Data Sufficiency

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


1. The bucket currently contains 9 lit of water.
2.If 3 lit 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.

I picked the answer as B by reducing it to the foll equation, but I'm not sure if that's right equation for the stataemnt 2. Can someone help me reduce the statement 2 ina equatin format.

My equation was, if x was max capticty of the bucket,

then x/2 + 3 = 4/3x; but I'm not sure if 4/3x is the correct value representing "amount of water increased by 1/3"

I would take the second statement as --> adding 3 liters increases the content 1/3 times what is in it which is (1/2)x where x is the total capacity..(since statement says bucket is half full)

so 3 = (1/3)*(1/2)x
x= 18

The OG 11 explanation has it as x + 3 = 4/3(1/2)*x
that is, x + 3 = (2/3)x; I didnt quite understand the logic.

Statement (2):

If x is the capacity of the bucket, then x/2 is the current amount of water in the bucket.

x/2 + 3 represents adding three gallons to the current amount.

Increasing the current amount (x/2) by 1/3 is equivalent to multiplying the current amount (x/2) by 4/3, or x/2*4/3.

Equating these two, we get x/2 + 3 = x/2*4/3

In your original post, you multiplied the total capacity (x) by 4/3 instead of the current amount (x/2).

Thanks for your response. One question in general I have is, whenever we see a fraction of an increase or a question saying fraction more, do we need to consider it as "fraction of the original".


Eg; If x is 3 more then y; Here, x = y +3;
If x is 1/3 more then y, do we say x= y +1/3y = 4/3y. Are there any exceptions for this rule?

Appreciate your response.