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

It is currently 22 Nov 2019, 10:21

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 & Y are Positive integers and X^2+Y^2 is odd, which of the..

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

Hide Tags

Find Similar Topics 
Senior Manager
Senior Manager
User avatar
P
Joined: 10 Jan 2017
Posts: 330
Location: India
Reviews Badge CAT Tests
If X & Y are Positive integers and X^2+Y^2 is odd, which of the..  [#permalink]

Show Tags

New post 20 Oct 2019, 04:53
1
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

72% (01:14) correct 28% (01:21) wrong based on 18 sessions

HideShow timer Statistics

If X & Y are Positive integers and X^2+Y^2 is odd, which of the following is must be odd?

1>X+2y
2>3x+9Y
3>2X+Y
4>XY
5>XY-3X

_________________
Good, better, best. Never let it rest. 'Till your good is better and your better is best.
Please hit +1 Kudos if you like my Post.
Intern
Intern
avatar
B
Joined: 15 Aug 2018
Posts: 2
GMAT 1: 710 Q49 V38
Re: If X & Y are Positive integers and X^2+Y^2 is odd, which of the..  [#permalink]

Show Tags

New post 20 Oct 2019, 05:33
2
J2S2019
If X & Y are Positive integers and X^2+Y^2 is odd, which of the following is must be odd?

We know that a positive no. is even then its square will also be even. Similarly, If a positive no. is odd then its square will also be odd.

We are given that X^2+Y^2 is odd.

This means that one of them is even and the other is odd. If both X and Y were Even/Odd, then the sum of their Squares would not be odd as odd+odd=even and even+even=even.

But keep in mind we don't know the signs X and Y. We can just deduce that when X is even, Y will be odd and When X is odd Y will be even.




Now we examine the options
1>X+2y
If X is even, then the expression becomes even

2>3x+9Y
Here both X and Y are multiplied with Odd numbers, So the even no. when multiplied with 3/9 will yield an even no. and the odd no. when multiplied with 3/9 will yield an odd no., Thus the overall expression will be Odd+Even= Odd.

3>2X+Y
If Y is even, then the expression will be even

4>XY
As we know one of them is even, So Even*odd=Even

5>XY-3X
We know XY is even from the previous case, further when X is even, XY -3X will be even.
Manager
Manager
User avatar
S
Joined: 22 Jun 2018
Posts: 85
Location: Ukraine
Concentration: Technology, Entrepreneurship
GMAT 1: 600 Q44 V28
GMAT 2: 630 Q42 V34
GMAT 3: 660 Q48 V34
GPA: 4
Re: If X & Y are Positive integers and X^2+Y^2 is odd, which of the..  [#permalink]

Show Tags

New post 20 Oct 2019, 09:10
1
There are a few tricks about even/odd nature of integers:
(1) EVEN * X --> always EVEN
(2) EVEN + X --> EVEN plays no role: if X is EVEN, the sum will always be EVEN; If X is ODD, the sum will be ODD.
(3) ODD * X --> ODD plays no role: if X is EVEN, the product will be EVEN; if X is ODD, the product will be ODD.

And the last, already mentioned by @adityapanda: power does not impact even-odd nature: X and X^2, X^3, X^4, etc. will have same even-odd nature. Let's ensure with example:
2 2^2=4 2^3=8... all powers of 2 are even
3 3^2=9 3^3=27... all powers of 3 are odd

Taking this into account, let's first analyze information from question stem:
X^2+Y^2 is odd, as power does not affect e-o nature, this implies that X+Y is odd, and this implies that X and Y are of different even-odd nature.

Taking (1)-(3) in mind, quickly looking on the answer choices: option B states 3x+9Y and we know that multiplication on ODD does not play any role, so 3X+9Y will have same even-odd nature as X+Y and we know from the information in question stem that X+Y is ODD. So, option B is correct answer choice.

Hope it helps.
GMAT Club Bot
Re: If X & Y are Positive integers and X^2+Y^2 is odd, which of the..   [#permalink] 20 Oct 2019, 09:10
Display posts from previous: Sort by

If X & Y are Positive integers and X^2+Y^2 is odd, which of the..

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





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