Question:The total revenue, in dollars, for a company selling x units of a product is given by the expression 18x^2....
GMAT Advanced Math : (Adv_Math) Questions
The total revenue, in dollars, for a company selling \(\mathrm{x}\) units of a product is given by the expression \(\mathrm{18x^2}\). The total cost, in dollars, of producing \(\mathrm{x}\) units is \(\mathrm{11x^2}\). The profit is the difference between the total revenue and the total cost. Which of the following expressions represents the profit, in dollars, from selling \(\mathrm{x}\) units?
- \(\mathrm{7x^4}\)
- \(\mathrm{29x^2}\)
- \(\mathrm{7x^2}\)
- \(\mathrm{29x^4}\)
1. TRANSLATE the problem information
- Given information:
- Total revenue for selling x units: \(18\mathrm{x}^2\) dollars
- Total cost for producing x units: \(11\mathrm{x}^2\) dollars
- Profit is defined as the difference between total revenue and total cost
- What this tells us: We need to subtract total cost from total revenue
2. TRANSLATE the profit definition into math
- "Profit is the difference between total revenue and total cost" means:
\(\mathrm{Profit} = \mathrm{Total\:Revenue} - \mathrm{Total\:Cost}\) - Substituting our expressions:
\(\mathrm{Profit} = 18\mathrm{x}^2 - 11\mathrm{x}^2\)
3. SIMPLIFY by combining like terms
- Both terms have the same variable part \(\mathrm{x}^2\), so they are like terms
- To combine like terms, subtract the coefficients: 18 - 11 = 7
- Keep the variable part unchanged: \(\mathrm{x}^2\)
- Result: \(\mathrm{Profit} = 7\mathrm{x}^2\)
Answer: C) \(7\mathrm{x}^2\)
Why Students Usually Falter on This Problem
Most Common Error Path:
Poor TRANSLATE reasoning: Students misinterpret "difference" to mean addition instead of subtraction.
They think "difference between revenue and cost" means "revenue plus cost" and calculate:
\(\mathrm{Profit} = 18\mathrm{x}^2 + 11\mathrm{x}^2 = 29\mathrm{x}^2\)
This leads them to select Choice B (\(29\mathrm{x}^2\)).
The Bottom Line:
This problem tests whether students can accurately translate business terminology into mathematical operations. The word "difference" specifically means subtraction, but in everyday language, students sometimes associate "difference" with any kind of comparison or combination. Success requires precise mathematical translation of the profit definition.