Questions about the world of GMAT Math from other sources and general math related questions.
mdh3000
 
 

Does this rule about factors and exponents ALWAYS hold true?

by mdh3000 Mon Jun 09, 2008 8:55 pm

OK, this was part of an explanation for a Official Guide problem (but I know I can't post the question, so I won't)....

The explanation was that if x^3 is divisible by 9, then x MUST BE divisible by 3.

Is this because we know that x^3 has 3^2 as a factor, and because x is the only source of factors, x must have at least one three as a factor?

So would this hold true for something like x^9 is divisible by 9, so x MUST BE divisible by 3?

I'm just trying to understand the theory as to why this is true and under what circumstances it's true.

Thanks!

mdh
Success
 
 

Yes, it holds true...WHY?

by Success Tue Jun 10, 2008 4:14 pm

For any 'x' to be divisible by 9, it 'MUST' be divisible by 3 twice. Thus, any number divisible by 9 will always be divisible 3.
There are also a few rules in the numbers strategy guide or so. Hope this helps.
StaceyKoprince
ManhattanGMAT Staff
 
Posts: 9360
Joined: Wed Oct 19, 2005 9:05 am
Location: Montreal
 

by StaceyKoprince Thu Jun 12, 2008 12:08 am

Yep, you guys have got it. If a number X is divisible by some other number Y, then X is also divisible by all of the factors of Y.
Stacey Koprince
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