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

It is currently 14 Oct 2019, 03:41

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If m and n are positive integers, what is the remainder when m^2 - n^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

Show Tags

New post 27 Jan 2018, 23:03
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

91% (01:16) correct 9% (01:43) wrong based on 75 sessions

HideShow timer Statistics

If m and n are positive integers, what is the remainder when m^2 - n^2 is divided by 10?

(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.

_________________
Retired Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1180
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

Show Tags

New post 27 Jan 2018, 23:34
1
1
gmatbusters wrote:
If m and n are positive integers, what is the remainder when
m^2 - n^2 is divided by 10?
(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.


\(\frac{m^2-n^2}{10}=\frac{(m+n)(m-n)}{10}\). we need to know the value of \(m\) & \(n\) to get the remainder

Statement 1: implies \(m=10k+3\). but nothing mentioned about \(n\). Insufficient

Statement 2: implies \(n=10q+3\). but nothing mentioned about \(m\). Insufficient

Combining 1 & 2: we have \(m-n=10k+3-10q-3=10(k-q)\) which is divisible by \(10\). Hence remainder will be \(0\). Sufficient

Option C
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 3536
Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

Show Tags

New post 28 Jan 2018, 18:21
1
Bunuel , would you please move this question to DS?
_________________
SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here.




Choose life.
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 7952
Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

Show Tags

New post 28 Jan 2018, 19:17
gmatbusters wrote:
If m and n are positive integers, what is the remainder when m^2 - n^2 is divided by 10?

(1) The remainder when m is divided by 10 is 3.
(2) The remainder when n is divided by 10 is 3.



Note :- Remainder when div by 10 means the units digit of the number.

\(m^2-n^2...(m-n)(m+n)\)..
Let's see the statements..

1) The remainder when m is divided by 10 is 3.
This means units digit of m is 3, but nothing about n.
Insufficient

(2) The remainder when n is divided by 10 is 3.[/quote]
This means units digit of n is 3, but nothing about m.
Insufficient

Combined..
Units digit of m and n both are 3, so m^2-n^2 will lead to units digit as 9-9=0
So it will be div by 10..
C
_________________
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1256
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If m and n are positive integers, what is the remainder when m^2 - n^2  [#permalink]

Show Tags

New post 28 Jan 2018, 19:25
GMAT Club Bot
Re: If m and n are positive integers, what is the remainder when m^2 - n^2   [#permalink] 28 Jan 2018, 19:25
Display posts from previous: Sort by

If m and n are positive integers, what is the remainder when m^2 - n^2

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne