Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Aug 2014, 00:17

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In the figure above, what is the value of x + y ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 2

Kudos [?]: 257 [0], given: 0

In the figure above, what is the value of x + y ? [#permalink] New post 18 Dec 2012, 05:08
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

64% (01:53) correct 36% (00:49) wrong based on 335 sessions
Attachment:
Triangles.png
Triangles.png [ 7.26 KiB | Viewed 3857 times ]
In the figure above, what is the value of x + y ?

(1) x = 70
(2) ABC and ADC are both isosceles triangles
[Reveal] Spoiler: OA
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24438 [2] , given: 2677

Re: In the figure above, what is the value of x + y ? [#permalink] New post 18 Dec 2012, 05:19
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Image
In the figure above, what is the value of x + y ?

(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Even when we consider both statements together we don't know the placement of points D and B. For example consider the diagram below:
Attachment:
Triangles2.png
Triangles2.png [ 10.79 KiB | Viewed 3572 times ]
As you can see we can have two different answers for x+y for two different placements of point D.

Answer: E.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: In the figure above, what is the value of x + y ? [#permalink] New post 27 Dec 2012, 01:30
Hi Bunuel, I see your point. However, what is the mistake when I follow this approach.

A: not sufficient
B: not sufficient

Taken together: <1+<2 = <3+<4 ==>since <2=<4; and therefore <1=<3

<1+<2+<3+<4+70 = 180
<2+<4=55

In triangle ADC <2+<4+y=180
from this we now know know y; we knew x.. so we get the answer.
Attachments

untitled.JPG
untitled.JPG [ 8.07 KiB | Viewed 3442 times ]

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24438 [1] , given: 2677

Re: In the figure above, what is the value of x + y ? [#permalink] New post 27 Dec 2012, 01:51
1
This post received
KUDOS
Expert's post
pavanpuneet wrote:
Hi Bunuel, I see your point. However, what is the mistake when I follow this approach.

A: not sufficient
B: not sufficient

Taken together: <1+<2 = <3+<4 ==>since <2=<4; and therefore <1=<3

<1+<2+<3+<4+70 = 180
<2+<4=55

In triangle ADC <2+<4+y=180
from this we now know know y; we knew x.. so we get the answer.


How did you get the red part above?
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: In the figure above, what is the value of x + y ? [#permalink] New post 27 Dec 2012, 01:57
Aah I see my mistake; i eqauted <1=<2 and <3=<4.

Spotted my error; thanks.
1 KUDOS received
Intern
Intern
avatar
Joined: 13 Apr 2013
Posts: 25
Followers: 0

Kudos [?]: 1 [1] , given: 3

In the figure above, what is the value of x + y ? [#permalink] New post 29 Apr 2013, 14:13
1
This post received
KUDOS
bhavinp wrote:
Answer is E

Here's a rough version of the image.
Image

Statement 1 is insufficient.
We know angle x is 70, but we know nothing about the placement of point D. The lower the placement of point D the greater the angle y, so y could really be any number of values. Remember we can't assume anything about the placement of a point, unless we are explicitly told about the placement in the question.

Statement 2 is insufficient.
x and y could be any number of values. For instance x could be 50 degrees or 70 degrees. All we know is that the triangles are isosceles, but we know nothing about the angles.

Statements 1 and 2 together are insufficient.
From statement 1 we know x is 70 and that angles BAC and BCA are both 55. But again we know nothing about the placement of point D. Point D could be very close to B in which case y would be close to 70 degrees or point D could be close to the segment AC in which case y would be close to 180 degrees.

I hope that helps!
Bhavin


Maybe this is a silly question - I understood this problem but I have one issue with the answer explanation. Why do both angles have to be 55? Isoceles triangles must have at least two equivalent angles, right? Why couldn't the angles have been 70/70/40? Doesn't change the answer from E, but still im curious :)
Senior Manager
Senior Manager
avatar
Joined: 21 Jan 2010
Posts: 348
Followers: 0

Kudos [?]: 67 [0], given: 12

Re: In the figure above, what is the value of x + y ? [#permalink] New post 29 Apr 2013, 15:51
Well, this is more of analytical question. When i looked at this question , i tried to remember a formula that i could use but unfortunately couldn't fit anything but looking at the image i see a very generic image. Their is no way to determine x + y. As infinite number of such triangles can be drawn, which will satisfy the given constraints. Hence E wins.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24438 [0], given: 2677

Re: In the figure above, what is the value of x + y ? [#permalink] New post 30 Apr 2013, 00:18
Expert's post
mokura wrote:
bhavinp wrote:
Answer is E

Here's a rough version of the image.
Image

Statement 1 is insufficient.
We know angle x is 70, but we know nothing about the placement of point D. The lower the placement of point D the greater the angle y, so y could really be any number of values. Remember we can't assume anything about the placement of a point, unless we are explicitly told about the placement in the question.

