Discussion
When digits of the number 13 are reversed, the number increases by 18. How many other two digit numbers increases by 18 when their digits are reversed?
Answer: B
6 other two digit numbers increase by 18.
For a number \(10a + b\), reversing gives \(10b + a\), and the increase is
\[ (10b + a) - (10a + b) = 9(b - a) = 18 \]
So the units digit must be 2 more than the tens digit: 13, 24, 35, 46, 57, 68 and 79. That is 7 numbers, and leaving out 13 itself, 6 others. The option 7 counts 13 as well, which the question excludes with the word 'other'.
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