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16 Sep 2014, 00:54
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A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?
A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%
A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%
16 Sep 2014, 00:54
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Bookmarks
Official Solution:
A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?
A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%
Say the price of the box is \($x\).
The original volume was \(5 \times 10 \times 20 = 1,000\) cubic centimeters, so the price per cubic centimeter was \(\frac{x}{1,000}\);
The new volume is \(6 \times 10 \times 20 = 1,200\) cubic centimeters, so the price per cubic centimeter now is \(\frac{x}{1,200}\);
Percent decrease is \(\frac{change}{original} \times 100 = \frac{\frac{x}{1,000} - \frac{x}{1,200} }{\frac{x}{1,000} } \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\).
Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is a Percent Word Problem question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: B
A fruit juice company altered its packaging from boxes measuring 5 x 10 x 20 centimeters to boxes measuring 6 x 10 x 20 centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?
A. 12.00%
B. 16.67%
C. 18.33%
D. 20.00%
E. 21.50%
Say the price of the box is \($x\).
The original volume was \(5 \times 10 \times 20 = 1,000\) cubic centimeters, so the price per cubic centimeter was \(\frac{x}{1,000}\);
The new volume is \(6 \times 10 \times 20 = 1,200\) cubic centimeters, so the price per cubic centimeter now is \(\frac{x}{1,200}\);
Percent decrease is \(\frac{change}{original} \times 100 = \frac{\frac{x}{1,000} - \frac{x}{1,200} }{\frac{x}{1,000} } \times 100 = \frac{1}{6} \times 100 \approx 16.67\%\).
Note that this is not a Geometry question. While it uses basic knowledge of lines and figures, it is a Percent Word Problem question. There are 8 questions within GMAT Prep Focus Edition that use similar principles. Here is one example.
Answer: B
