12 Days of Christmas GMAT Competition 2025 - Day 9: A point light

Intensity is inversely proportional to Distance

I = k*(1/D^2)

8 = k ( 1/6^2)

k = 288

Now let's look at option which satisfy I = 288/ D^2

288/4^2 = 18 ( Not on the table)

288/12^2 = 2 ( 2 is there)

So our answer is 12 & 2

asperioresfacere

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26 Dec 2025, 00:33

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Intensity (I) is inversely proportional to the square of the distance (d) from the source. this is expressed as I = k /d^2
We are given that when d = 6 meters , I = 8 units
8 = k/6^2
k= 8x36 = 288

Now test the options against our formula I = 288/d^2

Distance(d) = 12
I = 288/12^2= 288/144 = 2
Both 12 and 2 are on the list . Consistent Pair . ✅

If D = 4
I = 288/16 = 18 , Not in the list ❌
Likewise for other options.

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26 Dec 2025, 01:11

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Light intensity (I) is inversely proportional to the square of the distance (D) from the source,
$I*D^2 = k$ (some constant)

$8*6^2$

By testing options
$2*4^2$ doesn't give us the same constant.
$2*12^2$, gives us the same constant.

So intensity is 2, distance is 12.

Bunuel

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26 Dec 2025, 01:41

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Let I denotes Intensity in intensity units. R denotes distance in meters.

So , I = k/R^2

when R = 6 meters , I =8 units ,

k = 36*8 = 288 (intensity-m^2)

So , I = 288/R^2

So among the options R = 12 meters , I will be 2 units.

So the answer is Distance = 12 meters , Intensity = 2 units.

Bunuel

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26 Dec 2025, 01:44

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Let intensity be i and distance from the source d.

Therefore, i is proportional to 1/d^2 or i=k/d^2

We have 8= k/36 or k=8*36

From the given options, we can see that when d= 12, then I=8*36/144 =2 which is there among the option choices.

Therefore, Distance = 12 and Intensity = 2

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26 Dec 2025, 03:25

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Intensity = k* 1/distance^2 (k = constant)
8 = k/6^2 => k = 36*8 = 288

Scan the options:
Distance = 12 => Intensity = 288/144 = 2

Bunuel

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Bunuel

If I is inversely proportional to the square of the distance, we can say that $I = \frac{k}{d^2}$, where k is the constant of proportionality.

In the example, they have given I = 8 when d = 6.

Substituting the values in the above equation, we get $8 = \frac{k}{36}$ => $k = 288$
Therefore, $I = \frac{288}{d^2}$

We now substitute the values in the list as potential values of 'd' to see what we get:

d = 2, I = 72
d = 4, I = 18
d = 12, I = 2 (match)
For the other options for d, I would be less than 2.

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26 Dec 2025, 03:54

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based on the question => I = k/d^2
When d = 6, I =8 => 8 = k/6*6 => k=>288
=> I=288/d^2
=> Based on the choices when d = 12 => I = 288/144 = 2
Hence When d = 12, I = 2

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26 Dec 2025, 04:31

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I=(k/d^2)
d=6, I=8
8=(k/6^2)=(k/36)
k=288
I=288/d^2
d=2, 288/4=72 NO
d=4, 288/16=18 NO
d=12, 288/144=2 NO
d=16, 288/256=1.125 NO
d=24, 288/576=0.5 NO
d=32, 288/1024=0.28125 NO

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26 Dec 2025, 04:49

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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.

When the distance is 6 meters, the intensity is 8 units.

Select for Distance a distance in meters and select for Intensity an intensity in units that would be jointly consistent with the given information, Make only two selections, one in each column.

I = Intensity = k/(d^2)

8 = k/36 ----> k = 8 *36 = 288

Let's try all Distance and try to find Intensity :
D = 2,4,12,16,24, 32

I = 288/4 = 72
I = 288/16 = 72/4 = 18
I = 288/144 = 2 Answer ( I = 2 units, D=12 meters )
I = 288 / 256 < 2
I = 288/ (24*24) < 2
I = 288 / (32 *32) < 2

Reon

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26 Dec 2025, 05:37

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A point light source shines equally in all directions. The light intensity measured at a sensor is inversely proportional to the square of the distance from the source.
Intensity is inversely proportional to d^2.
Let, k is a constant
Intensity= k*(1/distance^2)
k= Intensity*Distance^2

When the distance is 6 meters, the intensity is 8 units
k= 8*6^2 = 8*36= 288

D=2; Intensity= 288/4 = 72 (Wrong)
D=4; Intensity= 288/16 =18 (Wrong)
D=12; Intensity= 288/144= 2 (Yes)

Distance= 12 meters
Intensity= 2 units

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26 Dec 2025, 06:14

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To assume proportionality lets assume the constant to be C such that,
Distance^2 inversely proportional to C / Intensity
Therefore,
6^2 = C / 8
C = 36 x 8
C = 288

Checking the values of intensity from options,
Intensity = 288 / Distance^2

Distance of 2, 4, 12, 16, 24, 32 gives us intensity of 72, 18, 2, 1.125, 0.5, 0.27 respectively

Only option matches is D = 12 with I = 2

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26 Dec 2025, 06:53

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We know that,
Intensity is inversely proportional to the square of distance d

=> I = k/d^2

We know that, when distance is 6 metres, intensity is 8 units
=> 8 = k/6^2
=> k = 288

=> I = 288/d^2

By matching the values from the given table to the equation above, we get,
I = 2
d = 12

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26 Dec 2025, 07:00

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D=6M
I= 8 units
8 x 6^2= 288 ; I= 288/D^2
We test D given; Lets try D =4
I=288/4^2=288/16=18 ;
18 is not in the intensity list
D= 12
I= 288/12^2=288/144=2
2 is i the intensity list so our correct answer will be
D=12 Metres
I=2 units

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26 Dec 2025, 07:04

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I = k/(d^2)

Calculate k:
8 = k/(6^2) = k/36
k = 36*8 = 288

I = 288/(d^2)

checking values:
2 = 288/(12^2)

Distance=12
Intensity=2

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26 Dec 2025, 07:18

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LI = K * 1/d2

LI is light intensity
K is proportional constant
d is distance of light source and sensor

Now we have given
8 = 1/6^2 * K
K = 8*36

Now we will go into option to set this up

so if we take distance as 12
then LI = 36*8/144
therefore LI = 2

Hence distance 12m and LI 2 units matches hence the answer

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Bunuel