Percentage MGMAT Q.

[hey_thr67]

Each light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and ten percent of the fluorescent bulbs are switched off. If eighty percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?

A: 22 (2/9)%
B: 16 (2/3)%
C: 11 (1/9)%
D: 10%
E: 5%

[Anurag@Gurome]

Each light bulb at Hotel California is either incandescent or fluorescent. At a certain moment, forty percent of the incandescent bulbs are switched on, and ten percent of the fluorescent bulbs are switched off. If eighty percent of all the bulbs are switched on at this moment, what percent of the bulbs that are switched on are incandescent?

Say, there are a total of 100 bulbs.
Hence, 80 bulbs are switched on at this moment.

Say, x bulbs are incandescent.
Hence, (100 - x) bulbs are fluorescent.

Therefore, 40% of the x bulbs and (100 - 10) = 90% of the (100 - x) bulbs are switched on. Hence, a total of (0.4x + 0.9(100 - x)) bulbs are switched on.

So, (0.4x + 0.9(100 - x)) = 80
--> (0.4x + 90 - 0.9x) = 80
--> 0.5x = 10
--> x = 20

Hence, number of incandescent bulbs that are switched on = 40% of 20 = 0.4*20 = 8

Hence, required percentage = (Number of incandescent bulbs that are switched on)/(Number of bulbs that are switched on) = 100*(8/80) = 10

The correct answer is D.

[hey_thr67]

Any other method with which I can guess ?

[dhonu121]

b = i+f.
Now switched ON bulbs = .4i+.9f
Now. (.4i+.9f) = .8(i+f). which solves to yield 4i=f.
We need to find, .4i/(.4i+.9f)*100 solving this using the equation above gives 10%.
Hence D

[minkathebest]

I did this using the 2x2 matrix method...

Our sets are
I / C
and Off / ON

Since we are working with percentages, let total = 100
off on T
I 0.6x 0.4x x

C 0.1(100-x) 100-x
=----------------------------------------------------
T 20 80 100


Now solve for 0.4 x / 80, so we need value of x

we do
0.6 + 0.1 (100-x) = 20
x = 20

Plug in x back into the (.4 (20) / 80 )*100 = 10

[Brent@GMATPrepNow]

I did this using the 2x2 matrix method...

Our sets are
I / C
and Off / ON

Since we are working with percentages, let total = 100
off on T
I 0.6x 0.4x x

C 0.1(100-x) 100-x
=----------------------------------------------------
T 20 80 100


Now solve for 0.4 x / 80, so we need value of x

we do
0.6 + 0.1 (100-x) = 20
x = 20

Plug in x back into the (.4 (20) / 80 )*100 = 10

I thought I'd point out that minkathebest is using a very useful technique called the Double Matrix Method. It can be used for most questions featuring a population in which each member has two criteria associated with it.
Here, the criteria are:
- type (incandescent or fluorescent)
- status (on or off)

For more information about this technique and some additional practice questions, check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent