Question

If A>B and B(B-A)>0, which of the following must be true?
I. B<0
II. A<0
III. AB<0

A: I only
B: II only
C: I and II
D: I and III

Answer 1

You know that B(B-A) is positive, so what does this tell you?

Answer 2

That B is positive?

Answer 3

Well if B is positive, then is B-A positive or negative?

Answer 4

Positive?

Answer 5

Ah, I get it, B is negative and A is positive. So it is D: I and III because A is greater than B and that means Positive X Negative = Negative

Answer 6

Kenny, how about this
given A > B , e.g. A = 10, B = 3
then what is B-A ?? would it not be -7

then, then for B(B-A) > 0 , B would have to be negative, so B ≠ 3, but B = -3 will work
and for the above example AB < 0 , so I and III are both correct

how about letting both A and B be negative, but still A > B
e.g. A = -5, B = -12
then B - A = -7
and for B(B-A) > 0 , B has to be negative
but then AB > 0 , which is false
so I is true, but III is false

What about I and II ?? true for this example, but not true for the first example

What is your final conclusion ??

Answer 7

B is negative, for that example you make it A = 10 B = -3, B - A is -3 - 10, which is -13 and then -3(-13) = 39 and 39 > 0.