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The table provides data about 12 different Persian rugs currently available for sale by a rug dealer. For each rug, the data includes the number of knots per square inch (KPSI) in the yarn, which is consistent throughout the rug.
| Type | Age | Width (ft) | Length (ft) | KPSI | Price |
|---|---|---|---|---|---|
| Ardabil | 45 | 9 | 13 | 112 | $3,952 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Isfahan | 25 | 10 | 15 | 158 | $3,930 |
| Isfahan | 35 | 10 | 14 | 158 | $3,470 |
| Kashan | 20 | 10 | 14 | 212 | $3,950 |
| Kashan | 20 | 10 | 12 | 162 | $3,852 |
| Kashan | 25 | 9 | 15 | 158 | $3,762 |
| Kashmar | 20 | 8 | 9 | 162 | $3,920 |
| Kashmar | 25 | 10 | 13 | 158 | $3,763 |
| Kashmar | 25 | 10 | 12 | 158 | $3,762 |
| Kerman | 20 | 10 | 14 | 280 | $3,530 |
| Mashad | 25 | 10 | 12 | 158 | $3,762 |
For each of the following statements, select T if it is true based on the information provided; otherwise, select F.
The rug with the least number of KPSI is the most expensive.
The 4 newest rugs are also the 4 rugs with the greatest numbers of KPSI.
The median age of Kashan rugs is greater than the median age of Kashmar rugs.
Let's start by understanding what we're working with. This table shows data about 12 Persian rugs with several key characteristics:
Looking at this data strategically, we can see potential relationships between age, quality (KPSI), and price. Before diving into calculations, let's note that we have multiple rugs of the same type (multiple Kashans and Kashmars), which will be important when analyzing subgroups.
Key insight: When analyzing this kind of comparative data, sorting will be our most powerful tool to quickly see patterns and relationships that would take much longer to find manually.
Original: "The rug with the least number of KPSI is the most expensive."
What we're looking for:
In other words: Does the lowest quality rug (by KPSI measure) have the highest price?
Let's use sorting to make this efficient. Rather than scanning all 12 rugs to find the minimum KPSI and then scanning again for the maximum price, we can:
Since the same rug (Ardabil) has both the lowest KPSI (112) and the highest price ($3,952), this statement is T.
Teaching callout: Notice how sorting eliminated the need to scan the entire dataset twice. Instead of comparing 12 KPSI values and 12 price values manually, two quick sorts revealed the answer instantly.
Original: "The 4 newest rugs are also the 4 rugs with the greatest numbers of KPSI."
What we're looking for:
In other words: Are the newest rugs also the ones with the highest quality?
Let's approach this efficiently:
These are exactly the same values we identified in our first sort. This means the 4 rugs with the highest KPSI values are the same as the 4 newest rugs.
Therefore, this statement is T.
Teaching callout: When comparing two sets like this, we don't need to track which specific rug is which - we just need to verify that the values match. This saves significant time compared to writing down all the details of each rug.
Original: "The median age of Kashan rugs is greater than the median age of Kashmar rugs."
What we're looking for:
In other words: Are Kashan rugs typically older than Kashmar rugs?
Let's use sorting to make this comparison straightforward:
Comparing the medians: Kashan median (20) is NOT greater than Kashmar median (25).
Therefore, this statement is F.
Teaching callout: Sorting by category made this subgroup analysis almost instantaneous. Instead of searching through all 12 rugs multiple times to find each type, one sort grouped everything we needed together.
Let's compile our findings:
Our answer is: T-T-F
Remember: The GMAT rewards strategic thinking, not manual calculation. By focusing on sorting and efficient data analysis techniques, we can solve table analysis questions with perfect accuracy while saving valuable time on the exam.
The rug with the least number of KPSI is the most expensive.
The 4 newest rugs are also the 4 rugs with the greatest numbers of KPSI.
The median age of Kashan rugs is greater than the median age of Kashmar rugs.