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# What is the value of (x+3y)/(3x-y)?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4904
GPA: 3.82
What is the value of (x+3y)/(3x-y)? [#permalink]

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05 Feb 2018, 01:12
00:00

Difficulty:

25% (medium)

Question Stats:

73% (00:53) correct 27% (01:22) wrong based on 30 sessions

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[GMAT math practice question]

What is the value of $$\frac{(x+3y)}{(3x-y)}$$?

$$1) x-2y = 1$$
$$2) x-2y = 0$$
[Reveal] Spoiler: OA

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Re: What is the value of (x+3y)/(3x-y)? [#permalink]

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05 Feb 2018, 07:05
MathRevolution wrote:
[GMAT math practice question]

What is the value of $$\frac{(x+3y)}{(3x-y)}$$?

$$1) x-2y = 1$$
$$2) x-2y = 0$$

(1) x-2y = 1 or x = 1+2y
Substituting this value of x in the fraction,

(1+2y + 3y) / [3(1+2y) - y] = (1 + 5y) / (3 + 5y)
But we cannot find this till we know the value of y. So not sufficient.

(2) x-2y = 0 or x = 2y
Substituting this in the fraction,

(2y + 3y) / (3*2y - y) = 5y/5y = 1. This is sufficient.

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4904
GPA: 3.82
Re: What is the value of (x+3y)/(3x-y)? [#permalink]

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06 Feb 2018, 23:45
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

When the question asks for a ratio, a fraction, a percent, a proportion or a rate, if one of conditions provides a ratio and the other condition provides a number, the condition with a ratio could be sufficient.

This question asks for a ratio.
Condition 1) provides a number and condition 2) provides the ratio, x/y = 2.
Thus, condition 2) is likely to be sufficient.

Condition 1) :
If $$x = 3$$ and $$y = 1$$, then $$\frac{(x+3y)}{(3x-y)}$$ = $$\frac{6}{8}$$ = $$\frac{3}{4}$$
If $$x = 5$$ and $$y = 2$$, then $$\frac{(x+3y)}{(3x-y)}$$ = $$\frac{16}{13}$$
Since we do not obtain a unique answer, condition 1) is not sufficient.

Condition 2) :
Since $$x = 2y$$, $$\frac{(x+3y)}{(3x-y)} = \frac{5y}{5y} = 1$$.
Condition 2) is sufficient.

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Intern
Joined: 08 Sep 2008
Posts: 12
Re: What is the value of (x+3y)/(3x-y)? [#permalink]

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07 Feb 2018, 02:55
Is this DS question valid? Both statements contradict each other.?

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Math Expert
Joined: 02 Sep 2009
Posts: 43864
Re: What is the value of (x+3y)/(3x-y)? [#permalink]

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07 Feb 2018, 04:23
vishalkazone wrote:
Is this DS question valid? Both statements contradict each other.?

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No it's not. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem. The question is flawed.
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Re: What is the value of (x+3y)/(3x-y)?   [#permalink] 07 Feb 2018, 04:23
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