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Scented or Unscented / Round or Square

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by kanha81 » Mon Mar 09, 2009 2:00 pm
I am having a tough time putting this problem in perspective in order to determine if it's solvable or not. Grateful, if you can please SHOW the logic in steps on how you solve the problem:

q: Each candle in a particular box is either rounder or square and either scented or unscented. If 60% of the candles are round; what is the probability that a candle selected randomly from the box will be unscented?

i) If a candle is scented, it has an 80% chance of being round
ii) If a candle is square, it has an 25% chance of being scented

Thanks a bunch!
I tried to solve this problem using the table approach; however, got confused while determining the unknowns.
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Re: Scented or Unscented / Round or Square

by Brent@GMATPrepNow » Mon Mar 09, 2009 5:52 pm
kanha81 wrote:I am having a tough time putting this problem in perspective in order to determine if it's solvable or not. Grateful, if you can please SHOW the logic in steps on how you solve the problem:

q: Each candle in a particular box is either rounder or square and either scented or unscented. If 60% of the candles are round; what is the probability that a candle selected randomly from the box will be unscented?

i) If a candle is scented, it has an 80% chance of being round
ii) If a candle is square, it has an 25% chance of being scented

Thanks a bunch!
I tried to solve this problem using the table approach; however, got confused while determining the unknowns.
I find it helps to show this visually.


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Re: Scented or Unscented / Round or Square

by rseeker2 » Mon Mar 09, 2009 9:28 pm
My take.. C

I did it this way...

Let 'a' be the number of round,scented candles
Let 'b' be the number of round,unscented candles
Let 'c' be the number of square,unscented candles
Let 'd' be the number of square,scented candles


Required -- the probability that a candle selected randomly from the box will be unscented i.e., b+c/a+b+c+d

Given -- 60% of the candles are round --> a+b/a+b+c+d = 60/100
which leads to 2(a+b) = 3(c+d) ------------- (i)

----------------------------------------------------------------------------

1) If a candle is scented, it has an 80% chance of being round

--> a/a+d = 80/100 --> a = 4d ------------ (ii)

Using (i) and (ii), b+c/a+b+c+d reduces to c-d/c+d, which cannot be determined

Hence, (1) alone is not sufficient


2) If a candle is square, it has a 25% chance of being scented

--> d/c+d = 25/100 --> c = 3d -------------- (iii)

Using (i) and (iii), b+c/a+b+c+d reduces to b+3d/10d, which cannot be determined

Hence, (2) alone is not sufficient


Combining both, if (iii) is used in c-d/c+d(arrived at using (i) and (ii)), we get 3d-d/3d+d = 1/2

Hence, both the statements together are needed to arrive at the answer
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