Find all School-related info fast with the new School-Specific MBA Forum

It is currently 05 Feb 2016, 15:06
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are integer, what is the remainder when x^2 + y^2

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31223
Followers: 5341

Kudos [?]: 62013 [0], given: 9426

Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 05 Jul 2013, 01:44
Expert's post
Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
2 KUDOS received
Director
Director
User avatar
Joined: 14 Dec 2012
Posts: 842
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 48

Kudos [?]: 915 [2] , given: 197

GMAT ToolKit User
Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 06 Jul 2013, 06:52
2
This post received
KUDOS
If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?

(1) When x-y is divided by 5, the remainder is 1

(2) When x+y is divided by 5, the remainder is 2

hi,

let a and b and c are 3 arbitray integers.

and if ==>a/c==>remainder x
and ===>b/c==>remainder is y

then
==>remainder of (a*b)/c=remainder of a*remainder of b
==>remainder of (a+b)/c=remainder of a+remainder of b
==>remainder of (a-b)/c=remainder of a-remainder of b

so using this clearly we can say that we need both the statement to solve this.
hence C
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...



GMAT RCs VOCABULARY LIST: vocabulary-list-for-gmat-reading-comprehension-155228.html
learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat- ... assessment
: http://www.youtube.com/watch?v=APt9ITygGss

Intern
Intern
avatar
Joined: 26 Mar 2014
Posts: 4
Followers: 0

Kudos [?]: 3 [0], given: 4

Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 26 Mar 2014, 21:26
from HTale's post on 17 May 2012: "You know that 2(x^2+y^2)= (x-y)^2 + (x+y)^2."

Please help: how does 2(x^2+y^2) factor to (x-y)^2 + (x+y)^2?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31223
Followers: 5341

Kudos [?]: 62013 [1] , given: 9426

Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 27 Mar 2014, 00:17
1
This post received
KUDOS
Expert's post
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8148
Followers: 417

Kudos [?]: 110 [0], given: 0

Top 10 in overall
Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 28 Mar 2015, 09:04
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

1 KUDOS received
Manager
Manager
User avatar
Joined: 12 Aug 2015
Posts: 231
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
Followers: 1

Kudos [?]: 55 [1] , given: 1104

CAT Tests
Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 21 Aug 2015, 01:25
1
This post received
KUDOS
hi

any shortcut to this problem? thanks
_________________

KUDO me plenty

Intern
Intern
avatar
Joined: 08 Oct 2015
Posts: 10
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 13 Nov 2015, 14:11
Bunuel wrote:
If x and y are integer, what is the remainder when x^2 + y^2 is divided by 5?

(1) When x-y is divided by 5, the remainder is 1 --> \(x-y=5q+1\), so \(x-y\) can be 1, 6, 11, ... Now, \(x=2\) and \(y=1\) (\(x-y=1\)) then \(x^2+y^2=5\) and thus the remainder is 0, but if \(x=3\) and \(y=2\) (\(x-y=1\)) then \(x^2+y^2=13\) and thus the remainder is 3. Not sufficient.

(2) When x+y is divided by 5, the remainder is 2 --> \(x+y=5p+2\), so \(x+y\) can be 2, 7, 12, ... Now, \(x=1\) and \(y=1\) (\(x+y=2\)) then \(x^2+y^2=2\) and thus the remainder is 2, but if \(x=5\) and \(y=2\) (\(x+y=7\)) then \(x^2+y^2=29\) and thus the remainder is 4. Not sufficient.

(1)+(2) Square both expressions: \(x^2-2xy+y^2=25q^2+10q+1\) and \(x^2+2xy+y^2=25p^2+20p+4\) --> add them up: \(2(x^2+y^2)=5(5q^2+2q+5p^2+4p+1)\) --> so \(2(x^2+y^2)\) is divisible by 5 (remainder 0), which means that so is \(x^2+y^2\). Sufficient.

Answer: C.

Hope it's clear.


