|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
TheUltimateWinner
Joined: 23 Feb 2015
Last visit: 30 Apr 2026
Posts: 2,465
Own Kudos:
Given Kudos: 1,990
Concentration: Finance, Technology
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,465
Kudos:
2,462
28 May 2019, 10:26
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
36% (01:44) correct
64%
(01:48)
wrong
based on 11
sessions
History
Date
Time
Result
Not Attempted Yet
Is natural number p prime?
1) \(2^p\)-1 is prime
2) \(p^2\)-12 has has an odd number of factors
1) \(2^p\)-1 is prime
2) \(p^2\)-12 has has an odd number of factors
This Question is Locked Due to Poor Quality
Hi there,
The question you've reached has been archived due to not meeting our community quality standards. No more replies are possible here.
Looking for better-quality questions? Check out the 'Similar Questions' block below
for a list of similar but high-quality questions.
Want to join other relevant Problem Solving discussions? Visit our Data Sufficiency (DS) Forum
for the most recent and top-quality discussions.
Thank you for understanding, and happy exploring!
28 May 2019, 14:56
Kudos
Bookmarks
Statement 1 is sufficient, but I think it's too hard a question for the GMAT. If we have a number 2^n - 1, and n is not prime, then we can write n = ab, where a and b are integers greater than 1. Then we can factor 2^(ab) - 1, as follows:
2^(ab) - 1 = (2^a)^b - 1 = [(2^a)^(b - 1) + (2^a)^(b-2) + ... 2^a + 1] * (2^a - 1)
So this number will never be prime, and so Statement 1 can only be true if p is prime.
Statement 1 does not seem to be consistent with Statement 2; if p^2 - 12 has an odd number of factors, then p^2 - 12 is a perfect square, so p^2 - 12 and p^2 are both perfect squares. That means p^2 is 16, since 4 and 16 are the only squares 12 apart, but then p = 4, which contradicts Statement 1.
So each statement is sufficient alone, but they produce contradictory answers (and contradictory values of p), so the question is badly designed, and is too hard for the GMAT anyway.
2^(ab) - 1 = (2^a)^b - 1 = [(2^a)^(b - 1) + (2^a)^(b-2) + ... 2^a + 1] * (2^a - 1)
So this number will never be prime, and so Statement 1 can only be true if p is prime.
Statement 1 does not seem to be consistent with Statement 2; if p^2 - 12 has an odd number of factors, then p^2 - 12 is a perfect square, so p^2 - 12 and p^2 are both perfect squares. That means p^2 is 16, since 4 and 16 are the only squares 12 apart, but then p = 4, which contradicts Statement 1.
So each statement is sufficient alone, but they produce contradictory answers (and contradictory values of p), so the question is badly designed, and is too hard for the GMAT anyway.
This Question is Locked Due to Poor Quality
Hi there,
The question you've reached has been archived due to not meeting our community quality standards. No more replies are possible here.
Looking for better-quality questions? Check out the 'Similar Questions' block below
for a list of similar but high-quality questions.
Want to join other relevant Problem Solving discussions? Visit our Data Sufficiency (DS) Forum
for the most recent and top-quality discussions.
Thank you for understanding, and happy exploring!
Moderators:
