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Re: If a two-digit positive integer has its digits reversed, the resulting
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12 Jan 2014, 14:28

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1

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 resulting
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18 Feb 2015, 21:12

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1

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.

Re: If a two-digit positive integer has its digits reversed, the resulting
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15 Jul 2016, 03:31

4

salr15 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

Let’s first label the original two-digit integer as N. We can then say that N = 10A + B, where A is the tens digit and B is the units digit of N.

If this is hard to see let’s try it with a sample number, say 24. We can say the following:

24 = (2 x 10) + 4

24 = 20 + 4

24 = 24

Getting back to the problem, we are given that if the integer N has its digits reversed the resulting integer differs from the original by 27. First let’s express the reversed number in a similar fashion to the way in which we expressed the original integer.

10B + A = reversed integer

Since we know the resulting integer differs from the original by 27 we can say:

10B + A – (10A + B) = 27

10B + A – 10A – B = 27

9B – 9A = 27

B – A = 3

Since B is the tens digit and A is the units digit, we can say that the digits differ by 3.

Re: If a two-digit positive integer has its digits reversed, the resulting
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20 Dec 2019, 14:29

Hi dodobolo,

As an example, if you take the number '85', then you can break that number down into two pieces (8)(10) and (5)(1).

Now, imagine you don't now what the two-digit number is... we can write that number as 'XY' where X represents the 'tens digit' and the Y represents the 'units digit. The value of 'XY' is (X)(10) +(Y)(1).

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