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by GMATCRUSHER » Thu Nov 26, 2009 1:33 pm
for any positive integer n, the length of n is defined as the number of prime factors whose product is n for example the length of 75 is 3 since 75 = 3x5x5. How many 2 digit positive integers have length of 6?

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by KapTeacherEli » Thu Nov 26, 2009 3:59 pm
We're looking for a number with a "length" of six, which means six prime factors--but it has to be two digits. That is an indicator that we want to start low, since even 3^6 is well above two digits (729)

The lowest sequence of six primes we can have is 2 x 2 x 2 x 2 x 2 x 2 = 2^6 = 64. That's one. Now, the next lowest involves upping one of those twos to a three. 2 x 2 x 2 x 2 x 2 x 3 = 32 x 3 = 96. It's pretty clear we can't go any higher than this and stay under two digits, so our answer is (C), two.
Eli Meyer
Kaplan GMAT Teacher
Cambridge, MA
www.kaptest.com/gmat

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by GMATCRUSHER » Fri Nov 27, 2009 4:25 pm
thank you!!
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