M12 Q36 : Retired Discussions [Locked]
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# M12 Q36

Author Message
Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 278
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 20

Kudos [?]: 124 [0], given: 48

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29 Nov 2010, 14:22
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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?
28
29
31
32
33

The official explanation says:
Multiples of 13: 13, 26, 39, ..., 195. 15 numbers.

Multiples of 12: 12, 24, 36, ..., 192. 16 numbers.

Multiples of both 12 and 13: 156. 1 number but it is counted twice.

The answer is 15+16-2 = 29

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What is a fast approach for such type of questions? I cannot imagine that one shall sit n count all 16 multiples of 200 and then 15 multiples of 13!
Manager
Status: I rest, I rust.
Joined: 04 Oct 2010
Posts: 122
Schools: ISB - Co 2013
WE 1: IT Professional since 2006
Followers: 17

Kudos [?]: 119 [1] , given: 9

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29 Nov 2010, 19:24
1
KUDOS
The direct way...divide 200/13= 15.x
divide 200/12= 16.x

now 13*12 = 156 - we have to exclude it twice

so 15 +16 -2
_________________

Respect,
Vaibhav

PS: Correct me if I am wrong.

Manager
Joined: 29 Oct 2010
Posts: 91
Followers: 1

Kudos [?]: 9 [0], given: 10

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30 Nov 2010, 14:45
B

Posted from my mobile device
Re: M12 Q36   [#permalink] 30 Nov 2010, 14:45
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# M12 Q36

Moderator: Bunuel

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