duahsolo wrote:If x^2 = y^2, is it true that x > 0?
(1) x = 2y + 1
(2) y <= -1
Statement 1: x = 2y+1
Substituting x = 2y+1 into x²=y², we get:
(2y+1)² = y²
4y² + 4y + 1 = y²
3y² + 4y + 1 = 0
(3y+1)(y+1) = 0.
Case 1: 3y+1 = 0, implying that y=(-1/3) and that x = 2(-1/3) + 1 = 1/3.
Case 2: y+1 = 0, implying that y=-1 and that x = 2(-1) + 1 = -1.
Since x>0 in Case 1 but x<0 in Case 2, INSUFFICIENT.
Statement 2: y≤-1
Substituting y=-1 into x²=y², we get:
x² = (-1)²
x² = 1
x = ±1.
Since it's possible that x>0 or that x<0, INSUFFICIENT.
Statements combined:
Of the two cases yielded in Statement 1, only Case 2 satisfies Statement 2.
In Case 2, x=-1.
Since x<0, the answer to the question stem is NO.
SUFFICIENT.
The correct answer is
C.
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
