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

 It is currently 16 Oct 2019, 22:39 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

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.  If x and y are positive integers, is x + y even?

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

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58391
If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

2
2 00:00

Difficulty:   35% (medium)

Question Stats: 71% (01:32) correct 29% (01:23) wrong based on 228 sessions

HideShow timer Statistics

Tough and Tricky questions: Number Properties.

If x and y are positive integers, is x + y even?

(1) xy is even

(2) x/y is even

Kudos for a correct solution.

_________________
Manager  Joined: 10 Sep 2014
Posts: 96
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
statement 1: not sufficient
If xy is even that means that at least one of them is even. This is not sufficient because if x=2 and y=3 then xy=6 and x+y=5, odd. But if x=4 and y = 4 then xy=16 and x+y=8, even.

statement 2: not sufficient
X=14 and y=7, x/y=2, even. x+y=21, odd.
x=8 and y=4, x/y=2, even. x+y=12, even.

If we combine statements, we still do not have enough information. The most we know is that one of them is even but we need to know for both x and y.

Manager  Status: Applied
Joined: 02 May 2014
Posts: 125
Location: India
Concentration: Operations, General Management
GMAT 1: 690 Q47 V38 GPA: 3.35
WE: Information Technology (Computer Software)
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
Take x=2 y=1; x+y=3=odd; statement 1-xy=even correct
Take x=2 y=4; x+y=6=even; statement 1-xy= even correct
hence statement 1 not sufficient
Take x=2 y=1; x+y=3=odd;statement 1-xy=even correct
Take x=4 y=2; x+y=6=even; statement 1-xy= even correct
Hence statement 2 not sufficient
Take x=2 and y=1 ;x+y=3=odd and take x=4 y=2; x+y=6=evenn
Not sufficient hence E.
Intern  Joined: 25 May 2014
Posts: 46
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

2
1
For x + y to be even, either both x and y has to be even or both has to be odd.

stmt1 : xy is even
This means that either both x and y are even OR one is even and other is odd.
why so?? because even * even = even AND even * odd = even.
Since we do not have suff information thus INSUFFICIENT.

stmt2: x/y is even
x/y = even------> x = even * y which means that x is even.
But we do not know is y is even or not thus INSUFFICIENT.

combining both statements also do not give sufficient information about x and y.
E.
_________________
Never Try Quitting, Never Quit Trying
Intern  Joined: 10 Mar 2014
Posts: 36
Concentration: General Management, Technology
GMAT 1: 650 Q47 V32 GPA: 4
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
Statement1: Even x Even = Even => Even + Even = Even
OR
Even x Odd = Even => Even + Odd = Odd
Hence Insufficient.

Statement2: Even / Even = Even => Even + Even = Even
OR
Even / Odd = Even => Even + Odd = Odd
Hence Insufficient.

Statement 1 and 2 combined also will give similar combination. So can't be determined. Hence answer is E.
Manager  Joined: 22 Sep 2012
Posts: 123
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
Question : If x and y are positive integers, is x + y even?

Statement 1: xy is even
If xy = 8,
Valid combination of x and y are , x= 4 and y =2 . x+y = 6 (true)
Another combination of x and y are , x= 8 and y =1 . x+y = 9 (false)

Insufficient

(2) x/y is even
If x/y = 8,
Valid combination of x and y are , x= 16 and y =2 . x+y = 18 (true)
Valid combination of x and y are , x= 8 and y =1 . x + y = 9 (false)

Insufficient

Combining both statements as well, we will not be able to solve the problem. Hence E) is the correct answer.
Intern  Joined: 22 Feb 2014
Posts: 29
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
x,y > 0; x+y = even if x,y = even or x,y = odd.

1) xy = even --- x or y or x & y - even. So x+y = odd or even. Not Sufficient
2) x/y = even --- x - even and y could be even or odd. So x+y = odd or even. Not Sufficient
1+2 ---- xy = even & x/y = even ---- we can eliminate x and y both odd. So x = even for sure. Y = even or odd. -- x+y = Even or Odd. So 1+2 not sufficient.

Intern  Joined: 20 Jan 2013
Posts: 33
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
statement 1:
If xy is even that means that at least one of them is even. This is not sufficient because if x=4 and y=5 then xy=20 and x+y=9, odd.
But if x=2 and y = 6 then xy=12 and x+y=8, even.
Hence Not Sufficient. Option A & D are out

statement 2:
X=12 and y=3, x/y=4, even. x+y=15, odd.
x=8 and y=4, x/y=2, even. x+y=12, even.
Hence Not Sufficient. Option B is out

If we combine statements, we still do not have enough information. The most we know is that one of them is even but we need to know for both x and y.

_________________
_________________

KUDOS is always a good way to thank anyone.
It encourages someone to post more questions and also answers.

KUDOS Please if My post helps you in anyway. Your Kudos keep me alive [/color]
Manager  Joined: 21 Jan 2014
Posts: 61
WE: General Management (Non-Profit and Government)
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

1
from statement 1: xy is even
as we know xy can be even in two cases
1) both x & y are even = x+y=EVEN
2) x is odd and y is even or vice versa. =x+y=ODD
SO its conflicting and no definite result hence INSUFFICIENT.

From statement 2: x/y is even
again x/y is even in following two scenarios
1) both x & y are even =x/y cane both odd and even
2) x is even and y is odd=x/y is even =x+y=ODD
This statement also contradicts and INSUFFICIENT.

Even combination of both statements is also not sufficient.

Math Expert V
Joined: 02 Sep 2009
Posts: 58391
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

Bunuel wrote:

Tough and Tricky questions: Number Properties.

If x and y are positive integers, is x + y even?

(1) xy is even

(2) x/y is even

Kudos for a correct solution.

Official Solution:

If x and y are positive integers, is x + y even?

For the sum of $$x$$ and $$y$$ to be even, the two variables must both be even or both be odd.

Statement (1): INSUFFICIENT. We know that at least one of the variables is even, but we do not know whether they are both even.

Statement (2): INSUFFICIENT. We know that $$x = y \times \text{(some even integer)}$$. Since an even integer multiplied by any other integer is also even, we know that $$x$$ is even. However, we do not know whether $$y$$ is even.

Statements (1) &amp; (2): INSUFFICIENT. Using both statements, we only know that $$x$$ is even. Meanwhile, y could be even, but it does not have to be. As a result, we cannot determine whether the sum of $$x$$ and $$y$$ is even or odd. All of these results can be confirmed by picking numbers.

_________________
Current Student D
Joined: 12 Aug 2015
Posts: 2568
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

There are a lot of ways to this one.
Given info =>
x,y are integers (This is a very important piece of info and should be always checked )
we need the even/odd nature of x+y
Statement 1=>
xy=even
=> (x,y)=> even,even => sum = even
even,odd => sum odd
odd,even => sum = odd

statement 2
x/y=even
hence x=y*even
so x must be even
but y can be even or odd
hence not sufficient

combining them two cases are possible
(x,y)=> even,even => sum=even
even,odd => sum =odd
hence not sufficient

Hence E
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13204
Re: If x and y are positive integers, is x + y even?  [#permalink]

Show Tags

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.
_________________ Re: If x and y are positive integers, is x + y even?   [#permalink] 08 Oct 2018, 12:52
Display posts from previous: Sort by

If x and y are positive integers, is x + y even?

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

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