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a and b are positive integers less than or equal to 9. If a

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a and b are positive integers less than or equal to 9. If a [#permalink] New post 03 Jan 2013, 05:47
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a and b are positive integers less than or equal to 9. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?

(A) 3
(B) 4
(C) 5
(D) 6
(E) none of the above
[Reveal] Spoiler: OA

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Last edited by Bunuel on 03 Jan 2013, 06:14, edited 1 time in total.
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Re: a and b are positive integers less than or equal to 9. If a [#permalink] New post 03 Jan 2013, 06:20
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daviesj wrote:
a and b are positive integers less than or equal to 9. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?

(A) 3
(B) 4
(C) 5
(D) 6
(E) none of the above


The sum of the digits of the six-digit number ababab is a+b+a+b+a+b=3(a+b), thus the sum of the digits is divisible by 3, which means that ababab must be divisible by 3.

Answer: A.
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Re: a and b are positive integers less than or equal to 9. If a [#permalink] New post 03 Jan 2013, 10:02
Since ab is in the number ababab 3 times and if the sum of any number is a multiple of 3 then 3 must be a factor of that number, the only answer choice that MUST be a factor of ababab is 3. Answer - A
Re: a and b are positive integers less than or equal to 9. If a   [#permalink] 03 Jan 2013, 10:02
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