Discussion
A two digit number is such that the product of its digits is 12. When 9 is added to the number, the digits interchanges their places, find the number.
Answer: B
The number is 34.
Let the number be \(10a + b\). Adding 9 reverses the digits:
\[ \begin{aligned} 10a + b + 9 &= 10b + a \\ 9(b - a) &= 9 \Rightarrow b = a + 1 \end{aligned} \]
Two consecutive digits with product 12 are 3 and 4, so the number is 34. Check: \(3 \times 4 = 12\) and \(34 + 9 = 43\).
43 has the right digits but adding 9 gives 52, not 34. 62 has product 12 but \(62 + 9 = 71\). 2 is not a two-digit number.
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