Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

It is currently 07 Jun 2020, 01:34

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.

Close

Request Expert Reply

Confirm Cancel

The figure shows the intersection of a Square ABCD and a Circle. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
GMAT ToolKit User CAT Tests
The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 07 Dec 2019, 18:00
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:20) correct 62% (01:52) wrong based on 113 sessions

HideShow timer Statistics

GMATBusters’ Quant Quiz Question -2


Image
The figure shows the intersection of a Square ABCD and a Circle. What is the Perimeter of the Square ABCD?
1) X = 1
2) AC and BD are perpendicular to each other

Attachment:
123.JPG
123.JPG [ 38.21 KiB | Viewed 1885 times ]

_________________
Most Helpful Expert Reply
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
GMAT ToolKit User CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 06 Jan 2020, 00:00
3
3
General Discussion
Intern
Intern
avatar
B
Joined: 11 Dec 2018
Posts: 12
Location: United States (NC)
Schools: HBS
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 07 Dec 2019, 18:39
Answer :E

I'm assuming in the given diagram the diameter passes through the intersection of the diagonals:

a= side of the square
d=diameter of the circle
Requirement is to find 4a ?
= 4(d-x)

1) x=1
for x=1 perimeters =4(d-1)
multiple answers as d changes hence insufficient.

2) This basically gives product information. In a square diagonal are perpendicular. Not sufficient.
Manager
Manager
avatar
S
Joined: 13 Apr 2019
Posts: 231
Location: India
Schools: Kellogg '22
GPA: 3.85
Premium Member
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 07 Dec 2019, 23:30
Here lets start by considering radius of circle as r. Let O be the center of circle and let M be the midpoint of side BC where Perpendicular from O meets BC.
By applying right angle property
(OB)^2 = (BM)^2 + (OM)^2
r^2 = (BM)^2 + (r-x)^2
on solving, we get (BM)^2 = x(2r-x)

since from 1 we know the value of x, we get value of (BM)^2 as 2r-1

so we cannot find the perimeter of square just from 1

(2) since its told that abcd is a square, we can already infer what is given in 2

Taking both 1 and 2, still we donot have enough information to find the value of r so answer is E
Intern
Intern
avatar
B
Joined: 15 Apr 2017
Posts: 37
GMAT 1: 570 Q49 V19
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 07 Dec 2019, 23:52
Ans: A
(1): from the mid point of the circle O draw radius to point B and C .Since the triangle OBC is an isosceles triangle with angle BOC = 90 degree. We can say sin 45 = OB/OX.
OX=radius-1
OB=radius.
Now we can find radius and hence the perimeter.
(2). This is a redundant info . Its given that the figure is square which implies that diagonals will intersect at 90 degree.
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 6333
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 08 Dec 2019, 00:01
#1
X=1 ;
insufficient as we dont know the center of circle also X=1 is the highest point of circle from square
#2
AC and BD are perpendicular to each other
the lines will intersect at center at 90* , but center of circle is not clear ; insufficient
from 1 &2
we can determine the sides of the digonals using 45:45:90 ; but will have unknow value of distance from center to circle side X=1
radius ; a+1 ; side of square ; 2a and perimeter ; 8a ; but value of a is not know
insufficient
IMO E


The figure shows the intersection of a Square ABCD and a Circle. What is the Perimeter of the Square ABCD?
1) X = 1
2) AC and BD are perpendicular to each other
Manager
Manager
User avatar
G
Status: On the journey of achieving
Affiliations: Senior Manager, CA by profession, CFA(USA) Level 2
Joined: 06 Feb 2016
Posts: 245
Location: India
Concentration: Finance, Finance
GMAT 1: 560 Q44 V21
GPA: 3.82
WE: Other (Commercial Banking)
Reviews Badge
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 08 Dec 2019, 00:05
Let us look at each statements one by one

1) X = 1
This statement does not provides us any information which will provide us the dimensions of the square, we cannot arrive at any side dimension length of the square hence statement 1 alone is not sufficient

2) AC and BD are perpendicular to each other

This statement does not provides us any information which will provide us the dimensions of the square, hence statement 1 alone is not sufficient

Even when we combine information in both the statements together, it won't give us any information about square dimensions or of the circle, hence both statements together are also not sufficient.
Answer is Option E, even both the statements together are also not sufficient.
Director
Director
avatar
V
Joined: 22 Feb 2018
Posts: 764
GMAT ToolKit User
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 08 Dec 2019, 02:05
The figure shows the intersection of a Square ABCD and a Circle. What is the Perimeter of the Square ABCD?

Tricky one for me, still i'll try.

1) X = 1,
Insufficient as we can't find the radius of the circle, which can give us diameter of the circle, which in turn could help to find side or diagonal of square.

2) AC and BD are perpendicular to each other
It implies that diagonals pass through the center of the circle. But still we can't find the radius/diameter of the circle/diagonal of the square/side of square. Hence insufficient.

1) + 2)
Square is inscribed from the circle as AC and BD are perpendicular to each other. Still can not find the side of square. Hence insufficient.

Imo. E
Intern
Intern
avatar
B
Joined: 17 Feb 2019
Posts: 27
Location: India
Schools: Tepper
GMAT 1: 610 Q43 V31
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 08 Dec 2019, 05:37
The answer is E.

