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

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

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New post 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
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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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

Answer: A

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?

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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

Answer: A

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.

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 19 Sep 2017, 21:51
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KUDOS
Expert's post
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:

Image

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.

Answer: E.

[Reveal] Spoiler:
Attachment:
Untitled.png
Untitled.png [ 2.03 KiB | Viewed 526 times ]

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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:

Image

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.

Answer: E.

[Reveal] Spoiler:
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?

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 19 Sep 2017, 23:49
1
This post received
KUDOS
Expert's post
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:

Image

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.

Answer: E.

[Reveal] Spoiler:
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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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Re: If A, B and C are distinct points, do line segments AB and BC have the [#permalink]

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New post 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.

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