"GRE数学习题1691解析：Mary购书小费问题解答"

Based on the information provided in the GRE math problem 1691, Mary paid for a book with a $10 bill and received the correct change, which was less than $3. This means that the total amount she paid for the book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. To solve this problem, we can set up the equation: Total amount = Price + Sales tax Since Mary paid with a $10 bill and received less than $3 in change, we can write: 10 - Change = Price + Sales tax Given that the sales tax is 4 percent of the price of the book, we can express it as: Sales tax = 0.04 * Price Substitute this into the previous equation: 10 - Change = Price + 0.04 * Price Rearranging the terms, we get: 10 - Change = 1.04 * Price We know that the change received by Mary is less than $3, so we can write: Change < 3 Substitute this back into the equation: 10 - 3 < 1.04 * Price Simplify: 7 < 1.04 * Price Price > 7/1.04 Price > 6.73 This means that the price of the book must be greater than $6.73. From the answer choices given, this confirms that statement B ("The price of the book was greater than $6.90") must be true. Additionally, since the sales tax is 4 percent of the price of the book, we can find the maximum sales tax: Sales tax = 0.04 * Price Sales tax < 3 0.04 * Price < 3 Price < 3 / 0.04 Price < 75 This means that the price of the book must be less than $75. Considering this, statement A ("The price of the book was less than $9.50") is also true. In conclusion, the statements that must be true are: A. The price of the book was less than $9.50. B. The price of the book was greater than $6.90.