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A Wagstaff prime is a prime number p such that p =
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Updated on: 12 Aug 2014, 06:03
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48% (01:24) correct 52% (01:29) wrong based on 252 sessions
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A Wagstaff prime is a prime number p such that \(p=\frac{2^q + 1}{3}\), when q is another prime. If p and q are positive integers, is p a Wagstaff prime? (1) p = q (2) q = (3^0)*3 Attachment:
Screen Shot 20140806 at 4.49.38 PM.png [ 21.72 KiB  Viewed 2419 times ]
OA below: Solution: B
Start with the easier statement first. If p = q, p and q could be any integer, but to answer the question we must know if both p and q are prime; statement (1) is INSUFFICIENT, as two different values satisfy the equation: p = q = 1 (which is not prime) and p = q = 3 (which is prime). Simplify statement (2): 30=1, and 1∗3=3, so q = 3. Now plug it into the formula given. ((23)+1)3 = 93=3, so p = 3. This is prime, so statement (2) is SUFFICIENT on its own; (B).
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Originally posted by pratikshr on 06 Aug 2014, 04:02.
Last edited by Bunuel on 12 Aug 2014, 06:03, edited 2 times in total.
Edited the question



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 04:03
Can't understand the OA.
Can some expert untangle this problem?



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 04:10
I think the answer should be C. 2 queries:
1) How can we assume that the value of P in Statement (2) is (2^q + 1) ? Is it not possible that P can take on any value?
2) Are we not assuming what we seek to prove? The question states that P is a Wagstaff Prime... and then in the answer choice we need to prove the same thing!



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 09:13
pratikshr wrote: I think the answer should be C. 2 queries:
1) How can we assume that the value of P in Statement (2) is (2^q + 1) ? Is it not possible that P can take on any value?
2) Are we not assuming what we seek to prove? The question states that P is a Wagstaff Prime... and then in the answer choice we need to prove the same thing! Answer is B A) 3P = 2^P + 1, If P=1, then 3=3 so P is not prime ( 1 is not prime). If P=3, then 9=9 so P is prime. > A doesnt hold B) Q= 3^0*3, so Q=3....Equation is 3P = 2^3 + 1....So P = 3, which is prime > B holds



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 10:33
Why cant the answer be D?
How is statement (1) not sufficient?
Only for the value of 3 we get P=Q=3. So (1) is sufficient too.
P=Q=1 is another value that satisfies (1) but both P and Q have to be prime.
Please correct me if I am wrong.



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 10:37
P is Wagstaff prime when Q is prime
So we cannot take P=Q=1.
So statement (1) is sufficient.



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 18:09
varunmb wrote: P is Wagstaff prime when Q is prime
So we cannot take P=Q=1.
So statement (1) is sufficient. You seem to be correct. I missed that P & Q must be prime.



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Re: A Wagstaff prime is a prime number p such that p =
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06 Aug 2014, 18:23
I think it should be D.
For P=Q=3 the condition is satisfied
Also for the the second stem it is satisfied.
Hence D
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Re: A Wagstaff prime is a prime number p
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27 Aug 2014, 22:16
Solution: B Start with the easier statement first. If p = q, p and q could be any integer, but to answer the question we must know if both p and q are prime; statement (1) is INSUFFICIENT, as two different values satisfy the equation: p = q = 1 (which is not prime) and p = q = 3 (which is prime). Simplify statement (2): 30=1, and 1∗3=3, so q = 3. Now plug it into the formula given. ((23)+1)3 = 93=3, so p = 3. This is prime, so statement (2) is SUFFICIENT on its own; (B). See: awagstaffprimeisaprimenumberpsuchthatp175863.html



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Re: A Wagstaff prime is a prime number p such that p =
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03 Feb 2015, 06:17
P=q=1 is not possible as it says q is another prime , here q is not a prime. So p=q=3 is the only possible solution for statement 1, correct me if i am wrong.
hence shouldn't the answer be D ,Someone please provide convincing explanation for B or Change the OA



