Math Olympiad 5

Multiple & Factor( Week 24 Evaluation)

1. Mary bought more than 3 apples. Counting by 3s, there are 2 apples left. Counting by 4s, there are 2 apples left too. At least, how many apples did she buy?

3. If x − 6 is a multiple of 7, which of the following must be the next greater multiples of 7?

4. Sofia, Josh, and Rene are riding a bike around a 1000 yards circular track. They start at the same place, same time and in the same direction, but each rides at different speed with Sofia at 769 yards per minute, Josh at 819 yards per minute, and Rene at 869 yards per minute. What is the least number of minutes will it take for all three to be together again?

5. A number is greater than 6. When the number is divided either by 13 or 15, the remainder is 6. What is the smallest possible even number that has the above property?

6. Curtis has a certain amount of money to spend on 3 types of gifts, and their prices are $5, $6, and $7 each respectively. If he spends all the money on any single type of gifts, there will all be $2 left. The amount of money Curtis has is more than $7. At least, how much (in dollars) money does Curtis have?

8. 72 apples are to be divided into equal piles. There are more than 1 but less than 72 apples in each pile. At most how many ways could the apples be divided?

9. A jar contains between 50 and 100 candies. If candies are taken out from the jar 7 at a time, there will be 6 candies left. If candies are taken out from the jar 6 at a time, there will be 5 candies left. How many candies are in the jar?

10. Steve collects coins and also loves math. When asked how many coins he had collected, he said the following: "If I arrange them in stacks of 6 each, none are left over. If I arrange them in stacks of 8 each, none are left over also. However, one is left over if I arrange them in stacks of 13 each". What is the smallest number of coins Steve could have collected?