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

It is currently 16 Oct 2019, 04:58

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

Is the prime number q equal to 29 ?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
Is the prime number q equal to 29 ?  [#permalink]

Show Tags

New post 25 Dec 2017, 05:42
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (02:16) correct 60% (02:19) wrong based on 92 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58390
Re: Is the prime number q equal to 29 ?  [#permalink]

Show Tags

New post 25 Dec 2017, 05:44
Bunuel wrote:
Is the prime number q equal to 29 ?

(1) q - 1 has exactly 6 positive factors.
(2) 2 and 3 are prime factors of q + 1


Similar questions to practice:
https://gmatclub.com/forum/is-the-prime ... 02096.html
https://gmatclub.com/forum/is-the-prime ... 74016.html
https://gmatclub.com/forum/is-the-two-d ... 28379.html
https://gmatclub.com/forum/is-the-prime ... 42249.html
https://gmatclub.com/forum/is-the-two-d ... 23951.html
_________________
Retired Moderator
User avatar
P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 484
GMAT ToolKit User
Re: Is the prime number q equal to 29 ?  [#permalink]

Show Tags

New post 25 Dec 2017, 08:42
Bunuel wrote:
Is the prime number q equal to 29 ?

(1) q - 1 has exactly 6 positive factors.
(2) 2 and 3 are prime factors of q + 1


i. Prime Numbers q with exactly 6 factors of q-1 are: 29, 53, 149, 173, …. Not sufficient
ii. Prime Numbers q with factors 2 and 3 in q+1 are: 5, 11, 23, 29, 47, 53, 59, ….. Not sufficient

i+ii: 29, 53, … Not sufficient

E
_________________
Hasan Mahmud
Manager
Manager
User avatar
G
Joined: 31 Jan 2019
Posts: 167
Location: Switzerland
Concentration: General Management
GPA: 3.9
Re: Is the prime number q equal to 29 ?  [#permalink]

Show Tags

New post 02 Sep 2019, 12:27
Hi everyone,

Is the prime number q equal to 29 ?

(1) q - 1 has exactly 6 positive factors.
This is valid for both 29 and 53. Hence insufficient

(2) 2 and 3 are prime factors of q + 1
This is both valid for 29 and 23. Hence insufficient

Taken together the statements are valid for 29 and 53.

Hence E
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is the prime number q equal to 29 ?  [#permalink]

Show Tags

New post 02 Sep 2019, 19:16
Bunuel wrote:
Is the prime number q equal to 29 ?

(1) q - 1 has exactly 6 positive factors.
(2) 2 and 3 are prime factors of q + 1


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we have 1 variable (\(q\)) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.

Condition 1)
We have \(q - 1 = a^5\) or \(q - 1 =a^2 \cdot b^3\) for prime numbers \(a\) and \(b\).
If \(q - 1 = 2^2 \cdot 7^1\), then we have \(q = 29\) and the answer is 'yes'.
If \(q - 1 = 2^2 \cdot 3^1\), then we have \(q = 13\) and the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)
Since \(2\) and \(3\) are prime factors of \(q+1\), \(q+1\) is a multiple of \(6\).
If \(q+1=30\), then we have \(q=29\) and the answer is 'yes'.
If \(q+1=24\), then we have \(q=23\) and the answer is 'no'.
Since condition 2) does not yield a unique solution, it is not sufficient.

Conditions 1) & 2)
We have \(q - 1 = a^5\) or \(q - 1 =a^2 \cdot b^3\) for prime numbers \(a\) and \(b\).
Since \(2\) and \(3\) are prime factors of \(q+1\), \(q+1\) is a multiple of \(6\).
If \(q - 1 = 2^2 \cdot 7^1\), then \(q+1=30\) is a multiple of \(6\) and we have \(q=29\) and the answer is 'yes'.
If \(q - 1 = 2^2 \cdot 13^1\), then \(q+1=54\) is a multiple of \(6\) and we have \(q=53\) and the answer is 'no'.
Since condition 1) does not yield a unique solution, it is not sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
GMAT Club Bot
Re: Is the prime number q equal to 29 ?   [#permalink] 02 Sep 2019, 19:16
Display posts from previous: Sort by

Is the prime number q equal to 29 ?

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





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