GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 31 May 2020, 02:30

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 x and y are positive integers, what is the remainder when (x^2 + y^

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 27 Nov 2018, 00:04
10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (01:52) correct 34% (01:34) wrong based on 174 sessions

HideShow timer Statistics

Most Helpful Community Reply
Manager
Manager
avatar
G
Joined: 24 Dec 2018
Posts: 107
Concentration: Entrepreneurship, Finance
Reviews Badge
Re: If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 29 Dec 2018, 03:18
4
1
Statement 1: if x & y are consecutive integers, \((x^2 + y^2)\) will be sum of square of one even positive integer and square of one odd positive integer. Now, square of even integer is always divisible by 4 since even integer will have 2 as a factor and since 2 is squared, it will be divisible by 4. Coming to the square of the odd integer, this number when divided by 4 will always give 1 as remainder. Let's understand why:

Odd integer can be written as 2n+1. Now \((2n+1)^2\)=4\(n^2\)+1+4n. When this expression is divided by 4, we get that 4\(n^2\)+4n to be divisible by 4 and 1/4 leaving a remainder of 1.

Thus, \((x^2 + y^2)\) when divided by 4, will always leave a remainder of 1. Hence, sufficient

Statement 2: This statement is a repeat of the same concept used in statement 1. Hence, by default this statement is also sufficient

Answer is D
General Discussion
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1153
If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 27 Nov 2018, 00:32
Bunuel wrote:
If x and y are positive integers, what is the remainder when (x^2 + y^2) is divided by 4 ?


(1) x and y are consecutive integers

(2) x is even and y is odd


To know this, we need to know the remainder of x^2 and y^2 when divided by 4.
As equations look a bit complex and our statements are very simple, we'll first try a few numbers.
This is an Alternative approach.

(1) As there are only 4 possible classes of integers with respect to 'remainder when divided by 4' (remainder = 0,1,2,3), checking the first 4 pairs is enough.
Say x = 1, y = 2. Then 1^2+2^2 = 5 which has remainder 1. Say x = 2, y = 3. Then 4 + 9 = 13 which has remainder 1. Say x = 3, y = 4. Then 9+16=25 which also has remainder 1. Last x = 4, y = 5 Which gives 16+25=41, remainder 1.
Then (1) is sufficient.

(2) Once again, there are only 4 options, depending on the remainder classes when divided by 4: x has remainder 0 and y remainder 1, x has remainder 0 and y remainder 3, x remainder 2 and y remainder 1 and x remainder 2 and y remainder 3. Looking at (1), we'll see what we've already checked: (4,5) is the first option, (4,3) is the second option, (2,1) is the third option and (2,3) the fourth option. So we'll get the same answer.
Sufficient.

(D) is our answer.
_________________
Manager
Manager
avatar
S
Joined: 24 Dec 2017
Posts: 180
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 27 Nov 2018, 04:17
\(\frac{x^2 + y^2}{4}\)= Remainder?

Statement 1: x and y are consecutive integers

Case 1 : \(\frac{2^2+3^2}{4}\)= \(\frac{13}{4}\){Remainder is 1}
Case 2: \(\frac{3^2+4^2}{4}\)= \(\frac{25}{4}\){Remainder is 1}

Helen Statment 1 is sufficient.

Statement 2: x = even & y = odd
Same as Statement 1. Hence it is sufficient too.

Answer IMO is D
Intern
Intern
avatar
B
Joined: 15 Sep 2018
Posts: 1
Re: If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 27 Nov 2018, 06:24
The remainder of (x^2 + y^2) divided by 4, is the remainder of x^2 divided by 4 + y^2 divided by 4.

St1:
-x or y must be an even number and a square of an even number divided by 4 have a remainder of 0.
-The other number must be odd, so square of an positive odd number should be: 1, 9, 25, 49.... all of them divided by 4 have a remainder of 1.

0+1 = 1

Statment 1 is sufficient.

Stat 2 = Sta 1 is sufficient.

D is the answer
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 64249
Re: If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 24 Dec 2018, 00:44
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15024
Re: If x and y are positive integers, what is the remainder when (x^2 + y^  [#permalink]

Show Tags

New post 18 Apr 2020, 01:24
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 Club Bot
Re: If x and y are positive integers, what is the remainder when (x^2 + y^   [#permalink] 18 Apr 2020, 01:24

If x and y are positive integers, what is the remainder when (x^2 + y^

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





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