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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

27 Apr 2012, 12:26

6

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

24% (02:11) correct
76% (01:31) wrong based on 153 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.

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 sides

Below is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15.

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 sides

Below is the only case possible to satisfy the following conditions: 1. Height is 10. 2. Shorter base is 15.

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.

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 ?

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 sides

Below 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 4871 times ]

As you can see we have two circles with different radii.
_________________

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 Non-Parallel side and 2 Parallel sides OR 2 Non-Parallel sides and 1 Parallel side.
_________________

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.??

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.??

Vertical line: |

The trapezoid is symmetrical about a vertical line (|) means that the trapezoid is isosceles.
_________________

Re: A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

29 Apr 2012, 06:23

1

This post received KUDOS

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 y-aixs if it was assumed that the trapezoid is symmetrical about a horizontal line because the non parallel sides will intersect at some point..
_________________

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 y-aixs if it was assumed that the trapezoid is symmetrical about a horizontal line because the non parallel sides will intersect at some point..

What you mean "nope"?

Stem says "a trapezoid is symmetrical about a vertical center line" which means that that the trapezoid is isosceles. All diagrams show trapezoids which are symmetrical about a vertical center line.
_________________

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..
_________________

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..

That's why I didn't understand your response. I guess all is clear then.
_________________

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 sides

Below 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.

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 sides

Below 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 ?

Re: A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

04 Jul 2012, 06:03

1

This post received KUDOS

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 sides

Below 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 non-parallel 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.

Re: A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

12 Dec 2013, 12:40

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.
_________________

Re: A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

13 Mar 2017, 00:58

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.
_________________

A trapezoid is symmetrical about a vertical center line. If [#permalink]

Show Tags

13 Mar 2017, 01:03

1

This post was BOOKMARKED

There are four basic ways this picture could look, as there are four sides of the trapezoid that could serve as the non-tangent 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 15-inch 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 198 times ]

_________________

Thanks & Regards, Anaira Mitch

gmatclubot

A trapezoid is symmetrical about a vertical center line. If
[#permalink]
13 Mar 2017, 01:03

There’s something in Pacific North West that you cannot find anywhere else. The atmosphere and scenic nature are next to none, with mountains on one side and ocean on...

This month I got selected by Stanford GSB to be included in “Best & Brightest, Class of 2017” by Poets & Quants. Besides feeling honored for being part of...

Joe Navarro is an ex FBI agent who was a founding member of the FBI’s Behavioural Analysis Program. He was a body language expert who he used his ability to successfully...