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If A, B, and C are distinct points

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If A, B, and C are distinct points [#permalink] New post 04 Jul 2012, 16:22
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

48% (01:00) correct 52% (01:02) wrong based on 130 sessions
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 is not equal to AC

Source: www.gmathacks.com
[Reveal] Spoiler: OA

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Re: If A, B, and C are distinct points [#permalink] New post 05 Jul 2012, 00:54
Expert's post
metallicafan 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 is not equal to AC

Source: http://www.gmathacks.com


Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Answer: E.
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Re: If A, B, and C are distinct points [#permalink] New post 05 Jul 2012, 06:56
Bunuel wrote:
Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Answer: E.


Bunuel, but the clue #1 says that ABCD is a rectangle. It is not necessary to evaluate whether it is a square or a rectangle.
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Re: If A, B, and C are distinct points [#permalink] New post 05 Jul 2012, 07:05
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metallicafan wrote:
Bunuel wrote:
Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Answer: E.


Bunuel, but the clue #1 says that ABCD is a rectangle. It is not necessary to evaluate whether it is a square or a rectangle.


I don't understand what you mean by the read part above.

As for the first statement: it says that ABCD is a rectangle, but since ALL squares are rectangles then ABCD could be a square or a rectangle which is not a square.
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Re: If A, B, and C are distinct points [#permalink] New post 05 Jul 2012, 12:12
Bunuel wrote:
metallicafan wrote:
Bunuel wrote:
Straight E:

If ABCD is a square, then AB=BC but if ABCD is NOT a square, so if it's just a rectangle, then AB and BC won't have the same length. Not sufficient.

Answer: E.


Bunuel, but the clue #1 says that ABCD is a rectangle. It is not necessary to evaluate whether it is a square or a rectangle.


I don't understand what you mean by the read part above.

As for the first statement: it says that ABCD is a rectangle, but since ALL squares are rectangles then ABCD could be a square or a rectangle which is not a square.


Ok, now I understand. I thought that, in the terminology, a rectangle could not be a "rectangle".
Thanks!
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Re: If A, B, and C are distinct points [#permalink] New post 06 Jul 2012, 06:24
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?
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Re: If A, B, and C are distinct points [#permalink] New post 06 Jul 2012, 07:49
Expert's post
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?


Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.
_________________

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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.


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Re: If A, B, and C are distinct points [#permalink] New post 12 Feb 2013, 19:57
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??
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Re: If A, B, and C are distinct points [#permalink] New post 13 Feb 2013, 00:35
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4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??


All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:
Square and Rectangle.png
Square and Rectangle.png [ 3.33 KiB | Viewed 1506 times ]
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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

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Re: If A, B, and C are distinct points [#permalink] New post 27 Mar 2013, 22:16
Bunuel wrote:
4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??


All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:
Square and Rectangle.png
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.


Sorry Bunuel for picking on this..just want to be completely sure. So unless it's specified that the figure is a square (or it forms a square), we are to assume that a rectangle means both a square and non-square?
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Re: If A, B, and C are distinct points [#permalink] New post 28 Mar 2013, 03:00
Expert's post
RMART wrote:
Bunuel wrote:
4112019 wrote:
I got little confused.......it is said that together with D, A, B, and C form a rectangle.....doesn't that mean AB and BC are not equal??


All squares are rectangles, so if ABCD IS a square then AB=BC. Look at the figures below:
Attachment:
Square and Rectangle.png
The first figure is a rectangle which IS a square, so in this case AB=BC and the second figure is a rectangle which is NOT a square, so in this case AB#BC.

Hope it's clear.


Sorry Bunuel for picking on this..just want to be completely sure. So unless it's specified that the figure is a square (or it forms a square), we are to assume that a rectangle means both a square and non-square?


If it's given that a figure is a rectangle, then it could be a square because all squares are rectangles (but not all rectangles are squares).
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If A, B, and C are distinct points [#permalink] New post 30 Mar 2014, 07:47
Bunuel wrote:
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?


Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.


But the real question is what is the order? Like for a triangle for example is P upper vertex then Q for the left vertex and R for the right vertex? And in a square do we go clockwise? Anticlockwise?

Thanks
Cheers
J
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Re: If A, B, and C are distinct points [#permalink] New post 30 Mar 2014, 10:11
Expert's post
jlgdr wrote:
Bunuel wrote:
metallicafan wrote:
Bunuel, another question:

When the question says: Together with point D, A, B, and C form a rectangle.
Is there a specific order in which the points are set?
For example, if we start in the left lower vertex of the rectangle as Point A and then continue to the left upper vertex as point B, and so on....¿would it be the correct order?

In general, when the GMAT says, for example, "a triangle ABC....", is there a specific vertex in which we should start and a orientation that we have to follow?


Generally when we are given "quadrilateral ABCD" or "triangle PQR", then it means that vertices are in that particular order only.


But the real question is what is the order? Like for a triangle for example is P upper vertex then Q for the left vertex and R for the right vertex? And in a square do we go clockwise? Anticlockwise?

Thanks
Cheers
J


Square ABCD means that the order of the vertices is A, B, C, D. Usually it does not matter whether you go clockwise or anticlockwise.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If A, B, and C are distinct points   [#permalink] 30 Mar 2014, 10:11
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