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M14-32

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M14-32  [#permalink]

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New post 16 Sep 2014, 00:54
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A
B
C
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E

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M14-32  [#permalink]

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New post 16 Sep 2014, 00:54
Official Solution:

If points A, B, C, and D form a quadrilateral, is AC longer than BD?

Statement (1) by itself is insufficient. Imagine a kite-shaped figure with an obtuse angle on top.

Statement (2) by itself is insufficient. S2 means that the quadrilateral is a rhombus.

Statements (1) and (2) combined are sufficient. S2 means that the quadrilateral is a rhombus, while S1 tells us which diagonal of the rhombus is longer.


Answer: C
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Re: M14-32  [#permalink]

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New post 05 Dec 2014, 22:14
Why does the angle determine the length of the diagonal?
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New post 06 Dec 2014, 06:37
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Re: M14-32  [#permalink]

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New post 21 Jun 2015, 10:08
Bunuel

Could you please show a case in which AC is shorter or equal to BD according to statement 1?
Having hard time seeing (kite-shaped as suggested) with obtuse angle BCD being less than angle ABC...

Thank you!!
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New post 06 Jan 2016, 13:17
me too :/ maybe someone wants to be really kind and draw it ....? :)
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Re: M14-32  [#permalink]

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New post 12 Jan 2016, 05:35
3
in the figure, as per statement, the angles are different but you can see the lengths different.
>> !!!

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Re: M14-32  [#permalink]

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New post 31 Jul 2016, 06:36
saran3129 wrote:
in the figure, as per statement, the angles are different but you can see the lengths different.


Hi Buneul,

Could you please elaborate on the explanation. If 4 sides are equal in a rhombus, won`t it have equal diagonals?

Cheers
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New post 01 Aug 2016, 02:20
Balajikarthick1990 wrote:
saran3129 wrote:
in the figure, as per statement, the angles are different but you can see the lengths different.


Hi Buneul,

Could you please elaborate on the explanation. If 4 sides are equal in a rhombus, won`t it have equal diagonals?

Cheers
Balaji


Not necessarily. If the diagonals of a rhombus are equal, then the rhombus is a square. Check rhombus with unequal diagonals below:
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Re: M14-32  [#permalink]

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New post 20 Mar 2017, 15:40
Bunuel, can you please explain the relationship between the measure of angles and the diagonals of a rhombus. In the figure above if angle ABC > angle BCD, how does that make the diagonal AC> diagonal BD?
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New post 21 Mar 2017, 03:57
vtomar20 wrote:
Bunuel, can you please explain the relationship between the measure of angles and the diagonals of a rhombus. In the figure above if angle ABC > angle BCD, how does that make the diagonal AC> diagonal BD?


Important properties of a triangle.
The shortest side is always opposite the smallest angle.
The longest side is always opposite the largest angle.
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Re: M14-32  [#permalink]

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New post 03 Jun 2017, 01:43
Hi Bunuel,

I have a doubt can't the first statement itself say that which diagonal is longer. If we are applying the property of triangle taking both the statements, can't it be taken individually.

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New post 23 Jun 2017, 05:56
Please Bunuel
may you elaborate on statement 1? Even with kite shaped figure i see that the bigger angle is opposite the biggest diagonal ? What is this i cant see?
It must be something obvious but i posted since someone else had the same doubt before..
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New post 23 Jun 2017, 11:20
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alexlovesgmat wrote:
Please Bunuel
may you elaborate on statement 1? Even with kite shaped figure i see that the bigger angle is opposite the biggest diagonal ? What is this i cant see?
It must be something obvious but i posted since someone else had the same doubt before..
Thanks


Consider the image below:
Attachment:
Untitled.png


In both figures \(\angle ABC \gt \angle BCD\) but in the first one \(AC>BD\) and in the second one \(AC<BD\).

Hope it helps.
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Re: M14-32  [#permalink]

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New post 24 Jun 2017, 10:18
Bunuel wrote:
Official Solution:

If points A, B, C, and D form a quadrilateral, is AC longer than BD?

