Algebra

Anonymous wrote:Is the value of a^2 - b^2 greater than the value of (3a + 3b)(2a - 2b) ?

(1) b < a

(2) a < -1


I assumed stmt 1 is enough to solve, using the followin method:
Deduced the given question as
Is a^2 - b^2 > 6(a^2 - b^2 )

Taking statement 1 - b<a, which means that the after performing the action of a^2 - b^2 the result is a positive no, which ultimately helps to answer the final question.
Stmt 2 insuff as b is not mentioned.

So, statement 1 is by itself sufficient, But the answer is C, anyone can explain why,how ???

Is a^2 - b^2 > 6(a^2 - b^2 )?

For this to be true, we need to know if a^2 - b^2 is negative or not... in other words,

Is a^2 < b^2? ............. (question)

statement(1): b < a
First consider values such that a^2 > b^2...
say a = 4 and b = -2
=> a^2 = 16 and b^2 = 4
=> a^2 - b^2 = 12
satisfies statement(1) doesn't satisfy question

Then consider values such that a^2 < b^2...
say a = 2 and b = -4
=> a^2 = 4 and b^2 = 16
=> a^2 - b^2 = -12
satisfies statement(1) and satisfies question

statement(1) Not Sufficient

Its quite obvious that statement (2) alone is Not Sufficient.

When you consider statement(1) and (2) together, if a is negative and greater than b, b has to be negative also... such that a^2 < b^2 is always true, and hence the answer is [C].