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

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How many positive integers less than 200 are there such that [#permalink]  23 Nov 2007, 05:07
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Question Stats:

63% (02:35) correct 38% (01:47) wrong based on 136 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
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Kudos [?]: 2605 [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
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Posts: 2756
Location: New York City
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Kudos [?]: 535 [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
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Kudos [?]: 62228 [0], given: 9444

Re: How many positive integers less than 200 are there such that [#permalink]  13 Dec 2014, 04:22
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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 $$(15-1)+(16-1)=29$$.

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Re: How many positive integers less than 200 are there such that [#permalink]  17 Jan 2016, 23:13
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Re: How many positive integers less than 200 are there such that   [#permalink] 17 Jan 2016, 23:13
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