lheiannie07 wrote:Is the value of a^2 - b^2 greater than the value of (3a + 3b) (2a - 2b) ?
(1) b < a
(2) a < -1
a²-b² > (3a+3b)(2a-2b)
a²-b² > 6a² - 6ab + 6ab - 6b²
a²-b² > 6a² - 6b²
5b² > 5a²
b² > a².
Question stem, rephrased:
Is b² > a²?
Statement 1:
Case 1: b=0, a=1
In this case, b² < a², so the answer to the question stem is NO.
Case 2: b=-1, a=0
In this case, b² > a², so the answer to the question stem is YES.
INSUFFICIENT.
Statement 2:
No information about b.
INSUFFICIENT.
Statements combined:
b < a < -1.
Since b and a are both negative, squaring both sides of b < a requires that we FLIP THE INEQUALITY, as follows:
b² > a².
Thus, the answer to the question stem is YES.
SUFFICIENT.
The correct answer is
C.
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