Statement 2 is insufficient.
x and y could be any number of values. For instance x could be 50 degrees or 70 degrees. All we know is that the triangles are isosceles, but we know nothing about the angles.

Statements 1 and 2 together are insufficient.
From statement 1 we know x is 70 and that angles BAC and BCA are both 55. But again we know nothing about the placement of point D. Point D could be very close to B in which case y would be close to 70 degrees or point D could be close to the segment AC in which case y would be close to 180 degrees.

I hope that helps!
Bhavin


Maybe this is a silly question - I understood this problem but I have one issue with the answer explanation. Why do both angles have to be 55? Isoceles triangles must have at least two equivalent angles, right? Why couldn't the angles have been 70/70/40? Doesn't change the answer from E, but still im curious :)


Merging similar topics.

As for your question: yes, ABC could be 70-70-40 triangle as well.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2025
Followers: 486

Kudos [?]: 1983 [1] , given: 29

Re: In the figure above, what is the value of x + y ? [#permalink] New post 01 May 2013, 09:13
1
This post received
KUDOS
Expert's post
Bunuel wrote:
Merging similar topics. As for your question: yes, ABC could be 70-70-40 triangle as well.

Bunuel and others,
I feel this question has a significant gap --- is the original diagram drawn to scale or not?

Of course, on the GMAT, we know "Figures are drawn as accurately as possible. Exceptions will be noted." I discuss this in a blog post.
http://magoosh.com/gmat/2012/gmat-trick ... -possible/
This is a crucial fact for students to keep in mind when interpreting GMAT diagrams.

IF this diagram is purporting to be drawn as accurate as possible, then it's an exceptionally poor diagram. That angle looks nothing like a 70 degree angle. If it's drawn to scale, though, we have to accept that the diagram is somewhat close to symmetrical, and therefore, the 70-70-40 triangle would not be possible.

IF the diagram is not drawn to scale, which I suspect was the intent of the author, that needs to be explicitly stated. Then, the 70-70-40 triangle would be possible. Any bilateral symmetry is out the window if it's not drawn to scale. Here's a scaled diagram of the figure with the 70-70-40 triangle.
Attachment:
isosceles triangles.JPG
isosceles triangles.JPG [ 25.57 KiB | Viewed 2949 times ]


I believe, either way, the answer would be (E). Nevertheless, I think this is a crucial issue for students to consider while analyzing the possibilities for a given diagram on the GMAT.

What do others think?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Intern
Intern
avatar
Joined: 15 Mar 2013
Posts: 6
Followers: 0

Kudos [?]: 1 [0], given: 4

Reviews Badge CAT Tests
Re: In the figure above, what is the value of x + y ? [#permalink] New post 22 Mar 2014, 05:50
Hello,

If we consider 2 statements together then:
Why can not these 2 triangles i.e. BAC and DAC are similar by SSS? BA/BC = DA/DC = AC\AC =1 and Hence , <x = <y
so then Ans is C.

Thanks.
Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 608
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 13

Kudos [?]: 264 [0], given: 647

Premium Member CAT Tests
Re: In the figure above, what is the value of x + y ? [#permalink] New post 26 Mar 2014, 00:33
manojISB wrote:
Hello,

If we consider 2 statements together then:
Why can not these 2 triangles i.e. BAC and DAC are similar by SSS? BA/BC = DA/DC = AC\AC =1 and Hence , <x = <y
so then Ans is C.

Thanks.

Hi Manoj,

How did you get the ratio of sides as one ?? Can you figure out which sides in the triangle are equal??

Please refer to the solutions above.

