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Re: DS: Value of P? [#permalink]
23 Sep 2007, 14:59
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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.
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
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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.”
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