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03 Sep 2020, 00:30
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ABCD is a quadrilateral. A rhombus is a quadrilateral whose sides are all congruent. BCEF is a rhombus and shares a common side with the quadrilateral ABCD. The area of which one is greater: ABCD or BCEF ?
(1) ABCD is a square.
(2) BCEF is not a square.
Are You Up For the Challenge: 700 Level Questions
(1) ABCD is a square.
(2) BCEF is not a square.
Are You Up For the Challenge: 700 Level Questions
03 Sep 2020, 01:22
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Given
ABCD is a quadrilateral.
BCEF is a rhombus.
Statement 1 - ABCD is a square.
Since ABCD and BCEF share a side BC, we can conclude that the lengths of sides are the same.
But we cannot conclude that BCEF is truly only a rhombus because every square is also a rhombus.
so, BCEF can be a square or a rhombus. So statement 1 is insufficient.
Statement 2 - BCEF is not a square.
This gives us a on clarity on BCEF but doesn't mention anything about ABCD
So statement 2 is insufficient.
Combining 1 and 2
we now know that ABCD is a square and BCEF is only a rhombus.
for a square and rhombus with equal sides, square will have max area.
IMO C
ABCD is a quadrilateral.
BCEF is a rhombus.
Statement 1 - ABCD is a square.
Since ABCD and BCEF share a side BC, we can conclude that the lengths of sides are the same.
But we cannot conclude that BCEF is truly only a rhombus because every square is also a rhombus.
so, BCEF can be a square or a rhombus. So statement 1 is insufficient.
Statement 2 - BCEF is not a square.
This gives us a on clarity on BCEF but doesn't mention anything about ABCD
So statement 2 is insufficient.
Combining 1 and 2
we now know that ABCD is a square and BCEF is only a rhombus.
for a square and rhombus with equal sides, square will have max area.
IMO C
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03 Sep 2020, 01:35
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Both ABCD and BCEF share 1 side
1) ABCD is a square
Case 1: BCEF is a square
Both ABCD and BCEF have same area.
Case 2: BCEF is a rectangle
ABCD have bigger area.(Since square have the greatest area among all quadrilaterals)
(Insufficient)
2) BCEF is not a square.
Case 1: ABCD is a square
ABCD have bigger area
Case 2: ABCD is also not a square, there are many possible figure of ABCD and BCEF, I.e. Rectangle, Trapezoid, Trapezium, Rhombus. Varying the area among each other.
(Insufficient)
Combining both.
ABCD is a square and BCEF is a non square.
Therefore area of ABCD is bigger.
(Sufficient)
Answer is C
Posted from my mobile device
1) ABCD is a square
Case 1: BCEF is a square
Both ABCD and BCEF have same area.
Case 2: BCEF is a rectangle
ABCD have bigger area.(Since square have the greatest area among all quadrilaterals)
(Insufficient)
2) BCEF is not a square.
Case 1: ABCD is a square
ABCD have bigger area
Case 2: ABCD is also not a square, there are many possible figure of ABCD and BCEF, I.e. Rectangle, Trapezoid, Trapezium, Rhombus. Varying the area among each other.
(Insufficient)
Combining both.
ABCD is a square and BCEF is a non square.
Therefore area of ABCD is bigger.
(Sufficient)
Answer is C
Posted from my mobile device
