Author 
Message 
TAGS:

Hide Tags

Retired Moderator
Joined: 10 May 2010
Posts: 813

A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
27 Apr 2012, 12:26
Question Stats:
30% (01:51) correct 70% (02:04) wrong based on 307 sessions
HideShow timer Statistics
A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle (1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long. Will appreciate an algebraic proof.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
The question is not can you rise up to iconic! The real question is will you ?



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
27 Apr 2012, 13:20
AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment:
Trapezoid.png [ 5.66 KiB  Viewed 6360 times ]
So, diameter of the circle is 10. Answer: C.
_________________
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



Intern
Joined: 28 Sep 2011
Posts: 26
Location: India
WE: Consulting (Computer Software)

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
27 Apr 2012, 20:39
I still have doubt. 1. If we consider, the height to be diameter, then wouldnt just A suffice Bunuel wrote: AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment: Trapezoid.png So, diameter of the circle is 10. Answer: C.
_________________
Kudos if you like the post!!!



Intern
Joined: 22 Jan 2012
Posts: 34

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
27 Apr 2012, 20:46
I too thought the same , then with 1 you can fix the distance between the parallel sides of the trapezoid , but will not be able to restrict the size of the trapezoid until unless there is some extra info to do that , which here is the shorter side in 2.



Retired Moderator
Joined: 10 May 2010
Posts: 813

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 02:53
If we consider the case when the circle touches the two equal sides of isosceles trapezium and the shorter side, here I am not able to prove rigorously that the distance between the two parallel sides must be more than 10.
_________________
The question is not can you rise up to iconic! The real question is will you ?



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 05:49
devpanda wrote: I still have doubt. 1. If we consider, the height to be diameter, then wouldnt just A suffice Bunuel wrote: AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment: The attachment Trapezoid.png is no longer available So, diameter of the circle is 10. Answer: C. Consider the diagram below for statement (1): Attachment:
1.png [ 6.92 KiB  Viewed 6233 times ]
As you can see we have two circles with different radii.
_________________
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: 25 Aug 2008
Posts: 174
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:08
I agree with Bunuel.. Both are needed to understand which combination of sides will be touching the circle. Is it 1 NonParallel side and 2 Parallel sides OR 2 NonParallel sides and 1 Parallel side.
_________________
Cheers, Varun
If you like my post, give me KUDOS!!



Intern
Joined: 17 Jan 2012
Posts: 2
Location: United States
Concentration: Operations, Marketing
GMAT Date: 05102012
WE: Engineering (Energy and Utilities)

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:18
I have a doubt.. there is also this statement in the question that "the trapezoid is symmetrical about a vertical line". But the solution is arrived by assuming it symmetrical about a horizontal line.??



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:21



Manager
Joined: 25 Aug 2008
Posts: 174
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:23
Nope.. The solutions is arrived by considering the statement that "the trapezoid is symmetrical about a vertical line". It cannot have non parallel sides on the yaixs if it was assumed that the trapezoid is symmetrical about a horizontal line because the non parallel sides will intersect at some point..
_________________
Cheers, Varun
If you like my post, give me KUDOS!!



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:27



Manager
Joined: 25 Aug 2008
Posts: 174
Location: India
WE 1: 3.75 IT
WE 2: 1.0 IT

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:30
Bunuel, The nope was for Prashant85 question that the solution is arrived by assuming it symmetrical about a horizontal line.. I think we both started answering at the same time and that's why I missed you answer while posting mine..
_________________
Cheers, Varun
If you like my post, give me KUDOS!!



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 06:34



Intern
Joined: 17 Jan 2012
Posts: 2
Location: United States
Concentration: Operations, Marketing
GMAT Date: 05102012
WE: Engineering (Energy and Utilities)

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
29 Apr 2012, 08:08
Thanks Bunuel and Varun... Its clear now.



