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

Danny Watts Jr

First need to simplify the equation by finding a common base (in this case, 2):
2^2(x+y) = 2^3(10)
Since the bases are equal, we can write the equation as:
2(x+y) = 30; or x + y = 15. So, we want to determine if the info given below is sufficient to solve x+y = 15.
Statement 1: x - y = 9 is NOT SUFFICIENT because the difference between the two figures do not always add to 15. For instance, x could be 20 and y could be 11, so x+y would = 31. A case in which x+y = 15 and x-y = 9 would be x=12 and y=3.
Statement 2 can be rearranged to x = 4y. Again, you can find an answer in which x+y=15 (x=12; y=3), but also answers in which this isn't the case (i.e. x=16; y=4). NOT SUFFICIENT
Together, since x-y = 9 and x = 4y; we can solve for y and would get 4y-y = 9; y = 3. Thus, the only possible answer for x is 12, so answer (C) is correct.

Apr 21, 2017 • Comment