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

It is currently 22 Jun 2018, 04:33

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If neither x nor y is divisible by 3, which of the following could be

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

Hide Tags

Expert Post
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
If neither x nor y is divisible by 3, which of the following could be [#permalink]

Show Tags

New post Updated on: 10 Mar 2018, 13:21
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (01:57) correct 60% (02:14) wrong based on 73 sessions

HideShow timer Statistics

[GMAT math practice question]

x and y are integers. If neither \(x\) nor \(y\) is divisible by \(3\), which of the following could be the value of \(x^2+y^2\)?

\(A. 333\)
\(B. 334\)
\(C. 335\)
\(D. 336\)
\(E. 337\)

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"


Originally posted by MathRevolution on 08 Mar 2018, 02:27.
Last edited by MathRevolution on 10 Mar 2018, 13:21, edited 1 time in total.
3 KUDOS received
PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1142
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If neither x nor y is divisible by 3, which of the following could be [#permalink]

Show Tags

New post 08 Mar 2018, 11:18
3
1
MathRevolution wrote:
[GMAT math practice question]

If neither \(x\) nor \(y\) is divisible by \(3\), which of the following could be the value of \(x^2+y^2\)?

\(A. 333\)
\(B. 334\)
\(C. 335\)
\(D. 336\)
\(E. 337\)


let \(x=3k+2\) or \(3k+1\) and \(y=3q+2\) or \(3q+1\), basically a number that is not divisible by \(3\)

you can take any combination and sum the squares of the resulting number -

if \(x=3k+1\) & \(y=3q+2\), then \(x^2+y^2=(3k+1)^2+(3q+2)^2\)

\(=>x^2+y^2=9k^2+6k+1+9q^2+12q+4= 3(3k^2+2k+3q^2+4q)+5=3(3k^2+2k+3q^2+4q)+3+2=3(3k^2+2k+3q^2+4q+1)+2\)

Hence \(x^2+y^2\) when divided by \(3\) will leave a remainder of \(2\).

Among the options only \(335\), when divided by \(3\) will leave a remainder of \(2\). Hence our answer

Option C

---------------------------------------
Essentially any number that is not divisible by 3, will leave a remainder of either 1 or 2 when divided by 3. on squaring those numbers, the remainders will also get squared to 1 or 4. so different remainder summation possible are 1+1=2, 1+4=5 & 4+4=8. Now when this number is divided by 3 it will leave a remainder of 2
Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5600
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: If neither x nor y is divisible by 3, which of the following could be [#permalink]

Show Tags

New post 11 Mar 2018, 18:32
1
2
=>

Consider the squares of the integers that are not divisible by 3:
\(1^2 = 1, 2^2 = 4, 4^2 = 16, 5^2 = 25, 7^2 = 49, 8^2=64\), ….
They all have a remainder of \(1\) when they are divided by \(3\).
Thus, the sum of the squares of two integers which are not divisible by \(3\) must have a remainder of \(2\) when it is divided by \(3\).

The only answer choice having this property is \(335\).

Therefore, C is the answer.

Answer: C
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Re: If neither x nor y is divisible by 3, which of the following could be   [#permalink] 11 Mar 2018, 18:32
Display posts from previous: Sort by

If neither x nor y is divisible by 3, which of the following could be

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


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

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

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®.