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If A, B and C are distinct points, do line segments AB and BC have the

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Joined: 15 Aug 2012
Posts: 29
Schools: AGSM '19
If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 10:08
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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
Intern
Joined: 15 Aug 2012
Posts: 29
Schools: AGSM '19
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 10:19
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.
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Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 15:05
rajudantuluri wrote:
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.

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

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?
Intern
Joined: 15 Aug 2012
Posts: 29
Schools: AGSM '19
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 16:05
Nikkb wrote:
rajudantuluri wrote:
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.

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

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?

I got this from one of Jeff Sackmann's question sets.
Math Expert
Joined: 02 Sep 2009
Posts: 47161
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 21:51
1
1
rajudantuluri wrote:
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

Check below:

The first figure is a square (so a rectangle too), AB ≠ AC and AB = BC;
The second figure is a rectangle, AB ≠ AC and AB ≠ BC.

Attachment:

Untitled.png [ 2.03 KiB | Viewed 1609 times ]

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Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 23:41
Bunuel wrote:
rajudantuluri wrote:
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

Check below:

The first figure is a square (so a rectangle too), AB ≠ AC and AB = BC;
The second figure is a rectangle, AB ≠ AC and AB ≠ BC.

Attachment:
Untitled.png

Bunuel : Does GMAT uses rectangle word for both square and rectangle ?
In questions where we have given suppose PQRS is a rectangle. In such cases we always assume measurement l*b and not a*a.
Is this wrong?
Math Expert
Joined: 02 Sep 2009
Posts: 47161
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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19 Sep 2017, 23:49
1
Nikkb wrote:
Bunuel wrote:
rajudantuluri wrote:
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

Check below:

The first figure is a square (so a rectangle too), AB ≠ AC and AB = BC;
The second figure is a rectangle, AB ≠ AC and AB ≠ BC.

Attachment:
Untitled.png

Bunuel : Does GMAT uses rectangle word for both square and rectangle ?
In questions where we have given suppose PQRS is a rectangle. In such cases we always assume measurement l*b and not a*a.
Is this wrong?

All squares are rectangles, so PQRS being a rectangle does not rule out possibility of it being a square.
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Intern
Joined: 15 Aug 2012
Posts: 29
Schools: AGSM '19
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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22 Sep 2017, 07:35
Thanks Bunuel! Those two figures make this a lot more clearer to me now. I just assumed a rectangle is a rectangle! Like you said, all squares are rectangles too. Broke the first rule of Geometry, DO NOT ASSUME!
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Joined: 19 Oct 2012
Posts: 340
Location: India
Concentration: General Management, Operations
GMAT 1: 660 Q47 V35
GMAT 2: 710 Q50 V38
GPA: 3.81
WE: Information Technology (Computer Software)
Re: If A, B and C are distinct points, do line segments AB and BC have the  [#permalink]

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23 Sep 2017, 09:29
While this is undisputed fact that all squares are rectangles, has there been an official question which has tested this notion? Bunuel, it would great if you can quote some questions from the top of your head.

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Re: If A, B and C are distinct points, do line segments AB and BC have the &nbs [#permalink] 23 Sep 2017, 09:29
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