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

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by Max@Math Revolution » Wed Sep 04, 2019 11:45 pm

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[GMAT math practice question]

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

1) 2x-y = 2
2) 3x-y = 0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Sep 08, 2019 5:26 pm
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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 = 1 and y = 0, then (3x+y)/(x-3y) = (3+0)/(1-0) = 3.
If x = 2 and y = 2, then (3x+y)/(x-3y) = (6+2)/(2-6) = 8/(-4) = -2.

Since we do not obtain a unique answer, condition 1) is not sufficient.

Condition 2) :
Since 3x = y, (3x+y)/(x-3y) = (3x+3x)/(x-9x) = 6x/(-8x) = -(3/4)
Condition 2) is sufficient.

Therefore, B is the answer.
Answer: B
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by deloitte247 » Fri Sep 13, 2019 7:43 am
Note that the question we are dealing with now is expressed in fraction, and as such, the condition will be fulfilled if we achieve a fraction result.
Let's keep a watch as we solve this problem
Statement 1: 2x - y = 2
if x=1 and y=0
2(1) - 0 = 2
$$So,\ for\ \frac{3x+y}{x-3y}\ where\ x=1\ and\ y=0$$
$$\frac{3x+y}{x-3y}\ =\frac{3\left(1\right)+0}{1-3\left(0\right)}=3$$
If x=2 and y=2
$$\frac{3x+y}{x-3y}\ =\frac{3\left(2\right)+2}{2-3\left(2\right)}=-2$$
The provided is not enought to arrive at a definite answer (improper fraction)

Statement 2: 3x - y =0
3x=y or y=3x
$$Therefore,\ \frac{3x+y}{x-3y}\ where\ y=3x$$
$$\ \frac{3x+y}{x-3y}\ =\frac{3x+3x}{x-9x}=\frac{6x}{-8x}=-\frac{3}{4}$$
Statement 2 is sufficient.

Since only statement 2 is sufficient, the answer to this problem is B.
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