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Difficulty:
35%
(medium)
Question Stats:
60% (01:04) correct
40%
(01:06)
wrong
based on 539
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Is quadrilateral ABCD a rhombus?
(1) AC is perpendicular to BD
(2) AB + CD = BC +AD
M11-05
(1) AC is perpendicular to BD
(2) AB + CD = BC +AD
M11-05
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Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
20 Dec 2014, 08:26
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Is quadrilateral \(ABCD\) a rhombus?
(1) \(AC\) is perpendicular to \(BD\).
This property holds true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(2) \(AB + CD = BC + AD\).
This property is also true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(1)+(2) Combining the two statements does not provide any additional information. Quadrilateral \(ABCD\) could still be either a rhombus or a kite. Not sufficient.
Refer to the image below for visualization:
Answer: E
(1) \(AC\) is perpendicular to \(BD\).
This property holds true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(2) \(AB + CD = BC + AD\).
This property is also true for both rhombi and kites, so this information alone is not sufficient to determine whether \(ABCD\) is a rhombus.
(1)+(2) Combining the two statements does not provide any additional information. Quadrilateral \(ABCD\) could still be either a rhombus or a kite. Not sufficient.
Refer to the image below for visualization:
Answer: E
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Kite and Rhombus.png [ 167.86 KiB | Viewed 19245 times ]
16 May 2017, 02:35
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(1) Line segments AC and BD are perpendicular bisectors of each other.
Perpendicular bisector means it would divide the line into half and thus the quadrilateral formed by joining A,B,C,D will have equal side and that is the property of rhombus
Perpendicular bisector means it would divide the line into half and thus the quadrilateral formed by joining A,B,C,D will have equal side and that is the property of rhombus
