The table shows the results of a survey of 1000 households conducted in 1996 and 2006. In 2006, participants were...

OWNING THE DATASET

Let's start by understanding the data we're working with. We have a table showing how 10 different products were rated on a necessity-luxury scale in both 1996 and 2006.

The table shows "necessity ratings" from 0-1000, where:

• Higher numbers (closer to 1000) = more people view the product as a necessity
• Lower numbers (closer to 0) = more people view the product as a luxury

Key insight: Any product with a necessity rating \(>500\) is considered a "necessity" by the majority of people, while those \(\leq 500\) are considered "luxuries" by the majority.

Looking at one example row: Automobile had a necessity rating of 930 in 1996 and 910 in 2006.

Dataset patterns we immediately notice:

• Most products increased in their necessity rating from 1996 to 2006
• The overall trend is toward items being viewed as more necessary over time
• There's a clear division between high-necessity and low-necessity products

This understanding will help us tackle the statements efficiently.

ANALYZING STATEMENT 2 (Starting here strategically)

Statement 2 Translation:
Original: "Exactly half of the products listed were considered necessities by a majority of Americans in 1996."
What we're looking for:

• Count products with necessity ratings \(>500\) in 1996
• Check if exactly 5 out of 10 products (half) were above this threshold

In other words: Were exactly 5 products rated above 500 in 1996?

Let's sort the table by the 1996 necessity rating (descending) to make this easy to visualize:

After sorting, we can quickly scan down the 1996 column and count:

• Automobile: 930 ✓ (\(>500\), necessity)
• Clothes washer: 920 ✓ (\(>500\), necessity)
• Car air conditioning: 770 ✓ (\(>500\), necessity)
• Clothes dryer: 620 ✓ (\(>500\), necessity)
• Microwave: 530 ✓ (\(>500\), necessity)
• Dishwasher: 430 ✗ (\(\leq 500\), luxury)
• Home computer: 320 ✗ (\(\leq 500\), luxury)
• Cell phone: 240 ✗ (\(\leq 500\), luxury)
• VCR: 180 ✗ (\(\leq 500\), luxury)
• Home air conditioning: 150 ✗ (\(\leq 500\), luxury)

We have exactly 5 products with necessity ratings above 500 in 1996, which is half of the 10 products.

Statement 2: Yes

Teaching tip: Notice how sorting instantly revealed the pattern we needed to see. We didn't need to create a list or do any calculations - just a quick visual count after sorting.

ANALYZING STATEMENT 1 (Continuing with our sorted view)

Statement 1 Translation:
Original: "Exactly one of the products listed was considered less of a necessity in 2006 than it was in 1996."
What we're looking for:

• Compare 2006 rating with 1996 rating for each product
• Count how many products show a decrease (2006 < 1996)
• Check if exactly one product decreased

In other words: Did exactly one product's necessity rating go down from 1996 to 2006?

Since we already have the table sorted by 1996 ratings, we can scan through and look for any products where the 2006 value is lower than the 1996 value:

• Automobile: \(930 \rightarrow 910\) ↓ (decreased)
• Clothes washer: \(920 \rightarrow 980\) ↑ (increased)
• Car air conditioning: \(770 \rightarrow 810\) ↑ (increased)
• Clothes dryer: \(620 \rightarrow 810\) ↑ (increased)
• Microwave: \(530 \rightarrow 680\) ↑ (increased)
• Dishwasher: \(430 \rightarrow 520\) ↑ (increased)
• Home computer: \(320 \rightarrow 670\) ↑ (increased)
• Cell phone: \(240 \rightarrow 490\) ↑ (increased)
• VCR: \(180 \rightarrow 190\) ↑ (increased)
• Home air conditioning: \(150 \rightarrow 560\) ↑ (increased)

We found exactly one product (Automobile) that decreased in its necessity rating. All other products increased.

Statement 1: Yes

Teaching tip: Instead of calculating exact differences for all 10 products, we looked for pattern violations - anything that doesn't follow the predominant trend of increasing values. This approach is much faster than calculating each change.

ANALYZING STATEMENT 3 (Leveraging our previous work)

Statement 3 Translation:
Original: "Of the products that were considered luxuries by a majority of Americans in 1996, 60 percent were considered necessities by a majority of Americans in 2006."
What we're looking for:

• Identify products that were luxuries in 1996 (\(\leq 500\) rating)
• Among those products, count how many became necessities in 2006 (\(>500\) rating)
• Calculate if that percentage equals 60%

In other words: Did 60% of the 1996 luxury products become necessity products by 2006?

From our work on Statement 2, we already know which 5 products were considered luxuries in 1996:

• Dishwasher: 430 in 1996
• Home computer: 320 in 1996
• Cell phone: 240 in 1996
• VCR: 180 in 1996
• Home air conditioning: 150 in 1996

Now let's check each of these products to see if their 2006 rating crossed the 500 threshold:

• Dishwasher: \(430 \rightarrow 520\) ✓ (became a necessity)
• Home computer: \(320 \rightarrow 670\) ✓ (became a necessity)
• Cell phone: \(240 \rightarrow 490\) ✗ (still a luxury)
• VCR: \(180 \rightarrow 190\) ✗ (still a luxury)
• Home air conditioning: \(150 \rightarrow 560\) ✓ (became a necessity)

Of these 5 former luxury products, 3 became necessities by 2006.
\(\frac{3}{5} = 60\%\)

Statement 3: Yes

Teaching tip: We leveraged our previous work from Statement 2 to quickly identify the luxury products from 1996. This allowed us to focus only on those 5 products instead of reviewing all 10 again.

FINAL ANSWER COMPILATION

Statement 1: Yes
Statement 2: Yes
Statement 3: Yes

The correct answer is: ALL THREE statements are Yes.

LEARNING SUMMARY

Skills We Used

• Strategic Sorting: We sorted the data once by 1996 necessity ratings, which helped us tackle two statements efficiently
• Pattern Recognition: We identified the overall trend (mostly increasing values) and looked for exceptions
• Visual Counting: After sorting, we could quickly count products above/below thresholds
• Fraction Recognition: We recognized \(\frac{3}{5} = 60\%\) without complex calculation

Strategic Insights

• Statement Order Matters: We started with Statement 2 because it gave us a clean division of the data that helped with other statements
• Leverage Previous Work: Our analysis of Statement 2 directly fed into our approach for Statement 3
• Look for Pattern Violations: When a statement says "exactly one," look for exceptions to the overall trend

Efficiency Gains

• We avoided creating separate lists for each statement
• We didn't calculate exact differences when only the direction of change mattered
• We focused only on relevant products rather than checking all 10 for each statement

Common Mistakes We Avoided

• Calculating unnecessary values (like exact differences for all products)
• Recounting the same information for each statement
• Processing statements in numerical order rather than strategic order
• Creating multiple sorted views when one strategic sort could address multiple statements

Remember that on GMAT table analysis questions, sorting is often your most powerful first move. It transforms a complex data set into a visually scannable pattern that makes insights jump out at you!