Nathan ([info]tischkid) wrote,
@ 2005-10-20 14:46:00
Previous Entry  Add to memories!  Share this!  Next Entry
Anyone want to relive those math nerd glory days???
So I've been wracking my brain for about an hour and I just can't figure this one out. Someone wrote in to us at The Princeton Review today asking about a question which he claims appeared on the GMAT he took recently. Keep in mind that there are no calculators allowed on the test. The questions reads as follows -

What is the greatest prime factor of 2^100 - 2^96?

Now, I know the answer...but I have NO IDEA how you're supposed to come up with it without a calculator...and tricks about powers of 2 that I should know about?

Come on...there must be someone out there who can crack this...

(2 comments) - (Post a new comment)


[info]jrust
2005-10-20 07:09 pm UTC (link)
Dude, I'm probably going to be TOTALLY wrong here, but I'll give it a shot.

If you treat 2^96 as x, then 2^100 = 16x.

2^96 = x
2^97 = x + x = 2x
2^98 = 2x+2x = 4x, etc.

If 2^100 = 16x, and 2+96 = x, then 2^100 - 2^96 = 16x - x = 15x. (15x = 15(2^96), just to catch up.)

We KNOW all the primes of 2^96 will be two, obviously, which leaves us with three and five, making 5 the greatest prime factor.

Right? Guys? Because I haven't taken a math class in 2.5 years.

(Reply to this)

answer
(Anonymous)
2005-10-21 03:01 am UTC (link)
2^100 - 2^96 = 2^96(2^4 - 1) = 2^96(15) = 2^96(5)(3)
Hence 5 is the answer

Visit www.gmatjj.blogspot.com for more questions ;)

(Reply to this)

(2 comments) - (Post a new comment)

Create an Account
Forgot your login or password?
Log in with OpenID
English • Español • Deutsch • Русский…