Hey Everyone!
Great responses, you guys did an incredible job and many of you got the right answer - answer choice C. The random winner for this week's round: highwyre237! Congratulations - I will PM you with instructions for collecting your prize. In the meantime, here's the answer breakdown:
Initially, it might seem like we do not have enough information to solve this problem; certainly, we are unable to determine the value of w, and hence n, on the basis of the prompt alone (or even the statements, for that matter). Still, let's take a look at a table of values of the powers of 4.
4^2 = 16
4^3 = 64
4^4 = 256
4^5 = 1024
4^6 = 4096
4^8 = 65536
4^10 = 1048576
Notice that the units digit of all the even powers of 4 is the same: 6. This is because all even powers of 4 are also powers of 42 = 16. Remember that—for the purposes of this problem—when we look at the units digit of a product, we need only consider the units digits of its factors; thus, the units digit of 44 = (42)2 = 16 × 16 will be 6, because the units digits of each factor is 6, and 6 × 6 = 36 has a units digit of 6. Similarly, the units digit of 46 = (44) × 42 = (44) × 16 will be 6, because the units digit of both (44) and 16 is 6, and 6 × 6 has a units digit of 6. (Do not be confused by all the 6's; to take a contrasting example, 7 × 7 = 49 has a units digit of 9.)
Having examined the prompt, we turn to the statements.
Statement 1 tells us that w is an even integer. Be careful, though. Although we found above that positive even integer exponents of 4 have a units digit of 6, the number zero is an even integer for which 4w does not have a units digit of 6; rather 40 = 1 has a units digit of 1. Thus, the fact that w is an even integer is not sufficient to determine the units digit of n. Eliminate answer choices A and D. The correct answer choice is B, C, or E.
Statement 2 tells us that w > 0. We have already seen that positive odd integer exponents yield a units digit of 4, while positive even integer exponents yield a units digit of 6. Thus, the fact that w is positive is not sufficient to solve for the units digit of n. (In fact, Statement 2 does not even specify whether w is an integer.) Eliminate answer choice B. The correct answer choice is either C or E.
Combined, Statements 1 and 2 tell us that w is a positive even integer. Thus, n must have a units digit of 6, as we found above. Both statements together are sufficient.
Answer choice C is correct.
Great participation, everyone! Take a look at some more great GMAT resources here:
https://www.knewton.com/gmat/free/Have a great weekend!