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What is a/ab+a+1 + b/bc+b+1 + c/ca+c+1?

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What is a/ab+a+1 + b/bc+b+1 + c/ca+c+1?

by Max@Math Revolution » Sun Mar 22, 2020 6:45 pm

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[GMAT math practice question]

What is a/ab+a+1 + b/bc+b+1 + c/ca+c+1?

1) abc = 1
2) a, b, and c are integers
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Source: — Data Sufficiency |
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Re: What is a/ab+a+1 + b/bc+b+1 + c/ca+c+1?

by Max@Math Revolution » Sun Mar 22, 2020 6:46 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.
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)
If we have abc = 1, then we have

a/ab+a+1 + ab/a(bc+b+1) + abc/ab(ca+c+1)
= a/ab+a+1 + ab/abc+ab+a + abc/abca+abc+ab
=a/ab+a+1 + ab/ab+a+1 + 1/ab+a+1 (substituting 1 for abc)
=ab+a+1/ab+a+1 = 1.
Since condition 1) yields a unique solution, it is sufficient.

Condition 2)
Since we don’t have any information about a, b and c, it is not sufficient.

Therefore, A is the answer.
Answer: A
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