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

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Carcass
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If p is a positive integer, which of the following could be [#permalink] New post   08 Mar 2020, 10:59
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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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Hm3105
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Re: If p is a positive integer, which of the following could be [#permalink] New post   09 Mar 2020, 22:27
Prime number is one which is only divisible by 1 and itself.
All the options except B when divided by 2 leave remainder 0 but B doesn't.

We can also solve this by choosing a value for 'p' checking options
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Re: If p is a positive integer, which of the following could be [#permalink] New post   09 Mar 2020, 22:45
B. The others can all have a factor of 2 pulled out

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Re: If p is a positive integer, which of the following could be [#permalink] New post   09 Mar 2020, 23:19
Carcass 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


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All of the options (A, C, D, and E) are multiple of 2:

8p = 2 * 4p
8p + 2 = 2 * (4p + 1)
8p + 4 = 2 * (4p + 2)
8p + 6 = 2 * (4p + 3)

Hence, they cannot be prime numbers (since prime numbers must only be divisible by 1 and itself)

Only option B: 8p + 1 does not apparently have any factors
Thus, it is the only one that CAN BE prime (it might not be prime as well - we cannot ensure that it is prime)

Option B
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Re: If p is a positive integer, which of the following could be [#permalink] New post   24 Jan 2022, 01:44
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8p = even integer
even + odd = odd
8p + 1 = odd integer

Answer B is the only choice that leads to an odd integer.

Also, 8(5) + 1 = 41
41 is a prime number
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