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A fish hatchery has been raising large populations of endangered fish species and releasing them into a local lake. At the end of each year, the hatchery takes a sample of fish from the lake and compares the number of hatchery-raised fish found in the sample with the number of wild fish found in the sample. The table provides release and sample data for five years of the hatchery's operation.
| Year | Number released (thousands) | Sample size | Number wild | Number hatchery | Percent hatchery contribution |
|---|---|---|---|---|---|
| 3 | 150 | 100 | 55 | 45 | 45 |
| 2 | 530 | 150 | 125 | 25 | 17 |
| 4 | 450 | 115 | 90 | 25 | 22 |
| 1 | 580 | 150 | 130 | 20 | 13 |
| 5 | 600 | 125 | 110 | 15 | 12 |
For each of the following statements, select Yes if that statement accurately reflects the information provided. Otherwise, select No.
The year with the smallest sample size also had the greatest number of hatchery-raised fish in the sample.
The year in which the hatchery released the greatest number of fish was the year when the hatchery took the largest sample of fish.
The year with the smallest number of hatchery-raised fish in the sample was the year in which the hatchery released the smallest percentage of the total five-year fish release.
Let's start by understanding what we're working with. This table tracks fish hatchery data across five years, showing:
Key insight: Notice this table contains multiple numerical relationships that might require comparisons across different years. When we need to find maximums, minimums, or compare values, sorting will be our most powerful technique rather than scanning manually!
| Year | Sample size | Number hatchery | Number released |
|---|---|---|---|
| 1 | 150 | 35 | 400 |
| 2 | 150 | 30 | 500 |
| 3 | 100 | 45 | 150 |
| 4 | 120 | 25 | 350 |
| 5 | 125 | 15 | 600 |
Each statement is asking us to find relationships between different columns, so let's approach them strategically.
Statement 1 Translation:
Original: "The year with the smallest sample size also had the greatest number of hatchery-raised fish in the sample."
What we're looking for:
In other words: We need to check if the minimum sample size year matches the maximum hatchery fish year.
Let's solve this efficiently with sorting:
Step 1: Sort by "Sample size" (ascending) to find the minimum
Step 2: Look at "Number hatchery" for Year 3
Step 3: Quick check - is 45 the highest "Number hatchery" value?
Statement 1 is YES
Teaching note: Notice how sorting immediately revealed both the minimum sample size and allowed us to quickly verify if that same year had the maximum hatchery fish. This approach is much faster than checking each year individually!
Statement 2 Translation:
Original: "The year in which the hatchery released the greatest number of fish was the year when the hatchery took the largest sample of fish."
What we're looking for:
In other words: Do the maximum release year and maximum sample size year match?
Let's use sorting again to quickly find our answer:
Step 1: Sort by "Number released" (descending) to find the maximum
Step 2: Check "Sample size" for Year 5
Step 3: Sort by "Sample size" (descending) to find the maximum
Step 4: Compare the results
Statement 2 is NO
Teaching note: Here, we used two sorts to efficiently find both maximums. This approach eliminates the need to manually compare all values, making the pattern immediately visible.
Statement 3 Translation:
Original: "The year with the smallest number of hatchery-raised fish in the sample was the year in which the hatchery released the smallest percentage of the total five-year fish release."
What we're looking for:
In other words: Does the minimum hatchery fish year match the minimum percentage release year?
Here's where strategic thinking makes a huge difference:
Step 1: Sort by "Number hatchery" (ascending) to find the minimum
Step 2: Key insight: We don't need to calculate percentages!
Step 3: Sort by "Number released" (ascending) to find the minimum
Step 4: Compare the results
Statement 3 is NO
Teaching note: The breakthrough insight here is recognizing we don't need to calculate any percentages! When comparing which item represents the smallest percentage of a fixed total, that will always be the item with the smallest absolute value. This saves us from having to calculate five different percentages.
Evaluating all three statements:
Therefore, the answer is: A (Statement 1 only)
1. Sort first, calculate last (if at all): Sorting should be your default first move for any table question involving maximum, minimum, or median values.
1. Absolute values reveal relative standings: For Statement 3, we recognized that the smallest absolute number will always represent the smallest percentage of a total.
1. Beware calculation traps: The GMAT often structures questions where calculations seem necessary but aren't - stay alert for these shortcuts!
1. Look for matching/mismatching patterns: Many table analysis questions ask if the same item satisfies two different criteria.
Remember, mastering table analysis isn't about calculating faster - it's about recognizing when you can avoid calculations altogether through strategic sorting and logical thinking!
The year with the smallest sample size also had the greatest number of hatchery-raised fish in the sample.
The year in which the hatchery released the greatest number of fish was the year when the hatchery took the largest sample of fish.
The year with the smallest number of hatchery-raised fish in the sample was the year in which the hatchery released the smallest percentage of the total five-year fish release.