Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
Pure beeswax has a density of 0.555 ounce per cubic inch. An online company sells pure beeswax at a price of $8.00 per ounce. What is the selling price, in dollars per cubic inch, for pure beeswax purchased from this company?
1. TRANSLATE the problem information
- Given information:
- Density: 0.555 ounce per cubic inch
- Price: $8.00 per ounce
- Need to find: selling price in dollars per cubic inch
2. INFER the solution strategy
- To get dollars per cubic inch, I need to combine the two given rates
- Since I have dollars/ounce and ounces/cubic inch, multiplying them will give me dollars/cubic inch
- The "ounces" units will cancel out: \(\mathrm{(dollars/ounce) \times (ounces/cubic\,inch) = dollars/cubic\,inch}\)
3. SIMPLIFY by performing the calculation
- Set up the multiplication: \(\mathrm{\$8.00/ounce \times 0.555\,ounces/cubic\,inch}\)
- Calculate: \(\mathrm{\$8.00 \times 0.555 = \$4.44}\) (use calculator)
- Result: $4.44 per cubic inch
Answer: $4.44
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak INFER skill: Students don't recognize that they need to multiply the two rates to get the desired unit.
Instead, they might try to divide (\(\mathrm{\$8.00 \div 0.555}\)) or add the numbers, not understanding how units combine through multiplication. They get confused about which operation connects "dollars per ounce" with "ounces per cubic inch" to produce "dollars per cubic inch."
This leads to confusion and guessing among the answer choices.
Second Most Common Error:
Poor SIMPLIFY execution: Students set up the problem correctly but make arithmetic errors in decimal multiplication.
They might calculate \(\mathrm{\$8.00 \times 0.555}\) incorrectly, perhaps getting $4.440 and rounding incorrectly, or making place value errors with the decimal point. Small calculation mistakes can lead to selecting an incorrect numerical answer.
The Bottom Line:
This problem tests whether students understand dimensional analysis - how units multiply and cancel to create new units. The mathematical setup is straightforward once students recognize that multiplying rates with complementary units gives them the rate they need.