AQA GCSE Additional Maths June 09 Question 3

In the following calculations each letter represents a different digit.

\(A \times A = BC\)

\(BC \times BC = DEC\)

Which digit does each letter represent?

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\(BC\) is a two digit square so is one of \(16,\ 25,\ 36,\ 49,\ 64,\ 81\), but \(BC \times BC\) is a three digut number so \( BC\lt \sqrt{1000} \), hence \(B\lt 4 \).

Which leaves us with the possibilities BC is one of \(16, \ 25, \ 36\), In which case the corresponding \(A\)s would be \(4, \ 5,\ 6\) but the latter two are not possible since that would make \(A=C\) which is not permitted.

Hence the solution is: \(A=4,\ B=1,\ C=6,\ D=2,\ E=5\).