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

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.

Answer: C.

Hope it's clear.
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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.

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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From (1) p = 4*(prime number), so p can be ANY number of the form 4*(prime number). I just listed only four of the infinitely many other possibilities. Plug any prime there and you get another possible value of p.

When we consider the statements together, we know that p = 4*(prime number) and that p is divisible by 3. 4 is not divisible by 3, so that prime of p must be divisible by 3. The only prime which is divisible by 3 is 3 itself (I hope you understand why).
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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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When you combine them, shouldn't stmt 2 p/3=prime as well? so if 12/3=4...4 isn't prime

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

C.

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

Statement II:insufficient
Numerous possibilities

Combined, P = 12

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

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

Thanks for the nice explanation, I got this question as part of my GMAT Prep-1 test yesterday.

Why? p is divisible by 3 just means that p/3 = integer, not necessarily prime.
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Either alone is of course not sufficient.

Combining we know people is 4 x 3 = 12

C for sure.

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.

(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.

Given: If p is a positive integer
Asked: What is the value of p?

(1) p/4 is a prime number.
p = 4q where q is a prime number
Since prime number is not known
p = 4*2 =8, 4*3=12 .....
NOT SUFFICIENT

(2) p is divisible by 3.[/quote]
p=3k
Possible values of p = 3,6,9,12...
NOT SUFFICIENT

Combining (1) & (2)
(1) p/4 is a prime number.
p = 4q where q is a prime number
(2) p is divisible by 3.[/quote]
p=3k
p = 4 * 3 = 12
SUFFICIENT

IMO C

(1) p/4 = prime => p = 4*prime
=> we have tons of prime numbers, such as: 3, 5, 7, ... ==> insufficient

(2) p = 3k
=> we have tons onf "k", such as: 1, 2, 3,... ==> insufficient

(1) & (2): p = 4*prime = 3k => prime = 3, k = 4 =>p = 12 => sufficient

C

Bunuel
For the first statement, I was struggling to see if there were other possibilities above 7. I realize that you listed out some of the possibilities, but how did you know when to stop at 7, did you test a few more values past 7? I was thinking that 52/4=13 so that also works. But then, I saw the next constraint to find the exact value for statement 2.

Is there a rule that you applied though to know that any other possibility could not be divisible by 3 except for one number?