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What is the average (arithmetic mean) mileage of 7 cars in a parking lot?

(1) If the 7 mileages were ordered from least to most, each would be 2.5 miles per gallon higher than the preceding car’s mileage.
(2) The range of the 7 mileages is 15 miles per gallon.
Explanation:

Let the mileage of the 7 cars be M1, M2, M3, M4, M5, M6, M7, such that M1 ≤ M2 ≤ M3 ≤ M4 ≤ M5 ≤ M6 ≤ M7.
Average mileage of 7 cars = (M1 + M2 + M3 + M4 + M5 + M6 + M7)/7.
We need to find whether the value “(M1 + M2 + M3 + M4 + M5 + M6 + M7)/7” can be determined.

Statement (1)

M1 = M1
M2 = M1 + 2.5
M3 = M1 + 2(2.5)
M4 = M1 + 3(2.5)
M5 = M1 + 4(2.5)
M6 = M1 + 5(2.5)
M7 = M1 + 6(2.5)

Average mileage of 7 cars
= (M1 + M2 + M3 + M4 + M5 + M6 + M7)/7
= [7(M1) + 28(2.5)]/7
= M1 + 10 (Equation I)

No information regarding the exact value of M1 is provided.

It is NOT possible to determine with certainty the average mileage of the 7 cars. Hence, Statement (1) is insufficient.

Statement (2)

M7 – M1 = 15 (Equation II)
No information regarding any of the mileage values is provided.

It is NOT possible to determine with certainty the average mileage of the 7 cars. Hence, Statement (2) is insufficient.

As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.

Statement (1) and Statement (2) combined

In order to determine the value of average mileage from Equation I, we need to find the exact value of M1.
Equation II does not provide any information that can be used to find the exact value of M1.

It is NOT possible to determine with certainty the average mileage of the 7 cars. Hence, Statement (1) and Statement (2) combined are insufficient.

E is the correct answer choice.
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