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# The average (arithmetic mean) weight of 5 crates is 250 pou

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The average (arithmetic mean) weight of 5 crates is 250 pou [#permalink]  05 Jun 2017, 02:18
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The average (arithmetic mean) weight of 5 crates is 250 pounds. The 2 lightest crates weigh between 200 and 205 pounds each, inclusive, and the 2 heaviest crates weigh between 300 and 310 pounds each, inclusive. If the weight of the fifth crate is x pounds, then x is expressed by which of the following?

A) 220 ≤ x ≤ 250

B) 230 ≤ x ≤ 260

C) 240 ≤ x ≤ 270

D) 250 ≤ x ≤ 270

E) 260 ≤ x ≤ 280
[Reveal] Spoiler: OA

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Re: The average (arithmetic mean) weight of 5 crates is 250 pou [#permalink]  11 Oct 2017, 05:17
We need to find an interval, thus we can proceed by first computing the sum of the crates weights as mean times number, i.e. 250*5 = 1250.

Now, we can derive x at the two extremes, i.e. when the lightest and heaviest crates have the higher weight and when they have the smaller weight.

In the first case, x = 1250-2*200-2*300= 250. This is the highest value of x because we have taken the minimum weight for the other crates.
In the second one, x = 1250-2*205-2*310= 220. This is the lowest value of x.

Thus the interval is 220-250. Answer A
Re: The average (arithmetic mean) weight of 5 crates is 250 pou   [#permalink] 11 Oct 2017, 05:17
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