EXPLANATION:

Please refer to the attached figure:
We have assumed a radius is drawn from B and C, meeting at the point which is coolinear to the point x distance is separated from the square. Hence, if the total distance is R, the point till the square edge (where x distance is separated from the circle), is r - x.

We can see, perimeter is:
r + k + 2l + r + k + 2l.

Also, we know, \( l = \sqrt{r^2 - (r-1)^2 } \)
Hence, L equals, \( \sqrt{2r - 1 } \)

Hence, solving the equation, we get perimeter as function of R as:
\( 4r - 2 + 4\sqrt{2r-1} \)

Since the value of R can vary, the perimeter can vary and have more than one answer.
Hence, E is the answer.
Attachments

File comment: Diagram
IMG_20191208_184450__01.jpg
IMG_20191208_184450__01.jpg [ 1.58 MiB | Viewed 1623 times ]

Intern
Intern
avatar
Joined: 02 Sep 2019
Posts: 10
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 08 Dec 2019, 10:04
4
In the above figure, let OB = OC = R. Let, OE = y, AB = 2a
Now, R = x + y ...(i)
R + y = 2a ...(ii)
In triangle OEB, R^2 = y^2 + a^2 ...(iii)

Substituting (i) in (iii), we get
(x+y)^2 = y^2 + a^2
x^2 + 2xy + y^2 = y^2 + a^2
x^2 + 2xy = a^2 ...(iv)

Substituting (i) in (ii), we get
x+2y = 2a

Multiplying above equation by x, we get

x^2 + 2xy = 2ax ... (v)

From (iv) and (v), we get

a^2 = 2ax

a=0 or a=2x

Since, a is a length, it can not be non - positive.

Therefore, a = 2x ... (vi)

(1) x = 1
Substituting in (vi), we get
a = 2. Therefore, perimeter = 8a = 16.
Clearly, statement 1 is sufficient.

(2) AC and BD are perpendicular to each other
Since, ABCD is a square AC and BD are perpendicular to each other. We do not get any information about the length of the square.
Therefore statement 2 is insufficient.

Choice A is the answer.
Attachments

20191208_231723.jpg
20191208_231723.jpg [ 1.39 MiB | Viewed 1576 times ]

Intern
Intern
avatar
Joined: 09 Dec 2019
Posts: 10
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 09 Dec 2019, 04:07
For every square and circle which exist as shown in the figure, distance x will be unique and no two combination of square and circle can have same value of x.

(1) For x=1, we have a unique figure and thus the perimeter of the square can be determined.
Therefore, statement 1 is sufficient.

(2) AC and BD are perpendicular to each other
ABCD is a square AC and BD are always perpendicular to each other.
Not sufficient.

A is the answer.
Intern
Intern
avatar
B
Joined: 22 May 2019
Posts: 11
CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 05 Jan 2020, 23:19
jhavyom can you explain how R+Y =2a in your explanation
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
GMAT ToolKit User CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 06 Jan 2020, 00:02
As per the jhyavyom solution, Side of the square is taken as 2a
Hence R+2a = side of the square = 2a

I hope it is clear, feel free to tag me in case of any doubt.

Happy Learning

saiprasanna wrote:
jhavyom can you explain how R+Y =2a in your explanation

_________________
Intern
Intern
avatar
S
Joined: 28 Jan 2017
Posts: 49
Premium Member Reviews Badge CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 02 Feb 2020, 12:42
Please expand on: R + y = 2a

How can that be true if R^2 = a^2 + y^2?

gmatbusters jhavyom
Intern
Intern
avatar
B
Joined: 13 Feb 2020
Posts: 2
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 16 Feb 2020, 03:36
GMATBusters
sorry for this but couldn`t understand how E lie on the diameter of the circle
Retired Moderator
User avatar
V
Joined: 27 Oct 2017
Posts: 1819
WE: General Management (Education)
GMAT ToolKit User CAT Tests
The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 16 Feb 2020, 04:09
By symmetry, it lies on diameter. It can be proved but better to use the principle of symmetry in GMAT.
Also, since the dimensioning line has 2 arrows, it means the max distance between the circle and circle, which is when E lies on diameter (otherwise the exact point on circle must have been specified).

sudhirgmat1 wrote:
GMATBusters
sorry for this but couldn`t understand how E lie on the diameter of the circle

_________________
Manager
Manager
avatar
B
Joined: 19 Sep 2018
Posts: 74
CAT Tests
Re: The figure shows the intersection of a Square ABCD and a Circle. What  [#permalink]

Show Tags

New post 05 May 2020, 12:29
Hi GMATBusters,

I had a doubt regarding the symmetry used here. We need to assume that the figure drawn is symmetrical?
Because based on that assumption, we get that EC and EB are S/2 and E lies on the diameter of the circle. I didn't make the assumption and ended up choosing E.
In what situations do we need to assume that the figure given is symmetrical?

Thanks and Regards,
Udit
GMAT Club Bot
Re: The figure shows the intersection of a Square ABCD and a Circle. What   [#permalink] 05 May 2020, 12:29

The figure shows the intersection of a Square ABCD and a Circle. What

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne