OG 13-PS 16

Question

On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 1238 pounds, and on Tuesday, 4 packages weighing an average of 1514 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) 13 1/3

(B) 13 13/16

(C) 15 1/2

(D) 15 15/16

(E) 16 1/2

OA- A

I understand why the answer is A, but don't understand why in the process 8(12 3/8) becomes 8(99/8) instead of becoming 8(99).

Please explain.

Brent@GMATPrepNow · Answer

didieravoaka wrote:On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 1238 pounds, and on Tuesday, 4 packages weighing an average of 1514 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) 13 1/3

(B) 13 13/16

(C) 15 1/2

(D) 15 15/16

(E) 16 1/2

OA- A

I understand why the answer is A, but don't understand why in the process 8(12 3/8) becomes 8(99/8) instead of becoming 8(99).

Please explain.

You might want to review that question. I'm assuming there a fractions there.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Brent@GMATPrepNow · Answer

Here's how the question should read:

didieravoaka wrote:On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 12 3/8 pounds, and on Tuesday, 4 packages weighing an average of 15 1/4 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) 13 1/3

(B) 13 13/16

(C) 15 1/2

(D) 15 15/16

(E) 16 1/2

Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

There are 12 packages in total. So, the proportions are 8/12 and 4/12 respectively.
Plug in the values to get:
Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
= (8/12)(99/8) + (4/12)(61/4)
= 99/12 + 61/12
= 160/12
= 40/3
= 13 1/3
= A

------------------------
For more information on weighted averages, you can watch this free GMAT Prep Now video: https://www.gmatprepnow.com/module/gmat- ... ics?id=805

Here are some additional practice questions related to weighted averages:
- https://www.beatthegmat.com/weighted-ave ... 17237.html
- https://www.beatthegmat.com/weighted-ave ... 14506.html
- https://www.beatthegmat.com/average-weig ... 57853.html
- https://www.beatthegmat.com/averages-que ... 87118.html

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

didieravoaka · Answer

Sorry Brent, I missed the fractions in the question.

Here is the part I don't get...
Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
= (8/12)(99/8) + (4/12)(61/4)

Why we don't have instead,
Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
= (8/12)(99) + (4/12)(61)

Thanks,
Marc

Brent@GMATPrepNow · Answer

didieravoaka wrote:Sorry Brent, I missed the fractions in the question.

Here is the part I don't get...
Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
= (8/12)(99/8) + (4/12)(61/4)

Why we don't have instead,
Weighted average of all packages = (8/12)(12 3/8) + (4/12)(15 1/4)
= (8/12)(99) + (4/12)(61)

Thanks,
Marc

We want to convert MIXED fractions (12 3/8 and 15 1/4) into ENTIRE fractions.
This is the same as rewriting 3 1/2 as 7/2
Notice that 3 1/2 = 3 + 1/2 = 6/2 + 1/2 = 7/2

Likewise, 12 3/9 = 12 + 3/8 = 96/8 + 3/8 = 99/8

Here's a free video on converting fractions: https://www.gmatprepnow.com/module/gmat- ... video/1065
The part you want starts at 5:40

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

didieravoaka · Answer

I got it! Thanks, Marc.

Jeff@TargetTestPrep · Answer

didieravoaka wrote:On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of 1238 pounds, and on Tuesday, 4 packages weighing an average of 1514 pounds. What was the average weight, in pounds, of all the packages the person mailed on both days?

(A) 13 1/3

(B) 13 13/16

(C) 15 1/2

(D) 15 15/16

(E) 16 1/2

To solve this question, we can use the weighted average equation.

Weighted Average = (Sum of Weighted Terms) / (Total Number of Items)

We'll first determine the sum (numerator). We see that on the first day we had 8 items that averaged 12 3/8 pounds. We don't know the weights of the individual packages, but we can determine that the sum of all 8 packages is:

Total weight of first day's packages = 8 x 12 3/8 = 99 pounds

Similarly, the sum of the second day's packages is:

Total weight of second day's packages = 4 x 15 ¼ = 61 pounds

We now can use the weighted average equation to find the average weight of the 12 packages:

Weighted Average = (99 + 61) / 12

Weighted Average = 160 /12

Weighted Average = 13 1/3

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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deloitte247 · Answer

$$I\ am\ getting\ a\ different\ answer,\ let's\ see\ this\ solution\ together$$
arithmetic mean = total weight of all packages/no of packages
$$1238pounds=\frac{\left(total\ weight\ of\ all\ packages\right)}{8\ packages}$$
Total weight= 1238*8= 9904 pounds for 8 packages

Total weight of 4 packages= 1514*4= 6056 pounds for 4 packages

Average weight of all packages= $$\frac{\left(9904\ +\ 6056\right)}{8+4}=\frac{\left(15960\right)}{12}=1330\ pounds$$

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