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If p is a positive integer, what is the value of p?
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Updated on: 09 Apr 2014, 01:17
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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.
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Originally posted by jimmyjamesdonkey on 23 Sep 2007, 11:46.
Last edited by Bunuel on 09 Apr 2014, 01:17, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




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Re: If p is a positive integer, what is the value of p? 1) p/4
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09 Apr 2014, 01:27
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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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?
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23 Sep 2007, 15:59
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
2ndinsuff, 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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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
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08 Apr 2014, 13:48
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
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09 Apr 2014, 03:12
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?
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28 Sep 2014, 14:28
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?
Thanks, snatch



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Re: If p is a positive integer, what is the value of p?
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28 Sep 2014, 23:46
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..
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Re: If p is a positive integer, what is the value of p?
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10 Aug 2015, 19:36
Thanks for the nice explanation, I got this question as part of my GMAT Prep1 test yesterday.



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Re: If p is a positive integer, what is the value of p?
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13 Jan 2018, 16:21
Bunuel wrote: 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. When you combine them, shouldn't stmt 2 p/3=prime as well? so if 12/3=4...4 isn't prime



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Re: If p is a positive integer, what is the value of p?
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13 Jan 2018, 16:24
rnz wrote: Bunuel wrote: 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. When you combine them, shouldn't stmt 2 p/3=prime as well? so if 12/3=4...4 isn't prime Why? p is divisible by 3 just means that p/3 = integer, not necessarily prime.
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Re: If p is a positive integer, what is the value of p?
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30 Oct 2018, 11:48
jimmyjamesdonkey wrote: 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. 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
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Re: If p is a positive integer, what is the value of p?
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30 Oct 2018, 13:07
jimmyjamesdonkey wrote: 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. Either alone is of course not sufficient. Combining we know people is 4 x 3 = 12 C for sure.



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Re: If p is a positive integer, what is the value of p?
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21 Dec 2018, 21:59
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.



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Re: If p is a positive integer, what is the value of p?
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22 Jan 2019, 16:52
(1) You can rewrite 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.



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Re: If P is a positive integer, what is the value of P? 1. P/4
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Re: If P is a positive integer, what is the value of P? 1. P/4
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