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a data from gmat club

by diebeatsthegmat » Tue Dec 21, 2010 2:41 pm
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

[spoiler]why the answer is C instead of D?
as i know a bisectore in ABCD will divide ABCD into 2 equal triangles, right? so A is also sufficient... ???[/spoiler]
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by Night reader » Tue Dec 21, 2010 7:53 pm
diebeatsthegmat wrote: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

[spoiler]why the answer is C instead of D?
as i know a bisectore in ABCD will divide ABCD into 2 equal triangles, right? so A is also sufficient... ???[/spoiler]
bisector may divide line segments into two separate and equal parts; since the diagonal divides not the line segment but angle in this case not sufficient.
Choice C suggests that the quadrilateral is rhombus, hence the angles bisected are equal.

p.s. when I was reading gmat hacks I was surprised how many elementary concepts I might not be sure of... yet I was solving 700-800 level questions correctly in MGMAT.
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by goyalsau » Wed Dec 22, 2010 6:32 am
diebeatsthegmat wrote: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

[spoiler]why the answer is C instead of D?
as i know a bisectore in ABCD will divide ABCD into 2 equal triangles, right? so A is also sufficient... ???[/spoiler]
HI! Buddy,

As i understand from your question, It ask whether Diagonal Divided the Quadrilateral in two equal part or not. ????

(1)
In Parallelogram diagonals divides the Parallelogram in to two congruent Triangles,

Hence Sufficient

(2) It simply Says Quadrilateral in a Rhombus...

Sufficient

I did some search on the net before posting this answer. and if somebody do not agree to me Please Share your source of reasoning......... I will be very Pleased...... I till be a new learning for me.........
Saurabh Goyal
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EveryBody Wants to Win But Nobody wants to prepare for Win.
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by diebeatsthegmat » Wed Dec 22, 2010 5:15 pm
goyalsau wrote:
diebeatsthegmat wrote: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

[spoiler]why the answer is C instead of D?
as i know a bisectore in ABCD will divide ABCD into 2 equal triangles, right? so A is also sufficient... ???[/spoiler]
HI! Buddy,

As i understand from your question, It ask whether Diagonal Divided the Quadrilateral in two equal part or not. ????

(1)
In Parallelogram diagonals divides the Parallelogram in to two congruent Triangles,

Hence Sufficient

(2) It simply Says Quadrilateral in a Rhombus...

Sufficient

I did some search on the net before posting this answer. and if somebody do not agree to me Please Share your source of reasoning......... I will be very Pleased...... I till be a new learning for me.........
i thought the same as you did and got the answer D but its C the OA. thats why i need an explanation why
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by Geva@EconomistGMAT » Thu Dec 23, 2010 1:42 am
diebeatsthegmat wrote:
goyalsau wrote:
diebeatsthegmat wrote:

I did some search on the net before posting this answer. and if somebody do not agree to me Please Share your source of reasoning......... I will be very Pleased...... I till be a new learning for me.........
i thought the same as you did and got the answer D but its C the OA. thats why i need an explanation why
https://www.merriam-webster.com/dictionary/bisector

According to webster, a bisector halves a line segment or angle, not a full figure. Here, the problem asks whether the line bisects the angles of the quadrilateral.

stat. (1): a diagonal will not bisect the angles of a regular parallelogram, but it will for a rhmbus, which is a specific case of a parallelogram. Insufficient, since we don't know either way.

Stat. (2): Without stat. (1), it is also possible to construct an equilateral trapezoid with perpendicular angles, for which the diagonals will not bisect the angles. Insufficient

combined : a parallelogram with perpendicular diagonals is a rhombus, in which the diagonals are also bisectors of the angles. Sufficient.
Geva
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by diebeatsthegmat » Thu Dec 23, 2010 7:09 pm
Geva@MasterGMAT wrote:
diebeatsthegmat wrote:
goyalsau wrote:
diebeatsthegmat wrote:

I did some search on the net before posting this answer. and if somebody do not agree to me Please Share your source of reasoning......... I will be very Pleased...... I till be a new learning for me.........
i thought the same as you did and got the answer D but its C the OA. thats why i need an explanation why
https://www.merriam-webster.com/dictionary/bisector

According to webster, a bisector halves a line segment or angle, not a full figure. Here, the problem asks whether the line bisects the angles of the quadrilateral.

stat. (1): a diagonal will not bisect the angles of a regular parallelogram, but it will for a rhmbus, which is a specific case of a parallelogram. Insufficient, since we don't know either way.

Stat. (2): Without stat. (1), it is also possible to construct an equilateral trapezoid with perpendicular angles, for which the diagonals will not bisect the angles. Insufficient

combined : a parallelogram with perpendicular diagonals is a rhombus, in which the diagonals are also bisectors of the angles. Sufficient.
thanks. i forgot about an equilateral :(
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