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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]

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23 Nov 2007, 06:07
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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, 05:22, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: How many positive integers less than 200 are there such that [#permalink]

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23 Nov 2007, 06:35
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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
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Re: How many positive integers less than 200 are there such that [#permalink]

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27 Nov 2007, 11:40
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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Re: How many positive integers less than 200 are there such that [#permalink]

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13 Dec 2014, 05:22
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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]

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18 Jan 2016, 00:13
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Re: How many positive integers less than 200 are there such that [#permalink]

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14 Mar 2016, 01:04
Great Question..
Focus the ording here => NOT BOTH
IF it says EITHER OR => 30
but here its 29
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Re: How many positive integers less than 200 are there such that [#permalink]

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20 Jan 2017, 11:24
1)Multiples of 12: (192-12)/12+1=16 2)Multiples of 13: (192-13)/13+1=16 3)Multiple of both 12 and 13 - 2*2*3*13=156 only 1 4)16-1+15-1=29
Re: How many positive integers less than 200 are there such that   [#permalink] 20 Jan 2017, 11:24
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# How many positive integers less than 200 are there such that

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