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How many positive integers less than 200 are there such that

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CEO
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How many positive integers less than 200 are there such that [#permalink] New post 23 Nov 2007, 05:07
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?


28
29
31
32
33
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 [#permalink] New post 23 Nov 2007, 05:35
Expert's post
B. 29

for 13: 13...195=13*15 ==> N13=13*15-13/13 +1 = 15
for 12: 12...192=12*16 ==> N13=12*16-12/12 +1 = 16

but there is one integer 13*12. so

N=(15-1)+(16-1)=29
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 [#permalink] New post 27 Nov 2007, 10:40
walker wrote:
B. 29

for 13: 13...195=13*15 ==> N13=13*15-13/13 +1 = 15
for 12: 12...192=12*16 ==> N13=12*16-12/12 +1 = 16

but there is one integer 13*12. so

N=(15-1)+(16-1)=29


very nice.

i did it the most ungraceful way possible.

200 / 12 = 16.xxxx
200 / 13 = 15.xxx

16 + 15 = 31

12 & 13 have one LCM under 200. didnt even both to calculate it since i know 12*12 =144.

subtract 2 since it shows up in both sets of multiples

31 - 2 = 29
  [#permalink] 27 Nov 2007, 10:40
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How many positive integers less than 200 are there such that

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