Discussion
The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, then the original number is
Answer: C
The original number is 39.
Let the tens digit be \(a\) and the units digit \(b\). Reversing the digits increases the number, so \(b > a\).
\[ \begin{aligned} (10b + a) - (10a + b) &= 54 \\ 9(b - a) &= 54 \\ b - a &= 6 \\ b + a &= 12 \end{aligned} \]
So \(b = 9\), \(a = 3\), and the number is 39; reversing it gives 93, which is 54 more. 93 is the reversed number, the trap. 75 and 48 have digits summing to 12 but differ from their reversals by 18 and 36.
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