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Geometry MGMAT question bank #6

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Gmat2Go
 Post subject: Geometry MGMAT question bank #6
 Post Posted: Tue Aug 14, 2007 11:59 pm 
Is quadrilateral ABCD a rectangle?
(1) Line segments AC and BD bisect one another.

(2) Angle ABC is a right angle.


OA is C.

From 2) I can see that its either square or rectangle so cross off b and d
From 1) I can still only see its a square

I can't tell why C tells me its rectangle but not a square? When the lines bisect each other, doesn't it create 45 degree angles, thus 45-45-90, making all sides x radical 2? THus, its a square? Please advise!
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givemeanid
 Post subject:
 Post Posted: Wed Aug 15, 2007 10:18 am 
Quote:
I can't tell why C tells me its rectangle but not a square? When the lines bisect each other, doesn't it create 45 degree angles, thus 45-45-90, making all sides x radical 2? THus, its a square? Please advise!


When diagonals bisect, they are not necessarily perpendicular bisectors of each other. For a rectangle to be a square, the diagonals have to be perpendicular bisectors, not just bisectors.
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Guest
 Post subject: follow-up
 Post Posted: Wed Aug 15, 2007 12:38 pm 
So just to follow up.

Is the Answer C or E?

If C, givemeanid, or someone else - can you please explain in further detail?

Thanks!
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givemeanid
 Post subject: Re: follow-up
 Post Posted: Wed Aug 15, 2007 2:43 pm 
Guest wrote:
So just to follow up.

Is the Answer C or E?

If C, givemeanid, or someone else - can you please explain in further detail?

Thanks!


1. When diagonals bisect each other, the quadrilateral is a parallelogram. However, this is not enough to say that the quad is a rectangle.
INSUFFICIENT.

2. Angle ABC = 90 degrees does not mean the quad is rectangle. We do not know anything else.
INSUFFICIENT.

Now, combining together, we know it is a parallelogram with one angle = 90 degrees. This is sufficient to say that the quad is a rectangle. (To figure this, since one angle is 90, the opposite angle is 90 too. In a parallelogram, opposite angles are equal. So, we have a pair of angles, each = 90. Since the sum of all 4 angles = 360, sum of the other pair = 360 - 90*2 = 180. Since, these angle are also equal to each other, they are also 90 degrees each. So, all angles are 90 degrees and diagonals bisect. The quad is a rectangle.)
SUFFICIENT.

Answer is C.
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Gmat2Go
 Post subject:
 Post Posted: Thu Aug 16, 2007 1:39 am 
Is it true that all squares are also rectangles?
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givemeanid
 Post subject:
 Post Posted: Thu Aug 16, 2007 8:59 am 
Gmat2Go wrote:
Is it true that all squares are also rectangles?


Yes. All squares are rectangles. However, the inverse is not true.
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StaceyKoprince
 Post subject:
 Post Posted: Sat Aug 18, 2007 3:22 pm 
Online
ManhattanGMAT Staff


Posts: 6068
Location: San Francisco
Nice, givemeanid. Keep up the great work!

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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tlc
 Post subject:
 Post Posted: Sun Jan 18, 2009 5:52 pm 
With the given two statements, couldn't the quadrilateral also be a rhombus? Definition of a rhombus: All sides are equal and opposite angles are equal.

Therefore,

(1) A rhombus can have line segments AC and BD bisect one another
(2) A rhombus can also have one right angle

Please explain why the two statements don't also suggest that the quadrilateral could be a rhombus.

Thanks-
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tlc
 Post subject:
 Post Posted: Wed Jan 21, 2009 8:47 pm 
Is anyone monitoring this post? Thanks-
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JonathanSchneider
 Post subject:
 Post Posted: Thu Jan 22, 2009 5:35 pm 
Offline
ManhattanGMAT Staff


Posts: 380
It COULD be a rhombus, but it doesn't have to be. A rhombus must have four equal side lengths. This is not known to be the case here. Furthermore, a rhombus does not have to have a right angle at its side (though it could - this would be called a square, which is an example of a rhombus). As a result, we only know that the shape is a rectangle.
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