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 350,000 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:

Is the reason why we know that p=4t is enough because there are only 4 possible remainders when 2^p is divided by 10 (2, 4, 8, 6)? Therefore 4 times a number will always end up in the 4th spot? In other words, if (B) said p=3t then it would be insufficient because every multiple of 3t would result in a different remainder (until you cycled through all 4 possibilities).

Plugging in is good here too, because it only takes a couple options to realize the remainder is always the same.

the last digit of 2^p should be 2, 4, 8,or 6, so the remainder should be one of these.

are their any other remainder generalizations such as this? I would've had to of done n amt. of probs like this to finally realize that.

Not necessarily for remainders, but it is good to know that a pattern occurs for every units digit that is raised to the nth power.

There is a pattern created. It is good to learn some and know that there is a pattern for all.
pattern of units digit when a number is raised to ^n
2^n 2,4,8,6
3^n 3,9,7,1
4^n 4,6,4,6
5^n 5,5,5,5
...and so on....

knowing the patterns exist helps with remainder questions

Social entrepreneurs aren't running charities : ‘It’s easy to think about it in terms of charity: it’s not. They are sustainable, trading, revenue-generating businesses. The benefit of them...