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GMAT Club > Tests > m01 > Q.35

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Math Expert
Joined: 02 Sep 2009
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Re: GMAT Club > Tests > m01 > Q.35 [#permalink]

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02 Jan 2010, 13:48
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vitaliy wrote:
Could you provide theory on the theme?

THANK'S!

Can you please post the question?
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Math Expert
Joined: 02 Sep 2009
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Kudos [?]: 106479 [2] , given: 11626

Re: GMAT Club > Tests > m01 > Q.35 [#permalink]

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02 Jan 2010, 14:23
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The symbol is just a symbol, it means nothing. In the question it denotes some function relationship.

The question defines "@x" as the number of distinct positive divisors of x. Say @6=4, as 6 have 4 distinct positive divisors: 1, 2, 3, 6.

@@90 --> $$90=2*3^2*5$$ the number of distinct factors (divisors) of 90 can be found by the formula: (1+1)(2+1)(1+1)=12. So @90=12 --> @12=? 12=2^2*3, again the number of distinct factors (divisors) of 12 can be found by the formula: (2+1)(1+1)=6.

General rule:

Finding the Number of Factors of an Integer

First make prime factorization of an integer $$n=a^p*b^q*c^r$$, where $$a$$, $$b$$, and $$c$$ are prime factors of $$n$$ and $$p$$, $$q$$, and $$r$$ are their powers.

The number of factors of $$n$$ will be expressed by the formula $$(p+1)(q+1)(r+1)$$. NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: $$450=2^1*3^2*5^2$$

Total number of factors of 450 including 1 and 450 itself is $$(1+1)*(2+1)*(2+1)=2*3*3=18$$ factors.

This question is about the number properties. You can check the Number Theory chapter in MathBook (link below), sorry it's not finished yet.
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Re: GMAT Club > Tests > m01 > Q.35 [#permalink]

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02 Jan 2010, 14:33
Great explanation ! Never came across this formula before. Another feather in the cap. Thanks !
Re: GMAT Club > Tests > m01 > Q.35   [#permalink] 02 Jan 2010, 14:33
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