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

It is currently 16 Oct 2019, 12:45

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 and y are positive integers, is the product xy even ?

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
Joined: 28 Jul 2004
Posts: 112
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

New post 29 Jan 2009, 05:47
6
26
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

71% (01:34) correct 29% (01:46) wrong based on 508 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
Most Helpful Community Reply
Current Student
avatar
B
Joined: 23 May 2013
Posts: 183
Location: United States
Concentration: Technology, Healthcare
GMAT 1: 760 Q49 V45
GPA: 3.5
GMAT ToolKit User
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 02 Aug 2016, 13:22
6
1
3
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.

Answer: D
General Discussion
SVP
SVP
User avatar
Joined: 29 Aug 2007
Posts: 1961
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 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.
_________________
Verbal: http://gmatclub.com/forum/new-to-the-verbal-forum-please-read-this-first-77546.html
Math: http://gmatclub.com/forum/new-to-the-math-forum-please-read-this-first-77764.html
Gmat: http://gmatclub.com/forum/everything-you-need-to-prepare-for-the-gmat-revised-77983.html


GT
VP
VP
User avatar
Joined: 07 Nov 2007
Posts: 1342
Location: New York
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 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
_________________
Your attitude determines your altitude
Smiling wins more friends than frowning
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4006
Location: Canada
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 03 Aug 2016, 10:29
3
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

Answer =

RELATED VIDEO

_________________
Test confidently with gmatprepnow.com
Image
Current Student
User avatar
Joined: 18 Oct 2014
Posts: 804
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 03 Aug 2016, 11:08
1
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.

D is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Intern
Intern
User avatar
Joined: 24 Nov 2015
Posts: 16
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 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

The answer is D
Manager
Manager
avatar
G
Joined: 12 Jun 2016
Posts: 212
Location: India
Concentration: Technology, Leadership
WE: Sales (Telecommunications)
GMAT ToolKit User
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 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
Manager
User avatar
B
Joined: 05 Oct 2014
Posts: 68
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

New post 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
Intern
Intern
avatar
Joined: 20 Dec 2018
Posts: 46
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 21 Dec 2018, 22:00
Statement 1. 5x – 4y is even i.e. 5x – 4y = 2k
Difference of two numbers is even if either both of them are odd or both of them are even.
Here, 4y is always even. So, 5x is also even.
Since 5x is even, we can say that x is even.
Now, xy will be even because the product of an even no with any positive integer is always even. Hence, Sufficient.
Statement 2. 6x + 7y is even.
6x is eve n because it is divisible by 2. So, 7y has to be even.
For 7y to be even, y has to be even.
We know the product of an even no with a positive integer is even.
Hence, xy is even. Hence, Sufficient.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13210
Re: If x and y are positive integers, is the product xy even ?  [#permalink]

Show Tags

New post 15 Jul 2019, 04:13
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.
_________________
GMAT Club Bot
Re: If x and y are positive integers, is the product xy even ?   [#permalink] 15 Jul 2019, 04:13
Display posts from previous: Sort by

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

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





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