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How many positive integers less than 200 are there such

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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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29
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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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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?

28
29
30
31
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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