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15 Aug 2018, 11:15
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
56% (01:44) correct
44%
(01:39)
wrong
based on 95
sessions
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A rectangle ABCD has E, F, G and H as mid-points of its sides AB, BC, CD and DA respectively. E, F, G, H are joined to form a quadrilateral EFGH. What is the area of quadrilateral EFGH in square units?
(1) AB = 8 units and BC = 6 units.
(2) GH = 5 units.
(1) AB = 8 units and BC = 6 units.
(2) GH = 5 units.
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
15 Aug 2018, 11:36
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amanvermagmat
As shown in Image,
Let AB = 2x and BC = 2y
Now as ABCD is a rectangle, that is angle A = angle B = angle C = angle D = 90 degrees,
Analyzing Statement 1 -
(1) AB = 8 units and BC = 6 units.
Now we know what is 2x and 2y from this. Subsequently we know x and y,
Therefore we can find area of the four triangles and subtract their sums from the complete rectangle.
This gives us the area of the quadrilateral formed.
Hence Sufficient.
Analyzing Statement 2 -
(2) GH = 5 units
Knowing GH will not help us find the area of the quadilateral . Also it will not help us in finding sides of the rectangle.
Hence Insufficient.
So IMO answer is A
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15 Aug 2018, 11:54
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amanvermagmat
The quadrilateral EFGH is a rhombus. (When we joint the midpoints of a rectangle, a rhombus is formed).
Question stem:- Area of the rhombus EFGH?
St1:- AB = 8 units and BC = 6 units.
We have diagonal of rhombus, HF=AB=3 unit & EG=BC=6 unit.
Area of the rhombus EFGH can be determined, Area=0.5*EG*HF
Sufficient.
St2:- GH = 5 units
Only length of sides of the rhombus is given, we need additional information such as angle etc.
Insufficient.
Ans. (A)
