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

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by mbawisdom » Tue Mar 06, 2018 9:06 am
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

[spoiler]OA=E[/spoiler].

How can I discard the rest of the options? Experts, can you give me some help? <i class="em em-pray"></i>
Lets look at each answer:

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!
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by [email protected] » Tue Mar 06, 2018 5:31 pm
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 B = 1/6
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...

Final Answer: E

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by Jeff@TargetTestPrep » Mon Mar 12, 2018 4:12 pm
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.

Answer: E

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