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"Length" of positive integer n.

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iiltaf
 Post subject: "Length" of positive integer n.
 Post Posted: Sun Jan 27, 2008 6:21 pm 
Hi,

I have purchased the full set of the ManhattanGMAT study guides and am currently working through the Number Properties Guide.
One of the OG Quant questions (# 103 from PS), is about the "length" of positive integer, referring to the following definition:

"For any positive integer n, n>1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n, For example, the length of 50 is 3 since 50 = 2 x 5 x 5."

Is this covered in any of the ManhattanGMAT material. I know the number properties book covers prime factorization etc etc ... but I didnt see anything around "length" of positive integers ...

Thanks.
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Guest
 Post subject:
 Post Posted: Sun Jan 27, 2008 10:39 pm 
The word "length" suggests that some real, mathematical function is at stake, but the concept is entirely made up for the purposes of the reasoning test.

The problem could have replaced length with many other words. It could have asked for the "meter" of n, the "crux" of n, or any other such thing.

The problem is really presenting a function in disguise.

f(x) = the number of terms in the complete prime factorization of x, where x>1.
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StaceyKoprince
 Post subject:
 Post Posted: Tue Jan 29, 2008 6:41 pm 
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ManhattanGMAT Staff


Posts: 6077
Location: San Francisco
Yep - they basically made up a term and a definition for that term. This can happen occasionally and, when it does, you won't have studied it before -- of course, because it's made up! This is just a test of whether you can follow directions.

As the previous guest noted, you have to decode this and figure out what math they're really talking about here. If you can complete the prime factorization of a number, then you can take the final step to calculate this "length" think they made up, so the problem is really about prime factorization.

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Stacey Koprince
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