is p a Wagstaff prime

[himu]

A Wagstaff prime is a prime number p such that
p=((2^q)+1)/3
, when q is another prime. If p and q are positive integers, is p a Wagstaff prime?


p=q
q=(3^0)*3

[aditya8062]

ur second statement is not clear !!

[aditya8062]

my take wud be D plz confirm the OA so as i may put the solution

[srcc25anu]

p and q are prime numbers > 0

1. p = q
p = (2^p +1) / 3

if we take p = q = 2,
2 = 5/3 (NOT TRUE)
if we take p = q = 3,
3 = 9/3 = 3 (TRUE)

Hence Not sufficient

2. q = 30*3 or 2 * 3^2 * 5

p = 2^90 + 1 / 3

for any p say 2, right hand side of the euation will be a very very big number such that even its division by 3 would never make it equal to p

2 = 2^90 + 1 / 3 ( a very huge number)

this will be true for any number.

hence p is NOT a WAGSTAFF PRIME
I would say B is sufficient

Answer would be B for me.

[himu]

[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. 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).[/spoiler]

[himu]

my ans was D:

1.since P & Q both are prime(given)...the only was p=q is that p=q=3.No other condition makes p=q which is given in statement 1..Hence sufficient.

But IT SEEMS THAT its ONLY given that Q is prime.HENCE THIS IS ACTUALLY INSUFFICIENT.

2.AS far as statement 2 goes,
q=(3^0)*3

means q=3, thus making p Wagstaff prime.

Hence B.

[aditya8062]

what is the source of this question

[himu]

All these are from Veritas Aditya.

[aditya8062]

well i really dont thing that answer of this is B .it has to be D .plz note that while following ST 1 we have to follow the basic equation given in the question .doing so will give us just one value of P and Q ,which is 3 .

we cannot take any random value of P being equal to Q and which is not satisfying the basic equation
yes if there does exist some other non prime for which P = Q and the basic eq also hold true then the answer can be B

[megamutter]

well i really dont thing that answer of this is B .it has to be D .plz note that while following ST 1 we have to follow the basic equation given in the question .doing so will give us just one value of P and Q ,which is 3 .

we cannot take any random value of P being equal to Q and which is not satisfying the basic equation
yes if there does exist some other non prime for which P = Q and the basic eq also hold true then the answer can be B

I have to disagree with you.
The basic goal of data sufficiancy is wether you can tell if a mathematical question can be answered with the constrains you have mentioned in the question.

The main question is: is p a Wgstaff prime. And in mathematical terms: Does p=((2^q)+1)/3 hold.

The first constraint is in the question stem: p and q are both positive and both integers.
And in A you also know that p and q are the same number. According to the Manhattan system you are looking for values where the question cant be answered for sure.

Now lets try to find cases that fit the constrains but result in different answers:

1) p=q=2 leads to the equation 2=5/3
so p is not a Wgstaff prime

2) p=q=3 leads to the equation 3=3
so is a Wgstaff prime

So A is insufficient

That B is sufficient is proven above.

The answer is: B