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

 It is currently 21 Oct 2018, 14:08

### 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 the product xy even

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 Jul 2004
Posts: 135
Location: Melbourne
Schools: Yale SOM, Tuck, Ross, IESE, HEC, Johnson, Booth
If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

29 Jan 2009, 05:47
6
15
00:00

Difficulty:

35% (medium)

Question Stats:

72% (01:38) correct 28% (01:46) wrong based on 596 sessions

### HideShow timer Statistics

If x and y are positive integers , is the product xy even

(1) 5x - 4y is even
(2) 6x + 7y is even

_________________

kris

Current Student
Joined: 23 May 2013
Posts: 188
Location: United States
Concentration: Technology, Healthcare
Schools: Stanford '19 (M)
GMAT 1: 760 Q49 V45
GPA: 3.5
If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

02 Aug 2016, 13:22
4
2
krishan wrote:
If x and y are positive integers , is the product xy even

(1) $$5x - 4y$$ is even
(2) $$6x + 7y$$ is even

1) $$4y$$ will always be even. Then we have $$5x - even = even$$. For this to be the case, $$5x$$ must be even. Since 5 can't be even, then x must be even. Thus the product $$xy$$ will be even. Sufficient.

2) $$6x$$ will always be even. Then we have $$even + 7y = even$$. Thus $$7y$$ is even, and $$y$$ is even, and $$xy$$ is even. Sufficient.

##### General Discussion
SVP
Joined: 29 Aug 2007
Posts: 2395
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

29 Jan 2009, 06:25
1
krishan wrote:
If x and y are positive integers , is the product xy even

(1) 5x - 4y is even
(2) 6x + 7y is even

D. in either case x and y has to be even.

(1) 5x - 4y is even: x has to be even. suff.
(2) 6x + 7y is even: y has to be even. suff.
_________________

Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT

SVP
Joined: 07 Nov 2007
Posts: 1687
Location: New York
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

29 Jan 2009, 07:43
1
krishan wrote:
If x and y are positive integers , is the product xy even

(1) 5x - 4y is even
(2) 6x + 7y is even

agree with D.

1) 5x - 4y is even -> x must be multiple of 2
5*2k-4y = 2*(any number) even
sufficient
2)6x + 7y is even[/
y should multiple of 2

even
sufficient
_________________

Smiling wins more friends than frowning

CEO
Joined: 12 Sep 2015
Posts: 3023
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

03 Aug 2016, 10:29
2
Top Contributor
krishan wrote:
If x and y are positive integers , is the product xy even

(1) 5x - 4y is even
(2) 6x + 7y is even

Target question: Is xy even?

Statement 1: 5x - 4y is even
Let's test all 4 cases
case a: x is even and y is even: In this case 5x-4y is EVEN
case b: x is even and y is odd: In this case 5x-4y is EVEN
case c: x is odd and y is even: In this case 5x-4y is ODD
case d: x is odd and y is odd: In this case 5x-4y is ODD
So, cases a and b are both possible.
In both cases the product xy is even
So, xy must be even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Aside: If anyone is interested, we have a video (below) on testing possible cases for these question types

Statement 2: 6x+7y is even
Let's test all 4 cases
case a: x is even and y is even: In this case 6x+7y is EVEN
case b: x is even and y is odd: In this case 6x+7y is ODD
case c: x is odd and y is even: In this case 6x+7y is EVEN
case d: x is odd and y is odd: In this case 6x+7y is ODD
So, cases a and c are both possible.
In both cases the product xy is even
So, xy must be even
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com

Current Student
Joined: 18 Oct 2014
Posts: 856
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

03 Aug 2016, 11:08
1
krishan wrote:
If x and y are positive integers , is the product xy even

(1) 5x - 4y is even
(2) 6x + 7y is even

For xy to be even, either x or y or both must be even.

(1) 5x - 4y is even
E-E=E
O-O=E

Since 4y is even, 5x has to be even. 5 is not even, hence x is even.

xy will be even.

(2) 6x + 7y is even
E+E= E
O+O=E

Since 6x is even, 7y has to be even. And because 7 is not even y has to be even.

xy will be even.

Both statements are sufficient.

_________________

I welcome critical analysis of my post!! That will help me reach 700+

Intern
Joined: 24 Nov 2015
Posts: 18
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

13 Jul 2017, 00:22
1
In my opinion, this type of problem is super easy if you really understand what you're being asked, and then re-frame the question to be more straightforward. It's more about the question than the math.

Given: (x,y) > 0, AND are integers

Original Question: Is xy even?

We know that any number multiplied by an even number is even, so the question is really asking: Do we know if either "X" or "Y" (or both, or neither) is even?

Reframing the question this way is better, in my opinion.

A.) 5x - 4y is even.

For 5x - 4y to be even, both 5x and 4y have to be of the same parity. ("Parity" is the word that describes whether a number is odd or even)
In other words, odd + odd, or even + even, produce even results.

5x - 4y

We know off the bat that "4y" is even, because 4 is even. 4 times anything would be even. So we have ( 5x - EVEN NUMBER = EVEN NUMBER. ) Therefore, we know that "5x" is also even, because 4y (even) and 5x have to be the same parity. (even minus even = even)

In order to make 5x even, "x" has to be even. That's because 5 is odd.

Knowing that "x" is even is enough to answer the question: Do we know if either "X" or "Y" (or both, or neither) is even?

SUFFICIENT.

B.) 6x + 7y is even

Same drill here. For 6x + 7y to be even, both terms have to be the same parity. Since 6 is even, we know that 6x is even. Since 6x is even, we know that 7y is even. Since 7y is even, we know that y is even (since 7 is odd).

Knowing that "y" is even is enough to answer the question: Do we know if either "X" or "Y" (or both, or neither) is even?

SUFFICIENT

Manager
Joined: 12 Jun 2016
Posts: 217
Location: India
WE: Sales (Telecommunications)
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

15 Nov 2017, 03:48
$$S1: 5x - 4y = even => 5x = even+4y => 5x = even => x = even => xy = even. Suff$$

$$S2: 6x+7y = even => 7y = even - 6x =>7y = even => y = even => xy = even. Suff$$

Both S1 and S2 are individually sufficient. Final answer = D
_________________

My Best is yet to come!

Manager
Joined: 05 Oct 2014
Posts: 56
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: If x and y are positive integers , is the product xy even  [#permalink]

### Show Tags

24 Dec 2017, 18:09
If x and y are positive integers, is the product xy even
(1) 5x - 4y is even
(2) 6x + 7y is even

1. for 5x-4y = Even, x must be even & y may or may not be even. Since x is even, we can conclude xy is even. SUFFICIENT.
Even – Even = Even
Even – Odd = Odd
Odd – Even = Odd
Odd – Odd = Odd

2. for 6x + 7y is even, y must be even. Since y is even, we can conclude xy is even. SUFFICIENT.
Even + Even = Even
Odd + Even = Odd
Even + Odd = Odd
Re: If x and y are positive integers , is the product xy even &nbs [#permalink] 24 Dec 2017, 18:09
Display posts from previous: Sort by