• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

## If m and n are positive integers...

tagged by: swerve

This topic has 1 expert reply and 0 member replies

### Top Member

swerve Master | Next Rank: 500 Posts
Joined
29 Oct 2017
Posted:
337 messages
Followed by:
4 members

#### If m and n are positive integers...

Wed Nov 08, 2017 7:10 am
If m and n are positive integers such that m>n, what is the remainder when m^2-n^2 is divided by 21?

1) The remainder when (m+n) is divided by 21 is 1.
2) The remainder when (m-n) is divided by 21 is 1.

The OA is C.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.

### GMAT/MBA Expert

Jay@ManhattanReview GMAT Instructor
Joined
22 Aug 2016
Posted:
1065 messages
Followed by:
22 members
470
Wed Nov 08, 2017 11:09 pm
swerve wrote:
If m and n are positive integers such that m>n, what is the remainder when m^2-n^2 is divided by 21?

1) The remainder when (m+n) is divided by 21 is 1.
2) The remainder when (m-n) is divided by 21 is 1.

The OA is C.

Please, can any expert explain this DS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
We have to get the remainder when (m^2 - n^2) is divided by 21.

1) The remainder when (m+n) is divided by 21 is 1.

Say m + n = 21a + 1; where a is any integer (quotient)

We cannot conclude on this basis whether (m^2 - n^2) is divisible by 21. Insufficient.

2) The remainder when (m-n) is divided by 21 is 1.

Say m - n = 21b + 1; where b is any integer (quotient)

We cannot conclude on this basis whether (m^2 - n^2) is divisible by 21. Insufficient.

(1) and (2) combined:

From both the statements, we get that m^2 - n^2 = (21a + 1)*(21b + 1) = 21^2.ab + 21b + 21a + 1

Since 21^2.ab + 21b + 21a is divisible by 21, the remainder when 21^2.ab + 21b + 21a + 1 divided by 21 is 1. Sufficient.

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Singapore | Doha | Lausanne | and many more...

### Top First Responders*

1 GMATGuruNY 70 first replies
2 Rich.C@EMPOWERgma... 42 first replies
3 Brent@GMATPrepNow 40 first replies
4 Jay@ManhattanReview 24 first replies
5 Terry@ThePrinceto... 10 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 GMATGuruNY

The Princeton Review Teacher

133 posts
2 Scott@TargetTestPrep

Target Test Prep

113 posts
3 Rich.C@EMPOWERgma...

EMPOWERgmat

111 posts
4 Jeff@TargetTestPrep

Target Test Prep

111 posts
5 Brent@GMATPrepNow

GMAT Prep Now Teacher

90 posts
See More Top Beat The GMAT Experts