Vincen wrote:If b is an even integer is b < 0 ?
(1) b^2 - 4b + 4 < 16
(2) b^2 > 9
The OA is A.
I know the option (2) alone is not sufficient, but I could not determine if the statement (1) is sufficient. Can any expert help me here.
Statement 1: b² - 4b + 4 < 16
Rephrased:
(b-2)² < 16.
If b=-2, then (b-2)² = (-2-2)² = (-4)² = 16.
If b=-4, then (b-2)² = (-4-2)² = (-6)² = 36.
If b=-6, then (b-2)² = (-6-2)² = (-8)² = 64.
Notice the PATTERN.
When b=-2, (b-2)² = 16.
As b becomes more negative, (b-2)² becomes BIGGER.
Implication:
There is no negative even value for b such that (b-2)² < 16.
Since b cannot be negative, the answer to the question stem is NO.
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