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Re: DS: Value of P? [#permalink]
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.

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

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

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

“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.”

gmatclubot

Re: If p is a positive integer, what is the value of p? 1) p/4
[#permalink]
09 Apr 2014, 02:12