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.
If b is greater than 1, which of the following must be...
This topic has expert replies

 Moderator
 Posts: 2228
 Joined: Sun Oct 15, 2017 1:50 pm
 Followed by:6 members
 EconomistGMATTutor
 GMAT Instructor
 Posts: 555
 Joined: Wed Oct 04, 2017 4:18 pm
 Thanked: 180 times
 Followed by:12 members
Hi LUANDATO,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.
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
(22)(21) = zero
We will discard this, since zero is neither positive nor negative.
Option B:
(b  1)/3b
For b = 2
(21)/3(2)=1/6 = POSITIVE
Discard option B.
Option C:
(1  b)^2
For b = 2
(12)^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 = (14)/2 = 3/2 = NEGATIVE
Therefore, Option E is correct.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
GMAT/MBA Expert
 Brent@GMATPrepNow
 GMAT Instructor
 Posts: 16207
 Joined: Mon Dec 08, 2008 6:26 pm
 Location: Vancouver, BC
 Thanked: 5254 times
 Followed by:1268 members
 GMAT Score:770
NOTE: this is one of those questions that require us to check/test each answer choice.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)Â²
D. (2  b)/(1  b)
E. (1  bÂ²)/b
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  bÂ²)/b
Factor the numerator to get: (1 + b)(1  b)/b [the numerator 1  bÂ² is a DIFFERENCE OF SQUARES, which can be factored]
Since b > 1, we know that...
(1+b) is POSITIVE
(1b) is NEGATIVE
b is POSITIVE
So, (1  bÂ²)/b = (1 + b)(1  b)/b
= (POSITIVE)(NEGATIVE)/(POSITIVE)
= (NEGATIVE)/(POSITIVE)
= NEGATIVE
Answer: E
Cheers,
Brent