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

A tech company sells two types of service plans: Basic and Enterprise. Last month, what percentage of the company's total revenue from these two service plans was generated by sales of the Enterprise plan?

(1) Last month, the price of an Enterprise plan was 250%250\% of the price of a Basic plan, and the number of Basic plans sold was 60%60\% greater than the number of Enterprise plans sold.
(2) Last month, total revenue generated from sales of the Basic plan was $120,000\$120,000.

  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.
Statement (1) establishes exact multiplier relationships for both price and quantity (PE=2.5PBP_E = 2.5 P_B and NB=1.6NEN_B = 1.6 N_E). When computing the proportion of revenue generated by the Enterprise plan, all unknown variables (PBP_B and NEN_E) cancel out cleanly, producing a single, deterministic percentage of 2541×100%\frac{25}{41} \times 100\%. Statement (2) only specifies the dollar revenue for the Basic plan, leaving the Enterprise plan's revenue completely unconstrained. Thus, Statement (1) alone is sufficient, while Statement (2) alone is not.

Step-by-Step Solution

1
Formulate the target ratio algebraically
Target percentage =RERE+RB×100%= \frac{R_E}{R_E + R_B} \times 100\%, where RE=PE×NER_E = P_E \times N_E and RB=PB×NBR_B = P_B \times N_B.
Total revenue is the sum of Enterprise revenue (RER_E) and Basic revenue (RBR_B).
2
Evaluate Statement (1)
PE=2.5PBP_E = 2.5 P_B and NB=1.6NEN_B = 1.6 N_E. Therefore, RE=2.5PBNER_E = 2.5 P_B N_E and RB=1.6PBNER_B = 1.6 P_B N_E. The revenue ratio is RERB=2.51.6=2516\frac{R_E}{R_B} = \frac{2.5}{1.6} = \frac{25}{16}.
Substituting these expressions into the target formula yields 25PBNE25PBNE+16PBNE=2541≈60.98%\frac{25 P_B N_E}{25 P_B N_E + 16 P_B N_E} = \frac{25}{41} \approx 60.98\%. Because a single, unique percentage is obtained, Statement (1) alone is sufficient.
3
Evaluate Statement (2)
RB=$120,000R_B = \$120,000, but RER_E remains unknown.
Knowing only the total revenue from Basic plans provides no information about the Enterprise revenue or its share of total revenue. Thus, Statement (2) alone is insufficient.

Key Concept

Data Sufficiency Evaluation of Percentages via Relative Variable Relationships
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Topics

Rates, Ratios, Percentages, and Applied Word Problems

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