John checks every 8th item for color, and Colin checks every 12th item for durability. If 1,920 items passed by both of them, how many items were checked by both John and colin?

How do I figure this?

1920/12 = 160

1920/8 = 240

Can you do anything with that?

still confused! do they want to know how many items were checked by BOTH john and calvin, meaning the same item?

John checks items

#8 #16 #24 #32 #40 .... #1920
the 8 means he checks item #8 , not 8 items
so isn't the above just like the times table for 8 ?
how many entries are there to get to 1920 ?
that would be 1920/8 or 160
So John had to check 160 items and that last item would be item # 1920.
Use the same argument for Colin.

So John checked 160 items and Colin checked 240 items
So number of items checked by BOTH John AND Colin = 400

(I assumed that they were not looking at the same items, if they are checking the same line , then we have to subtract all common items from the total.
A slightly more difficult question, but ...
what numbers would be divisible by both 8 and 24 ? )

Its a multible choice question and the choices are 20,40,60,80 and I still don't see how to come up with any of these answers

You are right, I should have taken the intersection of the two sets, I mis-read the question

so we are looking for numbers which are both divisible by 8 and by 12
the smallest of these would be the LCM of 8 and 12 which is 24
so the 24th is checked by both, the 48th is checked by both, etc
then 1920/24 = 80

To figure out how many items were checked by both John and Colin, you need to find the least common multiple (LCM) of 8 and 12. The LCM represents the smallest number divisible by both 8 and 12.

To find the LCM, you can use either prime factorization or the method of listing multiples.

Prime factorization:

- Prime factorize each number: 8 = 2^3 and 12 = 2^2 * 3
- Take the highest power of each prime factor: The LCM is 2^3 * 3 = 24.

Method of listing multiples:

- List the multiples of both 8 and 12 until you find the first common multiple: 8, 16, 24, 32... and 12, 24...
- The first common multiple is 24.

Therefore, the LCM of 8 and 12 is 24. This means that John and Colin will meet and check the same item every 24th item.

Now, to figure out the number of items checked by both John and Colin:

- Divide 1,920 by 24 (since they meet every 24th item).
- 1,920 ÷ 24 = 80.

So, John and Colin would have checked 80 items together.