A university offers its students on-campus housing in university-owned apartments. The majority of the apartments are unfurnished, but the university...

OWNING THE DATASET

Let's start by understanding this table showing apartment rental prices for different unit types across two years.

The table compares furnished vs. unfurnished prices for three apartment types (Studio, 1 Bedroom, 2 Bedroom) in two consecutive years. We have both the unfurnished and furnished prices for each apartment type in each year.

Key insights from our initial scan:

• Price differences between furnished and unfurnished units vary significantly by apartment type
• Just by glancing, we can see some price gaps look much larger than others
• The data is organized in a way that makes direct year-to-year and furnished/unfurnished comparisons straightforward

Note: When dealing with percentage comparisons like this table requires, remember we can use multiplication rather than division to check thresholds more efficiently.

ANALYZING THE QUESTION

The question asks: "For which apartment type was the price of a furnished unit more than 10% higher than the price of an unfurnished unit in both years?"

This requires us to:

1. Calculate the 10% threshold for each unfurnished price
2. Compare the furnished price against this threshold
3. Find which apartment type exceeds this threshold in BOTH years

Let's tackle each apartment type strategically, focusing on finding the answer as efficiently as possible.

ANALYZING APARTMENT TYPES

Studio Apartments Analysis

Step 1: Check Year 1

• Unfurnished price: \(\$705\)
• 10% threshold = \(\$705 \times 1.1 = \$775.50\)
• Furnished price: \(\$730\)
• Comparison: \(\$730 < \$775.50\)

Since \(\$730\) is less than \(\$775.50\), the furnished Studio apartment costs less than 10% more than the unfurnished one in Year 1.

Key insight: We can immediately eliminate Studio apartments as our answer because the question requires the price difference to be more than 10% in BOTH years. Since Year 1 already fails this test, we don't need to check Year 2 at all!

Studio apartments: ELIMINATED

1 Bedroom Apartments Analysis

Step 1: Check Year 1

• Unfurnished price: \(\$766\)
• 10% threshold = \(\$766 \times 1.1 = \$842.60\)
• Furnished price: \(\$867\)
• Comparison: \(\$867 > \$842.60\)

Since \(\$867\) is greater than \(\$842.60\), the furnished 1 Bedroom apartment costs more than 10% higher than the unfurnished one in Year 1.

Step 2: Check Year 2 (necessary since Year 1 passed the test)

• Unfurnished price: \(\$771\)
• 10% threshold = \(\$771 \times 1.1 = \$848.10\)
• Furnished price: \(\$893\)
• Comparison: \(\$893 > \$848.10\)

Since \(\$893\) is greater than \(\$848.10\), the furnished 1 Bedroom apartment costs more than 10% higher than the unfurnished one in Year 2 as well.

1 Bedroom apartments: MEETS CRITERIA for both years

2 Bedroom Apartments Analysis

Step 1: Check Year 1

• Unfurnished price: \(\$1,045\)
• 10% threshold = \(\$1,045 \times 1.1 = \$1,149.50\)
• Furnished price: \(\$1,112\)
• Comparison: \(\$1,112 < \$1,149.50\)

Since \(\$1,112\) is less than \$1,149.50\), the furnished 2 Bedroom apartment costs less than 10% more than the unfurnished one in Year 1.

Key insight: Just like with Studio apartments, we can immediately eliminate 2 Bedroom apartments as our answer because Year 1 already fails the test. We don't need to check Year 2!

2 Bedroom apartments: ELIMINATED

FINAL ANSWER

The only apartment type where the furnished unit was more than 10% higher in price than the unfurnished unit in BOTH years is: 1 Bedroom apartments.

Yes

LEARNING SUMMARY

Skills We Used

• The Early Termination Principle: We stopped checking an apartment type as soon as one year failed to meet our criteria, saving significant time.
• The Comparison Over Calculation Principle: Instead of calculating exact percentages, we created a 10% threshold by multiplying by 1.1, which is much faster.
• Strategic Testing Order: We tested one year first for each apartment type, only proceeding to test the second year if the first year met our criteria.

Strategic Insights

1. For "both years" questions: Always check one year first - if it fails, you can immediately eliminate that option.
2. For percentage threshold questions: Use multiplication (price × 1.1) rather than calculating exact percentages, which requires division.
3. Working efficiently: Notice how we only had to perform 4 calculations instead of 6 possible ones.

Common Mistakes We Avoided

• Unnecessary calculations: We didn't calculate Year 2 for Studio or 2 Bedroom apartments once we knew Year 1 didn't meet the criteria.
• Over-precision: We didn't calculate exact percentage differences (like 3.55% or 13.18%) when we only needed to know if they exceeded 10%.
• Missing visual cues: We recognized that some price differences were visibly smaller, helping us anticipate likely results before calculating.

Remember these strategies for any GMAT question that tests conditions across multiple categories or time periods - the early termination principle is a powerful time-saver!