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

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by Max@Math Revolution » Mon Feb 05, 2018 1:09 am
[GMAT math practice question]

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

$$\left(1\right)\ x-2y=1$$
$$\left(2\right)\ x-2y=0$$
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Source: — Data Sufficiency |
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by DavidG@VeritasPrep » Mon Feb 05, 2018 11:30 am
Max@Math Revolution wrote:[GMAT math practice question]

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

$$\left(1\right)\ x-2y=1$$
$$\left(2\right)\ x-2y=0$$
Statement 1: x - 2y = 1 --> x = 1+ 2y
Substituting, we get: (1 + 2y + 3y)/[(3(1 + 2y) -y]
(1 + 5y)/(3 + 6y -y)
(1 + 5y)/(3 + 5y)
Clearly insufficient. If y = 0, the expression equals 1/3; If y = 1, the expression equals 3/4. Because we cannot derive a single unique value, statement 1 alone is not sufficient to answer the question.

Statement 2: x -2y = 0 ---> x = 2y
Substituting we get (2y + 3y)/(3(2y) - y) = 5y/5y = 1. Because we have a unique value, this statement alone is sufficient to answer the question. The correct answer is B
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by Max@Math Revolution » Tue Feb 06, 2018 11:39 pm
=>

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

Condition 2) :
Since x = 2y, (x+3y)/(3x-y) = 5y/5y = 1.
Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B
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