Events & Promotions
|
|
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.
May 0608:30 AM PDT
-09:30 AM PDT
In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory....- May 08
08:00 AM PDT
-08:30 AM PDT
Join the special YouTube live-stream for selecting the winners of GMAT Club MBA Scholarships sponsored by Juno live. Watch who gets these coveted MBA scholarships offered by GMAT Club and Juno.
05 Feb 2021, 08:45
Kudos
Bookmarks
E
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:
63% (02:36) correct
37%
(02:38)
wrong
based on 116
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, is n^2 - n divisible by 12?
(1) n/11 is an integer
(2) n/19 is an integer
M36-82
(1) n/11 is an integer
(2) n/19 is an integer
M36-82
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
10 Nov 2021, 03:57
Kudos
Bookmarks
Bunuel
Official Solution:
If n is a positive integer, is \(n^2 - n\) divisible by 12?
(1) \(\frac{n}{11}\) is an integer
The above means that \(n\) is a multiple of 11.
If \(n=11\), then \(n^2 - n=n(n-1)=110=(not \ a \ multiple \ of \ 12);\)
If \(n=11*12\), then \(n^2 - n=(a \ multiple \ of \ 12) - (a \ multiple \ of \ 12)=(a \ multiple \ of \ 12).\)
Not sufficient.
(2) \(\frac{n}{19}\) is an integer
The above means that \(n\) is a multiple of 19.
If \(n=19\), then \(n^2 - n=n(n-1)=19*18=(not \ a \ multiple \ of \ 12);\)
If \(n=19*12\), then \(n^2 - n=(a \ multiple \ of \ 12) - (a \ multiple \ of \ 12)=(a \ multiple \ of \ 12).\)
Not sufficient.
(1)+(2) \(n\) is a multiple of both 11 and 19:
If \(n=11*19\), then \(n^2 - n=n(n-1)=11*19(11*19-1)=11*19*208=(not \ a \ multiple \ of \ 12);\)
If \(n=11*19*12\), then \(n^2 - n=(a \ multiple \ of \ 12) - (a \ multiple \ of \ 12)=(a \ multiple \ of \ 12).\)
Not sufficient.
Answer: E
General Discussion
05 Feb 2021, 10:46
Kudos
Bookmarks
Bunuel
\(n^2-n=n(n-1)\), that is product of two consecutive integers.
We are looking for whether n*(n-1) has factor as 12.
Both combined tells us that n is divisible by 11 or 19, but nothing much on 12. But we should still go into more details, if we have time in actuals.
1) n/11 is an integer
Say n is 11*12, then n(n-1) is divisible by 12.
But say n is 11, then n(n-1)=11*10. Not divisible by 12.
2) n/19 is an integer
Say n is 19*12, then n(n-1) is divisible by 12.
But say n is 19, then n(n-1)=19*18. Not divisible by 12.
Combined
Say n is 11*12*19, then n(n-1) is divisible by 12.
But say n is 11*19, then n(n-1)=11*19*(11*19-1)=11*19*208. Not divisible by 12.
E
