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# If a two-digit positive integer has its digits reversed, the

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

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27 Dec 2012, 08:29
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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
[Reveal] Spoiler: OA

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

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27 Dec 2012, 08:31
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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

Given that (10a + b) - (10b + a) = 27 --> 9a - 9b =27 --> a - b = 3.

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

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13 Oct 2013, 14:49
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runningguy wrote:
Bunuel 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

Given that (10a + b) - (10b + a) = 27 --> 9a - 9b =27 --> a - b = 3.

Do we use 10 because of the tens digit??

Yes, any two-digit integer ab can be expressed as 10a+b, for example: 45 = 10*4 + 5.

The same for 3, 4, 5, ... digit numbers. For example, 4-digit number 5,432 can be written as 5*1,000 + 4*100 + 3*10 + 2 = 5,432.

Hope it's clear.
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Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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18 Feb 2015, 22:12
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Hi All,

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.

[Reveal] Spoiler:
A

There are actually several ways to get to this answer: 14 and 41, 25 and 52, 36 and 63, 47 and 74, 58 and 85, 69 and 96.

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Rich
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Intern
Joined: 09 Sep 2013
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Re: If a two-digit positive integer has its digits reversed, the [#permalink]

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13 Oct 2013, 14:45
Bunuel 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

Given that (10a + b) - (10b + a) = 27 --> 9a - 9b =27 --> a - b = 3.

Do we use 10 because of the tens digit??

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

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12 Jan 2014, 15:28
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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.

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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
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