"GRE数学习题1692解析：Mary购买图书的金额与税金之间的关系"

The problem presented in GRE math question 1692 involves Mary making a purchase of a book, paying with a $10 bill and receiving less than $3 in change. The scenario is divided into two cases: one where the total amount Mary paid equals the price of the book, and another where the total amount paid includes a 4 percent sales tax on the price of the book. In the first case, the price of the book must be less than $10, as Mary received change. Given that the change was less than $3, it is safe to say that the price of the book was less than $7. Therefore, statement A - "The price of the book was less than $9.50" - must be true. In the second case, the total amount paid includes a 4 percent sales tax on the price of the book. Since Mary paid with a $10 bill and received less than $3 in change, it is reasonable to infer that the price of the book, including the tax, was greater than $7. Therefore, statement B - "The price of the book was greater than $6.90" - must also be true. Regarding statement C - "The sales tax was less than $0.45" - it is possible to calculate the maximum sales tax that meets the given conditions. If we assume the price of the book was $7, the 4 percent sales tax would be $0.28, which is indeed less than $0.45. Therefore, statement C must also be true. In conclusion, all of the statements A, B, and C are true based on the information provided in the GRE math question 1692. Mary paid for a book with a $10 bill, received less than $3 in change, and the total amount she paid equaled the price of the book plus a 4 percent sales tax. This analysis showcases the application of mathematical reasoning and logic in solving real-world problems.