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11 Jun 2020, 02:55
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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:
57% (01:33) correct
43%
(01:37)
wrong
based on 121
sessions
History
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Not Attempted Yet
If sides of a quadrilateral X are integers, then is X a square?
(1) Area of X is 324
(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.
Are You Up For the Challenge: 700 Level Questions
(1) Area of X is 324
(2) Areas of the triangles formed by the intersection of the diagonals of X are equal.
Are You Up For the Challenge: 700 Level Questions
11 Jun 2020, 06:17
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Bunuel
Using Statement 1, the quadrilateral could be a square with dimensions 18x18, or could be a rectangle with dimensions 1x324, among other possibilities.
Statement 2 is true of every rectangle (square or not) -- if you divide a rectangle into four triangles by drawing diagonals, the area of each triangle will be LW/4. So Statement 2 gives no useful information at all, and the answer is E.
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11 Jun 2020, 11:01
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Bunuel
Statement 1: Area of X is 324.
Now 324 = 18* 18.
So X could very well be a square.
But the dimensions of X could also be : 36*9 or 54*6. In this case X will be a rectangle.
So we cannot be sure of the shape of X.
So Insufficient.
Statement 2: Areas of the triangles formed by the intersection of the diagonals of X are equal.
The above statement again holds true for both square & rectangle.
So Insufficient.
Statement 1 + Statement 2: Even after combining both statements, we still wont have sufficient information as to whether X is a square or a rectangle.
So Answer Is E.
