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

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If p is a positive integer, what is the value of p? [#permalink] New post 23 Sep 2007, 10:46
00:00
A
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C
D
E

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77% (01:49) correct 23% (00:51) wrong based on 93 sessions
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, 00:17, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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 [#permalink] New post 23 Sep 2007, 13:33
C.

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

Statement II:insufficient
Numerous possibilities

Combined, P = 12
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Re: DS: Value of P? [#permalink] New post 23 Sep 2007, 14:59
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.
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 [#permalink] New post 23 Sep 2007, 19:27
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
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Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink] New post 08 Apr 2014, 12:48
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?
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Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink] New post 09 Apr 2014, 00:27
Expert's post
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.

Answer: C.

Hope it's clear.
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Re: If p is a positive integer, what is the value of p? 1) p/4 [#permalink] New post 09 Apr 2014, 02:12
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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Re: If p is a positive integer, what is the value of p? 1) p/4   [#permalink] 09 Apr 2014, 02:12
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