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# A Wagstaff prime is a prime number p such that p =

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A Wagstaff prime is a prime number p such that p = [#permalink]

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06 Aug 2014, 04:02
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Question Stats:

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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 2014-08-06 at 4.49.38 PM.png [ 21.72 KiB | Viewed 2263 times ]

OA below:
[Reveal] Spoiler:
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).
[Reveal] Spoiler: OA

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 = [#permalink]

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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 = [#permalink]

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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 = [#permalink]

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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!

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 = [#permalink]

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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 = [#permalink]

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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 = [#permalink]

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06 Aug 2014, 18:09
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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 = [#permalink]

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06 Aug 2014, 18:23
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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 [#permalink]

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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:
a-wagstaff-prime-is-a-prime-number-p-such-that-p-175863.html

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Re: A Wagstaff prime is a prime number p such that p = [#permalink]

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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 = [#permalink]

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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 = [#permalink]

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04 Feb 2015, 12:29
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Hi All,

This DS question is oddly-worded, 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.

[Reveal] Spoiler:
B

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Re: A Wagstaff prime is a prime number p such that p = [#permalink]

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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 2014-08-06 at 4.49.38 PM.png

OA below:
[Reveal] Spoiler:
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.

Thanks for clearing that, misunderstood the question.

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Re: A Wagstaff prime is a prime number p such that p = [#permalink]

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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 = [#permalink]

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14 Jan 2016, 22:20
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Expert's post
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 = [#permalink]

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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 = [#permalink]

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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 2014-08-06 at 4.49.38 PM.png

OA below:
[Reveal] Spoiler:
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".

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Re: A Wagstaff prime is a prime number p such that p =   [#permalink] 07 Sep 2017, 14:54
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