Discussion
If A and B represent digits and
\[ \begin{array}{r} A\,B\,A \\ \times\ 5 \\ \hline 4\,4\,B\,0 \end{array} \]
then which of the following is true?
Answer: D
The answer is A = 8, B = 9.
The product ends in 0, so A × 5 ends in 0 and A is even. The product 44B0 is at least 4400, so ABA is at least 880, which makes A = 8 (A = 9 is odd). Now write 8B8 × 5 out:
\[ \begin{aligned} (808 + 10B) \times 5 &= 4400 + 10B \\ 4040 + 50B &= 4400 + 10B \\ 40B &= 360,\ B = 9 \end{aligned} \]
Check: 898 × 5 = 4490. Option B (A = 9) fails because 9 × 5 ends in 5, and options A and C give products far below 4400.
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