those methods make sense. Appreciate the responses.
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Location: India
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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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02 Jul 2014, 00:31
$$\frac{x}{y} = \frac{2}{5}$$

We require to find $$\frac{y-x}{x+y} = \frac{y}{x+y} - \frac{x}{x+y}$$

$$\frac{y}{x} = \frac{5}{2}$$

$$\frac{y}{x+y} = \frac{5}{5+2} = \frac{5}{7}$$ ......... (a)

$$\frac{x}{x+y} = \frac{2}{5+2} = \frac{2}{7}$$ .......... (b)

(a) - (b)

$$= \frac{5}{7} - \frac{2}{7}$$

$$= \frac{3}{7}$$

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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)? [#permalink]

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28 Oct 2017, 03:02
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Re: If the ratio of x to y is 2 to 5, then (y-x)/(x+y)?   [#permalink] 28 Oct 2017, 03:02
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