Posted from my mobile device Image
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Intern
Intern
avatar
Joined: 15 Mar 2013
Posts: 6
Followers: 0

Kudos [?]: 1 [0], given: 4

Reviews Badge CAT Tests
Re: In the figure above, what is the value of x + y ? [#permalink] New post 26 Mar 2014, 03:31
(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Per the 2nd statement , I think AB= BC and AD = DC so AB/BC = AD/DC = 1 or AB/AD = BC/DC =1 And ofcourse AC/AC =1 so triangles are similar?? am I wrong here?

Thanks.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24438 [0], given: 2677

Re: In the figure above, what is the value of x + y ? [#permalink] New post 26 Mar 2014, 07:00
Expert's post
manojISB wrote:
(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Per the 2nd statement , I think AB= BC and AD = DC so AB/BC = AD/DC = 1 or AB/AD = BC/DC =1 And ofcourse AC/AC =1 so triangles are similar?? am I wrong here?

Thanks.


From AB/BC = AD/DC = 1 you cannot write AB/AD = BC/DC =1. AB/AD = 1 would mean that AB and AD have the same length which is obviously wrong.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 28 Apr 2014
Posts: 289
Followers: 0

Kudos [?]: 20 [0], given: 45

GMAT ToolKit User
Re: In the figure above, what is the value of x + y ? [#permalink] New post 18 May 2014, 09:14
mikemcgarry wrote:
Bunuel wrote:
Merging similar topics. As for your question: yes, ABC could be 70-70-40 triangle as well.

Bunuel and others,
I feel this question has a significant gap --- is the original diagram drawn to scale or not?

Of course, on the GMAT, we know "Figures are drawn as accurately as possible. Exceptions will be noted." I discuss this in a blog post.
http://magoosh.com/gmat/2012/gmat-trick ... -possible/
This is a crucial fact for students to keep in mind when interpreting GMAT diagrams.

IF this diagram is purporting to be drawn as accurate as possible, then it's an exceptionally poor diagram. That angle looks nothing like a 70 degree angle. If it's drawn to scale, though, we have to accept that the diagram is somewhat close to symmetrical, and therefore, the 70-70-40 triangle would not be possible.

IF the diagram is not drawn to scale, which I suspect was the intent of the author, that needs to be explicitly stated. Then, the 70-70-40 triangle would be possible. Any bilateral symmetry is out the window if it's not drawn to scale. Here's a scaled diagram of the figure with the 70-70-40 triangle.
Attachment:
isosceles triangles.JPG


I believe, either way, the answer would be (E). Nevertheless, I think this is a crucial issue for students to consider while analyzing the possibilities for a given diagram on the GMAT.

What do others think?
Mike :-)



Very important point Mike. I also presumed ( from the diagram in the question that Ab=BC and AD=DC. So how do we tackle such questions in real exam ? Do we not take it scale.
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2025
Followers: 486

Kudos [?]: 1983 [0], given: 29

Re: In the figure above, what is the value of x + y ? [#permalink] New post 18 May 2014, 14:06
Expert's post
himanshujovi wrote:
Very important point Mike. I also presumed ( from the diagram in the question that Ab=BC and AD=DC. So how do we tackle such questions in real exam ? Do we not take it scale.

Dear himanshujovi,
I'm happy to respond. :-)

On GMAT PS, unless noted, problems are always drawn to scale. Of course, things that look equal may be close by not exactly equal, things that look parallel or perpendicular may be not exactly, etc. For such exact things, you need to rely on what the problem explicitly tells you.

Geometry on the GMAT DS is much trickier, because the diagram could be drawn to scale or not even pretending to be drawn to scale. You need to have a strong visual imagination. One way to approach this --- given a rough DS diagram and the constraints in the question, practice drawing on paper as many variants as possible that are still totally consistent with the explicitly given constraints. It takes some practice to develop your visual intuition, but the more your practice, the more you will be able to see different geometric possibilities.

If, for a specific problem, you would like to see some geometric variants, then post the problem as a new thread in the Magoosh forum:
magoosh-324/
and I will post some diagrams of possible altenatives.

