GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 15 Dec 2018, 01:27

### 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

we will pick new questions that match your level based on your Timer History

Track

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

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

December 15, 2018

December 15, 2018

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.
• ### $450 Tuition Credit & Official CAT Packs FREE December 15, 2018 December 15, 2018 10:00 PM PST 11:00 PM PST Get the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # What is the remainder when 7^30 is divided by 100?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6639 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the remainder when 7^30 is divided by 100? [#permalink] ### Show Tags 06 Dec 2017, 00:12 00:00 Difficulty: 15% (low) Question Stats: 82% (01:23) correct 18% (02:19) wrong based on 82 sessions ### HideShow timer Statistics [GMAT math practice question] What is the remainder when $$7^{30}$$ is divided by $$100$$? A. $$19$$ B. $$29$$ C. $$39$$ D. $$49$$ E. $$59$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 06 Oct 2017
Posts: 10
Re: What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

06 Dec 2017, 05:57
2
7 has cyclicity of 4

7^4 =2401, when divided by 100 will leave remainder as 1

((7^4)^7*7^2)/100
=> 1*49/100
Remainder =49

D

Sent from my vivo 1609 using GMAT Club Forum mobile app
Intern
Joined: 26 Oct 2017
Posts: 27
Re: What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

06 Dec 2017, 09:56
1
1
MathRevolution wrote:
[GMAT math practice question]

What is the remainder when $$7^{30}$$ is divided by $$100$$?

A. $$19$$
B. $$29$$
C. $$39$$
D. $$49$$
E. $$59$$

Attachment:

IMG_20171206_232527.jpg [ 32.07 KiB | Viewed 970 times ]

Imo D

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
Intern
Joined: 11 Nov 2017
Posts: 12
Re: What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

06 Dec 2017, 11:03
MathRevolution wrote:
[GMAT math practice question]

What is the remainder when $$7^{30}$$ is divided by $$100$$?

A. $$19$$
B. $$29$$
C. $$39$$
D. $$49$$
E. $$59$$

Straight D.

Remainders when divided by 100 are
7^1 = 7
7^2 = 49
7^3 = 43
7^4 = 1
7^5 = 7

So, cyclicity of 4. 30%4=2
Remainder when divided by 100 is 49.
_________________

Cheers.

Never gonna give up!!!!

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6639
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

08 Dec 2017, 00:07
1
=>

The tens digit of $$7^k$$ cycles through $$0-->4-->4--->0--->0-->…..$$
The units digit of $$7^k$$cycles through $$7-->9-->3--->1--->7-->…..$$

Since $$30=4(7)+2, 7^{30}=7^{4(7)+2}$$ ends in $$49$$.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 07 Jul 2018
Posts: 7
What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

08 Jul 2018, 14:22
Question for the experts:
How does the cyclicity work?

I wonder if the cyclicity of the "powered up" numbers goes well beyond units or tens digits. Actually once I've computed one power can I reuse it? Illustration [inspired by math revolution post]:

The thousands digits of 7^k cycles through......?−−>?−−>?−−−>2−−−>?−−>…
The hundreds digits of 7^k cycles through.......?−−>?−−>3−−−>4−−−>?−−>…
The tens digit of 7^k cycles through.............0−−>4−−>4−−−>0−−−>0−−>…
The units digit of 7^k cycles through............7−−>9−−>3−−−>1−−−>7−−>…

The only calculation I've made are 7^3 and 7^4 and with that I've partly filled the 7 cycle up to the thousands! But then I've checked for 2401^2 but it doesn't work...

_________________

Welcoming critics is my way to improvement. So do not hesitate, tell me how I can improve. Thx

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4277
Location: India
GPA: 3.5
Re: What is the remainder when 7^30 is divided by 100?  [#permalink]

### Show Tags

09 Jul 2018, 06:51
jetmat wrote:
Question for the experts:
How does the cyclicity work?

I wonder if the cyclicity of the "powered up" numbers goes well beyond units or tens digits. Actually once I've computed one power can I reuse it? Illustration [inspired by math revolution post]:

The thousands digits of 7^k cycles through......?−−>?−−>?−−−>2−−−>?−−>…
The hundreds digits of 7^k cycles through.......?−−>?−−>3−−−>4−−−>?−−>…
The tens digit of 7^k cycles through.............0−−>4−−>4−−−>0−−−>0−−>…
The units digit of 7^k cycles through............7−−>9−−>3−−−>1−−−>7−−>…

The only calculation I've made are 7^3 and 7^4 and with that I've partly filled the 7 cycle up to the thousands! But then I've checked for 2401^2 but it doesn't work...

Please go through the discussion here

https://gmatclub.com/forum/cyclicity-on ... 13019.html
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Re: What is the remainder when 7^30 is divided by 100? &nbs [#permalink] 09 Jul 2018, 06:51
Display posts from previous: Sort by

# What is the remainder when 7^30 is divided by 100?

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.