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For each of 13 students who completed a vocational training program in the health-care field, the table provides the student's score on the program's entrance exam; the student's final rating upon completing the program, where a lower rating corresponds to better performance; and the number of documented errors during the student's first year of employment in the health-care field. The average (arithmetic mean) in each category is rounded to the nearest 0.1.
| Student number | Entrance exam score | Final rating | Number of first-year errors |
|---|---|---|---|
| 01 | 99 | 2 | 16 |
| 02 | 73 | 4 | 18 |
| 03 | 82 | 4 | 0 |
| 04 | 90 | 1 | 6 |
| 05 | 73 | 4 | 12 |
| 06 | 98 | 1 | 8 |
| 07 | 87 | 1 | 12 |
| 08 | 82 | 4 | 12 |
| 09 | 80 | 3 | 17 |
| 10 | 90 | 3 | 3 |
| 11 | 85 | 4 | 16 |
| 12 | 86 | 3 | 5 |
| 13 | 88 | 2 | 13 |
| Average | 85.6 | 2.8 | 10.6 |
For each of the following statements, select Yes if it is true based on the information provided; otherwise, select No.
Every student whose entrance exam score was below average had an above-average number of first-year errors.
Exactly half of the students who had an above-average number of first-year errors had a final rating of 4.
More than 50% of students who had a below-average number of first-year errors had final ratings of 3 or 4.
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:
Key insight: The averages are our benchmarks for comparison:
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.
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:
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.
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:
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.
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:
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.
Let's compile our findings:
The correct answer pattern is therefore: No, Yes, Yes (or B if using GMAT answer choice formatting).
By approaching table analysis questions with these strategies, you'll solve them more confidently and efficiently on test day.
Every student whose entrance exam score was below average had an above-average number of first-year errors.
Exactly half of the students who had an above-average number of first-year errors had a final rating of 4.
More than 50% of students who had a below-average number of first-year errors had final ratings of 3 or 4.