Math Olympiad 5

Multiple & Factor( Week 24 Evaluation)

1. Sofia bought more than 5 apples. Counting by 5s, there is one apple left. Counting by 6s, there is one apple left too. At least, how many apples did she buy?

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

4. Niconia, Ben, and Josh 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 Niconia at 745 yards per minute, Ben at 795 yards per minute, and Josh at 845 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 2. When the number is divided either by 5 or 7, the remainder is 2. What is the smallest possible even number that has the above property?

6. George has a certain amount of money to spend on 3 types of gifts, and their prices are $8, $9, and $10 each respectively. If he spends all the money on any single type of gifts, there will all be $6 left. The amount of money George has is more than $10. At least, how much (in dollars) money does George 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 120 and 180 candies. If candies are taken out from the jar 8 at a time, there will be 7 candies left. If candies are taken out from the jar 7 at a time, there will be 6 candies left. How many candies are in the jar?

10. Smith 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 9 each, none are left over also. However, one is left over if I arrange them in stacks of 7 each". What is the smallest number of coins Smith could have collected?