Fractions Problem

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balan88: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Wed Jun 04, 2014 10:21 am

by balan88 » Thu Jun 05, 2014 1:18 am

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

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Source: Beat The GMAT — Problem Solving | Thu Jun 05, 2014 1:18 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Thu Jun 05, 2014 2:15 am

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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Jun 05, 2014 2:21 am

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 the total weight of the filled vessel = 10 pounds.
Weight of the empty vessel = 10% of the total weight of the filled vessel = 1 pound.
Implication:
The filled vessel holds 9 pounds of paint.

The weight of the partially filled vessel = 1/2 the weight of the filled vessel = (1/2)(10) = 5 pounds.
Implication:
The partially filled vessel holds 4 pounds of paint.

Resulting fraction:
(weight of the paint in the partially filled vessel)/(weight of the paint in the filled vessel) = 4/9.

The correct answer is E.

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ceilidh.erickson: GMAT Instructor; Posts: 2095; Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members; Thanked: 1443 times

by ceilidh.erickson » Thu Jun 05, 2014 8:22 am

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.

Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

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