M7MBA wrote:Does x = 3?
(1) (x−3)(y−1)=0
(2) (x−3)^2+(y−1)^2=0
Statement 1: (x−3)(y−1) = 0
If y-1=0 -- implying that y=1 -- then x-3 can be equal to ANY VALUE.
For example:
x=3 and y=1, with the result that (x-3)(y-1) = (3-3)(1-0) = 0*0 = 0.
x=4 and y=1, with the result that (x-3)(y-1) = (4-1)(1-0) = 3*0 = 0.
Since the answer to the question stem is YES in first case but NO in the second case, INSUFFICIENT.
Statement 2: (x−3)² + (y−1)² = 0
Since the square of a value must be NONNEGATIVE, the equation above implies the following:
NONNEGATIVE + NONNEGATIVE = 0.
Since neither term can be negative, the equation in blue requires that both terms be equal to 0.
Thus:
(x-3)² = 0 and (y-1)² = 0, with the result that (x−3)² + (y−1)² = 0 + 0 = 0.
Since (x-3)² = 0, x=3.
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
B.
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
