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01 Jan 2020, 14:11
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C
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Difficulty:
95%
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Question Stats:
16% (00:47) correct
84%
(01:08)
wrong
based on 63
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Is there a diagonal in quadrilateral ABCD that is also a bisector in ABCD?
(1) ABCD is a parallelogram.
(2) The diagonals of ABCD intersect at right angles.
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Updated on: 04 Jan 2020, 21:24
Originally posted by freedom128 on 01 Jan 2020, 14:47.
Last edited by freedom128 on 04 Jan 2020, 21:24, edited 9 times in total.
Last edited by freedom128 on 04 Jan 2020, 21:24, edited 9 times in total.
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This is a kind of quant questions that look simple but need to read the whole statements carefully, in order to realize what is being asked.
After reading the whole statements, I realize that bisector asked here means that a diagonal bisects the other in BOTH equal length and equal angle.
1) Imagine a rectangle and a square as examples. Their diagonals bisect each other in equal length, but NOT necessarily in equal angle.
NOT SUFFICIENT
2) Imagine a kite and a square as examples. Although their diagonals intersect at right angle, they don't necessarily bisect each other in length.
NOT SUFFICIENT
1)+2)
We are certain that ABCD is a square. Thus, ABCD has a diagonal that is a bisector in both length and angle.
SUFFICIENT
FINAL ANSWER IS (C)
Posted from my mobile device
After reading the whole statements, I realize that bisector asked here means that a diagonal bisects the other in BOTH equal length and equal angle.
1) Imagine a rectangle and a square as examples. Their diagonals bisect each other in equal length, but NOT necessarily in equal angle.
NOT SUFFICIENT
2) Imagine a kite and a square as examples. Although their diagonals intersect at right angle, they don't necessarily bisect each other in length.
NOT SUFFICIENT
1)+2)
We are certain that ABCD is a square. Thus, ABCD has a diagonal that is a bisector in both length and angle.
SUFFICIENT
FINAL ANSWER IS (C)
Posted from my mobile device
02 Jan 2020, 01:43
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We are to determine if a diagonal in quadrilateral ABCD is a bisector.
Statement 1: ABCD is a parallelogram.
Statement 1 is sufficient. We know that the diagonals of a parallelogram are bisectors of the given parallelogram. Hence, if ABCD is a parallelogram, we can conclude that the diagonals of ABCD bisect ABCD into two congruent triangles, i.e. ABC and ADC; and ABD and CBD.
Statement 2: The diagonals of ABCD intersect at right angles.
From statement 2, we can determine that ABCD is either a square or a kite. While a square has two diagonals that are bisectors, a kite has only one diagonal that bisect ABCD into two congruent triangles. But the question is only asking us to verify if there is a (one) diagonal that bisects ABCD, so, statement 2 is also sufficient. This is because there is at least one diagonal that bisects ABCD in a kite and a square.
The answer is D.
Statement 1: ABCD is a parallelogram.
Statement 1 is sufficient. We know that the diagonals of a parallelogram are bisectors of the given parallelogram. Hence, if ABCD is a parallelogram, we can conclude that the diagonals of ABCD bisect ABCD into two congruent triangles, i.e. ABC and ADC; and ABD and CBD.
Statement 2: The diagonals of ABCD intersect at right angles.
From statement 2, we can determine that ABCD is either a square or a kite. While a square has two diagonals that are bisectors, a kite has only one diagonal that bisect ABCD into two congruent triangles. But the question is only asking us to verify if there is a (one) diagonal that bisects ABCD, so, statement 2 is also sufficient. This is because there is at least one diagonal that bisects ABCD in a kite and a square.
The answer is D.
