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Difficulty: MediumStatement Independence Evaluation and Statement Combination

A manufacturing facility produced two types of products, Type X and Type Y. In July, the total cost to produce NN units of Type X and MM units of Type Y was $4,200. What was the unit manufacturing cost of a Type X product?

  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.
Statement (2) alone provides sufficient data because the total cost for Type X products is given as 2,800for2,800 for N = 70 units.Dividing units. Dividing 2,800 by 70 gives a unique unit manufacturing cost of $40 for Type X products, completely independent of Statement (1) and without needing information regarding Type Y.

Step-by-Step Solution

1
Rephrase the target question
Let CxC_x be the unit cost of Type X and CyC_y be the unit cost of Type Y. Total cost is N⋅Cx+M⋅Cy=4200N \cdot C_x + M \cdot C_y = 4200. The target question asks for the unique value of CxC_x.
Clarify what specific variable needs to be solved for.
2
Evaluate Statement (1) independently
Statement (1) tells us Cy=30C_y = 30 and N=2MN = 2M. Substituting into the total cost equation gives N⋅Cx+(N/2)⋅30=4200N \cdot C_x + (N/2) \cdot 30 = 4200, which simplifies to N(Cx+15)=4200N(C_x + 15) = 4200. Since NN is unknown, CxC_x cannot be uniquely determined. Statement (1) alone is NOT sufficient.
Determine if Statement (1) yields a single unique numerical value for CxC_x.
3
Evaluate Statement (2) independently without carrying over information from Statement (1)
Statement (2) states that the total cost for Type X products is N⋅Cx=2800N \cdot C_x = 2800, and N=70N = 70. Solving for CxC_x gives Cx=2800/70=40C_x = 2800 / 70 = 40. This uniquely answers the question stem directly. Statement (2) alone IS sufficient.
Test Statement (2) strictly in isolation.

Key Concept

Evaluating Statement Independence in Data Sufficiency
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Topics

Statement Independence Evaluation and Statement Combination

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