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

A car dealership's inventory consists exclusively of sedans and SUVs. What is the ratio of the number of sedans to the number of SUVs in the inventory?

(1) The total number of sedans and SUVs in the inventory is 150150.
(2) The number of sedans in the inventory is 6060.

  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, but neither statement alone is sufficient.
Statement (1) gives S+U=150S + U = 150, which is insufficient by itself. Statement (2) gives S=60S = 60, which is also insufficient by itself. Together, we can deduce U=90U = 90, giving a unique ratio S:U=60:90=2:3S : U = 60 : 90 = 2 : 3. Therefore, both statements together are sufficient.

Step-by-Step Solution

1
Rephrase the target question.
Let SS be the number of sedans and UU be the number of SUVs. The target ratio is SU\frac{S}{U}.
Establishing explicit variable definitions simplifies statement analysis.
2
Evaluate Statement (1) independently.
S+U=150S + U = 150.
Knowing only the total does not fix the specific values of SS or UU, so the ratio SU\frac{S}{U} can take multiple values. Statement (1) is insufficient.
3
Evaluate Statement (2) independently.
S=60S = 60.
Without knowing UU, the ratio SU\frac{S}{U} cannot be evaluated. Statement (2) is insufficient.
4
Evaluate Statements (1) and (2) combined.
Substitute S=60S = 60 into S+U=150S + U = 150 to get 60+U=15060 + U = 150, so U=90U = 90. Thus, SU=6090=23\frac{S}{U} = \frac{60}{90} = \frac{2}{3}.
Combining both statements yields a single, definitive ratio value. Statements (1) and (2) together are sufficient.

Key Concept

Data Sufficiency evaluation for linear systems involving ratios and sums.
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Topics

Rates, Ratios, Percentages, and Applied Word Problems

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