length

Since they are asking us to find a 2-digit number with a length of 6 - we need to find numbers from 10-99 with the prime factors.

Since 2 is the lowest prime, try 2x2x2x2x2x2 = 6 factors of 2 = 64

Next try replacing one of the 2s with the next high prime number 3:
2x2x2x2x2x3 = 5 factors of 2 and one 3 = 96

Since we only need numbers from 10-99 no other number with 6 factors would be eligible.

Hope this helps.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pm; Thanked: 237 times; Followed by:25 members; GMAT Score:730

by logitech » Tue Jan 06, 2009 5:23 pm

Think about all the small primes, which ones will you keep it under 100 when you have 6 of them ?

2x2x2x2x2x2 = 64 is a good start.

Our next prime is 3

We can try to replace one of the 2's and try

2x2x2x2x2x3 = 96

This is very close to our border line of 99. and we know that if we ever replace another 2 with 3 , we will cross that line so we should stop here and choose TWO.

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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drewd313: Newbie | Next Rank: 10 Posts; Posts: 8; Joined: Fri Nov 14, 2008 8:31 pm

by drewd313 » Tue Jan 06, 2009 6:22 pm

Thanks for the responses.

This is actually the approach I took when doing the practice test. However, I had forgotten that 2 was a prime number for some reason and tried it with all 3's which results in a number bigger than 100. But, I understand it now thanks.