The table lists for each of 25 countries (A–Y) the ranking the country had in 2005 and the ranking it...

OWNING THE DATASET

Let's start by understanding this ranking table with the intention of "owning the dataset."

This table shows country rankings for various nations in two different years: 2005 and 2012. In any ranking system, the lower the number, the better the position (rank 1 is the best). This is our crucial insight for efficient analysis.

Looking at one example row helps us understand the structure:

Key insights about rankings:

• If \(2012 \text{ rank} < 2005 \text{ rank}\) → Country GAINED positions (improved)
• If \(2012 \text{ rank} > 2005 \text{ rank}\) → Country LOST positions (declined)
• If \(2012 \text{ rank} = 2005 \text{ rank}\) → Country maintained its position

Let's use this understanding to analyze the statements efficiently.

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "Countries K and L both gained positions in the rankings from 2005 to 2012."
What we're looking for:

• Did Country K's rank in 2012 (13) improve from its 2005 rank (23)?
• Did Country L's rank in 2012 (19) improve from its 2005 rank (21)?

In other words: We need to verify if both K and L have lower numerical rankings in 2012 than they had in 2005.

Let's use visual comparison rather than calculation:

For Country K:

• 2005 rank: 23
• 2012 rank: 13
• Visual check: Is \(13 < 23\)? YES → GAINED positions ✓

For Country L:

• 2005 rank: 21
• 2012 rank: 19
• Visual check: Is \(19 < 21\)? YES → GAINED positions ✓

Both countries K and L gained positions between 2005 and 2012.

Teaching note: Notice how we didn't need to calculate the exact number of positions gained (10 for K and 2 for L). We only needed to determine the direction of change through simple visual comparison, which is much faster.

Statement 1 is GAINED.

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "Country M gained positions in the rankings from 2005 to 2012."
What we're looking for:

• Did Country M's rank in 2012 (36) improve from its 2005 rank (4)?

In other words: We need to check if M has a lower numerical ranking in 2012 than it had in 2005.

Let's apply the same visual comparison technique:

For Country M:

• 2005 rank: 4
• 2012 rank: 36
• Visual check: Is \(36 < 4\)? NO → LOST positions ✗

Country M actually lost positions significantly between 2005 and 2012, as its ranking number increased.

Teaching note: Remember that with rankings, a higher number means a worse position. Country M went from a very good position (4th) to a much worse position (36th).

Statement 2 is LOST.

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "Of the three countries, only one gained positions in the rankings from 2005 to 2012."
What we're looking for:

• How many countries among K, L, and M gained positions?
• Is it exactly one country?

In other words: We need to count how many countries have 2012 ranks lower than their 2005 ranks, and check if that count equals exactly one.

Let's summarize our findings from the previous analyses:

Country K: 2005 rank (23) → 2012 rank (13) → GAINED ✓
Country L: 2005 rank (21) → 2012 rank (19) → GAINED ✓
Country M: 2005 rank (4) → 2012 rank (36) → LOST ✗

Count of countries that gained positions: 2 (Countries K and L)

Since two countries gained positions (not just one), this statement is false.

Statement 3 is LOST.

FINAL ANSWER COMPILATION

Reviewing our analysis:

• Statement 1: GAINED (Both countries K and L gained positions)
• Statement 2: LOST (Country M lost positions)
• Statement 3: LOST (Two countries gained positions, not just one)

Therefore, Statement 1 is the correct answer.

LEARNING SUMMARY

Skills We Used

• Visual comparison instead of calculation - We determined if rankings improved by simply checking if 2012 values were less than 2005 values, without calculating exact differences.
• Direction recognition - We focused on whether positions were gained or lost, not on how many positions changed.
• Pattern recognition - We quickly identified that lower numbers mean better rankings, which streamlined our analysis.

Strategic Insights

• Remember ranking direction - Always confirm if higher or lower numbers are better before proceeding with any analysis. In rankings, lower is better (rank 1 is best).
• Focus only on what's asked - We didn't waste time analyzing all countries in the table, just K, L, and M.
• Convert calculations to visual comparisons - "Is 13 less than 23?" is faster than "23 minus 13 equals 10."

Common Mistakes We Avoided

• Calculating exact position changes - We didn't need to compute that K gained 10 positions or L gained 2 positions; we only needed to know the direction of change.
• Misinterpreting ranking direction - We correctly recognized that higher numbers mean worse positions, avoiding a common trap.
• Over-analyzing the data - We didn't spend time on irrelevant information and focused only on the specific comparison needed.

This approach transforms what could be a calculation-heavy process into a rapid visual comparison task, maintaining accuracy while greatly improving efficiency.