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

 It is currently 16 Jan 2019, 02:25

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# In the figure shown, if the side of the square is 40, what is the radi

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52131
In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

13 Mar 2018, 23:11
00:00

Difficulty:

95% (hard)

Question Stats:

32% (02:15) correct 68% (02:11) wrong based on 74 sessions

### HideShow timer Statistics

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

Attachment:

Screenshot %2887%29.png [ 30.54 KiB | Viewed 932 times ]

_________________
Current Student
Joined: 18 Aug 2016
Posts: 623
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

13 Mar 2018, 23:27
Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

Attachment:
Screenshot %2887%29.png

DB is $$40\sqrt{2}$$
Diameter of bigger circle is 40
40\sqrt{2} = 2 * Diameter of small circle + 40(Diameter of bigger circle)
$$40\sqrt{2}$$ = 4 * radius of small circle + 40(Diameter of bigger circle)
Radius of small circle = $$(40\sqrt{2} - 40 ) / 4$$
A
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Manager
Joined: 23 Sep 2016
Posts: 214
In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

Updated on: 26 Mar 2018, 22:54
1
Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

Attachment:
Screenshot %2887%29.png

IMO C
AS the diameter of large circle is 40 as the side of square is also 40
then diagonal of square is $$40\sqrt{2}$$
and this diagonal will include 2 small circles and 1 large circle so radius of small circle is approx
$$\frac{(40\sqrt{2} - 40)}{2}$$( 40root2-40/2)
so $$20(\sqrt{2}-1)$$ (this will be a bit bigger than diameter of smaller circle)
we need radius then divide it by 2 which make bit bigger than radius as $$10(\sqrt{2}-1)$$

but as you can see both small circles are not touching in the corner of the square then the answer will be little less than the above answer
above answer in terms of value is 10*0.3=3 correct answer will be little less
A.10*0.3= 3 our answer were bith less than 3
B.6 way greater than 3 incorrect
C.6/2.3= 2.3 (bit less correct)
D.40*0.3= 12 (very large)
E.40*0.3/2.3= 5.3(greater than 3 incorrect)

-------------------------------------------------------------------------------------------------------------------------------

If you like my explanation than please give me KUDOS

Originally posted by rishabhmishra on 13 Mar 2018, 23:33.
Last edited by rishabhmishra on 26 Mar 2018, 22:54, edited 1 time in total.
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 642
GMAT 1: 740 Q50 V40
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

14 Mar 2018, 00:30
Bunuel wrote:

In the figure shown, if the side of the square is 40, what is the radius of the smaller circles?

A. $$10(\sqrt{2} - 1)$$

B. $$20(\sqrt{2} - 1)$$

C. $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

D. $$40(\sqrt{2} - 1)$$

E. $$\frac{40(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Source: ExpersGlobal

Attachment:
The attachment Screenshot %2887%29.png is no longer available

IMO C.

This is a nice tricky question and I took over 4 mins to solve it. Everyone who have tried a solution have got a different answer and I am excited to find out the OA.

Please refer to the attached figure. We have to find t ( radius of the small circle ) as in the figure.

The figure is zoomed into the 1/4th part of the larger square.

The distance between one corner of the square and the circle is diagonal of the square of side 20 minus the radius of inscribed large circle of radius 20.
I have called the distance x. And x = $$20\sqrt{2} - 20$$

This is the trap option!

However this distance x is split between the radius of the circle t and and distance between the center of small circle and corner of large square t\sqrt{2}.

Hence by multiplying the x in the correct ratio we can find radius t.

t =$$x * 1/{\sqrt{2}+1}$$

t = $$\frac{20(\sqrt{2} - 1)}{\sqrt{2}+1}$$

Hence C.

Attachments

radius of circle.jpg [ 541.21 KiB | Viewed 779 times ]

_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1195
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

25 Mar 2018, 04:23
1
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Attachments

IMG_20180325_175217.jpg [ 492.91 KiB | Viewed 566 times ]

_________________
Intern
Joined: 14 Mar 2017
Posts: 3
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

25 Mar 2018, 06:33
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????
Intern
Joined: 14 Mar 2017
Posts: 3
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

25 Mar 2018, 06:37
Dexter78424 wrote:
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????

Sent from my ONEPLUS A5000 using GMAT Club Forum mobile app
Senior PS Moderator
Status: It always seems impossible until it's done.
Joined: 16 Sep 2016
Posts: 642
GMAT 1: 740 Q50 V40
Re: In the figure shown, if the side of the square is 40, what is the radi  [#permalink]

### Show Tags

25 Mar 2018, 06:37
Dexter78424 wrote:
gmatbusters wrote:
OA should be C.
Side of the square = 40
Dia of big circle = 40.
Now diagonal of square = 40root 2,
Hence 40r*root2= 2*r*root2 + 2*r+40.

Solving we get r= 20(root2-1)/(root 2+1).

Shouldn't it 4r????

Hi Dexter78424,

Not quite clear what you are asking exactly. But the trick part of this question is - the ability to zoom in onto 1/4th of the larger square and focus on that.

You can see the detailed explanation in my post above & also in many other posts. The OA is correct -> Option (C)

Please go through those and ask specific doubts if you have any..

Best,
_________________

Regards,

“Do. Or do not. There is no try.” - Yoda (The Empire Strikes Back)

Re: In the figure shown, if the side of the square is 40, what is the radi &nbs [#permalink] 25 Mar 2018, 06:37
Display posts from previous: Sort by