Hi Hallmah_O,
Certain questions can be solved with some 'brute force' work - and that approach applies here. This question has some built-in patterns that you can take advantage of too - and that can help you to quickly narrow down answer choices.
To start, it's worth noting that when dealing with exponents, raising the exponent even a little bit will have a big impact on the total.
For example:
2^2 = 4
2^3 = 8
By raising the exponent by 1 here, we DOUBLE the total value. So for example, 2^10 and 2^11 are NOT 'close' to one another.
In this prompt, if we ignore all of the +1s and -1s for a moment, we'd end up with...
(2^2)(2^2)(2^4)(2^8) = 2^16
Now clearly that is NOT the actual product, but we can use it as an estimate to quickly eliminate Answers C, D and E (they're all far too BIG to be the product. So now we're left with Answers A and B...
Looking at the original equation, we can easily see that the first parentheses = 3, thus the product MUST be evenly divisible by 3.
Answer A: 2^16 - 1
Answer B: 2^16 + 1
These two numbers differ by just 2, so one of them IS divisible by 3 and the other one is NOT. If we can figure out the value of either calculation, then we'll be done... At this point, you can either 'count doubles' or rewrite the calculation...
2^16 = 4^8 = 8^4 = 64^2 = 4096
4096 - 1 = 4095
4096 + 1 = 4097
The first result is divisible by 3 and the second is not (you can use the 'rule of 3' to quickly figure that out).
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
