December 20, 2018 December 20, 2018 10:00 PM PST 11:00 PM PST This is the most inexpensive and attractive price in the market. Get the course now! December 22, 2018 December 22, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51302

Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
28 Apr 2015, 04:20
Question Stats:
39% (02:19) correct 61% (02:13) wrong based on 175 sessions
HideShow timer Statistics



Manager
Joined: 13 Dec 2013
Posts: 59
Location: Iran (Islamic Republic of)

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
28 Apr 2015, 06:36
Answer should be E
Data 1 ) we know that 3 sides out of 4 sides has equal length but we don't know the size of the last one. data 1 says that two lines (BC and AD ) are parallel
But we don't know the state of the 2 other sides . the quadrilateral could be a square or could be any other shape . so we can not determine the area of the shape.
Data 2 ) gives us only the size of one diameter we still are not sure about the shape of the quadrilateral , hence insufficient...
Combining the two statements , still we can not determine the shape of the quadrilateral , so we can not find the area surly,
Hence answer is E ...



Manager
Joined: 27 Dec 2013
Posts: 243

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
28 Apr 2015, 10:21
Option D for me. Giving 3 sides equal and sides BC and AD and parallel, I suppose the diagnols bisect each other. Bunuel wrote: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD. (2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Kudos for a correct solution.
_________________
Kudos to you, for helping me with some KUDOS.



Current Student
Joined: 24 Mar 2015
Posts: 35
Concentration: General Management, Marketing
GPA: 3.21
WE: Science (Pharmaceuticals and Biotech)

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
28 Apr 2015, 10:55
Bunuel wrote: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD. (2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Kudos for a correct solution. The question stem is asking us if we can find a definite area of quadrilateral ABCD, to do this we must know the exact shape of the quadrilateral including angles and appropriate side lengths. 1) This information tells us that it could be a square but without knowing that the side AD is also equal to 10 we cannot eliminate the possibility of the quadrilateral being a trapezoid which we would be unable to calculate the area of without further information regarding the shape. Not Sufficient eliminate answer choices A and D. 2) We still do not have information that would allow us to eliminate the possiblity of the shape being a trapezoid as we do not have the other diagonal that we would need to determine all angles and side lengths for the quadrilateral. Not Sufficient eliminate answer choice B. 1+2) Together we still do not have enough information without knowing more angles and lengths to determine the shape or respective area of the quadrilateral. Not Sufficient Select answer choice E.
_________________
Please pass me a +KUDOS if you liked my post! Thanks!
Do not compare yourself to others, compare yourself to who you were yesterday.



Senior Manager
Joined: 21 Jan 2015
Posts: 362
Location: India
Concentration: Strategy, Marketing
GMAT 1: 620 Q48 V28 GMAT 2: 690 Q49 V35
WE: Sales (Consumer Products)

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
29 Apr 2015, 21:47
(Ans: E) we can not specify the what type of quadrilateral it is so Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data is required to ans the question.
_________________
 The Mind is Everything, What we Think we Become.



Math Expert
Joined: 02 Sep 2009
Posts: 51302

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
04 May 2015, 03:37
Bunuel wrote: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD. (2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:We are told that three of the sides of quadrilateral ABCD have length 10. We are told nothing else about that quadrilateral, and we are asked for its area. A good way to visualize the constraints is to use “rubberband geometry.” Picture the three sides that we do know as stiff rods, each of length 10. They are hooked together with flexible hinges, because we know nothing about the angles in the polygon. Finally, the fourth side (AD) is a rubber band – it can stretch and shrink as we flex the hinged rods. Statement (1): BC is parallel to AD. Fiddle with the mental contraption of rods and hinges. To make rod BC parallel to the rubber band, you can make either a trapezoid or a parallelogram. This is because the two other sides (AB and CD) have the same length (= 10). The parallelogram will in fact be a rhombus: AD will also have length 10. Even if you knew which figure was in play, you don’t have a fixed height, so you don’t know the area. Statement (1) is NOT SUFFICIENT. Statement (2): Diagonal AC,which lies inside the quadrilateral, has length 10√3. This statement tells us that triangle ABC is fixed, and it looks something like this: We don’t need to know the exact angles; all we need to know is that the triangle is fixed in position (and thus has a fixed area). However, CD can swing through any number of angles, making the area of the other triangle (ACD) variable. Statement (2) is NOT SUFFICIENT. Statements (1) and (2) TOGETHER: We get the following pictures: Notice that either picture is possible, as long as the length of the diagonal is longer than that of a square with sides 10. That diagonal would have length 10√2. Since 10√3 is longer, we have the two possibilities above. The trapezoid actually contains the rhombus, so it has a larger area. Even together, the statements are not sufficient. The correct answer is E.Attachment:
1.gif [ 3.93 KiB  Viewed 3819 times ]
Attachment:
2.gif [ 3.5 KiB  Viewed 3822 times ]
Attachment:
3.gif [ 3.13 KiB  Viewed 3779 times ]
Attachment:
4.gif [ 5.09 KiB  Viewed 3808 times ]
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 01 Jun 2015
Posts: 218
Location: India
Concentration: Strategy, International Business

