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If x is a positive integer greater than 1, is x! + x + 1 a p

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Aug 18, 2019 10:25 pm
BTGmoderatorDC wrote:If x is a positive integer greater than 1, is x! + x + 1 a prime number?

(1) x < 10

(2) x is odd

OA B

Source: Manhattan Prep
Let's take each statement one by one.

(1) x < 10

Case 1: Say x = 2. We have x! + x + 1 = 2! + 2 + 1 = 5, a prime number;
Case 2: Say x = 3. We have x! + x + 1 = 3! + 3 + 1 = 10, a non-prime number

No unique answer. Insufficient.

(2) x is odd

Since x ≥ 3, x! will contain 2, thus, it is an even number. Thus, x! + x + 1 = Even + Odd + Odd = Even. The answer is no. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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