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The number 23A4534A01 is divisible by 11. How many values

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sarb
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The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   Updated on: 31 Aug 2013, 06:26
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The number 23A4534A01 is divisible by 11. How many values can “A” be substituted with?

A. 1
B. 4
C. 9
D. 10
E. Infinite
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D

Originally posted by sarb on 08 Jun 2012, 09:19.
Last edited by Bunuel on 31 Aug 2013, 06:26, edited 2 times in total.
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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   08 Jun 2012, 10:13
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sarb wrote:
The number 23A4534A01 is divisible by 11. How many values can “A” be substituted with?

A. 1
B. 4
C. 9
D. 10
E. Infinite


We want 2,3A4,534,A01 to be divisible by 11.

In order a number to be divisible by 11 the difference between the sum of the odd numbered digits (1st, 3rd, 5th...) and the sum of the even numbered digits (2nd, 4th...) must be divisible by 11.

The difference is: (2+A+5+4+0)-(3+4+3+A+1)=0. Now, since 0 is divisible by 11 then 2,3A4,534,A01 will be divisible by 11 irrespective of the value of A, so A can take all 10 values from 0 to 9, inclusive.

Answer: D.
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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   31 Aug 2013, 06:26
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Bumping for review and further discussion.
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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   01 Dec 2016, 16:54
This is a tricky one especially if it comes towards the end of quant section!
Thanks!!

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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   20 Nov 2019, 00:26
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Tricky question indeed. I would have gone for infinite if given in the exam :(

Sol:
The difference between its even & odd alternate is 0. S0 the number is divisible by 11 for any value of A. So A can take any digit value from 0-9 => 10
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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink] New post   13 Jul 2021, 07:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The number 23A4534A01 is divisible by 11. How many values [#permalink]
13 Jul 2021, 07:25
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