A logistics facility processes two types of parcels: Express packages and Standard package… — GMAT

A logistics facility processes two types of parcels: Express packages and Standard packages. Last week, what percentage of the total parcels processed were Express packages?

(1) The average weight of an Express package was $4.5$ kilograms, and the average weight of a Standard package was $2.5$ kilograms.
(2) The overall average weight of all parcels processed last week was $3.1$ kilograms.

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

Answer

Both statements together are sufficient, but neither statement alone is sufficient.

The correct response indicates that both statements together are sufficient, but neither statement alone is sufficient. Statement (1) provides only individual package weights, and Statement (2) provides only the overall average package weight. Neither statement alone reveals the mixture ratio. Combining both statements yields the weighted average equation

4.5E + 2.5S = 3.1(E + S)

, which simplifies to

1.4E = 0.6S

, establishing the unique ratio

\frac{E}{S} = \frac{3}{7}

. This uniquely determines that Express packages comprise

30\%

of the total.

Step-by-Step Solution

Define target variable and analyze the question stem

Let

E

be the number of Express packages and

S

be the number of Standard packages. The target question asks for the percentage

\frac{E}{E + S} \times 100\%

. Finding the ratio

\frac{E}{S}

is sufficient to determine this percentage.

Rephrasing a percentage target into a ratio target simplifies statement evaluation.

Evaluate Statement (1) independently

Statement (1) states that the average weight of an Express package is

4.5

kg and a Standard package is

2.5

kg. Without knowing the overall average weight or relative proportion,

\frac{E}{S}

cannot be determined.

Knowing individual component averages alone leaves the weighted ratio undetermined.

Evaluate Statement (2) independently

Statement (2) states that the overall average weight is

3.1

kg. Without the individual component weights, the relative breakdown cannot be determined.

Knowing the combined average weight alone provides no boundary values for individual component rates.

Evaluate Statements (1) and (2) together

Using weighted average principles:

4.5E + 2.5S = 3.1(E + S) \Rightarrow 4.5E + 2.5S = 3.1E + 3.1S \Rightarrow 1.4E = 0.6S \Rightarrow \frac{E}{S} = \frac{0.6}{1.4} = \frac{3}{7}

. The percentage of Express packages is

\frac{3}{3 + 7} \times 100\% = 30\%

Combining individual component averages with the overall weighted average determines a unique ratio of components.

Key Concept

Weighted Average Ratios in Data Sufficiency

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Key Concept

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