Bunuel wrote:

Is 4^(x+y) = 8^10?

Is \(4^{x+y}=8^{10}\)? --> is \(2^{2*(x+y)}=2^{3*10}\)? --> is \(2(x+y)=3*10\) --> is \(x+y=15\)?

(1) x-y=9. Clearly insufficient to answer the question whether \(x+y=15\). Consider \(x=9\) and \(y=0\) for a NO answer and \(x=12\) and \(y=3\) for an YES answer.

(2) y/x=1/4. Also insufficient. Consider \(x=4\) and \(y=1\) for a NO answer and \(x=12\) and \(y=3\) for an YES answer.

(1)+(2) We have two distinct linear equations with two unknowns (x-y=9 and y/x=1/4), so we can solve for \(x\) and \(y\) and answer the question. Sufficient.

Answer: C.

Hope it's clear.

by componendo-dividendo rule,

y/x=1/4

=>

(y+x)/x=5/4

so we get y+x..

is it not sufficient to answer the prompt..

Guess it is insufficient because we don't get the exact value of y+x..

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