Is there a diagonal in quadrilateral ABCD that is also a bisector in A

Question

Competition Mode Question

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.

Are You Up For the Challenge: 700 Level Questions

freedom128 · Answer

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

eakabuah · Answer

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.

Archit3110 · Answer

#1 ABCD is a parallelogram.
insufficient as ABCD can be square, rectangle or rhombus

#2
The diagonals of ABCD intersect at right angles
only possible when ABCD is a rhombus or square insufficient

from 1 & 2
ABCD can be square or rhombus
IMO E ;

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.

unraveled · Answer

Is there a diagonal in quadrilateral ABCD that is also a bisector in ABCD?

A bisector can intersect either perpendicularly or at any angle.

(1) ABCD is a parallelogram.
A parallelogram can have bisecting diagonals if it is a square, rectangle or a rhombus. So, SUFFICIENT.

(2) The diagonals of ABCD intersect at right angles.
The diagonals can be either equal or not but can intersect at right angles. Consider a trapezium whose diagonals insect in a perpendicular manner but are not bisectors.
Also, a quadrilateral can be formed whose diagonals are perpendicular. So both possibilities exist.

INSUFFICIENT.

Answer A.

unraveled · Answer

Going by the green highlighted part answer is C. Can you share something where it is mentioned that bisector means that.

freedom128 · Answer

https://www.mathopenref.com/bisector.html. A bisector is something that cuts an object into two equal parts. It is applied to angles and line segments. Where not mentioned specifically (angle or line segment length), it is prudent to assume that the diagonal bisects both angle and line segments. Bunuel , kindly explain

unraveled · Answer

Thanks for sharing a link but that is a known theory. May be i could not put my query properly.

As question is about a bisector and it is mentioned that a diagonal intersects, so questions asks 'can it be a bisector?'.

Hence i asked how is it known that we need to assume that both angle bisection and segment bisection are constraints within which we are required to answer.
I thought of only segment part thus the query.

ShankSouljaBoi · Answer

The bisector here is angle bisector or median ????
 VeritasKarishma

KarishmaB · Answer

The question needs to clarify what it is asking for. I would assume angle bisector here.

InaKi20 · Answer

I would assume answer A to be correct, because in a parallelogram, the diagonals bisect the whole quadrilateral into two equal triangles.
How do I know that this is not what it's asked for?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is there a diagonal in quadrilateral ABCD that is also a bisector in A

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards