Country Total Related to architecture, art, history Public ownership Private ownership Visitors per year Staff Austria 399 79 203 196...

OWNING THE DATASET

Let's start by understanding what we're working with in this table about museums in European countries. The table shows data for 8 European countries, including:

• Number of public museums
• Number of private museums
• Total museum visitors (in millions)
• Number of art/architecture/history museums
• Total number of museums

Key Insight: Before diving into calculations, let's identify any notable patterns or outliers:

• Public vs. private museum distribution varies dramatically across countries
• Croatia stands out with 220 public museums but only 1 private museum
• Museum visitors range from just 2.1M (Estonia) to 56.1M (Spain)
• France has the most total museums (1173), while Estonia has the fewest (245)

This initial scan will help us work more efficiently through each statement. Let's now analyze the statements in the most strategic order.

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "Estonia has the highest ratio of public museums to private museums among the given countries."

What we're looking for:

• Calculate or compare the ratio of public:private museums for each country
• Determine if Estonia has the highest ratio

In other words: Does Estonia have proportionally more public museums relative to private museums than any other country?

Our Approach:

Instead of calculating every ratio, let's first scan for extreme values that might immediately answer our question.

Looking at our data, Croatia immediately stands out with 220 public museums and only 1 private museum. This creates a \(220:1\) ratio, which is mathematically guaranteed to be the highest possible ratio in our dataset.

When we have such an extreme case (almost all public museums), we don't need to calculate ratios for all countries. No other reasonable distribution could produce a higher ratio than \(220:1\).

Key insight: Estonia's ratio would need to be higher than \(220:1\) for this statement to be true. Since that's mathematically impossible given the dataset (Estonia would need more than 220 public museums for each private museum), we can immediately determine this statement is False.

Teaching note: Always scan for extreme outliers before doing calculations for every data point. One extreme value can often answer comparison questions instantly!

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "A higher proportion of museums in France are art, architecture, or history museums than in the Netherlands."

What we're looking for:

• Calculate the percentage of art/architecture/history museums in France
• Calculate the percentage of art/architecture/history museums in Netherlands
• Compare these percentages

In other words: Does France have a higher percentage of its museums dedicated to art/architecture/history than the Netherlands does?

Our Approach:

Let's look at the relevant data:

• France: 780 art/architecture/history museums out of 1173 total museums
• Netherlands: 498 art/architecture/history museums out of 775 total museums

Instead of calculating exact percentages (which takes time and risks calculation errors), we can use cross-multiplication to compare these proportions:

• France proportion: \(\frac{780}{1173}\)
• Netherlands proportion: \(\frac{498}{775}\)

To compare these fractions without division, we can cross-multiply:

• \(780 \times 775 = 604,500\)
• \(498 \times 1173 = 584,154\)

Since \(604,500 > 584,154\), the proportion for France is higher.

Alternative approach: We can also see both ratios are close to \(\frac{2}{3}\):

• France ideal \(\frac{2}{3}\) would be: \(1173 \times \frac{2}{3} = 782\) (actual is 780, very close)
• Netherlands ideal \(\frac{2}{3}\) would be: \(775 \times \frac{2}{3} = 517\) (actual is 498, further below)

This confirms France's proportion is higher.

Therefore, Statement 1 is True.

Teaching note: Cross-multiplication eliminates the need for decimal calculations when comparing proportions. This technique saves time and reduces error potential on the GMAT.

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "Countries with more public museums tend to have more museum visitors."

What we're looking for:

• Check if there's a positive correlation between the number of public museums and the number of visitors
• Look for a general pattern rather than calculating exact correlation

In other words: Do countries with larger numbers of public museums generally have more museum visitors?

Our Approach:

Instead of analyzing all countries or calculating correlation coefficients, let's use strategic sampling by checking the countries at the extremes:

Countries with the most public museums:

• France (1053 public museums): 40.5M visitors
• Spain (973 public museums): 56.1M visitors
• Switzerland (960 public museums): 12.6M visitors

Countries with the fewest public museums:

• Estonia (163 public museums): 2.1M visitors
• Austria (203 public museums): 11.6M visitors
• Croatia (220 public museums): 2.4M visitors

Looking at these extremes, we can see a clear pattern: countries with more public museums generally have more visitors. The countries with the fewest public museums (Estonia, Croatia) have the lowest visitor numbers (2.1M, 2.4M), while countries with many public museums (France, Spain) have much higher visitor numbers (40.5M, 56.1M).

While there are some variations (Switzerland has many museums but fewer visitors than Spain), the overall trend shows a positive relationship between public museums and visitor numbers.

Therefore, Statement 3 is True.

Teaching note: For correlation questions, checking extreme values often reveals the pattern without needing to analyze every data point. This approach is much faster than calculating correlation coefficients.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: True (France has a higher proportion of art/architecture/history museums)
• Statement 2: False (Estonia does not have the highest public-to-private museum ratio; Croatia does)
• Statement 3: True (Countries with more public museums tend to have more visitors)

Therefore, our answer is: True False True

LEARNING SUMMARY

Skills We Used:

1. Outlier identification: Spotting Croatia's extreme \(220:1\) ratio immediately solved Statement 2
2. Cross-multiplication: Comparing fractions without calculating decimals for Statement 1
3. Strategic sampling: Testing extreme cases to establish patterns for Statement 3

Strategic Insights:

• Start with the clearest statement: Beginning with Statement 2 gave us a quick win
• Look before calculating: Visual inspection often reveals answers faster than calculations
• Use the appropriate level of precision: For Statement 1, we only needed to know which proportion was larger, not the exact percentages

Common Mistakes We Avoided:

• Calculating ratios for all countries when one extreme outlier provided the answer
• Computing exact percentages when cross-multiplication was faster and equally effective
• Analyzing every data point when checking extremes established the pattern

Transferable Strategies:

1. Always scan for outliers before calculating anything
2. Use cross-multiplication to compare fractions without division
3. Check extreme values first when looking for correlations
4. Sort mentally by key values to quickly identify patterns

These approaches will help you solve table analysis questions more efficiently across various topics and formats on the GMAT.