Decoding Number Properties on the GMAT - Part 2
Welcome to the 2nd installment of our dive into Number Properties. If you havent yet tried the first problem, start with the first article in the series.
Lets dive right into our second problem from the GMATPrep free exams:
*What is the greatest prime factor of [pmath]4^17[/pmath]- [pmath]2^88[/pmath]?(A) 2
(B) 3
(C) 5
(D) 7
(E) 11
You know the drill. First, whats going on?
Glance: PS. Ugly exponents. The answer choices are small / easy numbers.
Read: The question is pretty straightforward. Right up until we get to the ugly math. :P
Jot:
I definitely have to think about how to approach this.
My first thought: its annoying that the bases are different. Oh, but I can fix that! 4 is a multiple of 2.
Okaynow what? They probably want me to think that thats just [pmath]2^6[/pmath], in which case the answer would be 2. But you subtract the exponents when you're dividing the two bases. Here, the two bases are subtracted, so subtracting the exponents is an illegal move. The answer probably isnt 2; if I get stuck and have to guess, I wont guess (A).
Oh, this is ringing a bell. Ive seen something like this before. When I cant combine the terms using standard exponent rules, I should try pulling out a common term. That math is more annoying, but at least its something Im allowed to do.
Ive got it! 63 = (9)(7) = (3)(3)(7). So the prime factors of the whole thing are 2, 3, and 7. The largest one is 7; thats the answer!
The correct answer is (D).
Even if I hadnt figured out that last part, I still could have done a decent job of making an educated guess. 2 is a trap answer, as I found earlier. And if theyre asking for the greatest number, then the answer usually wont be the greatest number given, so I wouldnt have picked (E) either. Id have guessed among (B), (C), and (D), which gives me decent odds on a problem I dont know how to solve.
Key Takeaways for Divisibility and Primes on the GMAT:
(1) Exponents can be mixed in with divisibility and prime! Other topics also often get mixed up with Number Properties topics. Start looking out for other examples in your studies. (And know your exponent rules.)
(2) You can sometimes cross off answers by knowing what youre not allowed to do, as we did for answer (A). Start training yourself to think about trap answers, too, not just correct answers, and youll turn yourself into a better educated guesser.
(3) Weve got one more for you! Join us for the third, and final, installment of this series, when well try the hardest problem yet.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.