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Math Expert V
Joined: 02 Sep 2009
Posts: 58320

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Difficulty:   35% (medium)

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

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

(1) $$p$$ is prime.

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

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Math Expert V
Joined: 02 Sep 2009
Posts: 58320

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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 $$p=19$$).

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

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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  B
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)

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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  B
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GMAT Date: 06-14-2015
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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?
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Joined: 05 Jul 2006
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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 V
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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.
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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.
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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.

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Retired Moderator B
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U r right

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Intern  B
Joined: 04 Apr 2017
Posts: 17

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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
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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 V
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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).
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