GMAT1

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 218
Joined: Wed Dec 11, 2013 4:02 am
Thanked: 3 times
Followed by:4 members

GMAT1

by [email protected] » Sun Mar 30, 2014 9:33 am

GMAT/MBA Expert

User avatar
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

by Brent@GMATPrepNow » Sun Mar 30, 2014 9:38 am
If x,y and z are integers and xy+z is an odd number, is x an even integer?
1) xy + xz is an even integer.
2) y + xz is an odd integer.
Target question: Is x an even integer?

Given: xy+z is an odd number

Statement 1: xy+xz is an even integer.
Notice that statement 1 has an xy term, and the given information also has an xy term. We can use this to our advantage.
We know the property: Even - Odd = Odd
So, we can conclude that (xy + xz) - (xy + z) is odd
Simplify to get: xz - z is odd
Factor: z(x - 1) is odd
IMPORTANT: if the product of two integers is odd, then both of those integers must be odd as well.
So, z must be odd
And (x-1) must be odd, which means x must be even
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: y + xz is an odd integer.
There are several conflicting sets of values that meet this condition. Here are two:
Case a: x = 0, y = 1 and z = 1, in which case x is even
Case b: x = 1, y = 2 and z = 1, in which case x is odd
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image

User avatar
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

by GMATGuruNY » Sun Mar 30, 2014 1:25 pm
If x, y, and z are integers and xy+z is an odd integer, is x an even integer?

1) xy+xz is an even integer
2) y+xz is an odd integer
Statement 1: xy + xz is even
(xy + xz) - (xy + z) = even - odd
xz - z = odd
z(x-1) = odd.
Since odd*odd = odd, x-1 must be odd, implying that x itself is even.
SUFFICIENT.

Statement 2: y + xz is odd
(y + xz) + (xy + z) = odd + odd
y + x(z+y) + z = even
x(y+z) + (y+z) = even
(y+z)(x+1) = even.
Since it's possible that x+1 is even or that x+1 is odd, no way to determine whether x is even.
INSUFFICIENT.

The correct answer is A.
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