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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

we can eliminate d 21 which isnt a prime . 97 can be expreesed as 96 + 1
so 97^2 will leave a remainder of 1 so alll that remain are a,b, c . 7 leaves a remainder of 1 again so between 2 and 3 its 3

we can eliminate d 21 which isnt a prime . 97 can be expreesed as 96 + 1 so 97^2 will leave a remainder of 1 so alll that remain are a,b, c . 7 leaves a remainder of 1 again so between 2 and 3 its 3

we can eliminate d 21 which isnt a prime . 97 can be expreesed as 96 + 1 so 97^2 will leave a remainder of 1 so alll that remain are a,b, c . 7 leaves a remainder of 1 again so between 2 and 3 its 3

We have to find LARGEST Prime number that leaves remainder ~= 1

Start from
(E) : 97 is of the form (12n + 1 ) will always give remainder 1
(D) : 21 forget it Not Prime.
(C) : 7 -> 49 Remainder 1
(B) : 3 -> 9 Remainder 9
Thats it : (B) is the answer.

No need to look for (A) because even if that would be answer, 3 will always be greater than 2.

Assuming B is the final ans I will try to give a better explanation.

First off the question is about a prime number so 21 not being a prime is eliminated.

next 97 can be expressed as (96 + 1)^ 2 = 96^2 + 1 + 2*96*1
since (a + b)^2 = a^2 + b^2 + 2*a*b

so since 96 is divisible by 12 97^2/12 leaves a remainder of 1

7^2 / 12 = 49/12 leaves a remainder of 1 so the only 2 options left out are 2 and 3
2^2 / 12 leaves a remainder of 4 and
3^2/ 12 leaves a remainder of 9

but we are looking for the biggest prime number so its 3 between the 2 alternatives