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# M05 #20

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Manager
Joined: 12 Sep 2010
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27 Nov 2011, 16:27
If there is a remainder of 2 when integer P is divided by 7, is P divisible by 8?

1. P is divisible by 2 and 3
2. P<100

Can somone please explain how do to do this problem? I don't know how to handle "remainder of 2." Thanks.
Director
Joined: 28 Jun 2011
Posts: 890
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01 Dec 2011, 13:52
Math Expert
Joined: 02 Sep 2009
Posts: 39040
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Kudos [?]: 106488 [0], given: 11626

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14 Apr 2012, 15:44
Samwong wrote:
If there is a remainder of 2 when integer P is divided by 7, is P divisible by 8?

1. P is divisible by 2 and 3
2. P<100

Can somone please explain how do to do this problem? I don't know how to handle "remainder of 2." Thanks.

When positive integer p is divided by 7 the remainder is 2: $$p=7q+2$$, so p can be: 2, 9, 16, 23, 30, 37, 44, 51, 58, 65, 72, ...

(1) p is divisible by 2 and 3 --> p is a multiple of 6 --> p can be 30 (answer NO) or 72 (answer YES). Not sufficient.
(2) p<100. Clearly insufficient.

(1)+(2) p can still be 30 (answer NO) or 72 (answer YES). Not sufficient.

_________________
Re: M05 #20   [#permalink] 14 Apr 2012, 15:44
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# M05 #20

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