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
15 Feb 2017, 06:10
Bunuel wrote: Bunuel wrote: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD. (2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:We are told that three of the sides of quadrilateral ABCD have length 10. We are told nothing else about that quadrilateral, and we are asked for its area. A good way to visualize the constraints is to use “rubberband geometry.” Picture the three sides that we do know as stiff rods, each of length 10. They are hooked together with flexible hinges, because we know nothing about the angles in the polygon. Finally, the fourth side (AD) is a rubber band – it can stretch and shrink as we flex the hinged rods. Statement (1): BC is parallel to AD. Fiddle with the mental contraption of rods and hinges. To make rod BC parallel to the rubber band, you can make either a trapezoid or a parallelogram. This is because the two other sides (AB and CD) have the same length (= 10). The parallelogram will in fact be a rhombus: AD will also have length 10. Even if you knew which figure was in play, you don’t have a fixed height, so you don’t know the area. Statement (1) is NOT SUFFICIENT. Statement (2): Diagonal AC,which lies inside the quadrilateral, has length 10√3. This statement tells us that triangle ABC is fixed, and it looks something like this: We don’t need to know the exact angles; all we need to know is that the triangle is fixed in position (and thus has a fixed area). However, CD can swing through any number of angles, making the area of the other triangle (ACD) variable. Statement (2) is NOT SUFFICIENT. Statements (1) and (2) TOGETHER: We get the following pictures: Notice that either picture is possible, as long as the length of the diagonal is longer than that of a square with sides 10. That diagonal would have length 10√2. Since 10√3 is longer, we have the two possibilities above. The trapezoid actually contains the rhombus, so it has a larger area. Even together, the statements are not sufficient. The correct answer is E.Attachment: 1.gif Attachment: 2.gif Attachment: 3.gif Attachment: 4.gif Sir, Why did not you consider a square in statement A.



Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1143
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is
[#permalink]
Show Tags
16 Mar 2018, 21:40
we can consider Square also, But that's doesn't matter because it will not be unique answer. it can be square that there is not always a square. Hence insufficient. techiesam wrote: Bunuel wrote: Bunuel wrote: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is the area of quadrilateral ABCD?
(1) BC is parallel to AD. (2) Diagonal AC, which lies inside the quadrilateral, has length 10√3.
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:We are told that three of the sides of quadrilateral ABCD have length 10. We are told nothing else about that quadrilateral, and we are asked for its area. A good way to visualize the constraints is to use “rubberband geometry.” Picture the three sides that we do know as stiff rods, each of length 10. They are hooked together with flexible hinges, because we know nothing about the angles in the polygon. Finally, the fourth side (AD) is a rubber band – it can stretch and shrink as we flex the hinged rods. Statement (1): BC is parallel to AD. Fiddle with the mental contraption of rods and hinges. To make rod BC parallel to the rubber band, you can make either a trapezoid or a parallelogram. This is because the two other sides (AB and CD) have the same length (= 10). The parallelogram will in fact be a rhombus: AD will also have length 10. Even if you knew which figure was in play, you don’t have a fixed height, so you don’t know the area. Statement (1) is NOT SUFFICIENT. Statement (2): Diagonal AC,which lies inside the quadrilateral, has length 10√3. This statement tells us that triangle ABC is fixed, and it looks something like this: We don’t need to know the exact angles; all we need to know is that the triangle is fixed in position (and thus has a fixed area). However, CD can swing through any number of angles, making the area of the other triangle (ACD) variable. Statement (2) is NOT SUFFICIENT. Statements (1) and (2) TOGETHER: We get the following pictures: Notice that either picture is possible, as long as the length of the diagonal is longer than that of a square with sides 10. That diagonal would have length 10√2. Since 10√3 is longer, we have the two possibilities above. The trapezoid actually contains the rhombus, so it has a larger area. Even together, the statements are not sufficient. The correct answer is E.Attachment: 1.gif Attachment: 2.gif Attachment: 3.gif Attachment: 4.gif Sir, Why did not you consider a square in statement A.
_________________
Win GMAT CLUB Test Weekly Quant Quiz Contest Weekly Quant Quiz Questions Direct Download SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS




Re: Sides AB, BC, and CD of quadrilateral ABCD all have length 10. What is &nbs
[#permalink]
16 Mar 2018, 21:40






