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.
Sep 0201:00 PM EDT
-11:59 PM EDT
Take 30% off all study plans with code COURSEWORK - Expires on Monday 9/7
Sep 0301:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Sep 0410:00 AM PDT
-11:00 AM PDT
What does test anxiety really look like on the GMAT? For many test takers, it does not look like a panic attack. Instead, it shows up as brain fog, rereading, negative comparisons, mental noise....
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sundays Sept. 6, 2026.- Sep 07
12:01 AM PDT
-11:59 PM PDT
On the 7th, GMAT Club Tests will be Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT 
Sep 0712:30 AM EDT
-01:30 AM EDT
Tejas studied hard but kept repeating the same mistakes. After 3 attempts at 645, a focused 4-week strategy helped him identify and fix what was holding him back—leading to a 695 with just 12–15 hours of study per week.- Sep 09
07:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway 
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2108:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
06 Jul 2026, 08:00
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
75% (02:16) correct
25%
(02:19)
wrong
based on 487
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer, which of the following could be the remainder when n^2 - 8 is divided by 33?
I. 0
II. 15
III. 21
A. I only
B. II only
C. III only
D. II and III only
E. None of these
I. 0
II. 15
III. 21
A. I only
B. II only
C. III only
D. II and III only
E. None of these
|
⚠️ Important: GMAT Club does not allow AI-generated posts. AI-generated solutions are not eligible for kudos, and users who post them may face moderation action, including a ban.
M46-31
06 Jul 2026, 09:00
Kudos
Bookmarks
GMAT Club Official Solution:
If n is a positive integer, which of the following could be the remainder when n^2 - 8 is divided by 33?
I. 0
II. 15
III. 21
A. I only
B. II only
C. III only
D. II and III only
E. None of these
Since 33 is divisible by 3, first check what remainder n^2 - 8 can leave when divided by 3.
When n is divided by 3, the remainder can be 0, 1, or 2.
• If n leaves a remainder of 0, then n^2 - 8 leaves a remainder of 1 when divided by 3.
• If n leaves a remainder of 1, then n^2 - 8 = (3k + 1)^2 - 8 = 9k^2 + 6k - 7 leaves a remainder of 2 when divided by 3.
• If n leaves a remainder of 2, then n^2 - 8 = (3k + 2)^2 - 8 = 9k^2 + 12k - 4 leaves a remainder of 2 when divided by 3.
So n^2 - 8 can leave only a remainder of 1 or 2 when divided by 3.
Thus, n^2 - 8 can never be divisible by 3.
But 0, 15, and 21 are all divisible by 3. So if the remainder were any of those, we'd get:
n^2 - 8 = 33q + r = {a multiple of 3} + {a multiple of 3} = {a multiple of 3}
And since n^2 - 8 cannot be a multiple of 3, the remainder cannot be any of 0, 15, and 21.
Answer: E.
If n is a positive integer, which of the following could be the remainder when n^2 - 8 is divided by 33?
I. 0
II. 15
III. 21
A. I only
B. II only
C. III only
D. II and III only
E. None of these
Since 33 is divisible by 3, first check what remainder n^2 - 8 can leave when divided by 3.
When n is divided by 3, the remainder can be 0, 1, or 2.
• If n leaves a remainder of 0, then n^2 - 8 leaves a remainder of 1 when divided by 3.
• If n leaves a remainder of 1, then n^2 - 8 = (3k + 1)^2 - 8 = 9k^2 + 6k - 7 leaves a remainder of 2 when divided by 3.
• If n leaves a remainder of 2, then n^2 - 8 = (3k + 2)^2 - 8 = 9k^2 + 12k - 4 leaves a remainder of 2 when divided by 3.
So n^2 - 8 can leave only a remainder of 1 or 2 when divided by 3.
Thus, n^2 - 8 can never be divisible by 3.
But 0, 15, and 21 are all divisible by 3. So if the remainder were any of those, we'd get:
n^2 - 8 = 33q + r = {a multiple of 3} + {a multiple of 3} = {a multiple of 3}
And since n^2 - 8 cannot be a multiple of 3, the remainder cannot be any of 0, 15, and 21.
Answer: E.
General Discussion
ankushsambare
Joined: 13 Jun 2022
Last visit: 03 Sep 2026
Posts: 312
Given Kudos: 229
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
Products:
06 Jul 2026, 08:07
Kudos
Bookmarks
r be reminder when n^2 -8 by 33
then n^2 ~ r+ 8
check option which is giving perfect square when 8 is added.
I. r = 0
0+8 is not perfect square
II. r =15
15+8 not a prefect square
III. r =21
21+8 = 27 not a perfect square
So answer is E. I, II and III.
then n^2 ~ r+ 8
check option which is giving perfect square when 8 is added.
I. r = 0
0+8 is not perfect square
II. r =15
15+8 not a prefect square
III. r =21
21+8 = 27 not a perfect square
So answer is E. I, II and III.