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Senior Manager
Senior Manager
avatar
Joined: 28 Apr 2014
Posts: 289
Followers: 0

Kudos [?]: 20 [0], given: 45

GMAT ToolKit User
Re: In the figure above, what is the value of x + y ? [#permalink] New post 18 May 2014, 20:06
Thanks Mike.. As a matter of fact geometry was one of my favourite branch of Mathematics(after Calculus) during my pre engineering days. But then there was a very clear rule - Not to make any assumption at all from any figure unless explicitly mentioned. Looks like GMAT has played with this style of thinking or maybe I need to retune my neural cells [SMILING FACE WITH SMILING EYES]. Thanks anyways for the explanation


Regards
Himanshu


Sent from my iPhone using Tapatalk
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24438 [0], given: 2677

Re: In the figure above, what is the value of x + y ? [#permalink] New post 19 May 2014, 02:23
Expert's post
himanshujovi wrote:
mikemcgarry wrote:
Bunuel wrote:
Merging similar topics. As for your question: yes, ABC could be 70-70-40 triangle as well.

Bunuel and others,
I feel this question has a significant gap --- is the original diagram drawn to scale or not?

Of course, on the GMAT, we know "Figures are drawn as accurately as possible. Exceptions will be noted." I discuss this in a blog post.
http://magoosh.com/gmat/2012/gmat-trick ... -possible/
This is a crucial fact for students to keep in mind when interpreting GMAT diagrams.

IF this diagram is purporting to be drawn as accurate as possible, then it's an exceptionally poor diagram. That angle looks nothing like a 70 degree angle. If it's drawn to scale, though, we have to accept that the diagram is somewhat close to symmetrical, and therefore, the 70-70-40 triangle would not be possible.

IF the diagram is not drawn to scale, which I suspect was the intent of the author, that needs to be explicitly stated. Then, the 70-70-40 triangle would be possible. Any bilateral symmetry is out the window if it's not drawn to scale. Here's a scaled diagram of the figure with the 70-70-40 triangle.
Attachment:
isosceles triangles.JPG


I believe, either way, the answer would be (E). Nevertheless, I think this is a crucial issue for students to consider while analyzing the possibilities for a given diagram on the GMAT.

What do others think?
Mike :-)



Very important point Mike. I also presumed ( from the diagram in the question that Ab=BC and AD=DC. So how do we tackle such questions in real exam ? Do we not take it scale.


OG13, page 272:
A figure accompanying a data sufficiency problem will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2).
Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight.
You may assume that the positions of points, angles, regions, and so forth exist in the order shown and that angle measures are greater than zero degrees.
All figures lie in a plane unless otherwise indicated.

OG13, page 150:
Figures: A figure accompanying a problem solving question is intended to provide information useful in solving the problem. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Hope it helps.
_________________

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.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 253
Followers: 0

Kudos [?]: 10 [0], given: 22

Re: In the figure above, what is the value of x + y ? [#permalink] New post 24 May 2014, 09:33
Bunuel wrote:
Image
In the figure above, what is the value of x + y ?

(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Even when we consider both statements together we don't know the placement of points D and B. For example consider the diagram below:
Attachment:
Triangles2.png
As you can see we can have two different answers for x+y for two different placements of point D.

Answer: E.


Hi Bunuel,

If they had provided us additional information as such: AB=BC, AD=AC and ADC = 1/2 height of ABC. If that's the case, can we use the same inscribed angle rules we use for circle - can we assume that Y would've been 2x, therefore 140 degrees?

Would the answer change if AB & BC weren't equal and AD & AC weren't equal?

Thanks
Expert Post
Magoosh GMAT Instructor
User avatar
Joined: 28 Dec 2011
Posts: 2025
Followers: 486

Kudos [?]: 1983 [0], given: 29

Re: In the figure above, what is the value of x + y ? [#permalink] New post 24 May 2014, 16:12
Expert's post
russ9 wrote:
Bunuel wrote:
Image
In the figure above, what is the value of x + y ?

(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Even when we consider both statements together we don't know the placement of points D and B. For example consider the diagram below:
Attachment:
Triangles2.png
As you can see we can have two different answers for x+y for two different placements of point D.

Answer: E.


Hi Bunuel,

If they had provided us additional information as such: AB=BC, AD=AC and ADC = 1/2 height of ABC. If that's the case, can we use the same inscribed angle rules we use for circle - can we assume that Y would've been 2x, therefore 140 degrees?

Would the answer change if AB & BC weren't equal and AD & AC weren't equal?

Thanks

Dear russ9,
I'm happy to answer this. :-)

If we knew AB=BC and AD=AC, then we would know the triangles were isosceles, which would have added a tremendous amount of useful information to the problem.

