Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They...

1. Translate the problem requirements: We need to find the difference between the maximum possible range and minimum possible range when all 15 test scores (5 scores each from 3 people) are considered together. Individual ranges are 50, 80, and 120 points respectively.
2. Understand range mechanics: The range of combined scores depends on the highest and lowest scores across all three people, not just individual ranges.
3. Determine maximum combined range scenario: Position the individual score ranges to create the largest possible gap between the overall highest and lowest scores.
4. Determine minimum combined range scenario: Position the individual score ranges to create the smallest possible gap between the overall highest and lowest scores.
5. Calculate the difference: Subtract the minimum combined range from the maximum combined range.

Execution of Strategic Approach

1. Translate the problem requirements

Let's break down what we know in simple terms:

• Three people each took 5 GMAT practice tests
• All scores are between 500 and 750 (no one scored below 500 or above 750)
• Person A's range = 50 points (maybe they scored 600-650)
• Person B's range = 80 points (maybe they scored 550-630)
• Person C's range = 120 points (maybe they scored 500-620)

We need to find: What's the difference between the maximum possible range and minimum possible range when we look at all 15 scores together?

2. Understand range mechanics

Here's the key insight: When we combine all scores, the overall range depends on the highest score anyone got and the lowest score anyone got across all three people.

Think of it this way: If I have three groups of numbers, the range of all numbers combined is simply: (highest number from any group) - (lowest number from any group)

The individual ranges tell us how spread out each person's scores were, but they don't directly tell us the combined range.

3. Determine maximum combined range scenario

To get the maximum combined range, we want the three people's score ranges positioned as far apart as possible.

Let's think strategically:

• Person A (range 50): Put their scores at the high end, say 700-750
• Person B (range 80): Put their scores at the low end, say 500-580
• Person C (range 120): We could put them at either extreme

Actually, let's be more systematic. To maximize the overall range:

• We want someone's lowest score to be 500 (the minimum allowed)
• We want someone's highest score to be 750 (the maximum allowed)

This gives us a maximum combined range of \(750 - 500 = 250\) points.

4. Determine minimum combined range scenario

To get the minimum combined range, we want the three people's score ranges to overlap as much as possible.

Let's position them to minimize the gap between the overall highest and lowest scores:

The key insight: We want to cluster all the ranges together. Let's try to fit all three ranges within the smallest possible span.

If we stack the ranges optimally:

• Start with the largest range (120 points)
• Try to fit the other ranges (80 and 50) within this 120-point span

Actually, let's think about this more carefully. The minimum combined range occurs when the ranges overlap maximally. The minimum possible combined range would be 120 (the largest individual range), which occurs when all three people's score ranges are completely contained within a 120-point span.

5. Calculate the difference

Now we can find our answer:

• Maximum combined range = 250 points (when ranges are spread from 500 to 750)
• Minimum combined range = 120 points (when all ranges fit within a 120-point span)
• Difference = \(250 - 120 = 130\) points

Final Answer

The difference between the maximum and minimum possible ranges of all their scores put together is 130 points.

This matches answer choice E. 130.

Verification: Our answer makes sense because 130 represents the difference between the most spread out scenario (using the full 500-750 range) and the most clustered scenario (fitting within the largest individual range of 120 points).

Common Faltering Points

Errors while devising the approach

Faltering Point 1: Misunderstanding what "range of all their scores put together" means

Students often think this means adding up the individual ranges (\(50 + 80 + 120 = 250\)) rather than understanding it means the range when all 15 scores are combined into one dataset. The combined range is simply the difference between the highest score anyone achieved and the lowest score anyone achieved across all three people.

Faltering Point 2: Overlooking the constraint that scores must be between 500-750

Students may forget that all scores are bounded by 500-750 and try to use the full GMAT range of 200-800. This constraint is crucial because it limits how far apart we can position the ranges to maximize the combined range.

Faltering Point 3: Confusing individual ranges with positioning of ranges

Students may incorrectly assume that knowing someone has a range of 50 points tells us exactly where their scores fall (like 600-650). In reality, a 50-point range could be positioned anywhere within the 500-750 constraint (could be 500-550, 600-650, 700-750, etc.).

Errors while executing the approach

Faltering Point 1: Incorrectly calculating the minimum combined range

Students often struggle to visualize that the minimum combined range occurs when all individual ranges overlap maximally. They may incorrectly think the minimum is the smallest individual range (50) rather than understanding it's the largest individual range (120) when all ranges are nested within that span.

Faltering Point 2: Arithmetic errors in range calculations

When calculating maximum range (\(750 - 500 = 250\)) or the final difference (\(250 - 120 = 130\)), students may make simple arithmetic mistakes, especially when working under time pressure.

Errors while selecting the answer

Faltering Point 1: Selecting an individual range value instead of the difference

Students may calculate correctly but then select 120 (choice D) thinking it's the answer, forgetting that the question asks for the difference between maximum and minimum possible combined ranges, not just one of the component values in their calculation.