Between 20 and 28 students signed up for the chess club. The students could not be divided exactly into groups of 2, 3, 4, or 5. How many students signed up for the chess club?
2 divides 20,22,24,26,28
3 divides 21,24,27
4 divides 20,24,28
5 divides 20,25
So, which number has not been listed above?
So our number should not be divisible by 2,3,4,or 5
that is, it can't be a multiple of of these numbers
So for the range of 20 - 28
multiples of 2: 20, 22, 24, 26, 28
multiples of 2: 21, 24, 27
multiples of 4: 20, 24, 28
multiples of 5: 20, 25
I don't see the prime number 29, so that's it
Factor all numbers between 20 and 28.
20 = 2² ∙ 5
21 = 3 ∙ 7
22 = 2 ∙ 11
23 is a prime number
24 = 2³ ∙ 3
25 = 5²
26 = 2 ∙ 13
27 = 3³
28 = 2³ ∙ 7
The number 23 is the only number that can't be divided by 2, 3, 4, or 5.
23 students signed up for the chess club
good grief, how did I mess this one up, 29 is not even in the given range.
go with oobleck and bosnian,
it is obviously 23
To find the number of students who signed up for the chess club, we need to consider the range of 20 to 28 students and eliminate the numbers that can be divided evenly by 2, 3, 4, or 5.
First, let's eliminate numbers that can be divided evenly by 2. In this case, it means any even number. Therefore, we can eliminate 22, 24, 26, and 28.
Next, let's eliminate numbers that can be divided evenly by 3. In this range, we have 21, 23, 25, 27. Among these, only 21 and 27 cannot be divided evenly by 3.
Now, let's eliminate numbers that can be divided evenly by 4. In this range, we have 21, 23, and 25. None of these numbers can be divided evenly by 4, so we don't eliminate any numbers here.
Finally, let's eliminate numbers that can be divided evenly by 5. In this range, we have 21, 23, and 25. None of these numbers can be divided evenly by 5, so we don't eliminate any numbers here.
Now, let's analyze the remaining numbers: 20, 21, 23, 25, and 27.
Out of these, only the number 20 can be divided evenly by 2. Therefore, it is not possible for exactly 20 students to have signed up for the chess club.
Therefore, the number of students who signed up for the chess club must be either 21, 23, 25, or 27.