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Series problem

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.
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:

830×6000=1600\displaystyle\frac{8}{30}\times 6000= 1600
Original post by ghostwalker
Agreed:

830×6000=1600\displaystyle\frac{8}{30}\times 6000= 1600


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
Bump
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
Original post by ghostwalker
Agreed:

830×6000=1600\displaystyle\frac{8}{30}\times 6000= 1600


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.
(edited 7 years ago)
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 :laugh:

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