It is currently 19 Nov 2017, 01:53

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If p is a positive integer, what is the value of p?

Author Message
TAGS:

### Hide Tags

Director
Joined: 01 May 2007
Posts: 793

Kudos [?]: 385 [3], given: 0

If p is a positive integer, what is the value of p? [#permalink]

### Show Tags

23 Sep 2007, 11:46
3
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

77% (00:45) correct 23% (00:42) wrong based on 513 sessions

### HideShow timer Statistics

If p is a positive integer, what is the value of p?

(1) p/4 is a prime number.

(2) p is divisible by 3.
[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Apr 2014, 01:17, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

Kudos [?]: 385 [3], given: 0

Manager
Joined: 29 Jul 2007
Posts: 181

Kudos [?]: 39 [0], given: 0

### Show Tags

23 Sep 2007, 14:33
C.

Statement I: insufficient.
P=4*(any prime number)

Statement II:insufficient
Numerous possibilities

Combined, P = 12

Kudos [?]: 39 [0], given: 0

Director
Joined: 22 Aug 2007
Posts: 566

Kudos [?]: 72 [0], given: 0

Re: DS: Value of P? [#permalink]

### Show Tags

23 Sep 2007, 15:59
3
This post was
BOOKMARKED
jimmyjamesdonkey wrote:
If p is a positive integer, what is the value of p?

1) p/4 is a prime #.

2) p is divisible by 3.

OA to follow.

got C,

1st- insuff, can be any prime times 4
2nd-insuff, can be any prime (3) and non (6,9)

Both,

P/4= prime------------> P=prime*4
3N=P , where N is any intenger.

from both equations it follows

prime*4=3N------->3N/4=prime, where N must ne intenger, since this equation has only one possible value for N=4, there is only one possible value for P, cuz P=3N=3*4.

Kudos [?]: 72 [0], given: 0

GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5032

Kudos [?]: 452 [0], given: 0

Location: Singapore

### Show Tags

23 Sep 2007, 20:27
St1:
p/4 = prime.
P could be 44, or P could be 20...etc. Insufficient.

St2:
p could be 3,6,9,12,15....etc. Insufficient.

Using st1 and st2:
p = 12. The other choices will not result in p/4 = prime.

Sufficient.

Ans C

Kudos [?]: 452 [0], given: 0

Intern
Joined: 08 Apr 2014
Posts: 2

Kudos [?]: 1 [1], given: 2

Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink]

### Show Tags

08 Apr 2014, 13:48
1
KUDOS
In this case p can also be a different number?
What i mean is that it could be a very big number which we can not calculate so easy as 12. How we can be sure that 12 is the right answer, if what i refer is correct?

Kudos [?]: 1 [1], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132646 [2], given: 12326

Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink]

### Show Tags

09 Apr 2014, 01:27
2
KUDOS
Expert's post
9
This post was
BOOKMARKED
nikolas7 wrote:
In this case p can also be a different number?
What i mean is that it could be a very big number which we can not calculate so easy as 12. How we can be sure that 12 is the right answer, if what i refer is correct?

If p is a positive integer, what is the value of p?

(1) p/4 is a prime number --> p = 4*(prime number) --> p can be 4*2=8, 4*3=12, 4*5=20, 4*7=28, ... Not sufficient.

(2) p is divisible by 3 --> p can be 3, 6, 9, 12, 15, ... Not sufficient.

(1)+(2) From (1) we have that p = 4*(prime number) and from (2) that p is a multiple of 3. Now, for p = 4*(prime number) to be a multiple of 3 (prime number) must be 3, hence p = 4*(prime number) = 4*3 = 12. Sufficient.

Hope it's clear.
_________________

Kudos [?]: 132646 [2], given: 12326

Director
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 865 [0], given: 724

Location: India
GPA: 3.21
Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink]

### Show Tags

09 Apr 2014, 03:12
1
This post was
BOOKMARKED
nikolas7 wrote:
In this case p can also be a different number?
What i mean is that it could be a very big number which we can not calculate so easy as 12. How we can be sure that 12 is the right answer, if what i refer is correct?

If p is a positive integer, what is the value of p?

1) p/4 is a prime #.

2) p is divisible by 3.

Sol: St 1 P/4 is prime so p=8,12,20,28 and so on or P is an odd multiple of 4 (Barring 8 which is an even multiple of 4 and 2 is only even prime no ). Not Sufficient
St 2 p=3I where I is an integer so p=3,6,9,12 and so one

Combining we get p is a multiple of 3 and p/4 is prime. Only 12 fits. Note that you will not have a number where both the conditions are satsified.

Consider p/4= prime (11,23,29...)
p= 44,92,116
Thus p will be a multiple of 2 and 4 but not of 3.

If p is divisible by 3 then barring 12 for no other number can you get p/4 =prime
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 865 [0], given: 724

Intern
Joined: 21 Sep 2014
Posts: 8

Kudos [?]: 2 [0], given: 5

Re: If p is a positive integer, what is the value of p? [#permalink]

### Show Tags

28 Sep 2014, 14:28
Hallo Wounded Tiger,

You write "for no other number can you get p/4 = prime". But there are probably indefinitely many numbers greater than 12 and divisible by 4 as well as a multiple of 3. So how you know that none of These numbers will be a prime number?
Or does it suffice to not consider prime numbers greater than, let's say, 23?

Thanks,
snatch

Kudos [?]: 2 [0], given: 5

Director
Joined: 25 Apr 2012
Posts: 722

Kudos [?]: 865 [0], given: 724

Location: India
GPA: 3.21
Re: If p is a positive integer, what is the value of p? [#permalink]

### Show Tags

28 Sep 2014, 23:46
snatch123 wrote:
Hallo Wounded Tiger,

You write "for no other number can you get p/4 = prime". But there are probably indefinitely many numbers greater than 12 and divisible by 4 as well as a multiple of 3. So how you know that none of These numbers will be a prime number?
Or does it suffice to not consider prime numbers greater than, let's say, 23?

Thanks,
snatch

A prime number is one which has only 2 factors ie. 1 and itself...>Sure there are numbers which are divisible by 4 and multiple of 3( divisible by 3)...Any multiple of 12 will meet that requirement... so we have 12,24,36, 48,60 and so on
Now if you divide these numbers by 4 and consider St1 we get quotient 3,6,9,12,15...Now only 3 is a prime number (which meets your St 2 requirement) and there will be no other number for which p/4 will give you a prime number..
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Kudos [?]: 865 [0], given: 724

Intern
Joined: 09 Feb 2015
Posts: 31

Kudos [?]: 15 [0], given: 51

Location: United States (OR)
Concentration: Finance, Marketing
GMAT 1: 700 Q48 V37
WE: Information Technology (Computer Software)
Re: If p is a positive integer, what is the value of p? [#permalink]

### Show Tags

10 Aug 2015, 19:36
Thanks for the nice explanation, I got this question as part of my GMAT Prep-1 test yesterday.

Kudos [?]: 15 [0], given: 51

Non-Human User
Joined: 09 Sep 2013
Posts: 15706

Kudos [?]: 282 [0], given: 0

Re: If p is a positive integer, what is the value of p? [#permalink]

### Show Tags

07 Nov 2016, 08:27
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 282 [0], given: 0

Re: If p is a positive integer, what is the value of p?   [#permalink] 07 Nov 2016, 08:27
Display posts from previous: Sort by