Your application of the inscribed angle rule, unfortunately, is 100% incorrect. Among other things, if triangle ABC were inscribed in a circle, the center of that circle would NOT lie on side AC. If ADC = 1/2 height of ABC, then that would NOT mean that AD bisected angle BAC or that CD bisected angle BCA. If we had been told that those two segments were angle bisectors, then yes, it would have been true that y = 140.

Here's a real paradox: if we had been told the three pieces of information you suggested, those would uniquely determine triangle ADC, such that all of its angles would be mathematically determined. To find the measure of y would involves some sophisticated trigonometry and a calculator --- finding the numerical value of y would be well beyond anything the GMAT could expect you to do, but technically, y would be mathematically determined and one could find it, which means that information would be sufficient. In practice, the GMAT doesn't put you in that position --- it doesn't expect you to find as sufficient something that is uniquely determined mathematically but incalculable using ordinary GMAT math. The GMAT will only put you in the position of declaring something sufficient if you realistically could find it with ordinary GMAT math.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 253
Followers: 0

Kudos [?]: 10 [0], given: 22

Re: In the figure above, what is the value of x + y ? [#permalink] New post 27 May 2014, 14:41
mikemcgarry wrote:
russ9 wrote:
Bunuel wrote:
Image
In the figure above, what is the value of x + y ?

(1) x = 70.
(2) ABC and ADC are both isosceles triangles.

Even when we consider both statements together we don't know the placement of points D and B. For example consider the diagram below:
Attachment:
Triangles2.png
As you can see we can have two different answers for x+y for two different placements of point D.

Answer: E.


Hi Bunuel,

If they had provided us additional information as such: AB=BC, AD=AC and ADC = 1/2 height of ABC. If that's the case, can we use the same inscribed angle rules we use for circle - can we assume that Y would've been 2x, therefore 140 degrees?

Would the answer change if AB & BC weren't equal and AD & AC weren't equal?

Thanks

Dear russ9,
I'm happy to answer this. :-)

If we knew AB=BC and AD=AC, then we would know the triangles were isosceles, which would have added a tremendous amount of useful information to the problem.

Your application of the inscribed angle rule, unfortunately, is 100% incorrect. Among other things, if triangle ABC were inscribed in a circle, the center of that circle would NOT lie on side AC. If ADC = 1/2 height of ABC, then that would NOT mean that AD bisected angle BAC or that CD bisected angle BCA. If we had been told that those two segments were angle bisectors, then yes, it would have been true that y = 140.

Here's a real paradox: if we had been told the three pieces of information you suggested, those would uniquely determine triangle ADC, such that all of its angles would be mathematically determined. To find the measure of y would involves some sophisticated trigonometry and a calculator --- finding the numerical value of y would be well beyond anything the GMAT could expect you to do, but technically, y would be mathematically determined and one could find it, which means that information would be sufficient. In practice, the GMAT doesn't put you in that position --- it doesn't expect you to find as sufficient something that is uniquely determined mathematically but incalculable using ordinary GMAT math. The GMAT will only put you in the position of declaring something sufficient if you realistically could find it with ordinary GMAT math.

Does all this make sense?
Mike :-)


Hi Mike,

Thanks for the detailed response -- makes a lot of sense.

One point i'd like to bring up because I think that my original question wasn't phrased accurately:

1) If they give us that the height of ADC is 1/2 the height of ABC, doesn't that imply that the angle is doubled since AC is the same for both triangles? I meant to ask this and not bring in the "inscribed triangle" rule :)

Thanks!
Re: In the figure above, what is the value of x + y ?   [#permalink] 27 May 2014, 14:41
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic In the figure above, what is the value of x? fozzzy 4 03 Sep 2013, 23:44
8 In the figure above, what is the value of x? emmak 4 25 Mar 2013, 21:57
5 Experts publish their posts in the topic What is the value of x + y in the figure above? Walkabout 2 26 Dec 2012, 04:18
2 Experts publish their posts in the topic In the figure above, what is the value of x + y ? mydreammba 4 28 Dec 2011, 06:48
3 Experts publish their posts in the topic What is the value of x+y in the figure above? Baten80 3 08 Mar 2011, 13:16
Display posts from previous: Sort by

In the figure above, what is the value of x + y ?

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page    1   2    Next  [ 23 posts ] 



GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.