vipulgoyal wrote:Is | a | + | b | > | a + b| ?
(1) a^2 > b^2
(2) | a | × b < 0
My take E
Because both sides of the inequality in the question stem have absolute value, we can rephrase the question stem by squaring the inequality:
(|a| + |b|)² > |a+b|²
a² + 2|a||b| + b² > a² + 2ab + b²
2|a||b| > 2ab
|a||b| > ab.
The resulting inequality will be true only if a and b have different signs.
Question rephrased: Do a and b have different signs?
Both statements are satisfied if a=-2 and b=-1.
Both statements are satisfied if a=2 and b=-1.
Thus, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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
