Between 20 and 28 students signed up for the chess club. The students could not be divided exactly into groups of 2, 3, 4 and 5. How many students signed up for the chess club? Show your work

You can eliminate the even numbers because they're divisible by 2. You can eliminate 25 because it's divisible by 5. Then eliminate 21 and 27, both divisible by 3. What is your answer?

To find the number of students who signed up for the chess club, we need to find the smallest number that is greater than 20 and cannot be divided exactly by 2, 3, 4, or 5 within the range from 20 to 28.

Let's start by checking the numbers between 20 and 28 one by one.

21: Can be divided by 3 and 7 (not allowed).
22: Can be divided by 2 (not allowed).
23: Cannot be divided by any of the given numbers (allowed).
24: Can be divided by 2, 3, 4 (not allowed).
25: Can be divided by 5 (not allowed).
26: Can be divided by 2 (not allowed).
27: Can be divided by 3 (not allowed).

We have found our answer: 23 students signed up for the chess club.

Explanation of the method:
To check if a number can be divided exactly by another number, we check if the remainder is 0 when we divide the first number by the second number. If the remainder is 0, then the number is divisible.

In this case, we checked each number between 20 and 28 and determined if there were any divisors among the given numbers of 2, 3, 4, and 5. Any number that could be divided exactly by any of these numbers was not a valid answer. The first number that could not be divided exactly by any of these numbers was 23, so that is our answer.