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 in this rug dataset. The table contains information about 12 different rugs with details about their type, age, dimensions (length and width in feet), and KPSI (knots per square inch).

Key insights from our initial review:

• We have 6 different rug types (including Kashan and Kashmar)
• The rugs vary in age (with some being as new as 20 years old)
• Dimensions are given in feet, but KPSI is per square inch
• To calculate total knots, we need to convert feet to inches (× 12) and multiply:
  Total knots = KPSI × length × width × 144 (where \(144 = 12^2\) to convert sq ft to sq inches)

This quick data understanding will help us efficiently analyze each statement without getting lost in unnecessary calculations.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "The rug with the greatest KPSI has more than 5,500,000 knots"
What we're looking for:

• Identify which rug has the highest KPSI value
• Calculate if this rug's total knots exceed 5,500,000

In other words: Does the rug with the most knots per square inch have more than 5.5 million knots in total?

Let's approach this efficiently by sorting the data:

1. Let's sort by KPSI (in descending order)

This immediately shows us the rug with the highest KPSI at the top of our sorted list - a Kerman rug with 280 KPSI, measuring 10×14 feet.

Now, we need to determine if this rug has more than 5,500,000 knots total. Rather than calculating the exact number, we can use a quick approximation:

Area in square inches = \(10 \times 14 \times 144 = 20,160\) sq inches
Total knots ≈ \(280 \times 20,160 \approx 5,644,800\) knots

Since \(5,644,800 > 5,500,000\), this statement is T.

Teaching Callout: Notice how sorting instantly identified our target rug! Instead of manually comparing all 12 KPSI values, a simple sort command gave us the answer immediately. Also, we used approximation when precise calculation wasn't necessary - this saves valuable time on the GMAT.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "The median KPSI of the 4 newest rugs is 162"
What we're looking for:

• Identify the 4 rugs with the lowest age values (newest rugs)
• Find the median KPSI value of these 4 rugs
• Check if this median equals 162

In other words: If we arrange the KPSI values of the 4 youngest rugs, is the middle value (median) 162?

Again, sorting is our most efficient approach:

1. Let's sort by Age (in ascending order)

After sorting, we can immediately see the 4 newest rugs (all 20 years old) at the top of our list. Their KPSI values are: 212, 162, 162, and 280.

To find the median of these 4 values, we arrange them: 162, 162, 212, 280
Since we have an even number of values, the median is the average of the middle two:
Median = \(\frac{162 + 212}{2} = \frac{374}{2} = 187\)

Since \(187 \neq 162\), this statement is F.

Teaching Callout: Sorting by age made it incredibly easy to identify our subset of interest! Instead of scanning the entire table for the newest rugs, they were all grouped together at the top. Once we had our relevant data subset, finding the median became straightforward.

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "The median length of Kashan rugs equals the median length of Kashmar rugs"
What we're looking for:

• Find all Kashan rugs and determine the median of their lengths
• Find all Kashmar rugs and determine the median of their lengths
• Compare these two median values

In other words: Is the middle value of Kashan rug lengths the same as the middle value of Kashmar rug lengths?

The most efficient approach is to group the rugs by type:

1. Let's sort by Type

After sorting, all rugs of the same type appear together, making it easy to analyze each group:

For the Kashan section (3 rugs), the lengths are 14, 12, and 15 feet.
The median of 3 values is simply the middle value = 14 feet.

For the Kashmar section (3 rugs), the lengths are 9, 13, and 12 feet.
The median of these 3 values is the middle value = 12 feet.

Since \(14 \neq 12\) feet, this statement is F.

Teaching Callout: Sorting by type created visual groups that made our analysis much faster! We didn't need to write out the values separately or scan back and forth through the table. Also, when you have just 3 values, the median is simply the middle value - no calculation needed.

FINAL ANSWER COMPILATION

After analyzing all three statements:

• Statement 1: T (The rug with the greatest KPSI does have more than 5,500,000 knots)
• Statement 2: F (The median KPSI of the 4 newest rugs is 187, not 162)
• Statement 3: F (The median length of Kashan rugs is 14 feet, while the median length of Kashmar rugs is 12 feet)

The answer is therefore A: Statement 1 ONLY is true.

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: Each statement became dramatically simpler after sorting by the relevant column
• Approximation: When comparing to a threshold value, we used quick estimation rather than exact calculation
• Visual Grouping: Sorting created natural groups that made patterns immediately apparent
• Minimal Math: For the median of 3 values, we recognized that it's simply the middle value

Strategic Insights

• The Sort-First Principle: Your first action in table analysis questions should almost always be to sort the column most relevant to the statement
• Efficiency Hierarchy: Sorting → visual scanning → approximation → calculation (in that order of preference)
• Know Your Median Shortcuts: With 3 values, the median is the middle value; with 4 values, it's the average of the middle two

Common Mistakes We Avoided

• Manually scanning for maximum values instead of sorting
• Writing out multiple values before finding medians
• Performing exact calculations when approximations would suffice
• Treating each statement as an isolated problem without leveraging table manipulations

Remember: In table analysis questions, how you approach the data is often more important than the calculations themselves. Sorting is your superpower - it instantly transforms complicated searches into simple visual scans!