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# M20-25

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Math Expert
Joined: 02 Sep 2009
Posts: 44290

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16 Sep 2014, 01:09
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15% (low)

Question Stats:

70% (00:22) correct 30% (00:23) wrong based on 113 sessions

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What is the remainder when a positive integer $$p$$ is divided by 2?

(1) $$p$$ is a prime integer

(2) $$p \gt 10$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 44290

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16 Sep 2014, 01:09
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Official Solution:

What is the remainder when a positive integer $$p$$ is divided by 2?

Notice that a positive integer can yield only two remainders upon division by 2: 0 (when the dividend is even) and 1 (when the dividend is odd). So, we are basically asked whether $$p$$ is even or odd.

(1) $$p$$ is a prime integer. $$p$$ could be 2, so even, as well as 3 (for example), so odd. Not sufficient.

(2) $$p \gt 10$$. Clearly insufficient.

(1)+(2) Any prime number greater than 10 is odd and thus leaves the remainder of 1 when divided by 2. Sufficient.

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18 Oct 2017, 18:28
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Quote:
(1)+(2) Any odd number greater than 10 is odd and thus leaves the remainder of 1 when divided by 2. Sufficient.

I believe that correct statement is:
Any prime number greater than 10
Math Expert
Joined: 02 Sep 2009
Posts: 44290

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18 Oct 2017, 21:08
OleksandrGureiev wrote:
Quote:
(1)+(2) Any odd number greater than 10 is odd and thus leaves the remainder of 1 when divided by 2. Sufficient.

I believe that correct statement is:
Any prime number greater than 10

Edited the typo. Thank you!
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Re: M20-25   [#permalink] 18 Oct 2017, 21:08
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# M20-25

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