Challenge Problems( Week 50 Evaluation) 1. 7 copies of a book cost less than $8. However, 8 copies of the same book cost more than $8. At least how many cents would a single copy of the book cost? 2. In a math countdown contest with 72 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. Sofia 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 110 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 19 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 Alice's home and her school is 2800 meters. Alice 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 Alice walks 30 meters more than her sister per minute, what is Alice's speed (in meter/minute)? 8. From the natural numbers 1 to 61, pick any two numbers whose sum is less than 62. How many ways are there to pick? 9. The distance between place A and place B is 83 miles. George and Kevin started out from place A to place B, while David started out from place B to place A. They started out at the same time. George drove at an average speed of 43 mph, Kevin drove at an average speed of 47 mph, and David drove at an average speed of 32 mph. In how many hours after they start would Kevin be on the mid-point of the distance between George and David? |