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

 It is currently 24 May 2019, 18:33

### 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

# If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

### Show Tags

27 Jul 2017, 01:10
1
2
00:00

Difficulty:

15% (low)

Question Stats:

81% (00:50) correct 19% (01:00) wrong based on 70 sessions

### HideShow timer Statistics

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

1) $$x+y$$ is odd
2) $$x^y$$ is even

_________________
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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 04 Dec 2015 Posts: 751 Location: India Concentration: Technology, Strategy WE: Information Technology (Consulting) If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e [#permalink] ### Show Tags 27 Jul 2017, 01:16 1 MathRevolution wrote: If x and y are positive integers, is xy even? 1) $$x+y$$ is odd 2) $$x^y$$ is even 1) $$x+y$$ is odd $$Even + Odd = Odd$$ Therefore either $$x$$ or $$y$$ has to be even. Hence $$xy$$ will be Even. I is Sufficient. 2) $$x^y$$ is even Even raised to any integer is even. Odd raised to any integer will be odd. $$x$$ is even. Therefore $$xy$$ will be even. II is Sufficient. Answer (D)... _________________ Please Press "+1 Kudos" to appreciate. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7372 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e [#permalink] ### Show Tags 30 Jul 2017, 18:56 ==> If you modify the original condition and the question, in order to get xy=even, it can either be x=even? or y=even?. For con 1), from (x,y)=(odd,even),(even,odd), you always get yes, hence it is sufficient. For con 2), you always get x=even, hence it is yes and sufficient. The answer is D. Answer: D _________________ 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$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Joined: 02 Sep 2018
Posts: 24
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

### Show Tags

02 Apr 2019, 10:00
sashiim20 wrote:
MathRevolution wrote:
If x and y are positive integers, is xy even?

1) $$x+y$$ is odd
2) $$x^y$$ is even

1) $$x+y$$ is odd

$$Even + Odd = Odd$$

Therefore either $$x$$ or $$y$$ has to be even.

Hence $$xy$$ will be Even.

I is Sufficient.

2) $$x^y$$ is even

Even raised to any integer is even.

Odd raised to any integer will be odd.

$$x$$ is even. Therefore $$xy$$ will be even.

II is Sufficient.

_________________
Please Press "+1 Kudos" to appreciate.

When u r saying that x^y , for any number the answer will be even if x is even and odd if x is odd.

So in this case y can be odd or even .

hence the product xy can be even or odd .
So how come the condition is sufficint
Manager
Joined: 21 Feb 2019
Posts: 118
Location: Italy
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e  [#permalink]

### Show Tags

02 Apr 2019, 10:16
aaggarwal191 wrote:
sashiim20 wrote:
MathRevolution wrote:
If x and y are positive integers, is xy even?

1) $$x+y$$ is odd
2) $$x^y$$ is even

1) $$x+y$$ is odd

$$Even + Odd = Odd$$

Therefore either $$x$$ or $$y$$ has to be even.

Hence $$xy$$ will be Even.

I is Sufficient.

2) $$x^y$$ is even

Even raised to any integer is even.

Odd raised to any integer will be odd.

$$x$$ is even. Therefore $$xy$$ will be even.

II is Sufficient.

_________________
Please Press "+1 Kudos" to appreciate.

When u r saying that x^y , for any number the answer will be even if x is even and odd if x is odd.

So in this case y can be odd or even .

hence the product xy can be even or odd .
So how come the condition is sufficint

Even * Even = Even
Even * Odd = Even
Odd * Even = Even
Odd * Odd = Odd

Given: $$x^y$$ even. Hence, $$x$$ is even. If it was odd, it would be: $$odd * odd * odd$$ y times, which would give us an odd number.
Regardless of $$y$$ nature (even or odd), $$xy$$ will be always even.

Hope it's clear.
_________________
If you like my post, Kudos are appreciated! Thank you.

MEMENTO AUDERE SEMPER
Re: If x and y are positive integers, is xy even? 1) x+y is odd 2) xy is e   [#permalink] 02 Apr 2019, 10:16
Display posts from previous: Sort by