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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: 2597
Location: New York City
How many positive integers less than 200 are there such that  [#permalink]

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Updated on: 13 Dec 2014, 04:22
19
00:00

Difficulty:

55% (hard)

Question Stats:

67% (02:17) correct 33% (02:29) wrong based on 335 sessions

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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

Originally posted by bmwhype2 on 23 Nov 2007, 05:07.
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.
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Joined: 02 Sep 2009
Posts: 52451
Re: How many positive integers less than 200 are there such that  [#permalink]

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13 Dec 2014, 04:22
2
6
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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##### General Discussion
CEO
Joined: 17 Nov 2007
Posts: 3438
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: How many positive integers less than 200 are there such that  [#permalink]

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23 Nov 2007, 05:35
1
2
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: 2597
Location: New York City
Re: How many positive integers less than 200 are there such that  [#permalink]

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27 Nov 2007, 10:40
2
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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14 Mar 2016, 00:04
1
Current Student
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Re: How many positive integers less than 200 are there such that  [#permalink]

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20 Jan 2017, 10:24
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
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Re: How many positive integers less than 200 are there such that  [#permalink]

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17 Mar 2018, 20:10
There is no other way around this question. Use the formula and calculate carefully. The last step is quite easy, look at the unit number only.
Re: How many positive integers less than 200 are there such that &nbs [#permalink] 17 Mar 2018, 20:10
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