Data Sufficiency Practice Questions — GMAT — Page 14

Question 261Question →

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 $4,000 for Office buildings and$ 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.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: Statement (1) ALONE is sufficient, but statement (2) alone is 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 (

4,000 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 (

3:2

), 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

O

be the number of Office buildings and

R

be the number of Retail centers. The average monthly maintenance cost across all properties is

\frac{4000O + 2500R}{O + R} = 2500 + 1500\left(\frac{O}{O + R}\right)

. Thus, finding the proportion

\frac{O}{O + R}

or the ratio

\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

\frac{O}{R} = \frac{3}{2}

. This implies

\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 = 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 \cdot O = 72,000

, which gives

O = 18

. However, no information is given regarding

R

, the number of Retail centers. Since

R

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

Question 262Question →

A fitness club offers two annual membership tiers: Standard and Premium. Last year, what percentage of the fitness club's total annual membership revenue came from Premium memberships?

(1) Last year, the annual price of a Premium membership was $50\%$ greater than the annual price of a Standard membership.

(2) Last year, the ratio of the number of Standard memberships sold to the number of Premium memberships sold was $3$ to $2$ .

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answer

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Rephrasing the question stem shows that finding the percentage of total revenue from Premium memberships depends solely on the product of the quantity ratio

\frac{N_S}{N_P}

and the price ratio

\frac{P_S}{P_P}

. Statement (1) gives

\frac{P_S}{P_P} = \frac{2}{3}

and Statement (2) gives

\frac{N_S}{N_P} = \frac{3}{2}

. Neither statement alone provides both ratios, but combining both statements gives a product of

1

, which uniquely determines that Premium memberships generated exactly

50\%

of total revenue. Therefore, both statements together are sufficient.

Step-by-Step Solution

1

Rephrase the target question algebraically.

Let

N_S

and

N_P

be the number of Standard and Premium memberships sold, and

P_S

and

P_P

be their respective prices. Total revenue

R = N_S P_S + N_P P_P

. The fraction of revenue from Premium memberships is

\frac{N_P P_P}{N_S P_S + N_P P_P} = \frac{1}{\left(\frac{N_S}{N_P}\right)\left(\frac{P_S}{P_P}\right) + 1}

. Thus, knowing the product of ratios

\left(\frac{N_S}{N_P}\right)\left(\frac{P_S}{P_P}\right)

is sufficient.

Simplifying the stem target shows that only the relative overall ratio of Standard revenue to Premium revenue is needed, not individual numerical values.

2

Evaluate Statement (1) independently.

Statement (1) states

P_P = 1.5 P_S = \frac{3}{2} P_S

, which gives

\frac{P_S}{P_P} = \frac{2}{3}

. However,

\frac{N_S}{N_P}

is unknown.

Without the quantity ratio, the overall percentage of revenue cannot be calculated. Statement (1) alone is NOT sufficient.

3

Evaluate Statement (2) independently.

Statement (2) states

\frac{N_S}{N_P} = \frac{3}{2}

. However,

\frac{P_S}{P_P}

is unknown.

Without the price ratio, the overall percentage of revenue cannot be calculated. Statement (2) alone is NOT sufficient.

4

Evaluate Statements (1) and (2) together.

Using both statements,

\left(\frac{N_S}{N_P}\right)\left(\frac{P_S}{P_P}\right) = \left(\frac{3}{2}\right)\left(\frac{2}{3}\right) = 1

. Substituting this into the rephrased expression gives

\frac{1}{1 + 1} = \frac{1}{2} = 50\%

.

A single numerical answer (

50\%

) is uniquely determined. Both statements together are sufficient.

Key Concept

Data Sufficiency Rephrasing for Weighted Revenue Ratios

Question 263Question →

A boutique winery produces and sells only two types of wine: Pinot Noir and Chardonnay. Last year, was the total revenue generated from the sales of Pinot Noir greater than the total revenue generated from the sales of Chardonnay?

(1) Last year, the number of bottles of Pinot Noir sold was 20 percent greater than the number of bottles of Chardonnay sold.
(2) Last year, the average price per bottle of Chardonnay sold was 15 percent greater than the average price per bottle of Pinot Noir sold.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

Show answer & explanation

Answer: BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Answer

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Combining both statements provides the exact ratio of quantities sold (6:5) and the exact ratio of unit prices (20:23). Multiplying these two ratios yields a total revenue ratio of 24:23, which is strictly greater than 1. This establishes a definitive 'Yes' answer to whether Pinot Noir sales revenue exceeded Chardonnay sales revenue.

Step-by-Step Solution

1

Rephrase the question stem algebraically.

Let

N_P

and

N_C

be the number of bottles sold of Pinot Noir and Chardonnay, respectively. Let

P_P

and

P_C

be their respective average prices per bottle. Total revenues are

R_P = N_P \times P_P

and

R_C = N_C \times P_C

. The question asks whether

R_P > R_C

, which is equivalent to asking if

\frac{R_P}{R_C} > 1

, or

\left(\frac{N_P}{N_C}\right) \times \left(\frac{P_P}{P_C}\right) > 1

.

Simplifying the target question into a single product of ratios clarifies the data required for sufficiency.

2

Evaluate Statement (1) alone.

Statement (1) states

N_P = 1.20 N_C

, which gives

\frac{N_P}{N_C} = \frac{6}{5}

. However, no information is given regarding

P_P

and

P_C

. If

P_P = P_C

, then

R_P > R_C

(Yes). If

P_C = 2 P_P

, then

R_P < R_C

(No). Statement (1) ALONE is not sufficient.

Knowing only the quantity ratio leaves the price ratio unconstrained.

3

Evaluate Statement (2) alone.

Statement (2) states

P_C = 1.15 P_P

, which gives

\frac{P_P}{P_C} = \frac{1}{1.15} = \frac{20}{23}

. However, no information is given regarding

N_P

and

N_C

. Statement (2) ALONE is not sufficient.

Knowing only the price ratio leaves the quantity ratio unconstrained.

4

Evaluate Statements (1) and (2) together.

Combining both statements gives

\frac{R_P}{R_C} = \left(\frac{N_P}{N_C}\right) \times \left(\frac{P_P}{P_C}\right) = \left(\frac{6}{5}\right) \times \left(\frac{20}{23}\right) = \frac{24}{23}

. Since

\frac{24}{23} > 1

,

R_P

is definitively greater than

R_C

. The answer to the question is a definitive Yes.

Combining both ratios yields a unique, definitive revenue ratio greater than 1.

Key Concept

Data Sufficiency Value vs. Yes/No decision logic applied to weighted percentage and ratio word problems.

Data Sufficiency

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Answer

Step-by-Step Solution

Key Concept

Common Mistakes