Discussion
If A + B = C + D and A + D > B + C, then which one of the following is wrong ?
Answer: D
The statement that is wrong is B > D.
Rearrange the two conditions:
\[ \begin{aligned} A + B = C + D &\Rightarrow A - C = D - B \\ A + D \gt B + C &\Rightarrow A - C \gt B - D \end{aligned} \]
Substituting the first into the second gives \(D - B \gt B - D\), so \(D \gt B\). Therefore B > D must be wrong. It also follows that \(A - C = D - B \gt 0\), so A > C is true.
A > B and C > D are not fixed by the data either way, so they cannot be called wrong; only B > D contradicts the conditions.
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