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

Oldest

Best Reply

Author

Message

TAGS:

Senior Manager

Joined: 08 Aug 2005

Posts: 261

Followers: 1

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

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

06 May 2006, 05:31

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: 177

Location: Somewhere in Wisconsin!

Followers: 1

Kudos [?]: 1 [0], given: 0

[#permalink]

07 May 2006, 11:40

(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: 405

Followers: 1

Kudos [?]: 14 [0], given: 0

[#permalink]

08 May 2006, 09:52

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, 10:48

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, 10:48

		Similar topics	Author	Replies	Last post
Similar Topics:		Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the	johnycute	7	20 Nov 2006, 06:53
		Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the	goalsnr	1	10 Aug 2007, 10:53
	5	Is x^2+y^2 divisible by 5? 1). When x-y is divided by 5, the	ctrlaltdel	11	14 Nov 2009, 18:56
	15	If x and y are integer, what is the remainder when x^2 + y^2	kt750	22	26 Apr 2012, 20:58
	2	What is the remainder when x^2 - y^2 is divided by 3?	manishuol	2	29 Apr 2013, 12:05

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources