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Even though this question might seem a little strange, you do NOT need to do any excessive math to get to the correct answer. With just a bit of 'playing around' you can use 'brute force' to get to the answer.

We're told that a 2-digit number has its digits reversed and the difference between those two numbers is 27.

IF we use.... 11 and 11, then the difference is 0 - this is NOT a match

12 and 21, then the difference = 9 - this is NOT a match

13 and 31, then the difference = 18 - this is NOT a match (notice the pattern though? The difference keeps increasing by 9!!!!! I wonder what the next one will be???)

14 and 41, then the difference = 27 = this IS a match

The question asks for the difference in the two DIGITS. The difference between 1 and 4 is 3.

Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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12 Jan 2014, 15:28

1

This post was BOOKMARKED

Walkabout wrote:

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 27. By how much do the two digits differ?

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

The answer has to be a factor of 27, the only option that's a factor of 27 is 3.

Sice \((10x + y) - (10y + x) = 27\), you can simplify this relationship by subtracting with a common factor --> 9x - 9y = 27 ---> 9(x - y) = 27 ---> here, you already notice that the difference has to be a factor of both 9 and 27, but you can simplify further ---> x - y = 3, and thus we have the answer.

But these last steps are superfluous if you already notice that the answer has to be a factor of 27, this way you save time without having to calculate.

Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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18 Feb 2015, 21:57

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Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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24 Nov 2015, 04:21

Hey guys, I was wondering if it is true to say that for any AB and BA ==> 9 is always a factor of (A-B) or (B-A) which ever is bigger, and so we can directly divide 27/9 to yield 3 then we can check numbers for a match: 41-14 = 27

==>So if we were given AB - BA = 54 ==> 54/9 = 6 check numbers: 71- 17 = 54 Is this reasoning always correct?
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Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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06 Jan 2017, 16:06

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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