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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

3

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.

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.”

Re: If p is a positive integer, what is the value of p? [#permalink]
28 Sep 2014, 13:28

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?

Re: If p is a positive integer, what is the value of p? [#permalink]
28 Sep 2014, 22:46

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.”

gmatclubot

Re: If p is a positive integer, what is the value of p?
[#permalink]
28 Sep 2014, 22:46