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19 Sep 2017, 10:08
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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:
65%
(hard)
Question Stats:
51% (01:44) correct
49%
(01:36)
wrong
based on 94
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If A, B and C are distinct points, do line segments AB and BC have the same length?
(1) Together with point D, A, B and C form a rectangle.
(2) AB ≠ AC
(1) Together with point D, A, B and C form a rectangle.
(2) AB ≠ AC
19 Sep 2017, 10:19
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I thought since A B C and D form a rectangle, there is no way AB = BC no matter how you draw it. Shouldn't the answer be A?
Official explanation as below:
Explanation: Statement (1) is insufficient. If AB and BC are two sides
of a rectangle, they might be equal, but they might not be. Also, it's possible
that they are not both sides of a rectangle: it's possible that one of them is a
diagonal of the resulting rectangle.
Statement (2) is also insufficient. This tells us nothing about BC.
Taken together, the statements are still insufficient. If AB, AC, and BC are
all sides of a rectangle, we know that AB and AC are one each of the different
dimensions. However, we don't know that BC has the same length as AB; it
could have the same length as AC. And further, there is still the possibility that
one of these segments is the diagonal of the rectangle. Choice (E) is correct.
Statement 1 doesn't make sense for me since if AB and BC are considered two sides that are equal how would you even form a rectangle with D?
Is this a poor made question?
Bunuel, would appreciate your thoughts here.
Official explanation as below:
Explanation: Statement (1) is insufficient. If AB and BC are two sides
of a rectangle, they might be equal, but they might not be. Also, it's possible
that they are not both sides of a rectangle: it's possible that one of them is a
diagonal of the resulting rectangle.
Statement (2) is also insufficient. This tells us nothing about BC.
Taken together, the statements are still insufficient. If AB, AC, and BC are
all sides of a rectangle, we know that AB and AC are one each of the different
dimensions. However, we don't know that BC has the same length as AB; it
could have the same length as AC. And further, there is still the possibility that
one of these segments is the diagonal of the rectangle. Choice (E) is correct.
Statement 1 doesn't make sense for me since if AB and BC are considered two sides that are equal how would you even form a rectangle with D?
Is this a poor made question?
Bunuel, would appreciate your thoughts here.
19 Sep 2017, 15:05
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rajudantuluri
AB and BC are 2 line segments.
statement 1 : D ,A,B, C forms a rectangle : So only two combinations of rectangle can be formed : if we go clockwise 1: ABCD or 2: ABDC.
In both cases as formed figure is rectangle opposite sides are equal and adjacent sides are not equal. Also length, breadth and diagonal have different lengths.
So in all cases: Whether AB and BC forms 2 sides of rectangle or 1 form a side and other 1 is diagonal, AB never equals to BC.
Sufficient
Statement 2: AB != AC . Just tells about 2 sides of ABC triangle.
Insufficient
Answer: A
rajudantuluri : As per official explanation , we will not get the answer by statement 1 if we consider the point that " All rectangles are squares but all squares are not rectangle"
So by this if question stem says ABCD is a rectangle : it can be a rectangle(opp sides equal) or it can be a square(all sides equal).
But i am not sure if this point need to be considered here.
May you please tell source of the question?
