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

A corporate cafeteria serves only two types of lunches: hot meals and cold salads. On Tuesday, what was the ratio of the number of hot meals served to the number of cold salads served?

(1) The total number of lunches served on Tuesday was 200.
(2) On Tuesday, the number of hot meals served was 60% of the total number of lunches served.

  1. A
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.Answer
  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 (2) ALONE is sufficient, but statement (1) alone is not sufficient.
The correct choice is the option stating Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Statement (1) gives only the total volume of lunches served (200), which allows for multiple possible combinations of hot meals and cold salads, resulting in different ratios. Statement (2) establishes that hot meals comprise 60% of the total, meaning cold salads comprise the remaining 40%. The ratio of hot meals to cold salads is therefore fixed at 60% to 40%, which simplifies to 3:2. Thus, Statement (2) alone provides sufficient information to answer the question uniquely.

Step-by-Step Solution

1
Define variables and target expression
Let HH be the number of hot meals and CC be the number of cold salads. Total lunches T=H+CT = H + C. Target is to find the ratio HC\frac{H}{C}.
Rephrasing the question stem algebraically clarifies what information is needed.
2
Evaluate Statement (1)
Statement (1) states T=H+C=200T = H + C = 200. Without knowing the proportion of either HH or CC, HC\frac{H}{C} could be 19010=19\frac{190}{10} = 19 or 100100=1\frac{100}{100} = 1.
A single total count does not fix the internal ratio of the two components.
3
Evaluate Statement (2)
Statement (2) states H=0.60TH = 0.60T. Since T=H+CT = H + C, then C=T−0.60T=0.40TC = T - 0.60T = 0.40T. The ratio HC=0.60T0.40T=0.600.40=32\frac{H}{C} = \frac{0.60T}{0.40T} = \frac{0.60}{0.40} = \frac{3}{2}.
Statement (2) yields a single, definitive numerical value for the ratio.

Key Concept

Data Sufficiency logic for percentage components and ratio determination
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Topics

Rates, Ratios, Percentages, and Applied Word Problems

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