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

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Manager
Joined: 05 May 2005
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If b is greater than 1, which of the following must be [#permalink]  20 Aug 2007, 21:03
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
Director
Joined: 11 Jun 2007
Posts: 932
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Kudos [?]: 80 [0], given: 0

Re: Which must be negative? [#permalink]  20 Aug 2007, 21:28
above720 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

by plugging in using POE, the answer is E
CEO
Joined: 29 Mar 2007
Posts: 2585
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Re: Which must be negative? [#permalink]  20 Aug 2007, 22:17
above720 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

Plug in numbers. Try using an integer 3 and then a non-integer 1.5

When using 3 for B. A holds, and E holds. Now using 1.5 only E holds.

Ans E
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5068
Location: Singapore
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Set b to 8

a) (-6)(7) -> +ve
b) (7)/24 -> +ve
c) (-7)^2 -> +ve
d) (-6)/(-7) -> +ve
e) (-63)/8 -> -ve

Ans E
Senior Manager
Joined: 03 Jun 2007
Posts: 384
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I am not sure on this. A and E seem to be negative for certain cases of b. Is there a typo in the question ?
Director
Joined: 26 Jul 2007
Posts: 541
Schools: Stern, McCombs, Marshall, Wharton
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dahcrap wrote:
I am not sure on this. A and E seem to be negative for certain cases of b. Is there a typo in the question ?

A can be negative is some cases e.g. b=3 and positive in others e.g. b=1.5

E is negative in all cases and therefore the answer to the question of which must be negative.
Manager
Joined: 04 May 2007
Posts: 111
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dahcrap wrote:
I am not sure on this. A and E seem to be negative for certain cases of b. Is there a typo in the question ?

dahcrap,

they are asking what must be negative - so A is a trick. E is always neg
Senior Manager
Joined: 03 Jun 2007
Posts: 384
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gmatiscoming wrote:
dahcrap wrote:
I am not sure on this. A and E seem to be negative for certain cases of b. Is there a typo in the question ?

dahcrap,

they are asking what must be negative - so A is a trick. E is always neg

Aah There u go. I tend to miss this trick more often than not.
Manager
Joined: 18 Jun 2007
Posts: 88
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Kudos [?]: 1 [0], given: 0

Checking for values.. The only equation that comes as negative for all values of b is E
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