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If p is a positive integer, which of the following could be a prime nu

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Joined: 02 Sep 2009
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If p is a positive integer, which of the following could be a prime nu  [#permalink]

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08 Mar 2019, 03:14
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92% (00:49) correct 8% (00:50) wrong based on 38 sessions

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If p is a positive integer, which of the following could be a prime number?

A. 8p
B. 8p + 1
C. 8p + 2
D. 8p + 4
E. 8p + 6

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Re: If p is a positive integer, which of the following could be a prime nu  [#permalink]

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08 Mar 2019, 03:46
Bunuel wrote:
If p is a positive integer, which of the following could be a prime number?

A. 8p
B. 8p + 1
C. 8p + 2
D. 8p + 4
E. 8p + 6

THE REQUIRED PRIME NUMBER MUST BE AN ODD NUMBER AS IN EACH OF THE OPTIONS 8 IS MULTIPLIED WITH p.
ONLY OPTION B HAS AN ODD NUMBER, REST OF ALL ARE EVEN NUMBERS.
HENCE, OPTION B 8p+1
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Re: If p is a positive integer, which of the following could be a prime nu  [#permalink]

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08 Mar 2019, 04:52
Bunuel wrote:
If p is a positive integer, which of the following could be a prime number?

A. 8p
B. 8p + 1
C. 8p + 2
D. 8p + 4
E. 8p + 6

Option B) 8*2 + 1 = 17. here p=2.

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Re: If p is a positive integer, which of the following could be a prime nu  [#permalink]

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11 Mar 2019, 09:40
Bunuel wrote:
If p is a positive integer, which of the following could be a prime number?

A. 8p
B. 8p + 1
C. 8p + 2
D. 8p + 4
E. 8p + 6

We see that 8p is an even number greater than 2, so 8p + 2, 8p + 4 and 8p + 6 will each be an even number greater than 2, which means none of them could be a prime number since even numbers greater than 2 are not prime numbers. Therefore, the only expression that could be a prime number is 8p + 1. This is borne out by recalling that even + odd = odd.

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Re: If p is a positive integer, which of the following could be a prime nu   [#permalink] 11 Mar 2019, 09:40
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