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Math Expert V
Joined: 02 Sep 2009
Posts: 57281
For a light that has an intensity of 60 candles at its sourc  [#permalink]

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16 00:00

Difficulty:   5% (low)

Question Stats: 87% (02:00) correct 13% (02:20) wrong based on 483 sessions

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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

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

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

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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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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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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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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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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
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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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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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.
Math Expert V
Joined: 02 Sep 2009
Posts: 57281
Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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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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Joined: 01 Aug 2016
Posts: 27
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Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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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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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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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 !
Manager  S
Joined: 15 Jul 2016
Posts: 91
GMAT 1: 690 Q48 V36 Re: For a light that has an intensity of 60 candles at its sourc  [#permalink]

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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.

Bunuel egmat VeritasKarishma please help!
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Please give Kudos if you agree with my approach :) Re: For a light that has an intensity of 60 candles at its sourc   [#permalink] 10 Aug 2019, 23:02
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