Discussion
A number consists of two digits. If the digits interchanges place and then the new number is added to the original number, then the resultant number will be divisible by:
Answer: D
The sum is always divisible by 11.
Write the number as \(10a + b\), where \(a\) and \(b\) are its digits. Interchanging the digits gives \(10b + a\). Adding the two:
\[ \begin{aligned} (10a + b) + (10b + a) &= 11a + 11b \\ &= 11(a + b) \end{aligned} \]
For example, \(47 + 74 = 121 = 11 \times 11\). The sum is divisible by 3, 5 or 7 only when \(a + b\) happens to be, so none of those holds for every number: \(12 + 21 = 33\) is not divisible by 5 or 7.
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