Max@Math Revolution wrote:[GMAT math practice question]
$$If\ \ x>y>0,\ is\ y<2?$$
1) $$\frac{1}{x}=\frac{1}{2}$$
2) $$\frac{1}{x}+\frac{1}{y}=1$$
Statement 1:
1/x = 1/2
x=2.
Substituting x=2 into x>y>0, we get:
2>y>0.
Thus, y<2, so the answer to the question stem is YES.
SUFFICIENT.
Statement 2:
Test whether it's possible that y≥2.
Case 1: y=2
Substituting y=2 into 1/x + 1/y = 1, we get:
1/x + 1/2 = 1
1/x = 1/2
x=2.
In this case, x=y.
Not viable, since the prompt requires that x>y.
Case 2: y=3
Substituting y=3 into 1/x + 1/y = 1, we get:
1/x + 1/3 = 1
1/x = 2/3
x=3/2.
In this case, x < y.
Not viable, since the prompt requires that x>y.
The cases above illustrate that it is not possible that y≥2.
Thus, y<2, so the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
D.
An algebraic approach to Statement 2:
1/x + 1/y = 1
1/x = 1 - (1/y)
1/x = (y-1)/y
x = y/(y-1).
Substituting x = y/(y-1) into x>y, we get:
y/(y-1) > y
1/(y-1) > 1
1 > y-1
2 > y.
Thus, the answer to the question stem is YES.
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
