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Zorluk: OrtaRates, Ratios, Percentages, and Applied Word Problems

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.

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

Cevap

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.

Adım Adım Çözüm

1
Rephrase the question stem algebraically.
Let NPN_P and NCN_C be the number of bottles sold of Pinot Noir and Chardonnay, respectively. Let PPP_P and PCP_C be their respective average prices per bottle. Total revenues are RP=NP×PPR_P = N_P \times P_P and RC=NC×PCR_C = N_C \times P_C. The question asks whether RP>RCR_P > R_C, which is equivalent to asking if RPRC>1\frac{R_P}{R_C} > 1, or (NPNC)×(PPPC)>1\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 NP=1.20NCN_P = 1.20 N_C, which gives NPNC=65\frac{N_P}{N_C} = \frac{6}{5}. However, no information is given regarding PPP_P and PCP_C. If PP=PCP_P = P_C, then RP>RCR_P > R_C (Yes). If PC=2PPP_C = 2 P_P, then RP<RCR_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 PC=1.15PPP_C = 1.15 P_P, which gives PPPC=11.15=2023\frac{P_P}{P_C} = \frac{1}{1.15} = \frac{20}{23}. However, no information is given regarding NPN_P and NCN_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 RPRC=(NPNC)×(PPPC)=(65)×(2023)=2423\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 2423>1\frac{24}{23} > 1, RPR_P is definitively greater than RCR_C. The answer to the question is a definitive Yes.
Combining both ratios yields a unique, definitive revenue ratio greater than 1.

Anahtar Kavram

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