How many positive integers less than 200 are there such

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rakeshd347: Master | Next Rank: 500 Posts; Posts: 391; Joined: Sat Mar 02, 2013 5:13 am; Thanked: 50 times; Followed by:4 members

How many positive integers less than 200 are there such

by rakeshd347 » Thu Oct 17, 2013 7:29 pm

How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pm; Location: Bangalore, India; Thanked: 97 times; Followed by:26 members; GMAT Score:750

by ganeshrkamath » Thu Oct 17, 2013 7:41 pm

rakeshd347 wrote:How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?

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Multiples of both 12 and 13 = 156 => 1
Multiples of 12 = 12,24,....,192 => 16
Multiples of 13 = 13,26,....,195 => 15
Required answer = 16 + 15 - 1 - 1 = 29

Choose B

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pm; Thanked: 448 times; Followed by:34 members; GMAT Score:650

by theCodeToGMAT » Thu Oct 17, 2013 8:26 pm

12 * 13 will be the only common multiple = 156

Number of 12's multiple in 200 = 200/12 = 16
Number of 13's multiple in 200 = 200/13 = 15

So, numbers 16 + 15 - 2 = 29

Answer [spoiler]{B}[/spoiler]

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by Scott@TargetTestPrep » Fri Nov 22, 2019 11:15 am

rakeshd347 wrote:How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 12 but not both?

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29
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32

The number of multiples of 13 is:

(195 - 13)/13 + 1 = 15

The number of multiples of 12 is:

(192 - 12)/12 + 1 = 16

There is also one multiple of both 12 and 13, which is 12 x 13 = 156.

Thus, the number of multiples of 12 or 13 but not both that are also less than 200 is 15 + 16 - 1 - 1= 29.

Answer: B

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