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Manager
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Modules [#permalink] New post 01 Apr 2007, 12:15
Is B>=0?

1) B * |B| = B^2
2)|B| + B!=2

What is the answer and why?
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 [#permalink] New post 01 Apr 2007, 12:27
(D) for me :)

B >= 0

From 1
B * |B| = B^2

As B^2 >= 0 by definition, we have:
B * |B| >= 0
<=> B >= 0 as |B| >= 0 by definition too.

SUFF.

From 2
|B| + B!=2 >>> By definition of the factorial, B must be a positive integer or 0.

SUFF.
Director
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 [#permalink] New post 01 Apr 2007, 12:31
The question asks whether B is either a positive number or zero

Statement 1: B * |B| = B^2

The only case for this is when B is either positive becuase B^2 must be positive So both B and |B| are either positive or negative OR when B is zero and zero x zero = zero. Since |B|, by definition, is always positive --> B is positive or zero.

statement 1 is sufficient


Statement 2: |B| + B!=2

|B| is by definition positive. Because |B| + B! result in a positive integer, B! can either be a negative number that is smaller than B or a positive number. By definition, B! is positive non-zero number because factorials are valid of positive numbers only and the resulting factorial can never equal zero. Therefore, YES, B is a positive number.

Statement 2 is sufficient


Answer: D
Senior Manager
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 [#permalink] New post 01 Apr 2007, 23:53
Quote:
Is B>=0?

1) B * |B| = B^2
2)|B| + B!=2


Taking (1):
B * |B| = B^2 = B*B

B * |B| = B*B

|B| = B*B/B = B

|B| = B Since |B| is always +ve so B is a positive integer SUFF

(2) Fig wrote:
Quote:
From 2
|B| + B!=2 >>> By definition of the factorial, B must be a positive integer or 0. SUFF.


Earlier, I was confused with stmt (2) but thanks Fig!

Hence the answer is D :)

Last edited by Summer3 on 02 Apr 2007, 00:09, edited 1 time in total.
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 [#permalink] New post 02 Apr 2007, 00:02
D from me

regards,

Amardeep
  [#permalink] 02 Apr 2007, 00:02
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