GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 18:33

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# M14-30

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58320

### Show Tags

16 Sep 2014, 00:54
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:53) correct 29% (02:01) wrong based on 58 sessions

### HideShow timer Statistics

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

(1) $$p$$ is prime.

(2) The units digit of $$p$$ is not prime.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58320

### Show Tags

16 Sep 2014, 00:54
Official Solution:

Even when we consider the statements together, we can have an YES (for example if $$p=11$$) as well as a NO answer (for example if $$p=19$$).

_________________
Manager
Joined: 22 Feb 2016
Posts: 84
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57

### Show Tags

21 Nov 2016, 09:27
Isnt statement 1 sufficient?
If p=2 then 2p+1=5 prime
if p=3 then 2p+1=7 prime

Hence if p is prime then 2p+1 is prime??
Intern
Joined: 14 Apr 2015
Posts: 29
Location: United States
Concentration: Nonprofit, Entrepreneurship
GMAT Date: 06-14-2015
GPA: 3.93
WE: Marketing (Non-Profit and Government)

### Show Tags

16 Dec 2016, 12:22
AmritaSarkar89 wrote:
Isnt statement 1 sufficient?
If p=2 then 2p+1=5 prime
if p=3 then 2p+1=7 prime

Hence if p is prime then 2p+1 is prime??

Since there are so many primes in the early numbers, try testing a larger prime.

if p=17 then 2p+1= 35 Not Prime

Also notice that for any value of p, 2p+1 will be odd. And then you can ask yourself, are all odds prime numbers? No. But that number pattern doesn't emerge until you getting to larger numbers
Intern
Joined: 14 Apr 2015
Posts: 29
Location: United States
Concentration: Nonprofit, Entrepreneurship
GMAT Date: 06-14-2015
GPA: 3.93
WE: Marketing (Non-Profit and Government)

### Show Tags

16 Dec 2016, 12:42
This problem took me 8 minutes. Although I got it correct I feel like I must be missing something. Can anyone explain a fast way to arrive at the answer?
Retired Moderator
Joined: 05 Jul 2006
Posts: 1456

### Show Tags

16 Dec 2016, 14:20
Bunuel wrote:
If $$p$$ is a positive integer, is $$2p + 1$$ prime?

(1) $$p$$ is prime.

(2) The units digit of $$p$$ is not prime.

from 1

if p = 2 the 2p+1 = 5 ... prime and if p = 7 thus 2p+1 = 15 not prime ... insuff

from 2

if p = 14 then 2p+1 = 29 prime if p = 12 thus 2p+1 = 25 not prime ... insuff

both
p is a prime >= 11 that ends ( units digit ) in a non prime and since all primes after 5 ends in 1 , 3 , 7,9 then we are looking for primes that end in 9 or 1

11 and 19

if p= 11 thus 2p+1 = 23 prime ... if p = 19 thus 2p+1 = 39 not prime ... insuff

E
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1333
Location: Viet Nam

### Show Tags

17 Dec 2016, 02:50
1
meshackb wrote:
This problem took me 8 minutes. Although I got it correct I feel like I must be missing something. Can anyone explain a fast way to arrive at the answer?

I guess that you want to solve this one by using algebric way? No need to do that. In actual GMAT, you could simply find 2 cases satisfied statements but lead to 2 different results. This won't cost much time.

For example:

(1) p is prime.

p=2 so 2p+1=5 is prime
p=3 so 2p+1=7 is also a prime
p=5 so 2p+1=11 is also a prime

It seems good.

Now if p=7 so 2p+1=15 is not a prime. Hence (1) is out.

(2) The units digit of p is not prime.
So units digit of p could be 0, 1, 4, 6, 8, 9.

If p=1 then 2p+1=3 is a prime
If p=4 then 2p+1=9 is not a prime
Hence (2) is also out.

Now, combine (1) and (2).