Question for Bunuel. Theoretically, could you have used only q or p to represent the qoutient in this example. Wouldn't they represent the same whole factor of times that 5 can go into each statement?
Senior Manager
Senior Manager
avatar
Joined: 29 Oct 2013
Posts: 274
Concentration: Finance
Schools: Johnson
GMAT 1: 750 Q V
GPA: 3.7
WE: Corporate Finance (Retail Banking)
Followers: 12

Kudos [?]: 265 [0], given: 178

GMAT ToolKit User
If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 14 Dec 2015, 06:03
IMO this question is a walk in the park if we know the following rules:

You can always ignore the original number for remainder calculation. If you know a/n gives remainder p and b/n gives remainder of q then-
i) remainder of (a+b)/n = remainder of (p+q)/n
ii) remainder of (a-b)/n = remainder of (p-q)/n
iii) remainder of (a^2+b^2)/n = remainder of (p^2+q^2)/n
iv) remainder of (a^2-b^2)/n = remainder of (p^2-q^2)/n
v) remainder of (a*b)/n = remainder of (p*q)/n
vi) remainder of (a/b)/n = remainder of (p/q)/n
.
.
.
etc

But Im not quite sure about the accuracy of these rules.

So Moderators and Math Experts:

How do the above rules look neat or preposterous ?;) Any corrections, additions, exceptions? Thanks
_________________

Please consider giving 'kudos' if you like my post and want to thank :)

1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Mar 2014
Posts: 2198
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 67

Kudos [?]: 823 [1] , given: 612

Re: If x and y are integer, what is the remainder when x^2 + y^2 [#permalink] New post 16 Dec 2015, 11:46
1
This post received
KUDOS
NoHalfMeasures wrote:
IMO this question is a walk in the park if we know the following rules:

You can always ignore the original number for remainder calculation. If you know a/n gives remainder p and b/n gives remainder of q then-
i) remainder of (a+b)/n = remainder of (p+q)/n
ii) remainder of (a-b)/n = remainder of (p-q)/n
iii) remainder of (a^2+b^2)/n = remainder of (p^2+q^2)/n
iv) remainder of (a^2-b^2)/n = remainder of (p^2-q^2)/n
v) remainder of (a*b)/n = remainder of (p*q)/n
vi) remainder of (a/b)/n = remainder of (p/q)/n
.
.
.
etc

But Im not quite sure about the accuracy of these rules.

So Moderators and Math Experts:

How do the above rules look neat or preposterous ?;) Any corrections, additions, exceptions? Thanks


The best way would be to check them yourself by following the method shown below for (1).

You are given the following ,

a=nA+p and
b=nB+q

Thus, (a+b) = n(A+B) + p+q , or in other words, you will get a remainder of p+q when you divide a+b by n.

You can come up with similar relations based on method above. Additionally, you should not be remembering these relations and should be applying them as and when needed from first principles. Learning these obscure and not that common relations will only end up confusing you.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Re: If x and y are integer, what is the remainder when x^2 + y^2   [#permalink] 16 Dec 2015, 11:46

Go to page   Previous    1   2   [ 29 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
For integers x and y, 2^x+2^y=2^30. What is the value of x+y? A. 30 B shasadou 0 08 Jan 2016, 22:07
If (x−y)2=x2−y2, what is the value of nonzero integer xy? (1) x=5 (2) shasadou 0 07 Dec 2015, 03:50
11 Experts publish their posts in the topic If (x-y)^2=x^2-y^2, what is the value of nonzero integer xy? pratikshr 18 31 Jul 2014, 06:03
2 If x^2 - y^2 = 27, what is the value of (x + y)^2 ? avohden 3 01 Nov 2013, 23:47
2 Experts publish their posts in the topic What is the remainder when x^2 - y^2 is divided by 3? manishuol 6 29 Apr 2013, 11:05
Display posts from previous: Sort by

If x and y are integer, what is the remainder when x^2 + y^2

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.