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Six Digit Number

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by dtweah » Tue May 26, 2009 3:19 pm
a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above
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Re: Six Digit Number

by Brent@GMATPrepNow » Tue May 26, 2009 4:55 pm
dtweah wrote:a, b, and c are positive integers. If a, b, and c are assembled into the six-digit number abcabc, which one of the following must be a factor of abcabc?

(A) 16
(B) 13
(C) 5
(D) 3
(E) none of the above
Nice question - where did you find it?
It might help matters if we recognize that abcabc can be written as abc000 + abc
If we do this, we see that we can factor out abc
We get:
abcabc = abc000 + abc
= abc(1000+1)
= abc(1001)
Now we need to notice that 1001 = 13x7x11
So, continuing, we get:
= abc(13)(7)(11)
So we can see that abcabc must be divisible by 13.
It must also be divisible by 7 and 11
The correct answer is B
Brent Hanneson - Creator of GMATPrepNow.com
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