Algebra

Guest · Posted: Fri Aug 17, 2007 7:15 am Post subject: Algebra

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 ???

gabriel · Posted: Fri Aug 17, 2007 11:49 am Post subject:

...a^2-b^2 will be greater than 6(a^2-b^2) if a^2-b^2 is negative ... so the question further reduces to is a^2-b^2<0 ..

statement 1 says b<a .. eg b =1 and a =2 .. a^2-b^2 = 4 -1 =3 > 0 ..
eg b = -3 and a = -2 in which case a^2-b^2 = 4 - 9 = -5 < 0 .. so 2 different possibilities .. so this statement alone is insufficient ..

statement 2 says a< -1 .. it says nothing about b .. so insufficient ..

combine the two statements we get b< a and a<-1 so if a = -2 , b can be -3 .. so a^2-b^2 = 4 - 9 = -5 .. which gives us a defnite answer so ans is C ..

bingojohn · Posted: Fri Aug 17, 2007 12:02 pm Post subject: Re: Algebra