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MBA Applicant 2007/8
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Post subject: For any positive integer n, the length of n is defined as  Posted: Sat Jul 07, 2007 12:25 pm |
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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 = 3 x5x5. How many two digit positive integers have length 6?
A)None
B)One
C)Two
D)Three
E)Four
Can you please a) show the strategy to do this in less than 2 min and describe the range of difficulty of this problem?
I chose B (the incorrect answer) since 2^6 = 64 But the correct answer is C.
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StaceyKoprince
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Post subject: Posted: Mon Jul 09, 2007 6:08 pm |
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| ManhattanGMAT Staff |
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Posts: 5788
Location: San Francisco
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You need to use a little bit of logic to bound things here so that you can get through this in 2 minutes.
They give us the boundaries; we just have to understand what they mean. First, I'm only using 2-digit positive integers, so 10 to 99 inclusive. Second, I'm only using prime numbers. Third, I need to have a length of 6, so I need to multiply 6 prime numbers together.
The smallest prime number is two, so the first thing I try is six 2's (2*2*2*2*2*2) which equals 64. I know I can't get anything smaller than that, because two is the smallest prime. My next thought, then, is how to create the next-smallest possibility. To do that, I want to keep as many 2's as possible, but I have to change at least one of them to get a different product. The next smallest prime after 2 is 3, so I substitute a 3 for one of the 2's (2*2*2*2*2*3) which equals 96. That's still within the stated boundaries of the problem.
The next smallest possibility can be calculated by replacing one more 2 with a 3. If I think about it, I can tell that doing this will put me over 99 (though if I'm not sure, I can do the math to check) - so I'm done. There are two possibilities.
The key is to think about this logically and within the boundaries so that you know you've found all of the possibilities.
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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ogbeni
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Post subject: Re: For any positive integer n, the length of n is defined as Posted: Fri Jul 03, 2009 5:34 pm |
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Posts: 3
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..
Last edited by ogbeni on Tue Sep 01, 2009 1:42 pm, edited 1 time in total.
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RonPurewal
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Post subject: Re: For any positive integer n, the length of n is defined as Posted: Fri Jul 10, 2009 6:59 am |
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| ManhattanGMAT Staff |
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Posts: 6765
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ogbeni wrote: LOL - This is such a trick question!!! Arghhh these test makers are a crafty bunch!! they are. incidentally, it's fundamentally important that you grasp this mentality: they are "a crafty bunch", and the "clever" aspect of gmat problems should not be underestimated (especially on data sufficiency problems). if you plod through gmat problems trying to solve them as if they were "normal homework for school", you are not going to have a good time, to say the least.
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sukriteez
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Post subject: Re: For any positive integer n, the length of n is defined as Posted: Mon Oct 18, 2010 4:20 am |
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MBA Applicant 2007/8 wrote: 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 = 3 x5x5. How many two digit positive integers have length 6?
A)None
B)One
C)Two
D)Three
E)Four
Can you please a) show the strategy to do this in less than 2 min and describe the range of difficulty of this problem?
I chose B (the incorrect answer) since 2^6 = 64 But the correct answer is C. Wow! MGMAT staff is a genius!! such an easy soln n i spent over 4 minutes guessin numbers juz to get the ans as "only 96" Thanku stacey!!
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mschwrtz
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Post subject: Re: For any positive integer n, the length of n is defined as Posted: Tue Oct 19, 2010 3:30 pm |
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| ManhattanGMAT Staff |
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Posts: 506
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Yeah, Stacey did some nice clean work there. Glad you liked it.
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