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19 Nov 2014, 00:31
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E
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:
54% (01:14) correct
46%
(01:34)
wrong
based on 373
sessions
History
Date
Time
Result
Not Attempted Yet
Is quadrilateral ABCD a parallelogram?
(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC
(1) Area of triangle ABC is equal to area of triangle ACD
(2) AD=DC
19 Nov 2014, 10:40
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anant07
In order to prove that a quadrilateral is a parallelogram at least one of the following should be true:--
1. Two pairs of opposite sides are equal or parallel
2. One pair of opposite side is equal and parallel
3. Both the pairs of opposites angles are equal
4. Diagonals bisect each other
Considering the problem
STAT1 : Area of Triangle ABC = Area of Triangle ACD
From this we just know that there is a diagonal AC and on it's two sides there are two triangles which have same area. IF we would have given that the base of these two triangles are equal and parallel then we could prove that the quadrilateral is a parallelogram. But not we can't.
STAT2: It just tells us that two adjacent are equal. Which is of no use to us.
Combining these two also doesn't give us any concrete information to prove that the figure is a parallelogram.
So, INSUFFICIENT
Hence, Answer will be E
Hope it helps!
General Discussion
19 Nov 2014, 11:28
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We just need to find out if ABCD has 2 sets of parallel sides since we know that it is a quadrilateral.
statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.
statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides
Together, ABCD must be either a square or a rhombus, both of which are paralellograms.
Answer C!
statement 1: not sufficient
This is true for a square, which is a parallelogram, and also a trapezoid, which is not a parallelogram.
statement 2: not sufficient
No info on if ABCD has 2 sets of parallel sides
Together, ABCD must be either a square or a rhombus, both of which are paralellograms.
Answer C!
