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GMAT - Data Sufficiency - Exponents

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

Is 4x y = 810
(1) x - y = 9
(2) y/x = 1/4

To prove

4x+y = 810

22(x+y) = 230

we need to prove x + y = 15

(1) x - y = 9

adding 2y to both sides

x + y = 9 + 2y

since y can be any integer, 9 +2y and x + y can have a many values including 15 (for y = 3)

Insufficient


(2) y/x = 1/4

x = 4y

x + y = 5y

since y can be any integer, 5y and x + y can have a many values including 15 (for y = 3)

Insufficient

 

Combining both

x - y = 9

x = 4y

subsituting

3y = 9

y = 3

x = 12

x + y = 15

 

sufficient