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Director  Joined: 01 May 2007
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If p is a positive integer, what is the value of p?  [#permalink]

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3
20 00:00

Difficulty:   15% (low)

Question Stats: 76% (01:22) correct 24% (01:10) wrong based on 476 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.

Originally posted by jimmyjamesdonkey on 23 Sep 2007, 11:46.
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.
Math Expert V
Joined: 02 Sep 2009
Posts: 56306
Re: If p is a positive integer, what is the value of p? 1) p/4  [#permalink]

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8
9
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.
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Manager  Joined: 29 Jul 2007
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C.

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

Statement II:insufficient
Numerous possibilities

Combined, P = 12
Director  Joined: 22 Aug 2007
Posts: 510
Re: DS: Value of P?  [#permalink]

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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.
GMAT Club Legend  Joined: 07 Jul 2004
Posts: 4513
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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
Intern  Joined: 08 Apr 2014
Posts: 2
Re: If p is a positive integer, what is the value of p? 1) p/4  [#permalink]

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1
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?
Director  Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
Re: If p is a positive integer, what is the value of p? 1) p/4  [#permalink]

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1
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
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Intern  Joined: 21 Sep 2014
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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

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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..
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Location: United States (OR)
Concentration: Finance, Marketing
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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Thanks for the nice explanation, I got this question as part of my GMAT Prep-1 test yesterday.
Intern  B
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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Bunuel wrote:
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.

When you combine them, shouldn't stmt 2 p/3=prime as well? so if 12/3=4...4 isn't prime
Math Expert V
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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rnz wrote:
Bunuel wrote:
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.

When you combine them, shouldn't stmt 2 p/3=prime as well? so if 12/3=4...4 isn't prime

Why? p is divisible by 3 just means that p/3 = integer, not necessarily prime.
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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jimmyjamesdonkey wrote:
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.

Here is a simpler way to do this problem.

Satememnt (1) says p/4 is a prime number.
ok, p is 4 times a prime number.
hmm...
4 x 2 = 8
4 x 3 = 12
4 x 5 = 20
4 x 7 = 28
4 x 11 = 44
etc.
plenty of values. not sufficient.

Stament (2) says p is divisible by 3.
ok...
3
6
9
12
etc.
plenty of values. not sufficient.

--

together:
well, looking back at my first list, i see "4" times an ascending list of primes. in other words, i'm never going to see the number "3" again.
looks like it's 12.
sufficient.

Posted from my mobile device
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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jimmyjamesdonkey wrote:
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.

Either alone is of course not sufficient.

Combining we know people is 4 x 3 = 12

C for sure.
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Posts: 49
Re: If p is a positive integer, what is the value of p?  [#permalink]

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Statement 1. p/4 is a prime no. i.e. p = 4k where k is a prime no.
So, p could be anything like 8, 12, 20,………
Hence, Insufficient.
Statement 2. P = 3a
P could be any positive integer. Hence, Insufficient.
Statement 1 & 2 together.
P = 4k where k is a prime no and p = 3a
So, k = 3. Hence, P = 4 x 3 = 12.
Hence, Sufficient.
Intern  Joined: 26 Jan 2016
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Re: If p is a positive integer, what is the value of p?  [#permalink]

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(1) You can re-write the equation to make it simpler to test numbers: P = 4 * Prime Number
Try a few prime numbers: P = 4 * 3 = 12 (positive integer, works); P = 4 * 5 = 20 (positive integer, works)
One alone is insufficient
(2) List integers divisible by 3: 3, 6, 9, 12
Two alone is insufficient
(1) + (2) Same exercise as (1): P = 4 * 3 = 12 (divisible by three, works); P = 4 * 5 = 20 (not divisible by three, doesn't work)
I had a hard time with the logic here, so I had to prove it out:
4 clearly isn't divisible by 3, so whatever 4 is being multiplied by MUST be divisible by 3. 3 clearly is but anything above three CANNOT be because since it will be a prime number, it will only be divisible by 1 and itself.
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Re: If P is a positive integer, what is the value of P? 1. P/4  [#permalink]

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