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# How many positive integers less than 200 are there such that

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CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
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Kudos [?]: 347 [0], given: 4

How many positive integers less than 200 are there such that [#permalink]  23 Nov 2007, 05:07
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65% (hard)

Question Stats:

57% (02:22) correct 43% (02:09) wrong based on 63 sessions
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?

A. 28
B. 29
C. 31
D. 32
E. 33

M12-36
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Dec 2014, 04:22, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
CEO
Joined: 17 Nov 2007
Posts: 3578
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 405

Kudos [?]: 2132 [1] , given: 359

Re: How many positive integers less than 200 are there such that [#permalink]  23 Nov 2007, 05:35
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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
CEO
Joined: 21 Jan 2007
Posts: 2764
Location: New York City
Followers: 9

Kudos [?]: 347 [0], given: 4

Re: How many positive integers less than 200 are there such that [#permalink]  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
Math Expert
Joined: 02 Sep 2009
Posts: 27053
Followers: 4183

Kudos [?]: 40309 [0], given: 5420

Re: How many positive integers less than 200 are there such that [#permalink]  13 Dec 2014, 04:22
Expert's post
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bmwhype2 wrote:
How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?

A. 28
B. 29
C. 31
D. 32
E. 33

M12-36

# of multiples of 13 in the given range $$\frac{(\text{last-first})}{\text{multiple}}+1=\frac{195-13}{13}+1=15$$;

# of multiples of 12 in the given range $$\frac{(\text{last-first})}{\text{multiple}}+1=\frac{192-12}{12}+1=16$$;

# of multiples of both 13 and 12 is 1: $$13*12=156$$. Notice that 156 is counted both in 15 and 16;

So, # of multiples of 13 or 12 but not both in the given range is $$(15-1)+(16-1)=29$$.

_________________
Re: How many positive integers less than 200 are there such that   [#permalink] 13 Dec 2014, 04:22
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