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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]  03 Jan 2013, 04:47
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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, 05:14, edited 1 time in total.
Edited the question.
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Kudos [?]: 62027 [2] , given: 9426

Re: a and b are positive integers less than or equal to 9. If a [#permalink]  03 Jan 2013, 05:20
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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.

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Kudos [?]: 48 [0], given: 0

Re: a and b are positive integers less than or equal to 9. If a [#permalink]  03 Jan 2013, 09:02
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
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Re: a and b are positive integers less than or equal to 9. If a [#permalink]  25 Aug 2014, 03:02
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Kudos [?]: 252 [0], given: 27

Re: a and b are positive integers less than or equal to 9. If a [#permalink]  26 Jun 2015, 19:25
Dear Bunnel,

What about if I take a=4 b=5.

It's not divisible by 3 please assist.
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Kudos [?]: 0 [0], given: 17

Re: a and b are positive integers less than or equal to 9. If a [#permalink]  26 Jun 2015, 20:52
It works even when you use 4 and 5.
4=a
5=b
so the number is 454545.
Adding up all 3(4) + 3(5) = 3(9) = 27.
This is divisible by 3.
The of the question essence lies the data point that ab is repeated thrice.
hence should be divisible by 3
Hope this helps
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Kudos [?]: 811 [0], given: 40

a and b are positive integers less than or equal to 9. If a [#permalink]  26 Jun 2015, 22:59
Expert's post
vikasbansal227 wrote:
Dear Bunnel,

What about if I take a=4 b=5.

It's not divisible by 3 please assist.

454545 when divided by 3 gives the result 151515

$$\frac{454545}{3} = 151515$$

CONCEPT: Rule of Divisibility of 3 is "If sum of the digits of the Number is divisible by 3 then the number will be divisible by 2

SUm of the digits of No. 454545 is 27 which is divisible by 3 hence the Number 454545 will be divisible by 3

I hope it helps!
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a and b are positive integers less than or equal to 9. If a   [#permalink] 26 Jun 2015, 22:59
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