The average (arithmetic mean) weight of 5 crates is 250 pounds. The two lightest crates weight between 200 and 205...

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Princeton Review

The average (arithmetic mean) weight of 5 crates is 250 pounds. The two lightest crates weigh between 200 and 205 pounds each, inclusive, and the two heaviest crates weigh between 300 and 310 pounds each, inclusive. If the weight of the 5 crates is x pounds, then x is expressed by which of the following?

A. \(220 \le x \le 250\)
B. \(230 \le x \le 260\)
C. \(240 \le x \le 270\)
D. \(250 \le x \le 270\)
E. \(260 \le x \le 280\)

OA A

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Princeton Review

The average (arithmetic mean) weight of 5 crates is 250 pounds. The two lightest crates weigh between 200 and 205 pounds each, inclusive, and the two heaviest crates weigh between 300 and 310 pounds each, inclusive. If the weight of the 5 crates is x pounds, then x is expressed by which of the following?

A. \(220 \le x \le 250\)
B. \(230 \le x \le 260\)
C. \(240 \le x \le 270\)
D. \(250 \le x \le 270\)
E. \(260 \le x \le 280\)

OA A

(Note: The correct wording of the question should be: If the weight of the 5th crate is x pounds, then x is expressed by which of the following?”)

The total weight of the 5 crates is 250 x 5 = 1250 lbs. The minimum total weight of the two lightest crates and the two heaviest crates is 2 x 200 + 2 x 300 = 400 + 600 = 1000 lbs. The maximum total weight of the two lightest crates and the two heaviest crates is 2 x 205 + 2 x 310 = 410 + 620 = 1030 lbs. Therefore, the weight of the 5th crate must be between 1250 - 1000 = 250 lbs and 1250 - 1030 = 220 lbs, inclusive. That is, 220 ≤ x ≤ 250.

Answer: A