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On Monday, a person mailed 8 packages weighing an average

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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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New post 03 May 2020, 22:39
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On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of \(12\frac{3}{8}\) pounds, and on Tuesday, 4 packages weighing an average of \(15\frac{1}{4}\) pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) \(13\frac{1}{3}\)

(B) \(13\frac{13}{16}\)

(C) \(15\frac{1}{2}\)

(D) \(15\frac{15}{16}\)

(E) \(16\frac{1}{2}\)

We're going to make weighted average of \(12\frac{3}{8}\) (with 8 packages) and \(15\frac{1}{4}\) (4 packages). So, the correct answer must be between these two numbers. Choice C,D, and E are beyond of these two numbers, so they are out.
We're going to make the weighted average, but choice B is simply the ''regular'' average (\(12\frac{3}{8}\) + \(15\frac{1}{4}\))/2= \(13\frac{13}{16}\), which indicates choice B. So, B is out. Correct choice is A.
Hope it helps.
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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New post 28 May 2020, 09:41
Quote:
On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of \(12\frac{3}{8}\) pounds, and on Tuesday, 4 packages weighing an average of \(15\frac{1}{4}\) pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) \(13\frac{1}{3}\)

(B) \(13\frac{13}{16}\)

(C) \(15\frac{1}{2}\)

(D) \(15\frac{15}{16}\)

(E) \(16\frac{1}{2}\)


It's a weighted average question. So, the weight must be between \(12\frac{3}{8}\) and \(15\frac{1}{4}\) i.e. 99/8 and 122/8. It would be towards 99/8 as 8 packages are sent with that weight.

Only A and B are contenders and rest are eliminated.
As B is normal average of the two, A is the answer.

Bunuel There's Economist GMAT Tutor in this question. Can you please check.
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Re: On Monday, a person mailed 8 packages weighing an average   [#permalink] 28 May 2020, 09:41

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