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:

Re: What is the units digit of 9^19 - 7^15? [#permalink]

Show Tags

31 Aug 2017, 18:18

alanforde800Maximus wrote:

What is the units digit of 9^19 - 7^15?

a) 2 b) 4 c) 5 d) 6 e) 7

For cycle questions such as these you simply use division to find the units digit

9 occurs in cycles of 2: 9,1 so you divide the exponent- 19/2 - whatever the remainder is will be the answer - so in this case the remainder is 1 so the units digit will be the first digit in the series "9." When there is no remainder, then the units digit is always the last number in the series. Always start with the number it self- so in a cycle of 7 start with 7 ,9 , 3 1 or in a cycle of 9 you go 9,1,9,1

The table above gives the cyclicity of any number. If needed, memorize this table for numbers 2,3,7,8 which have the cyclicity of 4.

However, if we need to derive the cyclicity for number 9 and 7 we can do so by this method

For this problem Units digit \(9^odd\) = 9 \(9^even\) = 1 \(7^1\) = 7 \(7^2\) = 9 \(7^3\) = 3 \(7^4\) = 1

From the above table, we can clearly say that \(9^19 - 7^15\). Since 9^19 has units digit 9 and 7^15 has units digit 3, we will have units digit for the expression as 9-3(6)(Option D) _________________