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

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If a two-digit positive integer has its digits reversed, the [#permalink] New post 14 Apr 2007, 16:54
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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

Last edited by Bunuel on 12 Oct 2012, 09:22, edited 1 time in total.
Edited the question.
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 [#permalink] New post 14 Apr 2007, 18:33
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A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)
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 [#permalink] New post 15 Apr 2007, 14:16
salr15 wrote:
ricokevin wrote:
A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)


how did you get 10x + y?


34 = (3 x 10) + 4
If xy = 34 then this explains it.
HTH
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 [#permalink] New post 15 Apr 2007, 15:25
techjanson wrote:
salr15 wrote:
ricokevin wrote:
A?

Let x be the tenth digit and y be the units digit.

Then, the original number is 10x+y and the reversed number is 10y+x.

The difference between the two is 27. (reversed - original)

Thus, (10y+x)-(10x+y)=27
solve the above eq.
10y+x-10x-y=27
9y-9x=27
9(y-x)=27
y-x=3

Thus the two digits differ by 3.

:)


how did you get 10x + y?


34 = (3 x 10) + 4
If xy = 34 then this explains it.
HTH


Great thanks! :oops:
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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 12 Oct 2012, 08:32
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This is a tricky number properties question. Note that you can use two variables a and b to represent each of the digits.

In terms of expressing them in values - the total value would be (10a + b).

For example, for a number 37, a = 3 and b=7..then the expression 10a+b = 30 + 7 = 37.

Please refer to the video explanation here:
http://www.gmatpill.com/gmat-practice-t ... stion/2397


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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 08 Jan 2014, 20:10
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Re: If a two-digit positive integer has its digits reversed, the   [#permalink] 08 Jan 2014, 20:10
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