Challenge Problems( Week 50 Evaluation) 1. 7 copies of a book cost less than $8. However, 9 copies of the same book cost more than $9. At least how many cents would a single copy of the book cost? 2. In a math countdown contest with 54 questions, each question can only be answered by one player whether the player answers it correctly or not. 10 points were given for each correct answer and 5 points were deducted for each incorrect ansewer. Helen is always able to answer two questions correctly out of every three questions. How many questions will she need to answer in order to make sure that she wins the countdown contest? 3. Which of the following is larger than ? 4. Each term after the first term in a sequence is 6 less than of the preceding term. If x is the first term of the sequence and x is not equal 0, what is the ratio of the second term to the first term? 5. There are two natural numbers that are larger than 1. The square of their sum is 28 more than the sum of their squares. What are the two numbers? Write only the numbers separated by a comma. 6. There were a certain number of people meeting in a room at the very beginning. During the meeting process, of the people left the meeting and 35 new people joining the meeting. The number of people in the meeting at the end is of the number at the very beginning. How many people left the meeting during the process? 7. The distance between Helen's home and her school is 2575 meters. Helen started walking from home to school, and five minutes later, her sister started walking from school to home. Ten minutes after her sister started out, they met each other. If Helen walks 10 meters more than her sister per minute, what is Helen's speed (in meter/minute)? 8. From the natural numbers 1 to 95, pick any two numbers whose sum is less than 96. How many ways are there to pick? 9. The distance between place A and place B is 340 miles. Ben and Josh started out from place A to place B, while Rene started out from place B to place A. They started out at the same time. Ben drove at an average speed of 33 mph, Josh drove at an average speed of 38 mph, and Rene drove at an average speed of 25 mph. In how many hours after they start would Josh be on the mid-point of the distance between Ben and Rene? |