1. The problem involves understanding the truth values of statements about SAT scores of freshman students. 2. Let's analyze each statement logically: - Statement 1: "Some students had a score of exactly 1100." - Statement 2: "All students had a score of 1100 or above." - Statement 3: "Next year at least one student will have a score of at least 1100." - Statement 4: "Some students had a score of more than 950." - Statement 5: "Fewer than half had a score of 1100 or below." - Statement 6: "None of the above statements are true." 3. The problem states that none of the above statements are true. 4. This means: - No student had exactly 1100 (negation of statement 1). - Not all students had 1100 or above (negation of statement 2). - It is not guaranteed that next year any student will have at least 1100 (negation of statement 3). - No student had more than 950 (negation of statement 4). - At least half had a score of 1100 or below (negation of statement 5). 5. From these, we deduce the SAT scores last year were all below 1100 (since no one had exactly 1100 and not all had 1100 or above), and no one scored more than 950, so all scores were 950 or below. 6. Therefore, the average or mean SAT score last year was at most 950. 7. The problem is about logical deduction rather than a numerical calculation. Final conclusion: Given the negations, the SAT scores last year were all 950 or below, so the average SAT score was at most 950.