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# Series problem watch

1. Of 1, 2, 3,... 6000 how many are not multiples of 2, 3 or 5?
I'm coming up with 1600 but since there's no answer available I want to see what you guys get and how you get it.
2. (Original post by Student1256)
Of 1, 2, 3,... 6000 how many are not multiples of 2, 3 or 5?
I'm coming up with 1600 but since there's no answer available I want to see what you guys get and how you get it.
Agreed:

3. (Original post by ghostwalker)
Agreed:

wondering why it doesnt work if you do (2/10)*6000. what would define when the cycle is at a complete? because the cycle hasnt completed at 10 so it gives a faulty answer
4. Bump
5. (Original post by Student1256)
wondering why it doesnt work if you do (2/10)*6000. what would define when the cycle is at a complete? because the cycle hasnt completed at 10 so it gives a faulty answer
30 works bc its the LCM so the cycle completes then.

of course you could use cycles of 60,90,120 etc and it would also work fine
6. (Original post by ghostwalker)
Agreed:

You can treat this as a Venn diagram problem in disguise (set A = 2, set B = 3, set C = 5).

Start with 6,000/(2 x 3 x 5) which gives you 2 union 3 union 5 (or A union B union C) in the middle of the Venn and work outwards. Then add up the total of multiples and deduct this from 6,000. This gives you the set of integers from 1 to 6000 that are not members of the sets of A, B, or C.
7. (Original post by BrasenoseAdm)
You can treat this as a Venn diagram problem in disguise (set A = 2, set B = 3, set C = 5).

Start with 6,000/(2 x 3 x 5) which gives you 2 union 3 union 5 (or A union B union C) in the middle of the Venn and work outwards. Then add up the total of multiples and deduct this from 6,000. This gives you the set of integers from 1 to 6000 that are not members of the sets of A, B, or C.
Interesting approach! didn't expect an Oxford admissions representative on tsr to reply but it made my day haha

Ironically this problem is from an at interview test from trinity college

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