Question

You have a summer job working at Magic Spring water park. On "Towel Day," every person gets a free towel with the park logo. You work at the entrance, where they hand out towels. Mr. Whipple asks you to arrange the towels in stacks with the same number of towels in each stack. Also, every stack must have more than one towel, and there must be more than one stack of towels. (It’s Mr. Whipple, so you don’t ask why.) Look at the number of towels for each color. Which of these could be arranged into more than one stack with the same number of towels in each stack?

A) 60 blue towels
B) 29 green towels
C) 37 orange towels
D) 42 white towels

Answer 1

Options A (60 blue towels) and D (42 white towels) are the only numbers that can be arranged into more than one stack with the same number of towels in each stack because they are divisible by numbers greater than 1.

Step-by-step explanation:

The question is asking which set of towels can be arranged into more than one stack with the same number of towels in each stack, while ensuring each stack has more than one towel and that there are more than one stack. To determine if a number of towels can be divided into such stacks, we need to check if the number is divisible by any number greater than 1 (which would be the number of towels per stack).

• 60 blue towels - This number is divisible by many numbers: 2, 3, 4, 5, 6, etc. Hence, it can be arranged into multiple stacks with equal numbers of towels in each one.
• 29 green towels - This number is prime, which means it can only be divided by 1 and itself, so it cannot be arranged into multiple stacks with more than one towel per stack.
• 37 orange towels - Similarly, this number is also prime and cannot be arranged into the required stacks.
• 42 white towels - This number is divisible by 2, 3, 6, 7, and so on. It can therefore be arranged into multiple stacks with equal numbers of towels in each one.

Options A and D can be arranged into more than one stack with the same number of towels in each stack, but Options B and C cannot.