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 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 07
10:00 AM PDT
-11:00 AM PDT
A complete walkthrough of GMAT Club’s free 12-week GMAT study plan: what you study each week, how progress and goals are tracked, how the error log works, and how your practice unlocks paid tools at no cost. - 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 09
10:00 AM PDT
-11:00 AM PDT
Three MBA applications. Three rejections. No interview invites. A year later, Aman was admitted to Cambridge Judge, SMU, and IMD. In this episode of MBA Admit Stories, Aman shares how he rebuilt his MBA application... 
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
07 Jul 2026, 07:19
Kudos
Bookmarks
n^2 - 8 = 33*integer + remainder
Three cases:
n^2 - 8 = 33*integer + 0 -> n^2 = 33*integer + 8 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 8/3 is 2)
n^2 - 8 = 33*integer + 15 -> n^2 = 33*integer + 23 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 23/3 is 2)
n^2 - 8 = 33*integer + 21 -> n^2 = 33*integer + 29 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 29/3 is 2)
Testing possible values of the remainder of n^2 divided by 3:
n=3k -> remainder is 0
n=3k+1 -> n^2=9k^2+6k+1 -> remainder is 1
n=3k+2 -> n^2=9k^2+12k+4 -> remainder is 1
It is impossible that the remainder of n^2 divided by 3 is 2.
The answer is E
Three cases:
n^2 - 8 = 33*integer + 0 -> n^2 = 33*integer + 8 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 8/3 is 2)
n^2 - 8 = 33*integer + 15 -> n^2 = 33*integer + 23 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 23/3 is 2)
n^2 - 8 = 33*integer + 21 -> n^2 = 33*integer + 29 -> if such a n^2 exits, divided by 3 the remainder must be 2 (remainder of 29/3 is 2)
Testing possible values of the remainder of n^2 divided by 3:
n=3k -> remainder is 0
n=3k+1 -> n^2=9k^2+6k+1 -> remainder is 1
n=3k+2 -> n^2=9k^2+12k+4 -> remainder is 1
It is impossible that the remainder of n^2 divided by 3 is 2.
The answer is E
07 Jul 2026, 07:23
Kudos
Bookmarks
Tried using values for n a few, I know this is not a reliable method. But worked for me in this case.
07 Jul 2026, 07:36
Kudos
Bookmarks
We are to divide n^2 - 8 by 33 and find the possible remainder which could be between 0,15 and 21
Lets keep the remainder as r
=>n^2 - 8 = 33k + r where k is some integer
=> n^2 = 33k + (r + 8)
1 -> Check for remainder 0
n^2 = 33k + 8
=> We divide both sides by 3, since 33 is a multiple of 3, we can start of by checking with 3
=> 33k + 8 upon division by 3 would leave a remainder of 2
=> n^2 would also have to leave a remainder of 2
Now we know that, among the possibilities an integer here should be a multiple of 3, or 1 more than a multiple of 3 or 1 less than a multiple of 3
=> Their squares are
(3m)^2 = 9m^2 which leaves remainder of 0
(3m+1)^2 = 9m^2 + 6m + 1 which leaves a remainder of 1
(3m+2)^2 = 9m^2 + 12m + 4 which also leaves a remainder of 1
=> Perfect square only has 0 or 1 as remainder when divided by 3
=> 0 cant be remainder
2-> Remainder = 15
n^2 = 33k + 23
Upon dividing by 3 similarly as above,
We see 23 leaves remainder 2 upon division by 3
=> n^2 would also need remainder 2
We will again see the same thing occur
=> Remainder 15 is not possible
3-> Remainder = 21
n^2 = 33k +29
We see 29 leaves remainder 2 upon division by 3
=> n^2 would also need to leave remainder 2
Therefore we see the same thing as above
=> Remainder 21 is not possible
=> E. None of these
Lets keep the remainder as r
=>n^2 - 8 = 33k + r where k is some integer
=> n^2 = 33k + (r + 8)
1 -> Check for remainder 0
n^2 = 33k + 8
=> We divide both sides by 3, since 33 is a multiple of 3, we can start of by checking with 3
=> 33k + 8 upon division by 3 would leave a remainder of 2
=> n^2 would also have to leave a remainder of 2
Now we know that, among the possibilities an integer here should be a multiple of 3, or 1 more than a multiple of 3 or 1 less than a multiple of 3
=> Their squares are
(3m)^2 = 9m^2 which leaves remainder of 0
(3m+1)^2 = 9m^2 + 6m + 1 which leaves a remainder of 1
(3m+2)^2 = 9m^2 + 12m + 4 which also leaves a remainder of 1
=> Perfect square only has 0 or 1 as remainder when divided by 3
=> 0 cant be remainder
2-> Remainder = 15
n^2 = 33k + 23
Upon dividing by 3 similarly as above,
We see 23 leaves remainder 2 upon division by 3
=> n^2 would also need remainder 2
We will again see the same thing occur
=> Remainder 15 is not possible
3-> Remainder = 21
n^2 = 33k +29
We see 29 leaves remainder 2 upon division by 3
=> n^2 would also need to leave remainder 2
Therefore we see the same thing as above
=> Remainder 21 is not possible
=> E. None of these
