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If p is positive, is p prime? [#permalink]
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13 Dec 2016, 11:13
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Re: If p is positive, is p prime? [#permalink]
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13 Dec 2016, 11:23
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Here's is my solution to this one >
Given data > p>0 We are not told if p is an integer or not.
The question is asking us whether p is prime or not
Statement 1=> p^3 has 4 factors p=3 => yes,p is prime p=(15)^1/3=> p^3=15=> 4 factors => No,p is not prime
Hence not sufficient
Statement 2=> Here solving the equation => p^2 – p – 6 = 0. p= 1+5/2 => 3,2 as p>0 => p must be 3 So,p is prime Hence sufficient
Hence B
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Re: If p is positive, is p prime? [#permalink]
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17 Oct 2017, 02:28
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OK I got this question wrong (I answered B but the OA is D) but I am not far of from grasping this whole integer properties bit. Can someone please clarify:
Statement 2: p^3 has exactly 4 distinct factors
What exactly does this statement mean? What should I be thinking of here? The "4 distinct factors" is not clear to me.
Please please and thank you.



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Re: If p is positive, is p prime? [#permalink]
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24 Oct 2017, 12:46
I get that B is suff. But A? even if P weren't prime say (12)^3 = P^3 = 12 is not prime. On the other hand, (2)^3 says P is prime. So a prime cubed and non prime cubed both will have 4 distinct factors (say 2 cubed has 4,8,2,1). Can someone explain why is A sufficient?



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Re: If p is positive, is p prime? [#permalink]
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01 Nov 2017, 22:12
Answer is D.
For statement 1 p^3 has exactly 4 distinct factors: 1,p,p^2,p^3. Hence prime, therefore sufficient.
For statement 2 when you factorize the equation you get x=2,3. Both are prime, therefore sufficient.



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Re: If p is positive, is p prime? [#permalink]
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05 Nov 2017, 12:56
ToraTora wrote: Answer is D.
For statement 1 p^3 has exactly 4 distinct factors: 1,p,p^2,p^3. Hence prime, therefore sufficient.
For statement 2 when you factorize the equation you get x=2,3. Both are prime, therefore sufficient. For statement 2, you get x = 2, 3. sarahfiqbal wrote: OK I got this question wrong (I answered B but the OA is D) but I am not far of from grasping this whole integer properties bit. Can someone please clarify:
Statement 2: p^3 has exactly 4 distinct factors
What exactly does this statement mean? What should I be thinking of here? The "4 distinct factors" is not clear to me.
Please please and thank you. All "distinct factors" means all the positive, integer factors of a number counted only once. Distinct factors of 125 are 1, 5, 25, and 125. Madhavi1990 wrote: I get that B is suff. But A? even if P weren't prime say (12)^3 = P^3 = 12 is not prime. On the other hand, (2)^3 says P is prime. So a prime cubed and non prime cubed both will have 4 distinct factors (say 2 cubed has 4,8,2,1). Can someone explain why is A sufficient? Look below.
Last edited by BlueOwl on 05 Nov 2017, 13:12, edited 2 times in total.



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Re: If p is positive, is p prime? [#permalink]
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05 Nov 2017, 13:06
Bunuel wrote: If p is positive, is p prime? (1) p^3 has exactly 4 distinct factors (2) p^2 – p – 6 = 0. Let's start with 2, as it's easier. 2) Factoring: \(p^2 – p – 6 = 0\) Results in: \((p+2)(p3) = 0\) Therefore: \(p = 2\) or \(+3\) Since P is positive, P = 3, 3 is prime. Sufficient1) The only time \(p ^ 3\) will have 4 distinct factors is if p is prime. We can test this: If \(p = 2, 2 ^ 3 = 8.\) The distinct (unique) factors of 8 are: 1, 2, 4, 8 If \(p = 3, 3 ^ 3 = 27.\) The distinct (unique) factors of 27 are: 1, 3, 9, 27 If \(p = 4, 4 ^ 3 = 64.\) The distinct (unique) factors of 64 are: 1, 2, 4, 8, 16, 32, 64 If \(p = 5, 5 ^ 3 = 125.\) The distinct (unique) factors of 125 are: 1, 5, 25, 125 If \(p = 6, 6 ^ 3 = 216.\) The distinct (unique) factors of 216 are: 1, 2, 3, 4, 6, 8, 9... and so on. 1 is also sufficient.The answer is D.



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Re: If p is positive, is p prime? [#permalink]
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21 Nov 2017, 16:03
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Bunuel wrote: If p is positive, is p prime? (1) p^3 has exactly 4 distinct factors (2) p^2 – p – 6 = 0. Hi All, We're told that P is POSITIVE. We're asked if P is PRIME. This is a YES/NO question. To start, it's worth noting that we do NOT know whether P is an integer or not (and if you assume that P must be an integer, then you'll get this question wrong). 1) P^3 has exactly 4 distinct factors. To start, let's focus on numbers that have just 4 distinct factors. There are two that you should be able to find relatively easily: 6 (factors are 1, 2, 3 and 6) 8 (factors are 1, 2, 4 and 8) According to Fact 1, P^3 could be either of those 2 numbers.... IF.... P^3 = 6, then P is a NONINTEGER and the answer to the question is NO P^3 = 8, then P = 2 and the answer to the question is YES. Fact 1 is INSUFFICIENT 2) P^2  P  6 = 0 We can factor this equation into it's pieces and solve... P^2  P  6 = 0 (P3)(P+2) = 0 P = +3 or 2 The prompt tells us that P is POSITIVE, so there's only one solution here: +3... and the answer to the question is ALWAYS YES. Fact 2 is SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If p is positive, is p prime? [#permalink]
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24 Nov 2017, 13:50
Answer should be B.
The catch is p is positive, but need not be an integer
Statement 1 : \(p^3\) has 4 distinct factors if \(p\) is prime, then \(p^3\) has 4 distinct factors BUT if \(p = x^{1/3} * y ^ {1/3}\), where x and y are prime numbers, then \(p^3 = (x^{1/3} * y ^ {1/3})^3 = xy\) still has 4 distinct factors, in this case p is not prime.
Not Suff
Statement 2: from quad eqn we can p = 2 or 3, since p is positive, p = 3, prime > Suff
Answer (B)




Re: If p is positive, is p prime?
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24 Nov 2017, 13:50






