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| Country | Total | Related to architecture, art, history | Public ownership | Private ownership | Visitors per year | Staff |
|---|---|---|---|---|---|---|
| Austria | 399 | 79 | 203 | 196 | 11579900 | 7820 |
| Croatia | 221 | 65 | 220 | 1 | 2427703 | 1602 |
| Estonia | 224 | 67 | 163 | 61 | 2058817 | 2203 |
| France | 1173 | 780 | 1053 | 120 | 40469600 | 24500 |
| Hungary | 671 | 185 | 615 | 66 | 10123438 | 5807 |
| Netherlands | 775 | 498 | 713 | 62 | 19648000 | 27810 |
| Spain | 1455 | 679 | 973 | 482 | 56065370 | 15811 |
| Switzerland | 1061 | 291 | 960 | 101 | 12627700 | 5939 |
For each of the following statements, select True if the statement can be verified as true based on the information in the table. Otherwise, select False.
The proportion of museums in France related to architecture, art, or history is greater than the proportion of museums in the Netherlands devoted to art, architecture, or history.
The ratio of public museums to private museums is greatest for Estonia.
There is a positive correlation between the number of public museums and the number of visitors per year.
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:
Key Insight: Before diving into calculations, let's identify any notable patterns or outliers:
This initial scan will help us work more efficiently through each statement. Let's now analyze the statements in the most strategic order.
Original: "Estonia has the highest ratio of public museums to private museums among the given countries."
What we're looking for:
In other words: Does Estonia have proportionally more public museums relative to private museums than any other country?
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!
Original: "A higher proportion of museums in France are art, architecture, or history museums than in the Netherlands."
What we're looking for:
In other words: Does France have a higher percentage of its museums dedicated to art/architecture/history than the Netherlands does?
Let's look at the relevant data:
Instead of calculating exact percentages (which takes time and risks calculation errors), we can use cross-multiplication to compare these proportions:
To compare these fractions without division, we can cross-multiply:
Since \(604,500 > 584,154\), the proportion for France is higher.
Alternative approach: We can also see both ratios are close to \(\frac{2}{3}\):
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.
Original: "Countries with more public museums tend to have more museum visitors."
What we're looking for:
In other words: Do countries with larger numbers of public museums generally have more museum visitors?
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:
Countries with the fewest public museums:
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.
Let's compile our findings:
Therefore, our answer is: True False True
These approaches will help you solve table analysis questions more efficiently across various topics and formats on the GMAT.
The proportion of museums in France related to architecture, art, or history is greater than the proportion of museums in the Netherlands devoted to art, architecture, or history.
The ratio of public museums to private museums is greatest for Estonia.
There is a positive correlation between the number of public museums and the number of visitors per year.