On Monday, a person mailed 8 packages weighing an average (arithmetic

Question

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

(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}

EvaJager · Accepted Answer

Since the final average cannot be greater than  15\frac{1}{4} , answers C, D and E are out.

We can use the property of weighted averages.
 15\frac{1}{4}=15\frac{2}{8} , the distance between the two initial averages is almost 3.
Since the number of packages are in a ratio of 8:4 = 2:1, the differences between the final average and the initial averages are in a ratio 1:2.
So, the distance between  12\frac{3}{8}  and the final average is almost 1, close to  12\frac{3}{8}+1\approx{13}\frac{1}{4} .
The final answer should be close to  13\frac{1}{4} .

Answer A.

Bunuel · Answer

SOLUTION

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

(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}

The total weight of 8 packages is  8*12\frac{3}{8}=99  pounds;

The total weight of 4 packages is  4*15\frac{1}{4}=61  pounds;

The average weight of all 12 packages is  \frac{total \ weight}{# \ of \ packages}=\frac{99+61}{12}=13\frac{1}{3} .

Answer: A.

Gmbrox · Answer

There must be something easy that i just don't get for me : 
8*12(3/8) = 36 as you simplify the 8 between them. Therefore how do you manage to arrive at 99?

I guess it must be something different of spelling or something?

Thanks a lot for your help !

Bunuel · Answer

It's not 12 multiplied by 3/8. it's  12\frac{3}{8}=\frac{12*8+3}{8}=\frac{99}{8}  (the same way as  1\frac{1}{2}=\frac{3}{2} ).

AnsQ · Answer

I used ratio of packages, which is 2:1.
converted both to the same fractions, so
15 1/4 = 15 2/8

2x(12 3/8) + 1x( 15 2/8) = 24+15+ 6/8+2/8 = 39 and 8/8, 8/8 is also obviously 1. Could also be together 40 but that's not easily divisible with three and you know you're left with a remainder. Instead just:
39/3 + 1/3 = 13 and 1/3

PareshGmat · Answer

Total weight on Monday  = 8*12 + 8 * \frac{3}{8} = 96 + 3

Total weight on Tuesday  = 4*15 + 4 * \frac{1}{4} = 60 + 1

Average of all days  = \frac{96 + 60 + 4}{12} = 8 + 5 + \frac{4}{12} = 13\frac{1}{3}

Answer = A

JeffTargetTestPrep · Answer

Solution:

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:

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

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

Sum of second day's packages = 4 x 15 ¼ = 61

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

rencsee · Answer

Hey,

You need to know the common fractions in and out. Haven’t found the original post but pls see attached a picture from my notes. A lot of question will translate easy when you know the fractions and their decimal equivalent and reversely as well.

TheUltimateWinner · Answer

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.

totaltestprepNick · Answer

A https://www.youtube.com/watch?v=OOFxd7c3t_A Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience tutoring@totaltestprep.net

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