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

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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.

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by EconomistGMATTutor » Tue Nov 14, 2017 2:23 pm
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.
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by Brent@GMATPrepNow » Wed Nov 15, 2017 11:57 am
LUANDATO wrote: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 - b²)/b
NOTE: this is one of those questions that require us to check/test each answer choice.
In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

So, let's start with E: (1 - b²)/b
Factor the numerator to get: (1 + b)(1 - b)/b [the numerator 1 - b² is a DIFFERENCE OF SQUARES, which can be factored]

Since b > 1, we know that...
(1+b) is POSITIVE
(1-b) is NEGATIVE
b is POSITIVE

So, (1 - b²)/b = (1 + b)(1 - b)/b
= (POSITIVE)(NEGATIVE)/(POSITIVE)
= (NEGATIVE)/(POSITIVE)
= NEGATIVE

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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