For each of 13 students who completed a vocational training program in the health-care field, the table provides the student's...

OWNING THE DATASET

Let's start by understanding this healthcare training dataset with 13 students. When analyzing any data table, we want to quickly identify the structure and key metrics.

The table shows three critical metrics for each student:

• Entrance exam scores (higher is better)
• Final ratings (lower is better, on a 1-4 scale)
• First-year errors (lower is better)

Key insight: The averages are our benchmarks for comparison:

• Average entrance exam: 85.6
• Average rating: 2.8
• Average first-year errors: 10.6

These averages will be crucial for defining "above-average" and "below-average" in our analysis. Let's use sorting as our primary strategy to make patterns instantly visible.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "Every student with a below-average entrance score had an above-average number of first-year errors."
What we're looking for:

• Students with entrance scores \(< 85.6\)
• Check if ALL of these students had errors \(> 10.6\)

In other words: Do ALL students who scored poorly on entrance also make many errors?

Let's approach this efficiently. When evaluating "every" statements, we only need to find one counterexample to disprove them.

Step 1: Sort by entrance exam scores (ascending)
This immediately groups all below-average students at the top of our view.

Step 2: Identify the cutoff line at 85.6
The first 5 students have below-average entrance scores.

Step 3: Scan these 5 students for their error counts
We're looking for any student with errors \(≤ 10.6\) (below average).

Looking at the sorted data, Student 03 immediately stands out with 0 errors - which is obviously below the average of 10.6!

Teaching callout: Notice how sorting made this counterexample visually jump out. We didn't need to check all students or do any calculations - Student 03's 0 errors is dramatically below average and disproves the statement instantly.

Statement 1 is No. We found a student with below-average entrance score but below-average errors.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "Exactly half of the students with an above-average number of first-year errors had a rating of 4."
What we're looking for:

• Students with errors \(> 10.6\)
• Check if EXACTLY 50% of them had a rating of 4

In other words: Of the students who made many errors, did exactly half receive the worst possible rating?

Step 1: Sort by first-year errors (descending)
This immediately groups all above-average error students at the top.

Step 2: Identify the cutoff line at 10.6 errors
We can see that 8 students have above-average errors.

Step 3: Count how many of these 8 students have a rating of 4
Scanning the ratings column for these 8 students, we count exactly 4 students with a rating of 4.

Step 4: Check if this satisfies our "exactly half" condition
4 out of 8 is exactly 50% - exactly half.

Teaching callout: By sorting first, we quickly grouped all relevant students together. This eliminated the need to scan the entire table multiple times. Also, when working with "exactly half," we can just compare the raw numbers (4 vs 8) rather than calculating percentages.

Statement 2 is Yes. Exactly half (4 out of 8) of the students with above-average errors had a rating of 4.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "More than half of the students with a below-average number of first-year errors had a rating of 3 or 4."
What we're looking for:

• Students with errors \(< 10.6\)
• Check if MORE THAN 50% of them had ratings of 3 or 4

In other words: Of the students who made fewer errors, did most still receive poor ratings?

Step 1: Sort by first-year errors (ascending)
This immediately groups all below-average error students at the top.

Step 2: Count total below-average error students
We have 5 students with below-average errors (errors \(< 10.6\)).

Step 3: Determine our threshold
For 5 students, "more than half" means we need at least 3 students with ratings of 3 or 4.

Step 4: Count ratings 3-4 in this group
Scanning the ratings column for these 5 students, we count 3 students with ratings of either 3 or 4.

Step 5: Check if this meets our "more than half" condition
3 out of 5 is 60%, which is indeed more than half.

Teaching callout: For small groups, knowing simple thresholds helps us avoid calculations. With 5 students, we just needed to find at least 3 to exceed 50%. Once we reached 3, we could stop counting - no percentage calculation needed.

Statement 3 is Yes. More than half \(\frac{3}{5} = 60\%\) of the students with below-average errors had a rating of 3 or 4.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: No - We found a counterexample (Student 03)
• Statement 2: Yes - Exactly 4 out of 8 (50%) students with above-average errors had a rating of 4
• Statement 3: Yes - 3 out of 5 (60%) students with below-average errors had ratings of 3 or 4

The correct answer pattern is therefore: No, Yes, Yes (or B if using GMAT answer choice formatting).

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: We sorted the data in different ways to make patterns visible instantly
• Counterexample Finding: For "every" statements, we only needed one exception to disprove them
• Threshold Recognition: For small groups, we knew exactly how many items constituted "more than half"

Strategic Insights

1. Sort Before Analyzing: Sorting is your most powerful tool for table analysis questions - it groups similar data together, making patterns obvious.
2. Look for Extreme Values: After sorting, outliers like Student 03's 0 errors jump out visually, saving time.
3. Know Your Thresholds:
   • For 5 items: "more than half" means 3+
   • For 7 items: "more than half" means 4+
   • For 9 items: "more than half" means 5+
4. "Every" Statements Only Need One Exception: Don't waste time checking all cases once you find a counterexample.

Common Mistakes We Avoided

• We didn't manually check each student against multiple criteria - sorting made this unnecessary
• We didn't calculate percentages when simple counting would suffice
• We didn't waste time on exhaustive verification once we had sufficient evidence

By approaching table analysis questions with these strategies, you'll solve them more confidently and efficiently on test day.