Marcia's bucket can hold a maximum of how many liters of wat

(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3
Say the bucket contains (x/2) water. If 3 liters are added, then amount of water (which is x/2) will increase by 1/3 (i.e. 33.33%)
That means (1/3) of (x/2) corresponds to 3 liters -> x/6=3
Hence x = 18.

You can double check your answer -> half the capacity is 9 liters. If 3 liters are added, the water will increase from 9 to 12, i.e. increase by (1/3) or 33.33%.

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Marcia's bucket can hold a maximum of how many liters of water?

(1) The bucket currently contains 9 liters of water. This implies that the bucket can hold at least 9 liters of water. Not sufficient.

(2) If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3 --> x/2+3=x/2+x/2*1/3 --> we can find x. Sufficient.

Answer: B.
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I didn't understand that part.

Let x be the total capacity of the bucket.

1. insufficient

2. sufficient. x/2+3 is the volume of water when 3 liters are added
when the bucket is half full.

x/2 + 3 = x/2 * 4/3
x=18

So B

from the first statement clearly we cannot conclude.
From second statement ,
let x be the amount of water when it is half full
the amount of water in the bucket will increase by 1/3 'of its original volume' when 3 litters is added

so x/3=3 or x=9 hence capacity is 2x=18L HenceB

Can any one please explain the 2nd statement more clearly. I used real numbers and got the answers but still can't get around this equation and I don't want to miss out on an important concept by not clearly understanding how this equation was formed. Thanks.

The second statement basically says that 3 liters comprise 1/3 of the bucket when it is half full of water: 1/3*x/2 = 3.
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Dear aj0809

Since this is a DS question, you don't need to SOLVE it. You need to know, whether you can find its value. Since this is a quadratic equation of degree 1, the chances of getting two / more values of x are next to nil. Once you get the equation, it should be clear that we can get the value of x, thus this is sufficient.

Still, to give you a clarity, here's my take:

Let the water be X.
When 3L is added, the quantity = 3 + X,
The second question stem says that the water will increase by 1/3, i.e. it would be 4X/3
3+X = 4X/3
X = 9

When 3L is added, the bucket becomes half full.
Thus 9 + 3 = 12 = Half the capacity of bucket

Bucket's capacity = 24L

Hope this helps you...

Thanks a lot Bunuel and Thoughtosphere for the quick help

Solution

We need to determine the maximum number of liters that Marcia’s bucket can hold.

Statement One Alone:

The bucket currently contains 9 liters of water.

Only knowing that the bucket contains 9 liters of water is not enough information to determine the maximum capacity of the bucket. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

If 3 liters of water are added to the bucket when it is half full of water, the amount of water in the bucket will increase by 1/3.

Using the information in statement two we can create an equation in which b = the maximum capacity of the bucket. It follows that when the bucket is half full we can express the amount of water in the bucket as ½b.

3 + ½b= (1 + 1/3)(½b)

3 + ½b= 4/3(½b)

Without going further we see that we have enough information to determine the value of b, which is the maximum capacity of the bucket. Statement two alone is sufficient to answer the question.

Answer: B
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