help data sufficeny- algebraic question

[coolgirl26]

If ab=40, what is value of

AB(A+2B)?

1) A-B= -18

2) A^2B=18


The answer apparently is B, but I dont understand why, can someone please help me..btw thank you all for helping me so far its been a great help..

Can you also show me your algebraic manipulation on how to solve for these..I'm really having trouble

[DanaJ]

Well, since you know ab, then all you need to know is a + 2b.

1. this means that a = b - 18. Substitute that in ab = 40 to get:
b^2 - 18b = 40
b^2 - 18b - 40 = 0.
(b + 2)(b - 20) = 0, with 2 solutions:
b = -2 means that a = -20
b = 20 means that a = 2.
As you can see, you have two sets of answers for this, so 1 is not sufficient.

2. a^2*b = 18 means that a*(ab) = 18 or that 40*a = 18. This means that you can find an unique value for a (which will be 18/40 = 9/20), which in turn will yield an unique value for b. This means that 2 offers only one solution, so 2 is enough.