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
If p is a positive integer, is 2p + 1 prime?
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$$p \ge 1\,\,{\mathop{\rm int}} $$BTGmoderatorDC wrote:If p is a positive integer, is 2p + 1 prime?
(1) p is prime
(2) units digit of p is not prime
Source: Official Guide
$$2p + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$
Let´s go straight to (1+2): a BIFURCATION will guarantee (E) as the correct answer!
$$\left( {1 + 2} \right)\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,{\rm{p = 11}}\,\,\,\, \Rightarrow \,\,\,2p + 1 = 23\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,{\rm{p = 19}}\,\,\,\, \Rightarrow \,\,\,2p + 1 = 39\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr} \right.$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
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Given: p is a positive integer.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
Question: Is 2p + 1 prime?
Let's take each statement one by one.
(1) p is prime.
Case 1: Say p = 2, then 2P +1 = 5, a prime. The answer is Yes.
Case 2: Say p = 7, then 2P +1 = 15, not a prime. The answer is No.
No unique answer. Insufficient.
(2) Units digit of p is not prime.
Case 1: Say p = 11, then 2P +1 = 23, a prime. The answer is Yes.
Case 2: Say p = 19, then 2P +1 = 39, not a prime. The answer is No.
No unique answer. Insufficient.
(1) and (2) together
Both the cases discussed in Statement 2 are applicable here too.
No unique answer. Insufficient.
The correct answer: E
Hope this helps!
-Jay
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