A small business tracks its weekly profit changes from a baseline profit of $5,000. The changes recorded over 5 consecutive...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
A small business tracks its weekly profit changes from a baseline profit of \(\$5,000\). The changes recorded over 5 consecutive weeks were: \(+\$800\), \(-\$300\), \(+\$400\), \(+\$1,200\), and \(-\$100\). What is the range, in dollars, of the actual weekly profits during this 5-week period?
1. TRANSLATE the problem information
- Given information:
- Baseline profit: \(\$5{,}000\) each week
- Weekly changes: \(+\$800\), \(-\$300\), \(+\$400\), \(+\$1{,}200\), \(-\$100\)
- Need to find: range of actual weekly profits
2. INFER the approach needed
- To find range of actual profits, we need the actual profit values first
- Range = highest value - lowest value
- Strategy: Calculate each week's actual profit, then find max and min
3. SIMPLIFY by calculating actual weekly profits
Add each change to the \(\$5{,}000\) baseline:
- Week 1: \(\$5{,}000 + \$800 = \$5{,}800\)
- Week 2: \(\$5{,}000 + (-\$300) = \$4{,}700\)
- Week 3: \(\$5{,}000 + \$400 = \$5{,}400\)
- Week 4: \(\$5{,}000 + \$1{,}200 = \$6{,}200\)
- Week 5: \(\$5{,}000 + (-\$100) = \$4{,}900\)
4. INFER the maximum and minimum values
Looking at our calculated profits: \(\$5{,}800\), \(\$4{,}700\), \(\$5{,}400\), \(\$6{,}200\), \(\$4{,}900\)
- Maximum profit: \(\$6{,}200\) (Week 4)
- Minimum profit: \(\$4{,}700\) (Week 2)
5. SIMPLIFY to find the range
Range = Maximum - Minimum
\(\$6{,}200 - \$4{,}700 = \$1{,}500\)
Answer: C) 1,500
Why Students Usually Falter on This Problem
Most Common Error Path:
Poor TRANSLATE reasoning: Students calculate the range of the weekly changes instead of the actual profits.
They might think: "The changes go from \(+\$1{,}200\) (highest) to \(-\$300\) (lowest), so range = \(\$1{,}200 - (-\$300) = \$1{,}500\)." While this accidentally gives the correct numerical answer, the reasoning is fundamentally flawed and would fail on similar problems with different baselines.
Second Most Common Error:
Weak INFER skill: Students don't realize they need to calculate actual profit values first.
They might try to work directly with the changes, perhaps thinking the range is simply the difference between the largest positive change (\(+\$1{,}200\)) and the largest negative change (\(-\$300\)), leading to various incorrect calculations. This causes them to get stuck and guess among the answer choices.
The Bottom Line:
This problem tests whether students understand that "range" refers to the spread of the actual data values, not the changes themselves. The key insight is recognizing that you must first calculate what the problem is actually asking for the range of (the weekly profits) before you can find that range.