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Difficulty: MediumRates, Ratios, Percentages, and Applied Word Problems

A commercial real estate firm manages two types of properties: Office buildings and Retail centers. Last year, the average monthly maintenance cost per property was 4,000forOfficebuildingsand4,000 for Office buildings and 2,500 for Retail centers. What was the average monthly maintenance cost per property across all properties managed by the firm last year?

(1) Last year, the ratio of the number of Office buildings to the number of Retail centers managed by the firm was 3 to 2.
(2) Last year, the total monthly maintenance cost for all Office buildings managed by the firm was $72,000.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.Answer
  2. B
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. C
    BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
The overall average cost is a weighted average of the two individual property averages. To find a weighted average between two known values (4,000and4,000 and 2,500), only the relative ratio or percentage distribution of the two components is required. Statement (1) provides the exact ratio of Office buildings to Retail centers (3:23:2), which allows direct calculation of the weighted average ($3,400). Statement (2) only reveals that there are 18 Office buildings, leaving the number of Retail centers unknown, so the average cannot be calculated.

Step-by-Step Solution

1
Rephrase the question target algebraically.
Let OO be the number of Office buildings and RR be the number of Retail centers. The average monthly maintenance cost across all properties is 4000O+2500RO+R=2500+1500(OO+R)\frac{4000O + 2500R}{O + R} = 2500 + 1500\left(\frac{O}{O + R}\right). Thus, finding the proportion OO+R\frac{O}{O + R} or the ratio OR\frac{O}{R} is sufficient to determine the overall average cost.
Rephrasing shows that only the relative weighting of property types is required, not their absolute numbers.
2
Evaluate Statement (1) independently.
Statement (1) gives OR=32\frac{O}{R} = \frac{3}{2}. This implies OO+R=33+2=35=0.6\frac{O}{O + R} = \frac{3}{3 + 2} = \frac{3}{5} = 0.6. The overall average cost is 4000(0.6)+2500(0.4)=2400+1000=34004000(0.6) + 2500(0.4) = 2400 + 1000 = 3400. Thus, Statement (1) alone is sufficient.
Knowing the ratio provides the exact relative weights needed for the weighted average calculation.
3
Evaluate Statement (2) independently.
Statement (2) states that 4000⋅O=72,0004000 \cdot O = 72,000, which gives O=18O = 18. However, no information is given regarding RR, the number of Retail centers. Since RR can take any positive integer value, the weighted average cannot be determined. Thus, Statement (2) alone is not sufficient.
Knowing the quantity of one group without any information about the second group leaves the weighted average undefined.

Key Concept

Weighted Average and Ratio Sufficiency in Data Sufficiency
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Topics

Rates, Ratios, Percentages, and Applied Word Problems

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