A real estate agent sold 6 houses in Junction City and 3 houses

Question

A real estate agent sold 6 houses in Junction City and 3 houses in Uniontown. For each house he sold, he earned a commission of 7% of the selling price of the house. Was the total of his commissions for the houses he sold in Junction City greater than the total of his commissions for the houses he sold in Uniontown?

(1) The average (arithmetic mean) selling price of the 3 houses in Uniontown was more than twice the average selling price of the 6 houses in Junction City.

(2) The selling price of each of the 3 houses in Uniontown was more than twice the selling price of the most expensive of the 6 houses in Junction City.

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Official Answer

D

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Bunuel · Answer

A real estate agent sold 6 houses in Junction City and 3 houses in Uniontown. For each house he sold, he earned a commission of 7% of the selling price of the house. Was the total of his commissions for the houses he sold in Junction City greater than the total of his commissions for the houses he sold in Uniontown?

Note that the question essentially asks whether the sum of the 6 home prices in Junction City was greater than the sum of the 3 home prices in Uniontown.

(1) The average (arithmetic mean) selling price of the 3 houses in Uniontown was more than twice the average selling price of the 6 houses in Junction City.

This implies that (the sum of the 3 home prices in Uniontown)/3 > 2*(the sum of the 6 home prices in Junction City)/6, which simplifies to (the sum of the 3 home prices in Uniontown) > (the sum of the 6 home prices in Junction City). Sufficient.

(2) The selling price of each of the 3 houses in Uniontown was more than twice the selling price of the most expensive of the 6 houses in Junction City.

This implies that each house's selling price in Uniontown is more than double the highest selling price among the 6 houses in Junction City. Given this, the lowest possible total for the 3 houses in Uniontown (assuming each is just over double the price of Junction City's most expensive house) would still surpass the highest possible total for the 6 houses in Junction City. Hence, (the sum of the 3 home prices in Uniontown) > (the sum of the 6 home prices in Junction City). Sufficient.

Answer: D.

dibz101 · Answer

Bunuel

Case 2 says: "The selling price of each of the 3 houses in Uniontown was more than twice the selling price of the most expensive of the 6 houses in Junction City."

What if all the houses are $100k, the most expensive house in J will equal $100k and the commission in both sales would be equal. (It's not specifically mentioned that houses can have different prices).

Bunuel · Answer

I tried to decipher what you mean there, but unfortunately, I failed. Could you please provide the prices of 6 houses in Junction City and 3 houses in Uniontown that satisfy the second statement and yield equal commissions?

dibz101 · Answer

2) The selling price of each of the 3 houses in Uniontown was more than twice the selling price of the most expensive of the 6 houses in Junction City.

Possibility 1:
Price of houses in J: 100k, 100k, 100k, 100k, 100k, 100k (It's not mentioned in the passage that all houses cannot have the same price)
Price of most expensive house in J - 100k
Price of each of 3 houses in U - 200k

Sum of sale in U = Sum of sale in J

Possibility 2:
Price of houses in J: 100k, 99k, 99k, 99k, 99k, 99k 
Price of most expensive housee in J - 100k
Price of each of 3 houses in U - 200k

Sum of sale in U > Sum of sale in J

Not sufficient 
Am I missing something in the question?

Unless "the most" implies that there are no other houses in J equal to the one.

Bunuel · Answer

I see. Check the highlighted word in the second statement:

(2) The selling price of each of the 3 houses in Uniontown was  more  than twice the selling price of the most expensive of the 6 houses in Junction City.

So, if the most expensive of the 6 houses in Junction City was 100k, then the selling price of each of the 3 houses in Uniontown was  more  than 200k.

siddhantvarma · Answer

KarishmaB  is there a quicker way to evaluate statement 2? I started taking values and eventually found out that the selling price of all 3 houses in Uniontown would be more than that of 6 houses in Junction City but it took me a lot of time to get to the anwer this way.

KarishmaB · Answer

Spend time on the question stem to figure out exactly what is given. Then you will spend much less time on each option. 
6 houses sold in J and 3 in U. He got the same 7% commission on all houses.

Was Total commission from J > Total commission from U?

Think about it for a few seconds now. In J he sold 6 houses but in U he sold only 3. He got 7% commission from every house. So if houses in both cities are similarly priced, we obviously expect him to get from J twice the commission he got from U. But if houses in U are far more expensive (more than twice) than those in J, then we can expect that he got more commission from U. So we need to compare SP of 6 houses in J with SP of 3 houses in U. Which total SP is higher? That will give higher commission.

This question should be solved logically on test day without any of the work I am giving below. I am giving the work below to help you build your logic skills.

(1) The average (arithmetic mean) selling price of the 3 houses in Uniontown was more than twice the average selling price of the 6 houses in Junction City.

This tells us that average SP of the 3 houses in U was more than twice the average SP of the 6 houses in J. This should be enough to tell us that overall SP of houses in U is higher but if it is not obvious, see below:

Avg SP in U > 2 * Avg SP in J
3 * Avg SP in U > 6 * Avg SP in J
Total SP in U > Total SP in J

So overall SP of houses in U is higher so his commission from U will be higher. 
Hence this statement alone is sufficient.

(2) The selling price of each of the 3 houses in Uniontown was more than twice the selling price of the most expensive of the 6 houses in Junction City.

This option tells us that the SP of each house in U is twice more than the most expensive house of J. Every house of U is more than twice the price of the most expensive house in J

SP of House in U > 2 * SP of most expensive house in J
3 * SP of House in U > 6 * SP of most expensive house in J

The total SP of 6 houses in J will be less than 6* SP of most expensive house in J. So,

Total SP in U > Total SP in J

So overall SP of houses in U is higher so his commission from U will be higher. 
Hence this statement alone is sufficient.

Answer (D)

A real estate agent sold 6 houses in Junction City and 3 houses

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A real estate agent sold 6 houses in Junction City and 3 houses

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