Nice question - where did you find it?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
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
