If b is greater than 1, which of the following must be...

If b is greater than 1, which of the following must be negative?

A. (2 - b)(b - 1)
B. (b - 1)/3b
C. (1 - b)^2
D. (2 - b)/(1 - b)
E. (1 - b^2)/b

The OA is E.

Please, can any expert assist me with this PS question? I'm really confused with it. Thanks in advanced.

Hi LUANDATO,
Let's take a look at your question.

We will check each option one by one that if b is a number greater than 1, whether the result is negative or positive.

Lets start from Option A.
(2 - b)(b - 1)
Let b = 2
(2-2)(2-1) = zero
We will discard this, since zero is neither positive nor negative.

Option B:
(b - 1)/3b
For b = 2
(2-1)/3(2)=1/6 = POSITIVE
Discard option B.

Option C:
(1 - b)^2
For b = 2
(1-2)^2= (-1)^2 = 1 = POSITIVE
Discard Option C

Option D:
(2 - b)/(1 - b)
For b = 2
(2 - 2)/(1 - 2) = Zero
Discard option D, since zero is neither positive nor negative.

Option E:
(1 - b^2)/b
For b = 2
(1 - 2^2)/2 = (1-4)/2 = -3/2 = NEGATIVE

Therefore, Option E is correct.

Hope it helps.
I am available if you'd like any follow up.