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

 It is currently 14 Oct 2019, 18:29

### 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

# Consider a quarter of a circle of radius 16. Let r be the radius of th

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Oct 2011
Posts: 40
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

### Show Tags

21 Apr 2012, 10:28
3
1
19
00:00

Difficulty:

75% (hard)

Question Stats:

56% (02:29) correct 44% (02:28) wrong based on 123 sessions

### HideShow timer Statistics

Consider a quarter of a circle of radius 16. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

A. $$16*(\sqrt{2} -1)$$

B. $$8*(\sqrt{3} -1)$$

C. $$4*(\sqrt{7} - 1)$$

D. $$12* (\sqrt{7} -1)$$

E. None of these

A question from MBA Strategy course
Math Expert
Joined: 02 Sep 2009
Posts: 58320
Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

### Show Tags

21 Apr 2012, 12:09
2
7
JubtaGubar wrote:
Consider a quarter of a circle of radius 16. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

A. $$16*(\sqrt{2} -1)$$

B. $$8*(\sqrt{3} -1)$$

C. $$4*(\sqrt{7} - 1)$$

D. $$12* (\sqrt{7} -1)$$

E. None of these

A question from MBA Strategy course

Look at the diagram below:
Attachment:

Quarter of circle.png [ 5.62 KiB | Viewed 7048 times ]

The radius of a quarter of a circle equals to the diagonal of a square made by the radii of the inscribed circle plus the radius of that circle.

Now, since the sides of a square equal to $$r$$, then its diagonal equals to $$r\sqrt{2}$$, hence $$r\sqrt{2}+r=16$$ --> $$r=\frac{16}{\sqrt{2}+1}$$.

Rationalise by multiplying both numerator and denominator by $$\sqrt{2}-1$$: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}$$ --> apply $$(a+b)(a-b)=a^2-b^2$$ to the expression in the denominator: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{16(\sqrt{2}-1)}{2-1}=16(\sqrt{2}-1)$$.

Hope it's clear.
_________________
##### General Discussion
Intern
Joined: 23 Oct 2011
Posts: 40
Location: Ukraine
Schools: LBS '14 (M)
GMAT 1: 650 Q44 V35
WE: Corporate Finance (Mutual Funds and Brokerage)
Re: Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

### Show Tags

23 Apr 2012, 08:13
Thank you Bunuel!

I got 16/(sqr2 +1) and just forgot to multiply by (sqr2 -1).
Intern
Joined: 03 Jun 2019
Posts: 21
Re: Consider a quarter of a circle of radius 16. Let r be the radius of th  [#permalink]

### Show Tags

10 Jun 2019, 08:25
Bunuel wrote:
JubtaGubar wrote:
Consider a quarter of a circle of radius 16. Let r be the radius of the circle inscribed in this quarter of a circle. Find r.

A. $$16*(\sqrt{2} -1)$$

B. $$8*(\sqrt{3} -1)$$

C. $$4*(\sqrt{7} - 1)$$

D. $$12* (\sqrt{7} -1)$$

E. None of these

A question from MBA Strategy course

Look at the diagram below:
Attachment:
Quarter of circle.png

The radius of a quarter of a circle equals to the diagonal of a square made by the radii of the inscribed circle plus the radius of that circle.

Now, since the sides of a square equal to $$r$$, then its diagonal equals to $$r\sqrt{2}$$, hence $$r\sqrt{2}+r=16$$ --> $$r=\frac{16}{\sqrt{2}+1}$$.

Rationalise by multiplying both numerator and denominator by $$\sqrt{2}-1$$: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}$$ --> apply $$(a+b)(a-b)=a^2-b^2$$ to the expression in the denominator: $$r=\frac{16(\sqrt{2}-1)}{(\sqrt{2}+1)(\sqrt{2}-1)}=\frac{16(\sqrt{2}-1)}{2-1}=16(\sqrt{2}-1)$$.

Hope it's clear.

Hey,

how do you get to know that you will get a square instead of a rectangle.
Re: Consider a quarter of a circle of radius 16. Let r be the radius of th   [#permalink] 10 Jun 2019, 08:25
Display posts from previous: Sort by