Discussion
x is a three-digit natural number such that the difference between the number and its reverse is 99. Then what is the difference between the digit at the hundred's place and the digit at the unit's place of x ?
Answer: C
The difference between the hundreds digit and the units digit is 1.
Write \(x = 100a + 10b + c\), so its reverse is \(100c + 10b + a\).
\[ \begin{aligned} x - \text{reverse} &= 99a - 99c \\ &= 99(a - c) = 99 \\ a - c &= 1 \end{aligned} \]
The tens digit cancels out, so it can be anything. For example, \(201 - 102 = 99\) and \(2 - 1 = 1\). A difference of 0 would make \(x\) equal its reverse, and 2 or 3 would give differences of 198 or 297.
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