GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Dec 2019, 07:03 ### 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

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.  # Is the circumference of the largest circle above that can contain all

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59724
Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

2
8 00:00

Difficulty:   55% (hard)

Question Stats: 59% (02:06) correct 41% (02:00) wrong based on 128 sessions

### HideShow timer Statistics Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to $$16 + 16\sqrt{2}*\pi$$?

(1) The radius of one of the small circles is 8

(2) The area of all four circles is $$256\pi$$

Attachment: gmat-tip-circles-1.png [ 13.49 KiB | Viewed 1772 times ]

_________________
Manager  S
Joined: 02 May 2016
Posts: 75
Location: India
Concentration: Entrepreneurship
GRE 1: Q163 V154 WE: Information Technology (Computer Software)
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
$$16 + 16\sqrt{2}*\pi$$?

Well (1) and (2) gives the same information. So answer must be D or E.

Working out, I got the diameter of larger circle as $$16 + 16\sqrt{2}$$

Circumference of the circle will be 2*pi*r or pi*d
= $$16\pi + 16\sqrt{2}*\pi$$

Which is not equal to one given in prompt.

Hence D.

Am I correct?
I will elaborate once I get to know this is correct Bunuel: Your questions with suspense answers kill me GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1829
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
Bunuel wrote:
Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to $$16 + 16\sqrt{2}*\pi$$?

I'm curious about this question, because it might be an interesting problem, but I can't even begin to guess what it means. It asks about a circle "above", and tells us that circle "can contain all four circles ... above", which would mean the circle the question is talking about can contain itself. That doesn't make any sense.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Intern  B
Joined: 21 Jun 2017
Posts: 10
GMAT 1: 750 Q50 V41 Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
For a circle to encompass all 4 smaller circles, it has to be either tangent to those 4 or simply contain them. The question stem does not provide any info on this so I guess the answer is E?
Current Student B
Joined: 11 May 2015
Posts: 34
Location: United States
Concentration: Strategy, Operations
GPA: 3.44
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

IanStewart wrote:
Bunuel wrote:
Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to $$16 + 16\sqrt{2}*\pi$$?

I'm curious about this question, because it might be an interesting problem, but I can't even begin to guess what it means. It asks about a circle "above", and tells us that circle "can contain all four circles ... above", which would mean the circle the question is talking about can contain itself. That doesn't make any sense.

Same reaction here. Question is not clear. I dont see the "largest" circle"
Intern  B
Joined: 24 Jul 2016
Posts: 3
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
1

If all the four centres of the four circles are joined , it will form a square, we will have a square of length 16 units, from this the diagonal would be 16 √2 , the diameter of the bigger circle would be 16+16 √2 (adding the addtional radii to formulate the diameter). (Please refer the attached figure). This would give us the circumference of the bigger circle as (16+16 √2) π.

Since both 1 and 2 give the same data, each statement alone is sufficient as we have the radii of each circle and by forming a square we can find the diameter of the larger circle, thereby finding out the circumference of the circle.
Attachments image1.JPG [ 990.9 KiB | Viewed 1416 times ]

Intern  B
Joined: 04 Mar 2017
Posts: 28
GMAT 1: 200 Q48 V37 GPA: 1
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1

It doesn't say anywhere that all 4 circles have the same radius, so in statement I, we could have 1 circle at the provided radius and the other 3 at another. Statement II provides you with the area which you can calculate the required circumference.
Intern  B
Joined: 24 Jul 2016
Posts: 3
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
nrxbra001 wrote:

It doesn't say anywhere that all 4 circles have the same radius, so in statement I, we could have 1 circle at the provided radius and the other 3 at another. Statement II provides you with the area which you can calculate the required circumference.

How would you calculate the circumference of the bigger circle with the sum of areas of smaller circles?
The radii of each circle might differ,in that case you would not be able to find the radii of the bigger circle.

If the circles are not of the same size, then the answer would be E.
Intern  B
Joined: 05 Dec 2015
Posts: 4
Location: Brazil
GMAT 1: 720 Q50 V38 WE: Investment Banking (Investment Banking)
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

1
Statements I and II basically give you the same information:

The area of all four circles is 256π: 4π$$r^{2}$$= 256π -> $$r^{2}$$ = 64 -> r = 8

The distance X from the center of the imaginary bigger circle to the center of any smaller circle can be calculated using the Pythagorean theorem:
$$16^{2}$$ = $$x^{2}$$ + $$x^{2}$$ -> 2$$x^{2}$$ = 256 -> $$x^{2}$$ = 128

The circumference of the larger circle therefore is:
2π*(x + r) -> 2π (8$$\sqrt{2}$$ + 8) -> 16$$\sqrt{2}$$π + 16

Therefore, the correct answer is D.
Intern  B
Joined: 28 Nov 2014
Posts: 8
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

We need to know whether circles are identical or not? Incomplete question
GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1829
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

Bunuel wrote:
Is the circumference of the largest circle above that can contain all four circles in the figure above

I suspect sharmili has correctly guessed the intentions of the question designer, and if so, the question should be asking about the smallest circle that is not depicted above (the 'largest circle' that could contain all the other circles is infinitely big, so asking for the largest circle doesn't make sense), and there seems to be a π missing in the number at the end of the question. We do need information about whether the small circles are identical to solve anything here.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
Manager  B
Joined: 29 Sep 2016
Posts: 113
Re: Is the circumference of the largest circle above that can contain all  [#permalink]

### Show Tags

Bunuel wrote: Is the circumference of the largest circle above that can contain all four circles in the figure above equivalent to $$16 + 16\sqrt{2}*\pi$$?

(1) The radius of one of the small circles is 8

(2) The area of all four circles is $$256\pi$$

Attachment:
gmat-tip-circles-1.png

Hi Bunuel
The circles are nowhere mentioned as identical ones. How do I know that it isn't a usual 700 question trap.
That's why I choose option 'E'. Re: Is the circumference of the largest circle above that can contain all   [#permalink] 14 Sep 2019, 21:37
Display posts from previous: Sort by

# Is the circumference of the largest circle above that can contain all  