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Re: A Wagstaff prime is a prime number p such that p =
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04 Feb 2015, 06:39
D is the answer. It's clearly mentioned that P and q needs to be prime number. hence p=q=3 is the only possiblity



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Re: A Wagstaff prime is a prime number p such that p =
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04 Feb 2015, 12:29
Hi All, This DS question is oddlyworded, in that it describes a very specific set of conditions (the definition of a Wagstaff prime), but does NOT tell you that the variables involved are actually a part of that equation. Based on the prompt, there are 3 conditions that MUST be met for a Wagstaff prime to occur: 1) Q MUST be a prime number 2) The Wagstaff 'equation' must be used 3) The resulting value of P MUST be a prime number too. Consider the following possibilities: IF... Q = 3, then P = (2^3 + 1)/3 = 3, so YES, P IS a Wagstaff Prime IF... Q = 2, then P = (2^2 + 1)/3 = 5/3, so NO, P is NOT a Wagstaff Prime IF.... Q = 1, then no calculation is done, since Q is NOT a prime, so P is NOT a Wagstaff Prime (P can be ANY integer though, since it's not related to Q). We're told that P and Q are positive integers. The question asks if P is a Wagstaff prime. This is a YES/NO question. The answer depends ENTIRELY on the value of Q. Fact 1: P = Q Given the examples above, you can see 2 immediate possibilities: P = Q = 1 and the answer to the question is NO P = Q = 3 and the answer to the question is YES Fact 1 is INSUFFICIENT Fact 2: Q = (3^0)(3) This tells us that Q = 3. From the above example, we can see that P will = 3 when Q=3, so 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: A Wagstaff prime is a prime number p such that p =
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04 Feb 2015, 22:56
pratikshr wrote: A Wagstaff prime is a prime number p such that \(p=\frac{2^q + 1}{3}\), when q is another prime. If p and q are positive integers, is p a Wagstaff prime? (1) p = q (2) q = (3^0)*3 Attachment: Screen Shot 20140806 at 4.49.38 PM.png OA below: Solution: B
Start with the easier statement first. If p = q, p and q could be any integer, but to answer the question we must know if both p and q are prime; statement (1) is INSUFFICIENT, as two different values satisfy the equation: p = q = 1 (which is not prime) and p = q = 3 (which is prime). Simplify statement (2): 30=1, and 1∗3=3, so q = 3. Now plug it into the formula given. ((23)+1)3 = 93=3, so p = 3. This is prime, so statement (2) is SUFFICIENT on its own; (B). When a prime number p satisfies this condition: \(p=\frac{2^q + 1}{3}\) where q is also prime, p is called a Wagstaff prime. You are also given that p and q are positive integers. If p a Wagstaff prime? This will depend on q. If p satisfies \(p=\frac{2^q + 1}{3}\) and q is a prime number in this expression, then p is a Wagstaff prime. (1) p = q This just tells you that q = p. You know that p and q are positive integers. So if q is a prime number, p will be Wagstaff prime. If q = 1, p = 1 (p and q are not prime) . If q = 3, p = 3 (p and q both are prime) So in one case, p is a Wagstaff prime, in another it is not. (2) q = (3^0)*3 q = 3. In this case p = 3 is a Wagstaff prime. Sufficient alone. Answer (B)
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Re: A Wagstaff prime is a prime number p such that p =
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06 Feb 2015, 04:47
VeritasPrepKarishma wrote: pratikshr wrote: A Wagstaff prime is a prime number p such that \(p=\frac{2^q + 1}{3}\), when q is another prime. If p and q are positive integers, is p a Wagstaff prime? (1) p = q (2) q = (3^0)*3 Attachment: Screen Shot 20140806 at 4.49.38 PM.png OA below: Solution: B
Start with the easier statement first. If p = q, p and q could be any integer, but to answer the question we must know if both p and q are prime; statement (1) is INSUFFICIENT, as two different values satisfy the equation: p = q = 1 (which is not prime) and p = q = 3 (which is prime). Simplify statement (2): 30=1, and 1∗3=3, so q = 3. Now plug it into the formula given. ((23)+1)3 = 93=3, so p = 3. This is prime, so statement (2) is SUFFICIENT on its own; (B). When a prime number p satisfies this condition: \(p=\frac{2^q + 1}{3}\) where q is also prime, p is called a Wagstaff prime. You are also given that p and q are positive integers. If p a Wagstaff prime? This will depend on q. If p satisfies \(p=\frac{2^q + 1}{3}\) and q is a prime number in this expression, then p is a Wagstaff prime. (1) p = q This just tells you that q = p. You know that p and q are positive integers. So if q is a prime number, p will be Wagstaff prime. If q = 1, p = 1 (p and q are not prime) . If q = 3, p = 3 (p and q both are prime) So in one case, p is a Wagstaff prime, in another it is not. (2) q = (3^0)*3 q = 3. In this case p = 3 is a Wagstaff prime. Sufficient alone. Answer (B) Thanks for clearing that, misunderstood the question.



