Quick question Watch

7589200
Badges: 16
Rep:
?
#1
Report Thread starter 13 years ago
#1
From the numbers 1 to 6000, how many numbers aren't divisible by 2,3 or 5?
0
quote
reply
C4>O7
Badges: 5
Rep:
?
#2
Report 13 years ago
#2
Have you heard of the inclusion-exclusion principle?
0
quote
reply
7589200
Badges: 16
Rep:
?
#3
Report Thread starter 13 years ago
#3
No It is 125 numbers?
0
quote
reply
C4>O7
Badges: 5
Rep:
?
#4
Report 13 years ago
#4
You got the right answer but you could do it more systematically

Written in full:-

From 1-6000:
2|3000 numbers (this notation isn't recommended)
3|2000 ''
5|1200 ''

But
2,3|1000 ''
2,5|600 ''
3,5|400 ''

and
2,3,5|200 ''

So the number which ARE divisible by 2,3 or 5 is:
3000+2000+1200-1000-600-400+200 = 4400 (think about which are added and which subtracted)
6000-4400=1600
0
quote
reply
Chewwy
Badges: 15
Rep:
?
#5
Report 13 years ago
#5
crap method when you have more, but:

6000 - (6000/2+ 6000/3 + 6000/5) + (6000/6 + 6000/10 + 6000/15) - (6000/30) = 1600

the way i was told to do this kind of question, which i shun as being pretty much the same, is to right out the numbers 1-abc... where abc... is the product of all the numbers you want, and let it have a number of columns equal to one of the numbers. now cross out all the numbers that are factors, then times the number you're going up to by the fraction of the numbers that weren't crossed out.
0
quote
reply
7589200
Badges: 16
Rep:
?
#6
Report Thread starter 13 years ago
#6
No It is 125 numbers?
0
quote
reply
meef cheese
Badges: 10
Rep:
?
#7
Report 13 years ago
#7
1/2 x 2/3 x 4/5 x 6000 = 1600

Ok I copied it off Wrangler. I started a thread about this question. Search for it.
0
quote
reply
Chewwy
Badges: 15
Rep:
?
#8
Report 13 years ago
#8
(Original post by Vazzyb)
No It is 125 numbers?
no it's not. that's just silly. there are more primes than that (probably)...
0
quote
reply
7589200
Badges: 16
Rep:
?
#9
Report Thread starter 13 years ago
#9
No It is 125 numbers?

--------------

Well, i got 1600 to start with!

But then was asked a question if i was "using the right method" so i deleted it...

--------------

(Original post by e-unit)
1/2 x 2/3 x 4/5 x 6000 = 1600

Ok I copied it off Wrangler. I started a thread about this question. Search for it.
Ahh brilliant..
0
quote
reply
C4>O7
Badges: 5
Rep:
?
#10
Report 13 years ago
#10
Wrangler's method only works nicely if all the numbers are coprime and also if the large number is divisible by each the small numbers (as in this case).
0
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (197)
27.86%
No (510)
72.14%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise