A fish hatchery has been raising large populations of endangered fish species and releasing them into a local lake. At...

Owning the Dataset

Let's start by understanding what we're working with. This table tracks fish hatchery data across five years, showing:

• Sample size: Number of fish examined each year
• Number hatchery: How many hatchery-raised fish were in each sample
• Number released: Total fish released by the hatchery that year

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.

Analyzing Statement 1

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:

• Which year has the smallest sample size?
• Does this same year also have the greatest number of hatchery-raised fish?

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

• Year 3 immediately appears at the top with sample size = 100
• This is our year with the smallest sample size

Step 2: Look at "Number hatchery" for Year 3

• Year 3 has 45 hatchery-raised fish

Step 3: Quick check - is 45 the highest "Number hatchery" value?

• Scanning the column: 35, 30, 45, 25, 15
• Yes, 45 is the highest 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!

Analyzing Statement 2

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:

• Which year has the greatest number of released fish?
• Does this same year also have the largest sample size?

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

• Year 5 immediately appears at the top with 600 fish released
• This is our year with the greatest number of fish released

Step 2: Check "Sample size" for Year 5

• Year 5 has a sample size of 125

Step 3: Sort by "Sample size" (descending) to find the maximum

• Years 1 & 2 appear at the top, both with sample size = 150
• These are our years with the largest sample size

Step 4: Compare the results

• Maximum release year: Year 5
• Maximum sample size years: Years 1 & 2
• These are different years!

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.

Analyzing Statement 3

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:

• Which year has the smallest number of hatchery-raised fish?
• Which year released the smallest percentage of the total release across all five years?
• Do these years match?

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

• Year 5 immediately appears at the top with 15 hatchery fish
• This is our year with the smallest number of hatchery fish

Step 2: Key insight: We don't need to calculate percentages!

• The smallest percentage of the total will correspond to the smallest absolute number
• We just need to find which year had the smallest "Number released"

Step 3: Sort by "Number released" (ascending) to find the minimum

• Year 3 appears at the top with 150 fish released
• This is our year with the smallest release

Step 4: Compare the results

• Minimum hatchery fish year: Year 5
• Minimum release year: Year 3
• These are different years!

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.

Final Answer Compilation

Evaluating all three statements:

• Statement 1: YES
• Statement 2: NO
• Statement 3: NO

Therefore, the answer is: A (Statement 1 only)

Learning Summary

Skills We Used

• Strategic Sorting: We sorted the data in different ways to immediately reveal maximum and minimum values
• Logical Deduction: For Statement 3, we recognized that calculating percentages was unnecessary
• Visual Validation: After sorting, we used visual scanning to confirm our findings

Strategic Insights

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.

Common Mistakes We Avoided

• Unnecessary calculations: We didn't waste time calculating percentages for Statement 3
• Manual scanning: We didn't manually check each value in sequence
• Over-complication: We kept our approach straightforward by using strategic sorting and logical thinking

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!