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# Of the positive integers that are multiples of 30 and are less than or

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Joined: 02 Sep 2009
Posts: 58416
Of the positive integers that are multiples of 30 and are less than or  [#permalink]

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08 Mar 2019, 03:21
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Difficulty:

35% (medium)

Question Stats:

77% (01:49) correct 23% (01:58) wrong based on 87 sessions

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Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12?

A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 1/2

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Of the positive integers that are multiples of 30 and are less than or  [#permalink]

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Updated on: 08 Mar 2019, 06:33
Bunuel wrote:
Of the positive integers that are multiples of 30 and are less than or equal to 360, what fraction are multiples of 12?

A. 1/6
B. 1/5
C. 1/3
D. 2/5
E. 1/2

multiples of 30 upto 360 = 12
and multiple of 12 upto 360 which are multiple of 30:6
so fraction ; 6/12; 1/2
IMO E

Originally posted by Archit3110 on 08 Mar 2019, 05:08.
Last edited by Archit3110 on 08 Mar 2019, 06:33, edited 1 time in total.
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Re: Of the positive integers that are multiples of 30 and are less than or  [#permalink]

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08 Mar 2019, 06:23
I think the answer is E.

You have to first find the smallest common divisor, and then see what proportion of multiples of 30 are also multiples of that smallest common divisor.

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360 --- Total of 12

Out these numbers, only those that are multiples of 16 are also multiples of 12. 60, 120, 180, 240, 300, 360 --- Total of 6 numbers

Alternatively
360/30= 12
And 360/60 = 6

6/12 or 1/2

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Re: Of the positive integers that are multiples of 30 and are less than or  [#permalink]

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14 Mar 2019, 03:36
Vardan95 wrote:
I think the answer is E.

You have to first find the smallest common divisor, and then see what proportion of multiples of 30 are also multiples of that smallest common divisor.

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360 --- Total of 12

Out these numbers, only those that are multiples of 16 are also multiples of 12. 60, 120, 180, 240, 300, 360 --- Total of 6 numbers

Alternatively
360/30= 12
And 360/60 = 6

6/12 or 1/2

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Hi,

Please could you explain why the answer is not 2/5 (Option D)?

Regards,

Ritvik
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Re: Of the positive integers that are multiples of 30 and are less than or  [#permalink]

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09 Apr 2019, 09:57
menonrit wrote:
Vardan95 wrote:
I think the answer is E.

You have to first find the smallest common divisor, and then see what proportion of multiples of 30 are also multiples of that smallest common divisor.

Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360 --- Total of 12

Out these numbers, only those that are multiples of 16 are also multiples of 12. 60, 120, 180, 240, 300, 360 --- Total of 6 numbers

Alternatively
360/30= 12
And 360/60 = 6

6/12 or 1/2

Posted from my mobile device

Hi,

Please could you explain why the answer is not 2/5 (Option D)?

Regards,

Ritvik

I used a number line approach for this which I found to be simpler than actually listing the factors of 30.

I figured out the first multiple of 30 that is divisible by 12. So we found 2 multiples of 30 (30 and 60) to get a number divisible by 12. If you continue looking for the next factor that is divisible by 12 down the number line, you'll see a pattern. The next multiple of 30 is 90, which is not divisible by 12. But the fourth factor of 30, 120, is divisible by 120 again.

So we have, every 2nd factor of 30 is divisible by 12, otherwise 1:2.

Re: Of the positive integers that are multiples of 30 and are less than or   [#permalink] 09 Apr 2019, 09:57
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