Discussion
A two-digit number is such that the product of its digits is 14. When 45 is added to this number the digits interchange their position (like 12+9 = 21). What is that number ?
Answer: B
The number is 27.
Let the number be \(10a + b\). Adding 45 reverses the digits:
\[ \begin{aligned} 10a + b + 45 &= 10b + a \\ 9(b - a) &= 45 \\ b - a &= 5 \end{aligned} \]
With the product of the digits 14, the digits are 2 and 7 (\(2 \times 7 = 14\), and \(7 - 2 = 5\)), so the number is 27. Check: \(27 + 45 = 72\).
72 has the right digits but adding 45 gives 117, not 27. 54 and 36 have digit products of 20 and 18, not 14.
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