Anyone want to relive those math nerd glory days???

[tischkid]

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

Comments

[jrust]

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.

answer

[anonymous]

2^100 - 2^96 = 2^96(2^4 - 1) = 2^96(15) = 2^96(5)(3)
Hence 5 is the answer

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