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# Region Q, shown here, is defined by

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Senior RC Moderator
Status: It always seems impossible until it's done!!
Joined: 29 Aug 2012
Posts: 1141
Location: India
WE: General Management (Aerospace and Defense)
Region Q, shown here, is defined by [#permalink]

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25 Nov 2017, 12:11
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Difficulty:

85% (hard)

Question Stats:

45% (01:59) correct 55% (01:37) wrong based on 71 sessions

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Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:

Capture.PNG [ 25.12 KiB | Viewed 803 times ]
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Aug 2009
Posts: 5777
Re: Region Q, shown here, is defined by [#permalink]

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26 Nov 2017, 02:44
2
KUDOS
Expert's post
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
The attachment Capture.PNG is no longer available

Look at the attached figure..
Ans C

Join the parallel lines as shown..
Attachments

IMG_20171126_151118.jpg [ 1.48 MiB | Viewed 740 times ]

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Intern
Joined: 16 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
Re: Region Q, shown here, is defined by [#permalink]

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26 Nov 2017, 04:01
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
The attachment Capture.PNG is no longer available

As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =$$\pi * r^2$$ $$= 100 *\pi$$ = 300

The shaded region is around $$\frac{2}{3}$$ of the circle area => $$\frac{2}{3} * 300 = 200$$

Attachments

circle1.jpg [ 20.07 KiB | Viewed 719 times ]

Intern
Joined: 24 Jun 2017
Posts: 6
Re: Region Q, shown here, is defined by [#permalink]

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29 Nov 2017, 00:44
Vorovski wrote:
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG

As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =$$\pi * r^2$$ $$= 100 *\pi$$ = 300

The shaded region is around $$\frac{2}{3}$$ of the circle area => $$\frac{2}{3} * 300 = 200$$

Can you eloborate how you arrived at 2/3??
Intern
Joined: 24 Jun 2017
Posts: 6
Re: Region Q, shown here, is defined by [#permalink]

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29 Nov 2017, 00:45
chetan2u wrote:
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG

Look at the attached figure..
Ans C

Join the parallel lines as shown..

Expert can you post a clear cut solution... image is not that clear?
Intern
Joined: 16 Oct 2017
Posts: 30
Location: Ireland
Concentration: Healthcare, Finance
Re: Region Q, shown here, is defined by [#permalink]

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29 Nov 2017, 01:57
Vorovski wrote:
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG

As we can see the point (6,4) is a centre of the circle. The dash line is a radius wchich is 10. Circle area =$$\pi * r^2$$ $$= 100 *\pi$$ = 300

The shaded region is around $$\frac{2}{3}$$ of the circle area => $$\frac{2}{3} * 300 = 200$$

Can you eloborate how you arrived at 2/3??

The shaded region is around 70% of the circle and 70% is around 2/3.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8025
Location: Pune, India
Re: Region Q, shown here, is defined by [#permalink]

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29 Nov 2017, 03:20
2
KUDOS
Expert's post
Gnpth wrote:
Region Q, shown here, is defined by

$$(x−6)^{​2} +(y−4)^{2} \leq 100$$,

$$y\geq{0}$$, and $$x\geq{0}$$.

What is the approximate area of Region Q in square units?

A.between 75 and 125
B.between 125 and 175
C.between 175 and 225
D.between 225 and 275
E.between 275 and 325
Attachment:
Capture.PNG

The shaded region could be seen as sum of three areas: a quarter of a circle and two rectangles (the shaded region is a bit less)

Area of quarter of a circle $$= (\pi * r^2)/4 = (3.14 * 10^2)/4 = 314/4 = 75$$ approx

Area of each rectangle $$= 16*4 + 6*10 = 124$$

So total shaded area will be a bit less than 75 + 124 = 199

The reduced area at the top of the top rectangle is less than 6*2/2 = 6
The reduced area at the right of the lower triangle will be even less.

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Re: Region Q, shown here, is defined by   [#permalink] 29 Nov 2017, 03:20
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