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Re: A Wagstaff prime is a prime number p such that p =
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14 Jan 2016, 22:06
I picked B, but my concern is that:
p=(2^q+1)/3, when q is another prime some guys are selecting 1 but q is not a prime, thus it initially doesn't satisfy the condition. we must start with a q prime to get to a p prime... very confusing question...



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Re: A Wagstaff prime is a prime number p such that p =
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14 Jan 2016, 22:20
mvictor wrote: I picked B, but my concern is that:
p=(2^q+1)/3, when q is another prime some guys are selecting 1 but q is not a prime, thus it initially doesn't satisfy the condition. we must start with a q prime to get to a p prime... very confusing question... "A Wagstaff prime is a prime number p such that p=2^q+13, when q is another prime."  this is the definition of a Wagstaff prime. It doesn't tell us that variable p is a prime number. It just tells us that if q is prime and 2^q+13 is prime, it is equal to p and called a Wagstaff prime. "If p and q are positive integers,"  this is the given data about variables p and q. There are both positive integers. We don't know whether they are prime or not. They can take any positive integer value. "is p a Wagstaff prime?"  this is the question asked. Hence, q = 1 and p =1 are perfectly valid values.
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Re: A Wagstaff prime is a prime number p such that p =
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14 Jan 2016, 22:27
mvictor wrote: I picked B, but my concern is that:
p=(2^q+1)/3, when q is another prime some guys are selecting 1 but q is not a prime, thus it initially doesn't satisfy the condition. we must start with a q prime to get to a p prime... very confusing question... hi, the Q says "A Wagstaff prime is a prime number p such that p=((2^q)+1)/3, when q is another prime."... this means that if the conditions are met, that is, p and q are prime and p=((2^q)+1)/3, then p is a Wagstaff prime. This does not mean that other numbers cannot satisfy this condition or any one satisfying the condition has to be prime.. I think your query meant this only
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Re: A Wagstaff prime is a prime number p such that p =
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07 Sep 2017, 14:54
pratikshr wrote: A Wagstaff prime is a prime number p such that \(p=\frac{2^q + 1}{3}\), when q is another prime. If p and q are positive integers, is p a Wagstaff prime? (1) p = q (2) q = (3^0)*3 Attachment: Screen Shot 20140806 at 4.49.38 PM.png OA below: Solution: B
Start with the easier statement first. If p = q, p and q could be any integer, but to answer the question we must know if both p and q are prime; statement (1) is INSUFFICIENT, as two different values satisfy the equation: p = q = 1 (which is not prime) and p = q = 3 (which is prime). Simplify statement (2): 30=1, and 1∗3=3, so q = 3. Now plug it into the formula given. ((23)+1)3 = 93=3, so p = 3. This is prime, so statement (2) is SUFFICIENT on its own; (B). This last clause "when q is another prime" limits q to a prime number. Thus the answer is D. If q does not need to be prime, then the question should not state "when q is another prime". Bad question. Open to interpretation.
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