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## If b is an even integer is b < 0 ?

This topic has 1 expert reply and 2 member replies

### Top Member

Vincen Legendary Member
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#### If b is an even integer is b < 0 ?

Fri Sep 15, 2017 7:13 pm
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.

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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GMAT Score:
790
Fri Sep 15, 2017 7:36 pm
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: bÂ² - 4b + 4 < 16
Rephrased:
(b-2)Â² < 16.
If b=-2, then (b-2)Â² = (-2-2)Â² = (-4)Â² = 16.
If b=-4, then (b-2)Â² = (-4-2)Â² = (-6)Â² = 36.
If b=-6, then (b-2)Â² = (-6-2)Â² = (-8)Â² = 64.
Notice the PATTERN.
When b=-2, (b-2)Â² = 16.
As b becomes more negative, (b-2)Â² becomes BIGGER.
Implication:
There is no negative even value for b such that (b-2)Â² < 16.
Since b cannot be negative, the answer to the question stem is NO.
SUFFICIENT.

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Mo2men Legendary Member
Joined
25 Sep 2015
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Sat Sep 16, 2017 6:45 am
GMATGuruNY wrote:
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: bÂ² - 4b + 4 < 16
Rephrased:
(b-2)Â² < 16.
If b=-2, then (b-2)Â² = (-2-2)Â² = (-4)Â² = 16.
If b=-4, then (b-2)Â² = (-4-2)Â² = (-6)Â² = 36.
If b=-6, then (b-2)Â² = (-6-2)Â² = (-8)Â² = 64.
Notice the PATTERN.
When b=-2, (b-2)Â² = 16.
As b becomes more negative, (b-2)Â² becomes BIGGER.
Implication:
There is no negative even value for b such that (b-2)Â² < 16.
Since b cannot be negative, the answer to the question stem is NO.
SUFFICIENT.
Dear Mitch,

For statement 1:

If b = 0 ..........then 4 < 16

If b = 2...........then 0 < 16

If b = 4............then 4 <16

How come A is sufficient?????

Mo2men Legendary Member
Joined
25 Sep 2015
Posted:
579 messages
Followed by:
5 members
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Sat Sep 16, 2017 6:49 am
Mo2men wrote:
GMATGuruNY wrote:
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: bÂ² - 4b + 4 < 16
Rephrased:
(b-2)Â² < 16.
If b=-2, then (b-2)Â² = (-2-2)Â² = (-4)Â² = 16.
If b=-4, then (b-2)Â² = (-4-2)Â² = (-6)Â² = 36.
If b=-6, then (b-2)Â² = (-6-2)Â² = (-8)Â² = 64.
Notice the PATTERN.
When b=-2, (b-2)Â² = 16.
As b becomes more negative, (b-2)Â² becomes BIGGER.
Implication:
There is no negative even value for b such that (b-2)Â² < 16.
Since b cannot be negative, the answer to the question stem is NO.
SUFFICIENT.
Dear Mitch,

For statement 1:

If b = 0 ..........then 4 < 16

If b = 2...........then 0 < 16

If b = 4............then 4 <16

How come A is sufficient?????

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