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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 27 Dec 2012, 07:29
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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
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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 27 Dec 2012, 07:31
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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


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

Answer: A.
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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 13 Oct 2013, 13:49
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runningguy wrote:
Bunuel wrote:
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


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

Answer: A.


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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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 13 Oct 2013, 13:45
Bunuel wrote:
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


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

Answer: A.


Do we use 10 because of the tens digit??
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Re: If a two-digit positive integer has its digits reversed, the [#permalink] New post 12 Jan 2014, 14:28
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] 12 Jan 2014, 14:28
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