Statement (1) by itself is insufficient. Imagine a kite-shaped figure with an obtuse angle on top.

Statement (2) by itself is insufficient. S2 means that the quadrilateral is a rhombus.

Statements (1) and (2) combined are sufficient. S2 means that the quadrilateral is a rhombus, while S1 tells us which diagonal of the rhombus is longer.


Answer: C


Bunuel

A rhombus with equal sides means that the diagonals are equal. Choice B should be sufficient alone.

Why do you consider it wrong?
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New post 24 Jun 2017, 10:36
Mo2men wrote:
Bunuel wrote:
Official Solution:

If points A, B, C, and D form a quadrilateral, is AC longer than BD?

Statement (1) by itself is insufficient. Imagine a kite-shaped figure with an obtuse angle on top.

Statement (2) by itself is insufficient. S2 means that the quadrilateral is a rhombus.

Statements (1) and (2) combined are sufficient. S2 means that the quadrilateral is a rhombus, while S1 tells us which diagonal of the rhombus is longer.


Answer: C


Bunuel

A rhombus with equal sides means that the diagonals are equal. Choice B should be sufficient alone.

Why do you consider it wrong?


Please read the whole thread: https://gmatclub.com/forum/m14-184027.html#p1717536

P.S. Rhombus by definition has equal sides.
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Re: M14-32  [#permalink]

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New post 24 Jun 2017, 10:40
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Mo2men wrote:
Bunuel wrote:
Official Solution:

If points A, B, C, and D form a quadrilateral, is AC longer than BD?

Statement (1) by itself is insufficient. Imagine a kite-shaped figure with an obtuse angle on top.

Statement (2) by itself is insufficient. S2 means that the quadrilateral is a rhombus.

Statements (1) and (2) combined are sufficient. S2 means that the quadrilateral is a rhombus, while S1 tells us which diagonal of the rhombus is longer.


Answer: C


Bunuel

A rhombus with equal sides means that the diagonals are equal. Choice B should be sufficient alone.

Why do you consider it wrong?


Hi

A Rhombus is a quadrilateral that has all 4 sides equal, but that does NOT necessarily mean that its diagonals will also be equal.
Bunuel has already explained it in this thread by the means of a diagram before, please check.

A Rhombus whose diagonals are made equal, then becomes a Square.
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Re: M14-32  [#permalink]

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New post 07 Mar 2018, 23:54
can anyone please elaborate why statement A alone is not sufficient as we use property of triangle that larger angle will have opposite side larger which is conveyed by statement 1 and it straight away tell us AC>BD so answer must be A only because second statement tell us all sides equal then if its a square then we can say no and if its a rhombus then may be so insufficient please help he
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New post 08 Mar 2018, 01:46
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rishabhmishra wrote:
can anyone please elaborate why statement A alone is not sufficient as we use property of triangle that larger angle will have opposite side larger which is conveyed by statement 1 and it straight away tell us AC>BD so answer must be A only because second statement tell us all sides equal then if its a square then we can say no and if its a rhombus then may be so insufficient please help he
#bunuel Bunuel


AC and BC are NOT in the same triangle so you cannot apply this property here. You can check the diagram above which shows this clearly: https://gmatclub.com/forum/m14-184027.html#p1875155
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Re: M14-32  [#permalink]

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New post 08 Mar 2018, 04:32
Bunuel wrote:
rishabhmishra wrote:
can anyone please elaborate why statement A alone is not sufficient as we use property of triangle that larger angle will have opposite side larger which is conveyed by statement 1 and it straight away tell us AC>BD so answer must be A only because second statement tell us all sides equal then if its a square then we can say no and if its a rhombus then may be so insufficient please help he
#bunuel Bunuel


AC and BC are NOT in the same triangle so you cannot apply this property here. You can check the diagram above which shows this clearly: https://gmatclub.com/forum/m14-184027.html#p1875155

THANKS a lot sir
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Re: M14-32 &nbs [#permalink] 08 Mar 2018, 04:32
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