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0 < a < b < c. Is a < 3?

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by Max@Math Revolution » Sun Jun 09, 2019 11:06 pm

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[GMAT math practice question]

0 < a < b < c. Is a < 3?
1) 1/c > 1/3
2) 1/a + 1/b + 1/c = 1
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Jun 12, 2019 12:16 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.

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

We have 1/a > 1/b > 1/c, since we are given that 0 < a < b < c.

Condition 1) implies that c < 3. Therefore a < 3, and Condition 1) is sufficient.

Condition 2)
Since 1/a > 1/b > 1/c > 0, and 1/a + 1/b + 1/c = 1, we must have 1/a + 1/a + 1/a = 3/a > 1. Therefore, a < 3, and the answer is 'yes'.
Condition 2) is sufficient since it yields a unique answer.

Therefore, D is the answer.
Answer: D

This question is a CMT4(B) question: condition 1) is easy to work with and condition 2) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.
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