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

tagged by: Gmat_mission

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

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

OA=E.

How can I discard the rest of the options? Experts, can you give me some help?

### GMAT/MBA Expert

Elite Legendary Member
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Hi Gmat_mission,

We're told that B is greater than 1. We're asked which of the following MUST be negative (which really means "which of the following is ALWAYS NEGATIVE no matter how many different examples we can come up with"). This question can be solved by TESTing VALUES.

IF... B=2, then
Answer A = 0/1 = 0
Answer C = (-1)^2 = 1
Answer D = 0/-1 = 0

None of the first 4 answers is negative - and there's only one answer left...

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Senior | Next Rank: 100 Posts
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Gmat_mission 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 - b^2)/b

OA=E.

How can I discard the rest of the options? Experts, can you give me some help?

A. (2 - b)(b - 1): (+ or -)(+) --> answer can be + or -
B. (b - 1)/3b: (+)/(+) --> answer is +
C. (1 - b)^2 : square is never negative
D. (2 - b)/(1 - b): (+ or -)/(-) --> answer can be + or -
E. (1 - b^2)/b (-)/(+) --> answer is always negative as b^2 > 1!

### GMAT/MBA Expert

GMAT Instructor
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09 Apr 2015
Posted:
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39
Gmat_mission 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 - b^2)/b
Since b is greater than 1, (1 - b^2) will always be negative, and thus (1 - b^2)/b will always be negative.

_________________
Jeffrey Miller Head of GMAT Instruction

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