Problem Solving

Hi All,

We're told that an artist who needs to buy only paint and canvas finds that the cost of the canvas has decreased by 40 percent, the cost of paint has decreased by 60 percent and the paint previously accounted for 4 TIMES as much of the expense of painting as did canvas. We're asked for the percent decrease in the TOTAL cost for paint and canvas. This prompt is essentially a big 'Weighted Average' question; TESTing VALUES works perfectly here - but the answer choices are written in such a way that you actually avoid doing a lot of math IF you recognize the concepts involved.

To start, we know the decrease in the price of canvas was 40% and the decrease in price of the paint was 60%, so the OVERALL total decrease is something BETWEEN 40% and 60%, so we can eliminate Answers A and E.

IF we spent the SAME amount on canvas and paint, then the total percent decrease would be 50%. That didn't happen though (since the paint accounts for 4 TIMES of the TOTAL expense) - the overall average has to skew CLOSER to 60% than to 40%. There's only one answer that fits...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

AAPL wrote:An artist who needs to buy only paint and canvas finds that the cost of the canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent. If paint previously accounted for 4 times as much of the expense of painting as did canvas, by what percent did the total cost for paint and canvas decrease?

A. 40%
B. 44%
C. 50%
D. 56%
E. 60%

We can let the original cost of canvas = n and the original cost of paint = 4n, for a total cost of 5n.

The new cost of the canvas is 0.6n, and the new cost of paint is 0.4 x 4n = 1.6n, for a total cost of 2.2n.

So the percent decrease is:

(2.2n - 5n)/5n x 100 = -2.8/5 x 100 = -2.8 x 20 = -56 = 56 percent decrease

Answer: D