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:

What is the remainder, after division by 100, of 7^10 ?

(A) 1 (B) 7 (C) 43 (D) 49 (E) 70

The remainder when 7^10 is divided by 100 will be the last two digits of 7^10 (for example 123 divided by 100 yields the remainder of 23, 345 divided by 100 yields the remainder of 45).

\(7^{10}=(7^2)^5=49^5\) --> the units digit of 49^5 will be 9 (the units digit of 9^even is 1 and the units digit of 9^odd is 9).

So, we have that \(7^{10}=49^5\) has the units digit of 9, thus the units digit of the remainder must also be 9. Only answer D fits.

We have such a pattern 7 7*7=49 7*7*7=343 7*7*7*7=...1 7*7*7*7*7=7 So, the last number repeats every 5th time. 10/4 = 2, and remainder is 2. we choose 7*7 it means that 7*7*7*7*7*7*7*7*7*7=.......49 We divide by 100, it means .....,49 where 49 is a remainder.

this rule is general ? like if XXXXXX9^even the unit digit of the remainder is always 1 and XXXXX9^odd the unit digit of the remainder is always 9 ??

Thanks for your help

The units digit of 9^even is 1 and the units digit of 9^odd is 9.

If the units digit of a number is 1, then the remainder when this number will be divided by 100 will have the units digit of 1, for example 231 divided by 100 gives the reminder of 31.

If the units digit of a number is 9, then the remainder when this number will be divided by 100 will have the units digit of 9, for example 239 divided by 100 gives the reminder of 39.
_________________

What is the remainder, after division by 100, of \(7^{10}\) ?

1 7 43 49 70

PLZ EXPLAIN THE TRICK IN SOLVING THIS TYPE REMAINDER PROBLEM

Using Binomial theorem, last two digits of an exponent can be found as 7^(10)=7^(2*5)=49^5=(-1+50)^5=(-1)^5+5*(-1)^4*50=-1+50(Just considered last 2-digit of the product)=49

Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]

Show Tags

18 Dec 2012, 00:38

Ans:

7^10 can be written as 49^5 which can be written as (49^2)^2. 49 when divided by 100 it will give a remainder of (1)^2.49=49 answer (D).
_________________

Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]

Show Tags

17 Sep 2014, 10:13

kkalyan wrote:

What is the remainder, after division by 100, of 7^10 ?

(A) 1 (B) 7 (C) 43 (D) 49 (E) 70

sol:

7=7 7^2=..9 7^3=..3 7^4=1

now 10/4= 2 i.e. second from top of the pattern...which is 9 since we are dividing the number by 100 last number will be reminder check the answers....D is the only choice

Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]

Show Tags

10 May 2015, 00:53

Bunuel wrote:

thangvietnam wrote:

if we do not hav formular, how do I do?

What is the remainder, after division by 100, of 7^10 ?

(A) 1 (B) 7 (C) 43 (D) 49 (E) 70

The remainder when 7^10 is divided by 100 will be the last two digits of 7^10 (for example 123 divided by 100 yields the remainder of 23, 345 divided by 100 yields the remainder of 45).

\(7^{10}=(7^2)^5=49^5\) --> the units digit of 49^5 will be 9 (the units digit of 9^even is 1 and the units digit of 9^odd is 9).

So, we have that \(7^{10}=49^5\) has the units digit of 9, thus the units digit of the remainder must also be 9. Only answer D fits.

Answer: D.

excellent. I can not say a word for this wonderful explanation. thank you Buuney

Re: What is the remainder, after division by 100, of 7^10 ? [#permalink]

Show Tags

30 May 2016, 06:03

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...