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02 Jan 2010, 13:48
Kudos
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vitaliy
Can you please post the question?
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02 Jan 2010, 14:23
Kudos
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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.
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.
02 Jan 2010, 14:33
Kudos
Bookmarks
Great explanation ! Never came across this formula before. Another feather in the cap. 
Thanks !
Thanks !
Archived Topic
Hi there,
Archived GMAT Club Tests question - no more replies possible.
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for the latest questions.
Still interested? Check out the "Best Topics" block above for better discussion and related questions.
Thank you for understanding, and happy exploring!
