It is currently 23 Jan 2018, 10:13

### 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 June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4715
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:

79% (00:57) correct 21% (00:58) wrong based on 48 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. $$59$$
[Reveal] Spoiler: OA

_________________

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
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
KUDOS
1
This post was
BOOKMARKED
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: 28
Re: What is the remainder when 7^30 is divided by 100? [#permalink]

### Show Tags

06 Dec 2017, 09:56
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 371 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: 4715
GPA: 3.82
Re: What is the remainder when 7^30 is divided by 100? [#permalink]

### Show Tags

08 Dec 2017, 00:07
=>

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.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself

Re: What is the remainder when 7^30 is divided by 100?   [#permalink] 08 Dec 2017, 00:07
Display posts from previous: Sort by