Is quadrilateral a square? : GMAT Data Sufficiency (DS)
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03 Apr 2012, 06:27
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35% (medium)

Question Stats:

60% (01:22) correct 40% (11:46) wrong based on 52 sessions

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(1) Three angles of a quadrilateral are 90 degrees each.
(2) 3 sides of a quadrilateral are equal in length.
[Reveal] Spoiler: OA
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03 Apr 2012, 06:31
(1) Three angles of a quadrilateral are 90 degrees each.
(2)3 sides of a quadrrilateral are equal in length.

OA: C

(1) Three angles of a quadrilateral are 90 degrees each: Then the quadrilateral can be a rectangle or a square.
(2) 3 sides of a quadrrilateral are equal in length: Then the quadrilateral can be a rhombus or a square.
(1) + (2): The quadrilateral has to be a square.

Hence C.
Is my reasoning correct?
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03 Apr 2012, 07:23
#1: If all four sides are equal, it still may not be a square. For example, if all angles are not 90* then it is a Rhombus. Not sufficient.
#2: Three angles 90* means the fourth angle has to be 90* too. However, if a quadrilateral has all four angles equal to 90*, does it mean it is a square? No. It could be a rectangle. Not sufficient.

Combining #1 and #2: The quadrilateral must have all four angles 90*. Since 3 sides are equal, the fourth one must be equal to these three since the pair of opposite sides must be equal if all four angles are 90*. Hence, the quadrilateral must be a square.

Hope that was clear.
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05 Apr 2012, 01:55
balas wrote:

(1) Three angles of a quadrilateral are 90 degrees each.
(2)3 sides of a quadrrilateral are equal in length.

we need two things
1) sides are equal
2) all angles 90

from statement 1)

INSUFFICIENT

from statement 2)

INSUFFICIENT

FROM BOTH 1 AND 2

we have info both sides and angles

SUFFICIENT

Hence C.

Hope this helps...!!!
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26 Aug 2016, 07:07
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