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 0208:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
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.
Aug 2710:00 AM EDT
-11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Sep 0212:30 AM EDT
-01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
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 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, 08:52
Kudos
Bookmarks
We need to find the remainder could be 0 or 15 or 21 when (n^2 -8) is divided by 33.
ie. we need to see if (n^2-8) % 33 = 0 (% used as shorthand of remainder operator)
ie we need to see if n^2 -8 % 3 =0 (If it's divisible by 33 its divisible by 3)
ie we need to see if n^2 -2 %3 =0
ie we need to see if n^2 %3 =2 TRICK !!! But no square number leaves remainder 2 when divisible by 3. [to prove take n = 3k, 3k+1, 3k+2 and square them and see the remainder]
Lets check if n^2 -8 % 33 = 15 => n^2 -8 = 33k +15 => n^2 =33k +23 => n^2 =33k +21 +2 i.e. n^2 %3 = 2 [SAME TRICK!!!!! n^2 can't leave remainder 2 !!]
Lets check if n^2-8 % 33 = 21 => n^2 - 8 = 33k + 21 => n^2= 33k +29 = n^2 = 33k + 27 +2 ie n^2 %3 =2 [SAME TRICK !!!! n^2 can't leave remainder 2 for any n !!!]
Hence, (E) none of the options could be a remainder because if it were, n^2 would leave a remainder 2 when divided by 3 !
ie. we need to see if (n^2-8) % 33 = 0 (% used as shorthand of remainder operator)
ie we need to see if n^2 -8 % 3 =0 (If it's divisible by 33 its divisible by 3)
ie we need to see if n^2 -2 %3 =0
ie we need to see if n^2 %3 =2 TRICK !!! But no square number leaves remainder 2 when divisible by 3. [to prove take n = 3k, 3k+1, 3k+2 and square them and see the remainder]
Lets check if n^2 -8 % 33 = 15 => n^2 -8 = 33k +15 => n^2 =33k +23 => n^2 =33k +21 +2 i.e. n^2 %3 = 2 [SAME TRICK!!!!! n^2 can't leave remainder 2 !!]
Lets check if n^2-8 % 33 = 21 => n^2 - 8 = 33k + 21 => n^2= 33k +29 = n^2 = 33k + 27 +2 ie n^2 %3 =2 [SAME TRICK !!!! n^2 can't leave remainder 2 for any n !!!]
Hence, (E) none of the options could be a remainder because if it were, n^2 would leave a remainder 2 when divided by 3 !
06 Jul 2026, 08:53
Kudos
Bookmarks
My logic to this was that if I simplify n^2-8 it gives me (n+2*sqrt2)(n-2*sqrt2). Since both the numbers have a component of 2*sqrt2 added/subtracted, it is highly unlikely that upon division the numbers would give any remainder which might be a whole number. I know I am going wrong somewhere, but I dont know of a better way to do this
06 Jul 2026, 08:54
Kudos
Bookmarks
Bunuel
We need to find what the possible remainders must be when n2 - 8 is divided by 33.
Let's say the remainder is R, so n2 - 8 will have remainder R (mod 33).
Now we can break 33 as 3*11, right?
=> n^2 - 8 --> R (mod 3)
=> n^2 - 2 --> R (mod 3)
=> n^2 -> R+2 (mod 3) ------------------(1)
similarly,
=> n^2 - 8 --> R (mod 11)
=> n^2 --> R+8 (mod 11) -------------------(2)
Now we check all options:
I. R = 0 ❌ incorrect
put R=0
n^2 --> 0+2 --> 2 (mod 3).
the perfect square modulo 3 can only be 0^2-->0, 1^2-->1, 2^2-->1
it has no integer solution, so R = 0, can't be the remainder
II. R = 15 ❌ incorrect
put R = 15
n^2 --> 15+2 = 17 --> 2 (mod 3)
again the same situation as above, so no solution.
III. R = 21 ❌ incorrect
put R = 21
n^2 --> 21+2 = 23 --> 2 (mod 3)
againn!! no solution
THEREFORE -> option E: None of These
