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01 Apr 2007, 13:15
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Is B>=0?
1) B * |B| = B^2
2)|B| + B!=2
What is the answer and why?
1) B * |B| = B^2
2)|B| + B!=2
What is the answer and why?
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01 Apr 2007, 13:27
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(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.
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.
01 Apr 2007, 13:31
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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
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
