Source: Official Guide for GMAT Review 2016 Data Sufficiency ; #53


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

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

1 Explanation


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

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Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.

Section 6.3 Data Sufficiency

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