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If p is a positive integer, is 2p + 1 prime?

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If p is a positive integer, is 2p + 1 prime?

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If p is a positive integer, is 2p + 1 prime?

(1) p is prime

(2) units digit of p is not prime

OA E

Source: Official Guide

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BTGmoderatorDC wrote:
If p is a positive integer, is 2p + 1 prime?

(1) p is prime

(2) units digit of p is not prime

OA E

Source: Official Guide
Statements combined:
Case 1: p=11 --> p is prime, but its units digits is not prime
In this case, 2p+1 = 2*11 + 1 = 23.
Since 23 is prime, the answer to the question stem is YES.

Case 2: p=19 --> p is prime, but its units digit is not prime
In this case, 2p+1 = 2*19 + 1 = 39.
Since 39 is not prime, the answer to the question stem is NO.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

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