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a and b are positive integers less than or equal to 9. If a [#permalink]

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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?

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Last edited by Bunuel on 03 Jan 2013, 05:14, edited 1 time in total.

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.

Re: a and b are positive integers less than or equal to 9. If a [#permalink]

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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

Re: a and b are positive integers less than or equal to 9. If a [#permalink]

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25 Aug 2014, 03:02

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Re: a and b are positive integers less than or equal to 9. If a [#permalink]

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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

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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Re: a and b are positive integers less than or equal to 9. If a [#permalink]

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02 Jul 2016, 09:49

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