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GMAT Club > Tests > m01 > Q.35

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Re: GMAT Club > Tests > m01 > Q.35 [#permalink] New post 02 Jan 2010, 12:48
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Re: GMAT Club > Tests > m01 > Q.35 [#permalink] New post 02 Jan 2010, 13:23
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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.

Answer: D (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] New post 02 Jan 2010, 13:33
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, 13:33
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