BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

by fskilnik@GMATH » Tue Oct 30, 2018 6:40 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
$$p \ge 1\,\,{\mathop{\rm int}} $$
$$2p + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$

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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Tue Oct 30, 2018 10:01 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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
Given: p is a positive integer.
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
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review India | Mehdipatnam GMAT Coaching | Madhapur GMAT Courses | Manhattan Review Hyderabad | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Post new topic Post Reply
• Page 1 of 1