Intern
Joined: 03 Apr 2012
Posts: 24

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
01 May 2012, 12:50
Bunuel wrote: AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment: Trapezoid.png So, diameter of the circle is 10. Answer: C. Hi Bunuel, Why can't you have a circle touching the isosceles side, in which case the radius is 15. I did not understand your solution. could you please explain. thank you



Retired Moderator
Joined: 10 May 2010
Posts: 813

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
02 May 2012, 03:23
jayaddula wrote: Bunuel wrote: AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment: Trapezoid.png So, diameter of the circle is 10. Answer: C. Hi Bunuel, Why can't you have a circle touching the isosceles side, in which case the radius is 15. I did not understand your solution. could you please explain. thank you This is my doubt as well, I can see how it is true from the diagram. However when I try to prove it mathematically , i fail.
_________________
The question is not can you rise up to iconic! The real question is will you ?



Intern
Joined: 11 Jun 2011
Posts: 10

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
04 Jul 2012, 06:03
jayaddula wrote: Bunuel wrote: AbhiJ wrote: A trapezoid is symmetrical about a vertical center line. If a circle is drawn such that it is tangent to exactly three sides of the trapezoid and is enclosed entirely within the trapezoid, what is the diameter of the circle
(1) The parallel sides of the trapezoid are 10 inches apart. (2) Of the parallel sides of the trapezoid, the shorter side is 15 inches long.
Will appreciate an algebraic proof. Given; the circle is is entirely enclosed within the isosceles trapezoid, so that it is tangent to exactly three sidesBelow is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15. Attachment: Trapezoid.png So, diameter of the circle is 10. Answer: C. Hi Bunuel, Why can't you have a circle touching the isosceles side, in which case the radius is 15. I did not understand your solution. could you please explain. thank you Hi Jayaddula, If we take only option B, then the diameter is >15 and not 15, i.e. it can be any number, so we can't say B. Now for C If we have circles touching the isosceles sides, then the diameter will be >15 and not 10, i.e. the circle will not be inside the Trapezoid. This implies that circle will touch the parallel sides and not the nonparallel sides of the Trapezoid.Thus the two statements together are sufficient to answer the question. Hope I am clear.
_________________
_______________________________________________________________________________________________________________________________ If you like my solution kindly reward me with Kudos.



Director
Joined: 26 Oct 2016
Posts: 648
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
13 Mar 2017, 01:03
There are four basic ways this picture could look, as there are four sides of the trapezoid that could serve as the nontangent side: (1) INSUFFICIENT: If the circle is tangent to both of the parallel sides (Figure A or B), then the diameter must be 10. If the circle is tangent to only one of the parallel sides (Figure C or D), then the diameter is less than 10. Since we are left with multiple possibilities for the diameter of the circle, we do not have enough information to answer the original question. (2) INSUFFICIENT: Just knowing the length of the shorter parallel side is not enough to determine which of the basic figures above describes the correct situation. If Figure A or B represents the correct situation, the diameter of the circle is clearly determined solely by the distance between the parallel sides; the diameter is independent of the length of the shorter parallel side, so knowing that it is 15 inches long is not useful. If Figure C or D describes the correct situation, then the diameter would depend on not only the 15inch side but also the longer parallel side, which has an unknown length. (1) AND (2) SUFFICIENT: If the distance between the parallel sides is 10, and the shorter parallel side has a length of 15, then Figure A or B represents the correct situation and the diameter of the circle must equal 10. Alternatively, notice that Figure D could not represent our situation, since the circle would have to have a diameter larger than 15 inches in order to be tangent to the short parallel side and the nonparallel sides of the trapezoid. We know that the parallel sides of the trapezoid are only 10 inches apart, so the circle would be too large to be drawn entirely within the trapezoid as required. Similar logic explains why Figure C is also impossible when we consider (1) and (2) together. The correct answer is C.
Attachments
Trapezoid.PNG [ 222.45 KiB  Viewed 1555 times ]
_________________
Thanks & Regards, Anaira Mitch



NonHuman User
Joined: 09 Sep 2013
Posts: 8195

Re: A trapezoid is symmetrical about a vertical center line. If
[#permalink]
Show Tags
18 Apr 2018, 13:11
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: A trapezoid is symmetrical about a vertical center line. If &nbs
[#permalink]
18 Apr 2018, 13:11






