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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