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If ab≠0, √((5a+6b)/(a+3b))=?

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by Max@Math Revolution » Wed Jun 29, 2016 7:24 pm
If ab≠0, √((5a+6b)/(a+3b))=?
1) b/a=2/3
2) a+b=5

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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Jul 03, 2016 4:47 am
If one of conditions is "number" and the other is "ratio", the condition with "ratio" is the correct answer. Hence, the correct answer is A.

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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by 800_or_bust » Sun Jul 03, 2016 10:34 am
Max@Math Revolution wrote:If ab≠0, √((5a+6b)/(a+3b))=?
1) b/a=2/3
2) a+b=5

*An answer will be posted in 2 days.
(1) Given equation solved for a, a = 3b/2... Thus, √((5a+6b)/(a+3b)) = √((5(3b/2)+6b)/(3b/2+3b)) = √((15b/2+6b)/(3b/2+3b)) = √((27b/2)/(9b/2)) = √(3). SUFFICIENT.

(2) Given equation solved for a, a = 5-b. Thus, √((5a+6b)/(a+3b)) = √((5(5-b)+6b)/((5-b)+3b)) = √((25-5b+6b)/(5-b+3b)) = √((25+b)/(5+2b)). No way to eliminate b. NOT SUFFICIENT.

Just worked this out, because I wasn't satisfied with the solution. I certainly wouldn't recommend just applying rules without first testing the given information to verify its sufficiency (or lack thereof).
800 or bust!
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