The table provides data about 12 different Persian rugs currently available for sale by a rug dealer. For each rug,...

OWNING THE DATASET

Let's start by understanding what we're working with. This table shows data about 12 Persian rugs with several key characteristics:

• Type: Different varieties (Ardabil, Kashan, Kashmar, etc.)
• Age: How old each rug is (in years)
• KPSI: Knots per square inch (measure of quality/intricacy)
• Price: Cost in dollars

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.

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "The rug with the least number of KPSI is the most expensive."
What we're looking for:

• Find the rug with the minimum KPSI value
• Check if this same rug has the maximum price

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:

1. Sort by KPSI ascending (lowest values first)
   The first row now shows us the rug with the lowest KPSI - we can see it's the Ardabil rug with 112 KPSI and priced at $3,952.
2. Now sort by Price descending (highest values first)
   The first row shows us the most expensive rug - it's the same Ardabil rug at $3,952 with 112 KPSI.

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.

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "The 4 newest rugs are also the 4 rugs with the greatest numbers of KPSI."
What we're looking for:

• Identify the 4 newest rugs (lowest age values)
• Identify the 4 rugs with highest KPSI
• Check if these two sets contain exactly the same rugs

In other words: Are the newest rugs also the ones with the highest quality?

Let's approach this efficiently:

1. Sort by Age ascending (newest rugs first)
   We can now see the 4 newest rugs all have an age of 20 years. Let's note their KPSI values: 212, 162, 162, and 280.
2. Now sort by KPSI descending (highest values first)
   We can now see the top 4 KPSI values: 280, 212, 162, and 162.

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.

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "The median age of Kashan rugs is greater than the median age of Kashmar rugs."
What we're looking for:

• Find all Kashan rugs and determine their median age
• Find all Kashmar rugs and determine their median age
• Compare these two median values

In other words: Are Kashan rugs typically older than Kashmar rugs?

Let's use sorting to make this comparison straightforward:

1. Sort by Type (to group the rugs by their varieties)
   Now we can easily see all Kashan rugs grouped together and all Kashmar rugs grouped together.
2. Scan the Kashan group
   We can see Kashan rugs have ages: 20, 20, and 25 years.
   With three values, the median is the middle value: 20 years.
3. Scan the Kashmar group
   We can see Kashmar rugs have ages: 20, 25, and 25 years.
   With three values, the median is the middle value: 25 years.

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.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: T - The rug with lowest KPSI (Ardabil) is indeed the most expensive
• Statement 2: T - The 4 newest rugs are the same as the 4 rugs with highest KPSI
• Statement 3: F - The median age of Kashan rugs (20) is NOT greater than the median age of Kashmar rugs (25)

Our answer is: T-T-F

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: We used sorting as our primary analytical tool for all three statements
• Pattern Recognition: We identified matching sets of values without tracking individual items
• Subset Analysis: We isolated subgroups by sorting to analyze them efficiently
• Extreme Value Detection: We quickly found minimum and maximum values through sorting

Strategic Insights

1. Start with Sorting: Almost every table analysis question becomes easier after sorting by relevant columns
2. Min/Max Values: When looking for minimum or maximum values, one sort reveals them instantly
3. Medians After Sorting: Finding medians becomes trivial when values are sorted - just find the middle value
4. Subset Comparison: Sorting by categories makes comparing subgroups much more efficient
5. Value Matching: When comparing sets, focus on matching values rather than tracking individual items

Common Mistakes We Avoided

• Manually scanning all 12 rugs multiple times
• Calculating exact values when we only needed to compare
• Writing down excessive details about individual rugs
• Performing separate calculations for each subset

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.