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The table shows the results of a survey of 1000 households conducted in 1996 and 2006. In 2006, participants were asked to categorize each of 10 products and services as either luxury or a necessity; in 2006, 2 additional products and services were included, increasing the total number to 12.
| Product/Service | 1996 Luxury | 1996 Necessity | 2006 Luxury | 2006 Necessity |
|---|---|---|---|---|
| Automobile | 70 | 930 | 90 | 910 |
| Automobile air-conditioning | 590 | 410 | 409 | 591 |
| Cable TV | 833 | 167 | 671 | 329 |
| Cell phone | n/a | n/a | 517 | 483 |
| Clothes dryer | 375 | 625 | 166 | 834 |
| Clothes washer | 139 | 861 | 105 | 895 |
| Dishwasher | 871 | 129 | 656 | 344 |
| High-speed Internet | n/a | n/a | 715 | 285 |
| Home air-conditioning | 495 | 505 | 299 | 701 |
| Home computer | 741 | 259 | 472 | 528 |
| Microwave oven | 680 | 320 | 317 | 683 |
| TV set | 404 | 596 | 353 | 647 |
For each of the following statements about this data, select Yes if the statement can be inferred from the given information. Otherwise, select No.
Exactly one product or service was categorized as a necessity by fewer participants in 2006 than in 1996.
Exactly half of the products and services in the 1996 survey were categorized as a necessity by a majority of survey participants.
Of the products and services that were categorized as luxuries by a majority of the 1996 survey participants, exactly 60% were categorized as necessities by a majority of the 2006 survey participants.
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:
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:
This understanding will help us tackle the statements efficiently.
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:
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:
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.
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:
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:
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.
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:
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:
Now let's check each of these products to see if their 2006 rating crossed the 500 threshold:
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.
Statement 1: Yes
Statement 2: Yes
Statement 3: Yes
The correct answer is: ALL THREE statements are Yes.
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!
Exactly one product or service was categorized as a necessity by fewer participants in 2006 than in 1996.
Exactly half of the products and services in the 1996 survey were categorized as a necessity by a majority of survey participants.
Of the products and services that were categorized as luxuries by a majority of the 1996 survey participants, exactly 60% were categorized as necessities by a majority of the 2006 survey participants.