Discussion
Find the possible value of B.
\(\begin{array}{r} AB\\ +\ 37\\ \hline 6A\end{array}\)
Answer: C
The value of B is 5.
Write AB as 10A + B. The sum AB + 37 = 6A means 10A + B + 37 = 60 + A, so 9A + B = 23.
\[ 9A+B=23 \Rightarrow A=2,\ B=5 \]
Check: 25 + 37 = 62. B = 3, 4 or 6 would give no digit A that fits.
You can check by putting in the values: with A = 2 and B = 5 the sum is 25 + 37 = 62, which has the form 6A with A = 2. Trying B = 3 gives A = 20/9, which is not a digit, and B = 4 and B = 6 give no whole digit either, so B must be 5.
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