Question

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?

• A. 5
• B. 6
• C. 7
• D. 8
• E. 10

Hint:

Digit reversal problems reduce to linear conditions on digit differences.

Answer 1

The Correct Option is B

Let number = $10a + b$, reverse = $10b + a$. Difference: $(10b + a) - (10a + b) = 9(b-a) = 18 \Rightarrow b-a = 2$. $a$ can range from 1 to 7 (since $b \leq 9$), excluding $a=1$ for given 13 leaves 6 others. \[ \boxed{6} \]