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# A lighthouse emits a light that can be seen for 60 miles in all direct

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Manager
Joined: 08 Sep 2017
Posts: 65
A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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12 Jul 2018, 19:40
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Difficulty:

45% (medium)

Question Stats:

67% (01:16) correct 33% (02:05) wrong based on 45 sessions

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A lighthouse emits a light that can be seen for 60 miles in all directions. If the intensity of the light is strengthened so that its visibility is increased by 40 miles in all directions, by approximately how many square miles is its region of visibility increased?

A) 6,300
B) 10,000
C) 10,300
D) 20,000
E) 31,400

Kudos if you like the question please, thanks!

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Manager
Joined: 19 Nov 2017
Posts: 153
Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
GPA: 4
Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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12 Jul 2018, 20:27
radius = $$60$$ miles
area = $$3600π$$

radius (extended) = $$100$$ miles
area $$10000π$$

Increased area =$$6400π$$ square miles

$$π = \frac{22}{7}$$
$$6300*\frac{22}{7} = 19800$$. Approx $$20000$$.
D is correct
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Intern
Joined: 11 Jul 2018
Posts: 20
Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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12 Jul 2018, 20:50
vaibhav1221 wrote:
radius = $$60$$ miles
area = $$3600π$$

radius (extended) = $$100$$ miles
area $$10000π$$

Increased area =$$6400π$$ square miles

$$π = \frac{22}{7}$$
$$6300*\frac{22}{7} = 19800$$. Approx $$20000$$.
D is correct

I guess you meant 6400 and not 6300 in the end.
It is 6400*22/7 = 20114
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Joined: 04 Jan 2015
Posts: 1991
Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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13 Jul 2018, 05:14
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Solution

Given:
A lighthouse emits a light that can be seen for 60 miles in all directions
When the intensity of the light is increased, the visibility of light is increased by 40 miles in all directions

To find:
How many square miles is its region of visibility increased?

Approach and Working:
When emitted light can be seen up to 60 miles in all directions:
Area covered= $$π* (60)^2= 3600 π$$ miles
When intensity of light is increased further 40 miles:
Now, the light can be seen in 60+40= 100 miles
Area covered= $$π* (100)^2= 10000 π$$ miles
Hence, increase in area= $$10000 π- 3600 π= 6400 π$$= 6400*3.14 ≈ 20,000

Hence, the correct answer is option D.

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Manager
Joined: 19 Nov 2017
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Location: India
Schools: ISB
GMAT 1: 670 Q49 V32
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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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13 Jul 2018, 19:30
bangu wrote:
vaibhav1221 wrote:
radius = $$60$$ miles
area = $$3600π$$

radius (extended) = $$100$$ miles
area $$10000π$$

Increased area =$$6400π$$ square miles

$$π = \frac{22}{7}$$
$$6300*\frac{22}{7} = 19800$$. Approx $$20000$$.
D is correct

I guess you meant 6400 and not 6300 in the end.
It is 6400*22/7 = 20114

Hi!
I wrote 6300 intentionally, because, 6300 is divisble by 7. Finding an approximate answer is much faster than calculating the exact answer, which the question doesn't ask for.

Regards,
V

Posted from my mobile device
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Regards,

Vaibhav

Sky is the limit. 800 is the limit.

~GMAC

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Joined: 07 Feb 2017
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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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13 Jul 2018, 19:41
eazy peazy pie
pi 60^2
pi 100^2

10,000 pi - 3,600 pi

6,700 pi

Math Expert
Joined: 02 Aug 2009
Posts: 6787
A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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13 Jul 2018, 20:00
Carlgrc wrote:
A lighthouse emits a light that can be seen for 60 miles in all directions. If the intensity of the light is strengthened so that its visibility is increased by 40 miles in all directions, by approximately how many square miles is its region of visibility increased?

A) 6,300
B) 10,000
C) 10,300
D) 20,000
E) 31,400

Kudos if you like the question please, thanks!

So its a circle of radius 60 and (60+40)=100...See attached figure

we have to find area outside the inner circle and within the outer circle

so $$\pi*100^2-\pi*60^2=\pi*(100^2-60^2)=\pi(100-60)(100+60)=\pi*40*160=\pi*6400 = \frac{22}{7}*6400$$~22*900=19800 ~20000

D
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