AMC10-2016A真题.pdfVIP

1. What is the value of ? 2. For what value of does ? 3. For every dollar Ben spent on bagels, David spent cents less. Ben paid more than David. How much did they spend in the bagel store together? 4. The remainder can be defined for all real numbers and with by where denotes the greatest integer less than or equal to . What is the value of ? 5. A rectangular box has integer side lengths in the ratio . Which of the following could be the volume of the box? 6. Ximena lists the whole numbers through once. Emilio copies Ximenas numbers, replacing each occurrence of the digit by the digit . Ximena adds her numbers and Emilio adds his numbers. How much larger is Ximenas sum than Emilios? 7. The mean, median, and mode of the data values are all equal to . What is the value of ? 8. Trickster Rabbit agrees with Foolish Fox to double Foxs money every time Fox crosses the bridge by Rabbits house, as long as Fox pays coins in toll to Rabbit after each crossing. The payment is made after the doubling, Fox is excited about his good fortune until he discovers that all his money is gone after crossing the bridge three times. How many coins did Fox have at the beginning? 9. A triangular array of coins has coin in the first row, coins in the second row, coins in the third row, and so on up to coins in the th row. What is the sum of the digits of ? 10. A rug is made with three different colors as shown. The areas of the three differently colored regions form an arithmetic progression. The inner rectangle is one foot wide, and each of the two shaded regions is foot wide on all four sides. What is the length in feet of the inner rectangle? 11. What is the area of the shaded region of the given