If x and y are positive integers, is the product xy even?
1). 5x-4y is even 2). 6x+7y is even.
Number Systems -Odds & Evens
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Target question: Is xy even?sukhman wrote:If x and y are positive integers, is the product xy even?
1)5x-4y is even
2)6x+7y is 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 free video on testing possible cases for these question types: https://www.gmatprepnow.com/module/gmat- ... ies?id=839
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 = D
Cheers,
Brent
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Statement 1:sukhman wrote:If x and y are positive integers, is the product xy even?
1). 5x-4y is even 2). 6x+7y is even.
5x = EVEN + 4y = EVEN + EVEN = EVEN.
5x is even only if x is even.
Since x is even, xy is even.
SUFFICIENT.
Statement 2:
7y = EVEN - 6x = EVEN - EVEN = EVEN.
7y is even only if y is even.
Since y is even, xy is even.
SUFFICIENT.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- sukhman
- Master | Next Rank: 500 Posts
- Posts: 202
- Joined: Sun Sep 08, 2013 11:51 am
- Thanked: 3 times
- Followed by:2 members
Statement 1 case b: x is even and y is odd: In this case 5x-4y is EVEN
Staement 2 case b: x is even and y is odd: In this case 6x+7y is ODD
There is disrepancy among these two , in statement 1 and 2
what I did was since xy we need it to be even we can take 3 cases
x-even y-odd
x-odd y-even
x-even y-even
Brent please correct me if I am wrong (I know I am
Staement 2 case b: x is even and y is odd: In this case 6x+7y is ODD
There is disrepancy among these two , in statement 1 and 2
what I did was since xy we need it to be even we can take 3 cases
x-even y-odd
x-odd y-even
x-even y-even
Brent please correct me if I am wrong (I know I am