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

An agricultural supplier sells two grades of organic fertilizer: Premium grade and Standard grade. Last month, all inventory of both grades was sold. What percentage of the supplier's total revenue last month came from sales of Premium grade fertilizer?

(1) The price per bag of Premium grade fertilizer was 50%50\% higher than the price per bag of Standard grade fertilizer.
(2) The number of bags of Standard grade fertilizer sold last month was 20%20\% less than the number of bags of Premium grade fertilizer 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.Answer
  4. D
    EACH statement ALONE is sufficient.
  5. E
    Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

Both statements together are sufficient to determine the exact percentage of total revenue coming from Premium grade fertilizer, but neither statement alone is sufficient.
The correct choice identifies that neither statement alone gives both the price ratio and the quantity ratio required to calculate the percentage contribution to total revenue. Statement (1) provides only the relative prices (pPpS=1.5\frac{p_P}{p_S} = 1.5), while Statement (2) provides only the relative quantities sold (S=0.8PS = 0.8P). Combining both gives the combined revenue ratio S⋅pSP⋅pP=45×23=815\frac{S \cdot p_S}{P \cdot p_P} = \frac{4}{5} \times \frac{2}{3} = \frac{8}{15}, which allows calculating the exact percentage 1523\frac{15}{23}. Thus, both statements together are sufficient.

Step-by-Step Solution

1
Rephrase the question target algebraically.
Let PP and SS be the quantities of Premium and Standard bags sold, and let pPp_P and pSp_S be their respective unit prices. Total revenue is Rtotal=P⋅pP+S⋅pSR_{total} = P \cdot p_P + S \cdot p_S. The target percentage is P⋅pPP⋅pP+S⋅pS=11+S⋅pSP⋅pP\frac{P \cdot p_P}{P \cdot p_P + S \cdot p_S} = \frac{1}{1 + \frac{S \cdot p_S}{P \cdot p_P}}. Finding this percentage requires knowing the ratio of total revenues S⋅pSP⋅pP\frac{S \cdot p_S}{P \cdot p_P}, which simplifies to (SP)×(pSpP)\left(\frac{S}{P}\right) \times \left(\frac{p_S}{p_P}\right).
Simplifying the target expression reduces the problem from requiring four individual variable values to requiring only one combined ratio.
2
Evaluate Statement (1) independently.
Statement (1) states pP=1.5⋅pSp_P = 1.5 \cdot p_S, which gives pSpP=11.5=23\frac{p_S}{p_P} = \frac{1}{1.5} = \frac{2}{3}. However, no information is given regarding the ratio of quantities sold SP\frac{S}{P}. Statement (1) alone is NOT sufficient.
Knowing only the price ratio leaves the quantity ratio unknown.
3
Evaluate Statement (2) independently.
Statement (2) states S=0.8⋅PS = 0.8 \cdot P, which gives SP=0.8=45\frac{S}{P} = 0.8 = \frac{4}{5}. However, no information is given regarding the price ratio pSpP\frac{p_S}{p_P}. Statement (2) alone is NOT sufficient.
Knowing only the quantity ratio leaves the price ratio unknown.
4
Evaluate Statements (1) and (2) together.
Combining both statements yields S⋅pSP⋅pP=(45)×(23)=815\frac{S \cdot p_S}{P \cdot p_P} = \left(\frac{4}{5}\right) \times \left(\frac{2}{3}\right) = \frac{8}{15}. Substituting this into the target expression gives 11+815=1523≈65.2%\frac{1}{1 + \frac{8}{15}} = \frac{15}{23} \approx 65.2\%. Therefore, both statements together are sufficient.
Combining the relative prices and relative quantities provides the exact ratio of revenues.

Key Concept

Data Sufficiency Target Rephrasing for Percentage of Total Revenue
Estimated Time:2m 0s
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Topics

Rates, Ratios, Percentages, and Applied Word Problems

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