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## Math Test Scores - Answer

The order of grades from highest to lowest was Dallas, Aaron, Edgar, Carl and Benjamin.

Since no one predicted their own grade

• Statement (1) was made by Aaron or Dallas.
• Statement (2) was made by Benjamin or Edgar.
• Statement (3) was made by Benjamin or Dallas.
• Statement (4) was made by Aaron or Carl.
• Statement (5) was made by Dallas or Edgar.
• Therefore (4) must have been made by Carl and (1) by Aaron.

Assume Aaron is at the top. Then the order would be Aaron > Carl > Benjamin > Edgar. But then no possibility for Dallas results in three False-True and one False-False for the other statements. Therefore, Aaron cannot be at the top.

A similar line of reasoning shows that Carl is not at the top, also that neither Aaron nor Carl is at the bottom.

Therefore, the only possibilities are

• Benjamin top, Edgar bottom
• Edgar top, Benjamin bottom
• Dallas top, Benjamin bottom
• (Since a boy has the bottom grade, Dallas can't be bottom.)

Trial and error will show that only the above answer results in one True-True, three True-False and one False-False.

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