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For a light that has an intensity of 60 candles at its sourc

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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 \(S=\frac{60k}{d^2}\), 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

Problem Solving
Question: 91
Category: Algebra Applied problems
Page: 73
Difficulty: 600


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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 13 Feb 2014, 01:17
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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 \(S=\frac{60*2}{20^2}=\frac{3}{10}\).

Answer: A.
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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 13 Feb 2014, 10:30
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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=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

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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 13 Feb 2014, 21:38
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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 \(30(\frac{1}{100}) = \frac{3}{10} candles\)

Answer: (A)
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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 15 Feb 2014, 09:55
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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 sourc  [#permalink]

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New post 16 Feb 2014, 01:41
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 sourc  [#permalink]

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New post 16 Feb 2014, 23:56
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 \(S=\frac{60*2}{20^2}=\frac{3}{10}\).

Answer: A.
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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 30 Dec 2016, 16:18
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 \(S=\frac{60*2}{20^2}=\frac{3}{10}\).

Answer: A.


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 sourc  [#permalink]

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New post 31 Dec 2016, 01:42
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 \(S=\frac{60*2}{20^2}=\frac{3}{10}\).

Answer: A.


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 sourc  [#permalink]

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New post 31 Dec 2016, 02:39
60k/2^2 = 30 => k=2

So if d=20 then 60*2/20*20 == 3/10
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For a light that has an intensity of 60 candles at its source  [#permalink]

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New post 31 May 2017, 18:10
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

Answer: A
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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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New post 12 Oct 2018, 02:53
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

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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 sourc   [#permalink] 12 Oct 2018, 02:53
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