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# For a light that has an intensity of 60 candles at its source, the int

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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
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For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula $$S=\frac{60k}{d^2}$$, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(A) 3/10 candles
(B) 1/2 candles
(C) 1 1/3 candles
(D) 2 candles
(E) 3 candles

Using the formula $$S=\frac{60k}{d^2}$$, the ratio between light intensity at 2 feet and 20 feet $$=\frac{Light Intensity At 20 Feet}{Light Intensity At 2 Feet}=\frac{60k}{20^2}/\frac{60k}{2^2}= \frac{1}{100}$$
Given that light intensity at 2 feet equals 30 candles, the intensity of light at 20 feet is equal to $$30(\frac{1}{100}) = \frac{3}{10} candles$$

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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(A) 3/10 candles
(B) 1/2 candles
(C) 1 1/3 candles
(D) 2 candles
(E) 3 candles

30 = 60* k/4 => k =2
60*2/20*20 = 3/10 - Option A)
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
option A.
First we can calculate the value of k by putting S=30 and d=2 in
S=60k/d^2
From this k=2
Now we can calculate S=60*2/(20)^2
S=3/10
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
Bunuel wrote:
SOLUTION

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(A) 3/10 candles
(B) 1/2 candles
(C) 1 1/3 candles
(D) 2 candles
(E) 3 candles

The intensity of the light is 30 candles (S) at a distance of 2 feet (d) from the source: $$30=\frac{60k}{2^2}$$ --> $$k=2$$.

Therefore the intensity of the light at a distance of 20 feet from the source is $$S=\frac{60*2}{20^2}=\frac{3}{10}$$.

Hi, Bunuel. I chose C because I think candle can not be apart, that means the number of candle is integer. Why the number of candle can be fraction? Thanks in advance:)

It changed in the OG Quantitive 2017 where the choices are
A) 3/10 candle
B) 1/2 candle
C) 1 candle
D) 2 candles
E) 3 candles.
And the question remains the same.
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
Jez0612 wrote:
Bunuel wrote:
SOLUTION

For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

(A) 3/10 candles
(B) 1/2 candles
(C) 1 1/3 candles
(D) 2 candles
(E) 3 candles

The intensity of the light is 30 candles (S) at a distance of 2 feet (d) from the source: $$30=\frac{60k}{2^2}$$ --> $$k=2$$.

Therefore the intensity of the light at a distance of 20 feet from the source is $$S=\frac{60*2}{20^2}=\frac{3}{10}$$.

Hi, Bunuel. I chose C because I think candle can not be apart, that means the number of candle is integer. Why the number of candle can be fraction? Thanks in advance:)

It changed in the OG Quantitive 2017 where the choices are
A) 3/10 candle
B) 1/2 candle
C) 1 candle
D) 2 candles
E) 3 candles.
And the question remains the same.

Intensity is kind of a unit of a brightness, so it's not actual candles, so we can have an intensity in fractions.
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
60k/2^2 = 30 => k=2

So if d=20 then 60*2/20*20 == 3/10
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
rlevochkin wrote:
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d d feet from the source is given by the formula S=60k/d^2 60, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

A. 3/10 candles
B. 1/2 candles
C. 1 1/3 candles
D. 2 candles
E. 3 candles

We are given that for a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant.

For this direct variation problem, we first will use the given formula to solve for k, the constant of variation, and then we can answer the question.

30 = 60k/(2^2)

30 = 60k/4

120 = 60k

k = 2

We know that k is 2, and we use that fact to determine the intensity of the light at a distance of 20 feet from the source.

S = 60(2)/20^2

S = 120/400 = 12/40 = 3/10 candles

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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
WoundedTiger wrote:
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

Sol: For the given intensity S=30 candles at a distance of 2 feet we can find value of k as

30*d^2/60= k
30*4/60 so k=2

Now substituting the value of k and d=20 ft we get
S= 60*2/(20^2)
Or
120/400 = 3/10 candles

Ans A

Posted from my mobile device

HI !

Can someone please explain why Ks coeffficient ( 60 ) remains the same . Thats what threw me !
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
whelmedbynumbers wrote:
WoundedTiger wrote:
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

Sol: For the given intensity S=30 candles at a distance of 2 feet we can find value of k as

30*d^2/60= k
30*4/60 so k=2

Now substituting the value of k and d=20 ft we get
S= 60*2/(20^2)
Or
120/400 = 3/10 candles

Ans A

Posted from my mobile device

HI !

Can someone please explain why Ks coeffficient ( 60 ) remains the same . Thats what threw me !

I have the same question.

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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
whelmedbynumbers wrote:
WoundedTiger wrote:
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

Sol: For the given intensity S=30 candles at a distance of 2 feet we can find value of k as

30*d^2/60= k
30*4/60 so k=2

Now substituting the value of k and d=20 ft we get
S= 60*2/(20^2)
Or
120/400 = 3/10 candles

Ans A

Posted from my mobile device

HI !

Can someone please explain why Ks coeffficient ( 60 ) remains the same . Thats what threw me !

chetan2u Bunuel, I have the same question. Can you help clarify? Thank you!
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
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Argp wrote:
whelmedbynumbers wrote:
WoundedTiger wrote:
For a light that has an intensity of 60 candles at its source, the intensity in candles, S, of the light at a point d feet from the source is given by the formula S=60k/d^2, where k is a constant. If the intensity of the light is 30 candles at a distance of 2 feet from the source, what is the intensity of the light at a distance of 20 feet from the source?

Sol: For the given intensity S=30 candles at a distance of 2 feet we can find value of k as

30*d^2/60= k
30*4/60 so k=2

Now substituting the value of k and d=20 ft we get
S= 60*2/(20^2)
Or
120/400 = 3/10 candles

Ans A

Posted from my mobile device

HI !

Can someone please explain why Ks coeffficient ( 60 ) remains the same . Thats what threw me !

chetan2u Bunuel, I have the same question. Can you help clarify? Thank you!

Hi
The light is the same in all 3 calculations and has an intensity of 60 candles at the source. It decreases as we move away from light, so d, the distance, in the formula changes.
Rest everything remains the same.

Maybe if we were dealing with some other light that has an intensity of 30 candles AT THE SOURCE, the 60 would have changed but then too, it would be mention that 60 is the luminosity related to candles at the source.
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
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Re: For a light that has an intensity of 60 candles at its source, the int [#permalink]
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