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Is b-a positive?

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Is b-a positive?

by Max@Math Revolution » Mon Dec 23, 2019 5:16 pm
[GMAT math practice question]

Is b-a positive?

1) The solution set of (a - 3b)x + (b - 3a) < 0 is x > 5/3
2) ab < 0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Dec 25, 2019 4:54 am
=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Condition 1)
(a - 3b)x + (b - 3a) < 0
=> (a - 3b)x < (3a - b)
=> x > (3a - b) / (a - 3b) under the assumption a - 3b < 0.
Then, we have (3a - b)/(a - 3b) = 5/3 or 3(3a - b) = 5(a - 3b).
It is equivalent to 9a - 3b = 5a - 15b, 4a = -12b or a = -3b.
Since we have the assumption a - 3b < 0, we have (-3b) - 3b = -6b < 0 or b > 0. Since b is positive, a = -3b is negative.
Thus b - a is positive and condition 1) is sufficient, since it yields a unique solution.

Condition 2)
If a = 1 and b = -1, then b - a = (-1) - 1 = -2 is negative and the answer is 'no'.
If a = -1 and b = 1, then b - a = 1 - (-1) = 2 is positive and the answer is 'yes'.

Since condition 2) does not yield a unique solution, it is not sufficient.

Therefore, A is the answer.
Answer: A
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