The smallest positive number which is a prime and its units digit is not a prime is 11.
If p=11 then 2p+1=23 is a prime

The next prime is 13, 17, 19
13, 17 are out because these numbers don't satisfy (2).
Now 19 left. If p=19 then 2p+1=2*19+1=39 is not a prime

Clearly (1) + (2) is insufficient.
_________________
Intern
Joined: 30 Jul 2014
Posts: 38

### Show Tags

30 Dec 2016, 01:58
yezz wrote:
Bunuel wrote:
If $$p$$ is a positive integer, is $$2p + 1$$ prime?

(1) $$p$$ is prime.

(2) The units digit of $$p$$ is not prime.

from 1

if p = 2 the 2p+1 = 5 ... prime and if p = 7 thus 2p+1 = 15 not prime ... insuff

from 2

if p = 14 then 2p+1 = 29 prime if p = 12 thus 2p+1 = 25 not prime ... insuff

both
p is a prime >= 11 that ends ( units digit ) in a non prime and since all primes after 5 ends in 1 , 3 , 7,9 then we are looking for primes that end in 9 or 1

11 and 19

if p= 11 thus 2p+1 = 23 prime ... if p = 19 thus 2p+1 = 39 not prime ... insuff

E

In the second example, you cannot take p=12. Since the last digit is not prime, 12 is not an option. Take 17 and it gives us the answer.
Retired Moderator
Joined: 05 Jul 2006
Posts: 1456

### Show Tags

30 Dec 2016, 13:02
theincredible wrote:
yezz wrote:
Bunuel wrote:
If $$p$$ is a positive integer, is $$2p + 1$$ prime?

(1) $$p$$ is prime.

(2) The units digit of $$p$$ is not prime.

from 1

if p = 2 the 2p+1 = 5 ... prime and if p = 7 thus 2p+1 = 15 not prime ... insuff

from 2

if p = 14 then 2p+1 = 29 prime if p = 12 thus 2p+1 = 25 not prime ... insuff

both
p is a prime >= 11 that ends ( units digit ) in a non prime and since all primes after 5 ends in 1 , 3 , 7,9 then we are looking for primes that end in 9 or 1

11 and 19

if p= 11 thus 2p+1 = 23 prime ... if p = 19 thus 2p+1 = 39 not prime ... insuff

E

In the second example, you cannot take p=12. Since the last digit is not prime, 12 is not an option. Take 17 and it gives us the answer.

Sent from my iPhone using GMAT Club Forum mobile app
Retired Moderator
Joined: 05 Jul 2006
Posts: 1456

### Show Tags

30 Dec 2016, 13:02
U r right

Sent from my iPhone using GMAT Club Forum mobile app
Intern
Joined: 04 Apr 2017
Posts: 17

### Show Tags

30 Jun 2017, 11:51
Prime numbers can't be represented through linear equations. If that would have been the case, we wouldn't need super computers.
So, E is the answer.
Intern
Joined: 09 Aug 2012
Posts: 2

### Show Tags

10 Feb 2019, 03:03
I think this is a poor-quality question and I don't agree with the explanation. The question clearly says - if P is a positive integer. So in option 1 if P is prime, then P can only be equal to 2 (since that is the only even prime integer). Hence, 2*2+1 = 5 is a prime number.

However, for 2 if the unit digit of p is not prime and P is even (from the question) - so let's say 14 - 14*2+1 = 29 which is prime, however, 16 gives us 33 which is not prime. Hence, only solution 1 is sufficient.
Math Expert
Joined: 02 Sep 2009
Posts: 58320

### Show Tags

10 Feb 2019, 03:10
NilayanDasGupta wrote:
I think this is a poor-quality question and I don't agree with the explanation. The question clearly says - if P is a positive integer. So in option 1 if P is prime, then P can only be equal to 2 (since that is the only even prime integer). Hence, 2*2+1 = 5 is a prime number.

However, for 2 if the unit digit of p is not prime and P is even (from the question) - so let's say 14 - 14*2+1 = 29 which is prime, however, 16 gives us 33 which is not prime. Hence, only solution 1 is sufficient.

Why it's necessary in (1) p to equal to 2? Why it cannot be 11? Or 19? Both are prime integers and if p=11, then 2p+1 IS primes (23) but if p=19, then 2p+1 is NOT a prime (39).
_________________
M14-30   [#permalink] 10 Feb 2019, 03:10
Display posts from previous: Sort by

# M14-30

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne