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

 It is currently 03 May 2015, 17:49

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the remainder when x^2+y^2 is divided by 5, where x

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Senior Manager
Joined: 08 Aug 2005
Posts: 251
Followers: 1

Kudos [?]: 17 [0], given: 0

What is the remainder when x^2+y^2 is divided by 5, where x [#permalink]  06 May 2006, 04:31
What is the remainder when x^2+y^2 is divided by 5, where x and y are positive integer?

1). When x+y is divided by 5, the remainder is 1.
2). When x-y is divided by 5, the remainder is 2.
Manager
Joined: 09 Apr 2006
Posts: 173
Location: Somewhere in Wisconsin!
Followers: 1

Kudos [?]: 2 [0], given: 0

[#permalink]  07 May 2006, 10:40
(I) gives (x + y) = {1,11,21,...} or {6,16,26,...}
(II) gives (x - y) = {2,12,22,..} or {7,17,27,...}

(x^2 + y^2) = (x + y)^2 - 2xy = (x - y)^2 + 2xy

As we do not get any information about xy from either (I) or (II) we can rule out A and B.

Now combine them.

(x+y)^2(mod5) = 1 (as the last digit would be 1 or 6)
(x-y)^2(mod5) = 4 (as the last digit would be 4 or 9)

Add them and you would get 2(x^2 + y^2) on the LHS.

On the RHS you would get 1+4=5. So 2(x^2 + y^2)(mod 5) = 0 ==> (x^2 + y^2)(mod 5) = 0. So ans is C.
_________________

Thanks,
Zooroopa

Senior Manager
Joined: 29 Jun 2005
Posts: 403
Followers: 1

Kudos [?]: 15 [0], given: 0

[#permalink]  08 May 2006, 08:52
Agree with C
here is brutal and unneccessary approach:

From st1 we learned that x+y is a number that ends to 6 or 1
From st2 we learned that x-y ends to 7 or 2
So lets assume, that x+y=16, x-y=12. x=14, y=2. the remainder for x^2+y^2 is 0.
Now, lets assume that x+y=21, x-y=17. x=19, y=2. the remainder is 0.

from these, we can see that one of them will always end to 4 or 9, and the other to 1 or 4 respectively, which gives us 5 at the end of X^2+Y^2
Thus the remainder is always 0, and the answer is C
Intern
Joined: 03 May 2006
Posts: 27
Followers: 0

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

[#permalink]  08 May 2006, 09:48
Its C. Each individual is INSUFF. Combining. Square and add.
which gives 2(x^2 + y^2) = multiple of 5.
Since x and y are integers, (x^2+y^2) is multiple of 5.
[#permalink] 08 May 2006, 09:48
Similar topics Replies Last post
Similar
Topics:
2 What is the remainder when x^2 - y^2 is divided by 3? 6 29 Apr 2013, 11:05
60 If x and y are integer, what is the remainder when x^2 + y^2 24 26 Apr 2012, 19:58
If y = ( x^2 - y^2)/(x-y) where x not equal to y, then what 6 21 Nov 2007, 11:32
Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the 1 10 Aug 2007, 09:53
Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the 7 20 Nov 2006, 05:53
Display posts from previous: Sort by

# What is the remainder when x^2+y^2 is divided by 5, where x

 Question banks Downloads My Bookmarks Reviews Important topics

 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®.