Fractions Problem

balan88 wrote:An empty wooden vessel weighs 10% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

A, 3/5
B, 5/9
c, 1/24
D, 4/9
E, 2/5

Let's plug in some weights that meet the given conditions.

An empty wooden vessel weighs 10% of its TOTAL weight when filled with paint.
Let's say the TOTAL weight is 10 pounds.
This means that the empty wooden vessel weighs 1 pound.
And it means that the vessel can hold up to 9 pounds of paint.

If the weight of a partially filled vessel is one half that of a completely filled vessel....
So, the total weight of the partially filled vessel = 1/2 of 10 = 5 pounds
Since the empty wooden vessel weighs 1 pound, this partially filled vessel holds 4 pounds of paint.

...what fraction of the vessel is filled?
The vessel holds up to 9 pounds of paint.
So, the vessel is 4/9 filled

Answer: D

Cheers,
Brent

What is the source of this question? As written, "An empty wooden vessel weighs 10% of its total weight when filled with paint" is nonsensical. This implies that when it is filled with paint, an empty vessel weighs 10% of its weight. If it's filled with paint, it's not empty, and it can't weigh 10% of its own weight. To make any sense, this question would have to read "... weighs 10% of what it would weigh when filled with paint."

We can infer the likely meaning of the question and solve, as Brent and Mitch have done. But just know that you will never see a question on the GMAT quant that doesn't make grammatical sense! It's a bad idea to study from non-GMAT-like sources.