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If p is a positive integer, what is the value of p? [#permalink]
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23 Sep 2007, 11:46
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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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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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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]
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23 Sep 2007, 15:59
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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
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 [#permalink]
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08 Apr 2014, 13:48
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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]
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09 Apr 2014, 01:27
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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. 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]
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09 Apr 2014, 03:12
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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 #.
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? [#permalink]
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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? [#permalink]
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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? [#permalink]
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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? [#permalink]
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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? [#permalink]
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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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Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
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