A real estate agent sold 6 houses in Junction City and 3 houses in Uniontown. For each house he sold,...

Understanding the Question

We need to determine whether the agent's total commission from Junction City exceeds his total commission from Uniontown.

Given Information

• Junction City: 6 houses sold
• Uniontown: 3 houses sold
• Commission rate: 7% of selling price (same for all houses)

What We Need to Determine

Since the commission rate is constant at 7%, we're essentially asking: Is the total selling price of the 6 Junction City houses greater than the total selling price of the 3 Uniontown houses?

This is a yes/no question - we need a definitive answer about which city generated more commission.

Key Insight

The challenge here is comparing two groups of different sizes. Junction City has twice as many houses (6 vs 3), but that doesn't automatically mean higher total value. We need information about the relative prices to determine which total is greater.

Analyzing Statement 1

Statement 1 tells us: The average selling price in Uniontown was MORE than twice the average selling price in Junction City.

Let's think about this logically. If Junction City houses average $100,000, then Uniontown houses average MORE than $200,000.

Testing the Relationship

• Junction City total: \(6 \text{ houses} \times \$100{,}000 \text{ average} = \$600{,}000\)
• Uniontown total: 3 houses × MORE than $200,000 average = MORE than $600,000

Since Uniontown's total is definitely higher than Junction City's total, the commissions follow the same pattern.

The answer to our question is definitively NO - Junction City's commissions are NOT greater than Uniontown's.

[STOP - Statement 1 is Sufficient!]

Conclusion

Statement 1 is sufficient because it gives us a definitive answer.

This eliminates choices B, C, and E.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: Each of the 3 Uniontown houses sold for more than twice the price of the most expensive Junction City house.

This is even stronger than Statement 1! Let's reason through this.

Logical Analysis

If the most expensive Junction City house sold for $200,000, then:

• Each Uniontown house sold for MORE than $400,000
• Minimum total for 3 Uniontown houses: 3 × (more than $400,000) = MORE than $1,200,000
• Maximum possible total for 6 Junction City houses: \(6 \times \$200{,}000 = \$1{,}200{,}000\)

Since Uniontown's total exceeds $1,200,000 while Junction City's total cannot exceed $1,200,000, Uniontown definitely has the higher total (and thus higher commissions).

The answer is again NO - Junction City's commissions are NOT greater.

[STOP - Statement 2 is Sufficient!]

Conclusion

Statement 2 is sufficient because it also gives us a definitive answer of NO.

This eliminates choices A, C, and E.

The Answer: D

Both statements independently tell us that Uniontown's total commissions exceed Junction City's, just through different comparisons:

• Statement 1: Compares averages
• Statement 2: Compares individual prices to the maximum

Since each statement alone is sufficient to answer the question, the answer is D.

Answer Choice D: "Each statement alone is sufficient."