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

 It is currently 18 Jan 2019, 03:59

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

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.
• ### FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# What is the remainder when 2^k is divided by 10?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6811
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the remainder when 2^k is divided by 10?  [#permalink]

### Show Tags

12 Jan 2017, 17:16
00:00

Difficulty:

45% (medium)

Question Stats:

60% (01:18) correct 40% (01:28) wrong based on 85 sessions

### HideShow timer Statistics

What is the remainder when $$2^k$$ is divided by 10?

1) k is a positive multiple of 10
2) k is a positive multiple of 4

_________________

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 $149 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: 04 Jan 2017 Posts: 8 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 18:11 Hint lies in the cyclicity of 2 Sent from my SM-G610F using GMAT Club Forum mobile app Manager Joined: 17 Apr 2016 Posts: 88 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 12 Jan 2017, 19:10 1 1 What is the remainder when 2^k is divided by 10? 1) k is a positive multiple of 10 2) k is a positive multiple of 4 Solution:- 2^1=2 2^2=4 2^3=8 2^4=16 On continuing we observe that the last digit follows a cyclic pattern:- 2,4,8,6 Statement 1:- If k=10, the remainder will be 4. If k=20, the remainder will be 6. Hence the first statement is not sufficient. Statement 2:- K is multiple of 4. Hence if k=4, remainder is 6. If k=8, remainder is 6. Likewise for each k, the remainder is 6. Hence sufficient. Answer-B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6811 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the remainder when 2^k is divided by 10? [#permalink] ### Show Tags 15 Jan 2017, 17:36 1 ==> Modify the original condition and the question. The remainder dividing $$2^k$$ by $$10 is ~2^1=~2, ~2^2=~4, ~2^3=~8, ~2^4=~6.$$ Thus, when it comes to ones, 2-->4-->8-->6-->2… are repeated, which means they have a cycle of four. Hence, the answer is 2) and B. Answer: B _________________ 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Non-Human User
Joined: 09 Sep 2013
Posts: 9424
Re: What is the remainder when 2^k is divided by 10?  [#permalink]

### Show Tags

01 Nov 2018, 16:36
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.
_________________
Re: What is the remainder when 2^k is divided by 10? &nbs [#permalink] 01 Nov 2018, 16:36
Display posts from previous: Sort by