Question 530303
The easiest way to solve this is to think logically about the givens provided.  They narrow the potential solution set way down to a handful of possible answers.  Then picking the right answer becomes very obvious.
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The best clue is: the sum of the digits = 8.  Think of all the 2-digit numbers as an ordered pair of single digits.  For example, let's set:
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d1 = 1st digit,
d2 = 2nd digit
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That is, instead of thinking of the number as d1d2, think of it as d1, d2.  Then, going back to d1 + d2 = 8, the possible 2-digit numbers are:
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08 (0, 8)
17 (1, 7)
26 (2, 6)
35 (3, 5)
44 (4, 4)
53 (5, 3)
62 (6, 2)
71 (7, 1)
80 (8, 0)
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The next condition was adding 18 to the number reverses the digits.  So, add 18 to all of the numbers above:
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08 + 18 = 26
17 + 18 = 35
26 + 18 = 44
35 + 18 = 53 (which gives us the reversed digits)
44 + 18 = 62
53 + 18 = 71
62 + 18 = 80
71 + 18 = 89
80 + 18 = 98
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Hence, our original number is 35
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cheers,
Lee
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PS.  This could be easily solved with linear equations; however, not as quickly as this method, in this instance.  I can show you the other method if you like... 8-)