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

 It is currently 16 Oct 2019, 10:04

### 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

# What is the remainder when dividing 221 by 3?

Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 29 Apr 2015
Posts: 822
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

Updated on: 09 Jul 2015, 11:37
2
00:00

Difficulty:

25% (medium)

Question Stats:

74% (00:56) correct 26% (01:25) wrong based on 164 sessions

### HideShow timer Statistics

What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

_________________
Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Originally posted by reto on 09 Jul 2015, 11:36.
Last edited by Bunuel on 09 Jul 2015, 11:37, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 58381
What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

09 Jul 2015, 11:44
reto wrote:
What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

This cannot possibly be a GMAT question. When dividing by 3 we can have only 3 remainders: 0, 1, or 2. 0 is clearly out, 2 in any integer power cannot be a multiple of 3. So, we are left with 1 or 2. Then, simple testing will tell us that 2 in odd powers gives the remainder of 2 while 2 in even powers gives the remainder of 1 when dividing by 3.

_________________
Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300
Re: What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

09 Jul 2015, 11:44
reto wrote:
What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

2/3--->Remainder 2
2*2/3--->R=1
2*2*2/3--->R=2
2*2*2*2/3--->R=1

So Odd powers of 2 have a remainder of 2 on being divided by 3 and Even powers of 2 have a remainder of 2 on being divided by 3.

Since 21 is an Odd power, the remainder should be 2.

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2977
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

09 Jul 2015, 11:50
reto wrote:
What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

2 when divided by 3 leaves remainder = 2 [i.e. 2 is in excess of 2 to be a multiple of 3]

which in other words can also be written as

2 when divided by 3 leaves remainder = -1 [i.e. 2 is short of 1 to be a multiple of 3]

i.e when $$2^{21}$$ is divided by 3 the remainder will be $$(-1)^{21} = -1 i.e. 2$$

Please Note: remainders can be written in Positive as well as in Negative form

e.g. When 11 is divided by 7 remainder is 4 or remainder is (-3)
i.e. 11 has either excess of 4 or it is short by 3 to be a multiple of 7

e.g. When 39 is divided by 12 remainder is 3 or remainder is (-9)
i.e. 39 has either excess of 3 or it is short by 9 to be a multiple of 12

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4782
Location: India
GPA: 3.5
Re: What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

02 Feb 2018, 08:30
reto wrote:
What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

$$\frac{2^{21}}{3}$$

Or, $$\frac{2^{16}*2^5}{3}$$

$$2^{16}$$ will leave a remainder of 1 when divided by 3
$$2^5$$ will leave a remainder of 2 when divided by 3

Thus, the final remainder will be 2, answer will be (C)
_________________
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 )
VP
Joined: 07 Dec 2014
Posts: 1222
What is the remainder when dividing 221 by 3?  [#permalink]

### Show Tags

02 Feb 2018, 11:03
reto wrote:
What is the remainder when dividing $$2^{21}$$ by 3?

A. 4
B. 3
C. 2
D. 1
E. 0

exponent→ones unit cycle for 2:
2^1→2
2^2→4
2^3→8
2^4→6
thus, 2^21 gives a ones unit of 2
2/3 leaves a remainder of 2
C
What is the remainder when dividing 221 by 3?   [#permalink] 02 Feb 2018, 11:03
Display posts from previous: Sort by