\(\frac{ax+ay}{x+y}=\frac{a(x+y)}{x+y}=a\), so we can see that the value of the fraction given doesn't depend on the values of \(x\) and \(y\) as \(x+y\) is reduced.

(1) x=4 and y=5. Not sufficient.
(2) a=6. Sufficient.

Answer: B.
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Target question: What is the value of (ax + ay)/(x + y)?
This is a good candidate for rephrasing the target question.

Take the expression: (ax + ay)/(x + y)
Factor the numerator to get: a(x + y)/(x + y)
Simplify the fraction to get: a
Since (ax + ay)/(x + y) = a, we can rephrase the target question...
REPHRASED target question: What is the value of a?

Aside: the video below has tips on rephrasing the target question

Now that we've REPHRASED the target question, it should be easy to analyze the two statements.

Statement 1: x = 4 and y = 5
Since we have no information about a, we cannot answer the REPHRASED target question with certainty.
So, statement 1 is NOT SUFFICIENT

Statement 2: a = 6
PERFECT - this is exactly what we need.
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: B

RELATED VIDEO FROM OUR COURSE

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