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

It is currently 14 Dec 2018, 09:40

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
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Typical Day of a UCLA MBA Student - Recording of Webinar with UCLA Adcom and Student

     December 14, 2018

     December 14, 2018

     10:00 PM PST

     11:00 PM PST

    Carolyn and Brett - nicely explained what is the typical day of a UCLA student. I am posting below recording of the webinar for those who could't attend this session.
  • Free GMAT Strategy Webinar

     December 15, 2018

     December 15, 2018

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

If n is positive integer, is 21 a factor of n?

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If n is positive integer, is 21 a factor of n?  [#permalink]

Show Tags

New post 03 Jul 2018, 00:50
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

63% (00:59) correct 37% (01:48) wrong based on 47 sessions

HideShow timer Statistics

[GMAT math practice question]

If \(n\) is positive integer, is \(21\) a factor of \(n\)?

1) \(21\) is a factor of \(3n\)
2) \(21\) is a factor of \(n^2\)

_________________

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Senior Manager
Senior Manager
avatar
S
Joined: 04 Aug 2010
Posts: 310
Schools: Dartmouth College
Re: If n is positive integer, is 21 a factor of n?  [#permalink]

Show Tags

New post 03 Jul 2018, 03:03
MathRevolution wrote:
[GMAT math practice question]

If \(n\) is positive integer, is \(21\) a factor of \(n\)?

1) \(21\) is a factor of \(3n\)
2) \(21\) is a factor of \(n^2\)


Statement 1:
In other words, 3n is a multiple of 21:
3n = 21, 42, 63...
To get a list of options for n, divide every value above by 3:
n = 7, 14, 21...
If n=7, then the answer to the question stem is NO.
If n=21, then the answer to the question stem is YES.
INSUFFICIENT.

Statement 2:
Since n is a positive integer, n² must be a perfect square that is divisible by 21:
n² = 21², (2*21)², (3*21)²....
n² = 21², 42², 63²....
To get a list of options for n, take the square root of every value above:
n = 21, 42, 63...
In every case, n is divisible by 21, so the answer to the question stem is YES.
SUFFICIENT.


_________________

GMAT and GRE Tutor
Over 1800 followers
Click here to learn more
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If n is positive integer, is 21 a factor of n?  [#permalink]

Show Tags

New post 04 Jul 2018, 23:46
=>

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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
If \(n = 21\), then \(21\) is a factor of n and the answer is “yes”.
If \(n = 7\), then \(21\) is not a factor of n and the answer is “no”.
Since the solution is not unique, condition 1) is not sufficient.

Condition 2)
Since \(21 = 3*7\) is a factor of \(n^2\), each of \(3\) and \(7\) is a factor of \(n^2\).
If \(3\) is a factor of \(n^2\), then, since \(3\) is a prime number, \(3\) is a factor of \(n\).
If \(7\) is a factor of \(n^2\), then, since \(7\) is a prime number, \(7\) is a factor of \(n\).
Thus, \(21\) is a factor of \(n\).
Condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

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 $99 for 3 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: If n is positive integer, is 21 a factor of n? &nbs [#permalink] 04 Jul 2018, 23:46
Display posts from previous: Sort by

If n is positive integer, is 21 a factor of n?

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


Copyright

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®.