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When you reverse the digits of the number $13,$ the number increases by $18.$ How many other two digit numbers increase by $18$ when their digits are reversed?

1. $5$
2. $6$
3. $7$
4. $8$
5. $10$

Let 10x + y be a two digit number.

Its reverse = 10y + x

Now, 10y + x – 10x – y = 18

9(y – x) = 18

y – x = 2

Thus y and x can be (1, 3), (2, 4), (3, 5), (4, 6), (5, 7), (6, 8) and (7, 9)  Other than 13,

Hence, option (2)6 is the Answer.

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