GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 14 Aug 2018, 20:09

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 05 Nov 2013
Posts: 24
A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post Updated on: 12 Aug 2014, 06:03
2
5
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

48% (01:24) correct 52% (01:29) wrong based on 252 sessions

HideShow timer Statistics

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
Screen Shot 2014-08-06 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).

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
Intern
Intern
avatar
Joined: 05 Nov 2013
Posts: 24
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 06 Aug 2014, 04:03
Can't understand the OA.

Can some expert untangle this problem?
Intern
Intern
avatar
Joined: 05 Nov 2013
Posts: 24
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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!
Intern
Intern
avatar
Joined: 31 Jul 2014
Posts: 20
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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
Intern
Intern
avatar
Joined: 07 Mar 2013
Posts: 10
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 610 Q45 V29
GMAT 2: 690 Q49 V34
GMAT 3: 710 Q49 V38
Reviews Badge
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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.
Intern
Intern
avatar
Joined: 07 Mar 2013
Posts: 10
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 610 Q45 V29
GMAT 2: 690 Q49 V34
GMAT 3: 710 Q49 V38
Reviews Badge
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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.
Intern
Intern
avatar
Joined: 31 Jul 2014
Posts: 20
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 06 Aug 2014, 18:09
2
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.
Manager
Manager
avatar
Joined: 28 Apr 2014
Posts: 242
GMAT ToolKit User
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 06 Aug 2014, 18:23
1
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

Posted from my mobile device
Intern
Intern
avatar
Joined: 27 Aug 2014
Posts: 27
GMAT Date: 09-27-2014
GMAT ToolKit User
Re: A Wagstaff prime is a prime number p  [#permalink]

Show Tags

New post 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
Manager
Manager
avatar
Joined: 17 Mar 2014
Posts: 68
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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
Intern
Intern
avatar
Joined: 08 Jan 2015
Posts: 13
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12175
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 04 Feb 2015, 12:29
1
1
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.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 04 Feb 2015, 22:56
1
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:
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)
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Manager
Manager
avatar
Joined: 17 Mar 2014
Posts: 68
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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:
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.
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2717
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Premium Member Reviews Badge
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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...
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8184
Location: Pune, India
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 14 Jan 2016, 22:20
1
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.
_________________

Karishma
Veritas Prep GMAT Instructor

Save up to $1,000 on GMAT prep through 8/20! Learn more here >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6514
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Manager
Manager
User avatar
B
Status: GMAT Coach
Joined: 05 Nov 2012
Posts: 128
Location: Peru
GPA: 3.98
Re: A Wagstaff prime is a prime number p such that p =  [#permalink]

Show Tags

New post 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:
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.
_________________

Clipper Ledgard
GMAT Coach

Re: A Wagstaff prime is a prime number p such that p = &nbs [#permalink] 07 Sep 2017, 14:54
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.