Shawn and Rhonda bought identical boxes of stationery. Shawn used hers to write 1-sheet letters and Rhonda used hers to write 3-sheet letters. Shawn used all of the envelopes and had 50 sheets of paper left, while Rhonda used all of the paper and had 50 envelopes left. The number of sheets of paper in each box was:
The Superduper Supermarket has 128 crates of apples that have just arrived at the loading dock. Each crate contains at least 120 apples and at most 144 apples. What is the largest integer n you can find such that there must be at least n crates containing the same number of apples? (This means that, even if you make the number of apples in each crate as different as you can possibly make them, there are still going to be n crates with the same number of apples.)
Mike’s age right now is exactly 3 times his age 3 years hence minus 3 times his age 3 years ago. How old is Mike right now?
The average weight of the 5-man freshman basketball team was thought to be 60 kg. However, a mistake was made — one of the weights was written down wrong. Once the mistake was found, and that one weight was changed to the right value of 80 kg, the correct average turned out to be 70 kg. What was the mistaken value? That is, what was written down at first instead of 80 kg?
The average age of a group of 50 people is 45. Three members, ages 50, 60, and 72, leave the group. What is the average age of the remaining 47 people?
If x hens lay x + 1 eggs in x + 2 days, how many days will it take x + 3 hens to lay x + 5 eggs?
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Phoebe Beebe has an appointment with her orthodontist at 2:55 this afternoon. Her brother Led will drive her there, and they will leave right after school. If they go 60 kph (about 35 mph) the whole way, they will arrive 5 minutes early. But if they drive 40 kph (about 25 mph) the whole way, they will arrive 5 minutes late. What time does school get out, and how far do they have to drive? (The orthodontist’s name is Dr. Larry Filler; his nurse is Jane Pullam.)
If x is a perfect square (i.e., the square of some integer), then the next perfect square larger than x is:
Suppose x, y, and z are all counting numbers, and x + y = z. If two of these numbers are multiples of 7, is the third one also a multiple of 7? Show why or why not.
Let x be a positive integer. Consider the product x(x + 1)(x + 2). Name two prime numbers and one composite number that are always factors of this product, for any x. Can you explain why this is true?