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 what we're working with. This table shows rental prices for both furnished and unfurnished apartments across three types (Studio, 1 Bedroom, and 2 Bedroom) over two years.

Here's what a sample row tells us:

Apartment Type	Year	Unfurnished Price	Furnished Price
1 Bedroom	1	$766	$867

Key insights about this dataset:

• We can directly compare furnished vs. unfurnished prices for the same apartment type in the same year
• The price differences vary considerably across apartment types
• Some price differences appear visually small (like Studio apartments in Year 2)
• We can calculate the premium amount (furnished - unfurnished) to evaluate relationships

Rather than calculating percentages for everything, let's approach this strategically with direct comparisons.

QUESTION TRANSLATION

We need to determine which apartment types had furnished prices that exceeded unfurnished prices by more than 10% in both Year 1 and Year 2.

For a "Yes" answer, the apartment type must satisfy: \(\mathrm{Furnished\ Price} > \mathrm{Unfurnished\ Price} \times 1.10\) for BOTH years.
For a "No" answer, the apartment type fails this test in at least one year.

ANALYZING STATEMENT A: Studio Apartments

Statement A Translation:
Original: "For Studio apartments, the furnished price exceeded the unfurnished price by more than 10% in both years"
What we're looking for:

• For Year 1: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)
• For Year 2: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)

In other words: Did Studio apartments have a premium of more than 10% in both years?

Let's start with Year 2 since the optimized approach suggests this comparison is more obvious:

Year 2 Analysis:

• Unfurnished: $747
• Furnished: $752
• Just by looking at these numbers, we can see they're extremely close
• The difference is only $5 \(\$752 - \$747 = \$5\)
• 10% of $747 would be $74.70
• $5 is clearly much less than $74.70

Since the premium needs to exceed 10% in BOTH years, and we've already found one year where it doesn't, we can immediately conclude:

Statement A: No

Teaching callout: Notice how we strategically checked the most obvious year first! When evaluating "both years" conditions, finding a single counterexample immediately gives us our answer without needing to check the other year. This is called "early termination" and is a powerful time-saving technique.

ANALYZING STATEMENT B: 1 Bedroom Apartments

Statement B Translation:
Original: "For 1 Bedroom apartments, the furnished price exceeded the unfurnished price by more than 10% in both years"
What we're looking for:

• For Year 1: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)
• For Year 2: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)

In other words: Did 1 Bedroom apartments have a premium of more than 10% in both years?

We need to check both years:

Year 1 Analysis:

• Unfurnished: $766
• Furnished: $867
• Premium amount: \(\$867 - \$766 = \$101\)
• 10% of $766 = $76.60
• Is $101 > $76.60? Yes! ✓

Year 2 Analysis:

• Unfurnished: $771
• Furnished: $893
• Premium amount: \(\$893 - \$771 = \$122\)
• 10% of $771 = $77.10
• Is $122 > $77.10? Yes! ✓

Since the premium exceeds 10% in BOTH years:

Statement B: Yes

Teaching callout: When finding 10% of a value, we can simply move the decimal point one place to the left instead of multiplying by 0.10. This mental math shortcut makes these comparisons much faster!

ANALYZING STATEMENT C: 2 Bedroom Apartments

Statement C Translation:
Original: "For 2 Bedroom apartments, the furnished price exceeded the unfurnished price by more than 10% in both years"
What we're looking for:

• For Year 1: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)
• For Year 2: \(\mathrm{Furnished\ price} > \mathrm{Unfurnished\ price} \times 1.10\)

In other words: Did 2 Bedroom apartments have a premium of more than 10% in both years?

Let's check Year 1 first:

Year 1 Analysis:

• Unfurnished: $1045
• Furnished: $1112
• Premium amount: \(\$1112 - \$1045 = \$67\)
• 10% of $1045 = $104.50
• Is $67 > $104.50? No! ✗

Since the premium doesn't exceed 10% in Year 1, and we need it to exceed 10% in BOTH years, we can immediately conclude:

Statement C: No

Teaching callout: Again, we saved time by stopping after finding one year that fails to meet our condition. No need to check Year 2! This is critical for efficient problem-solving on the GMAT.

FINAL ANSWER COMPILATION

Let's summarize our findings:

• Statement A (Studio Apartments): No - Premium doesn't exceed 10% in Year 2
• Statement B (1 Bedroom Apartments): Yes - Premium exceeds 10% in both years
• Statement C (2 Bedroom Apartments): No - Premium doesn't exceed 10% in Year 1

The only apartment type with a furnished premium exceeding 10% in both years is 1 Bedroom Apartments.

LEARNING SUMMARY

Skills We Used

• Direct Comparison Instead of Percentages: Rather than calculating actual percentages, we compared the actual premium amount to 10% of the unfurnished price
• Visual Recognition: For Studio apartments in Year 2, we could quickly recognize that $747 and $752 are so close that the premium couldn't possibly be 10%
• Early Termination: Once we found a single year that didn't meet our condition, we immediately stopped checking that apartment type

Strategic Insights

• Check the most obvious cases first: For Studio apartments, Year 2 had numbers that were visibly close, making it an ideal first check
• Mental math shortcuts: Finding 10% is as simple as moving the decimal point left one place
• Subtract first, then compare: Finding the premium amount (furnished - unfurnished) makes the comparison clearer than calculating percentages

Common Mistakes We Avoided

• Unnecessary calculations: We didn't need to check both years for Studio and 2 Bedroom apartments
• Inefficient percentage calculations: We never calculated actual percentages (like 0.67% for Studio Year 2); we just compared the premium to 10% of unfurnished
• Over-complication: By using the "premium > 10% of unfurnished" approach, we simplified the problem considerably

Remember: For "AND" conditions (like "both years"), as soon as one part fails, the entire statement is false. This allows you to stop checking immediately after finding a counterexample!