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# If x is a prime number greater than 2, which of the following could be

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If x is a prime number greater than 2, which of the following could be  [#permalink]

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30 Oct 2018, 00:39
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If x is a prime number greater than 2, which of the following could be a prime number?

(A) $$x^2$$
(B) $$\frac{x}{2}$$
(C) $$3x$$
(D) $$x - 4$$
(E) $$x^2 + 1$$

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Re: If x is a prime number greater than 2, which of the following could be  [#permalink]

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30 Oct 2018, 01:29
IMO D. As it is “could be” question, plugin x=7, only D holds

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Re: If x is a prime number greater than 2, which of the following could be  [#permalink]

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06 Feb 2019, 07:57
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pushpitkc wrote:
If x is a prime number greater than 2, which of the following could be a prime number?

(A) $$x^2$$
(B) $$\frac{x}{2}$$
(C) $$3x$$
(D) $$x - 4$$
(E) $$x^2 + 1$$

A) is the square of a prime, which can't be prime by definition since it has 3 factors
B) all prime numbers besides 2 are odd, so dividing x by 2 results in a non-int
C) a prime x can only have factors of itself and 1, if x is 3 then 3*3=9, perfect square so again, more than 2 factors
D) subtracting an even from an odd number means that the result is odd, which could be prime (e.g. 7-4=3)
E) any prime squared is already not prime, adding 1 just means it will be even and obviously not a prime number
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If x is a prime number greater than 2, which of the following could be  [#permalink]

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06 Feb 2019, 12:40
If x is a prime number greater than 2, which of the following could be a prime number?

All prime numbers are integers.

The only factors of a prime number are that number and 1.

All prime numbers greater than 2 are odd.

Any even number greater than 2 is not prime.

(A) $$x^2$$

The factors of this number are 1, x, and $$x^2$$. So this number cannot be prime.

(B) $$\frac{x}{2}$$

Since all prime numbers greater than 2 are odd, $$\frac{x}{2}$$ is not an integer, and therefore will not be prime.

(C) $$3x$$

The factors of this number are 1, 3, x, and 3x. So this number cannot be prime.

(D) $$x - 4$$

An odd prime number minus 4 is an odd number. A odd number could be prime.

Example: 11 - 4 = 7

(E) $$x^2 + 1$$

A prime number greater than 2 is odd. The square of an odd number is an odd number. An odd number + 1 is an even number. An even number greater than 2 is not prime.

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If x is a prime number greater than 2, which of the following could be   [#permalink] 06 Feb 2019, 12:40
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