y = 0.25x^2 - 7.5x + 90.25 The equation gives the estimated stock price y, in dollars, for a certain...
GMAT Advanced Math : (Adv_Math) Questions
\(\mathrm{y = 0.25x^2 - 7.5x + 90.25}\)
The equation gives the estimated stock price y, in dollars, for a certain company x days after a new product launched, where \(\mathrm{0 \leq x \leq 20}\). Which statement is the best interpretation of \(\mathrm{(x,y) = (1,83)}\) in this context?
The company's estimated stock price increased $83 every day after the new product launched.
The company's estimated stock price increased $1 every 83 days after the new product launched.
1 day after the new product launched, the company's estimated stock price is $83.
83 days after the new product launched, the company's estimated stock price is $1.
1. TRANSLATE the problem information
- Given information:
- Equation: \(\mathrm{y = 0.25x^2 - 7.5x + 90.25}\)
- \(\mathrm{x}\) = days after new product launched (\(\mathrm{0 \leq x \leq 20}\))
- \(\mathrm{y}\) = estimated stock price in dollars
- Point: \(\mathrm{(x,y) = (1,83)}\)
2. TRANSLATE the coordinate pair
- In the ordered pair \(\mathrm{(x,y) = (1,83)}\):
- First number (1) = x-value = days after launch
- Second number (83) = y-value = stock price in dollars
3. INFER the contextual meaning
- Since \(\mathrm{x = 1}\) and \(\mathrm{y = 83}\):
- 1 day after the product launched
- The stock price was $83
Answer: C. 1 day after the new product launched, the company's estimated stock price is $83.
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students reverse the coordinates, thinking \(\mathrm{(1,83)}\) means \(\mathrm{x = 83}\) and \(\mathrm{y = 1}\).
This happens because they don't carefully track which variable goes with which position in the ordered pair. They might think "83 days after launch, the price is $1" instead of "1 day after launch, the price is $83."
This may lead them to select Choice D (83 days after the new product launched, the company's estimated stock price is $1).
Second Most Common Error:
Poor INFER reasoning: Students misinterpret the point as representing a rate of change rather than a specific value.
They might think \(\mathrm{(1,83)}\) means the stock price increases by $83 every 1 day, confusing a single data point with a rate of change pattern.
This may lead them to select Choice A (The company's estimated stock price increased $83 every day after the new product launched).
The Bottom Line:
This problem tests whether students can correctly interpret coordinate pairs in context. The key is remembering that in \(\mathrm{(x,y)}\), the first number always corresponds to the independent variable and the second to the dependent variable, regardless of the size of the numbers.
The company's estimated stock price increased $83 every day after the new product launched.
The company's estimated stock price increased $1 every 83 days after the new product launched.
1 day after the new product launched, the company's estimated stock price is $83.
83 days after the new product launched, the company's estimated stock price is $1.