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Math Expert V
Joined: 02 Sep 2009
Posts: 59623
On Monday, a person mailed 8 packages weighing an average  [#permalink]

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5
17 00:00

Difficulty:   5% (low)

Question Stats: 87% (01:56) correct 13% (02:40) wrong based on 1436 sessions

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

Practice Questions
Question: 16
Page: 154
Difficulty: 600

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Math Expert V
Joined: 02 Sep 2009
Posts: 59623
Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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

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 $$\frac{total \ weight}{# \ of \ packages}=\frac{99+61}{12}=13\frac{1}{3}$$.

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

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8
1
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 $$13\frac{1}{4}$$.

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##### General Discussion
Manager  Joined: 30 Sep 2009
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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a person mailed 8 packages=99 pounds (total of all 8 packages)

and on Tuesday, 4 packages=61 pounds (total of all 4 packages)

total weight =99+61 =160 pounds

the average weight =160/(8+4) =option a
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Bunuel wrote:
RESERVED FOR A SOLUTION.

Bunuel, had an off-topic request for you: Could you please post questions from non-OG sources as well? I'm not sure if that might breach a copyright arrangement bsaed on the source you use, and of course your comments on other's questions are supremely valuable for those of us subscribed to your daily updates - but if you could include occasional 700+ non-OG questions, would be much appreciated by your "followers" Intern  Joined: 03 Sep 2012
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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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 !
Math Expert V
Joined: 02 Sep 2009
Posts: 59623
Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Gmbrox wrote:
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 !

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 $$1\frac{1}{2}=\frac{3}{2}$$).
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Thank you a lot bunuel, Ok after reviewing the official book, i now got it, it is a mix number, it does not exists in france so that's why. If anyone has difficulties to understand like me :

12(3/8) = 12+3/8 and not 12x(3/8).

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

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I used weighted-averages to solve this as follows:

Let 12.375 be the lowest weight, therefore, (15.25 - 12.375) = 2.875, the difference in weights between the light and heavy packages.

Hence, the amount we need to add to 12.375 is:

(8x0 + 4x2.875)/(8+12) = 11.50 / 12 ~ 12/12 = 1 (Need to round final answer down a bit since I rounded numerator up)

Therefore, the average weight of all packages is approximately 12.375 + 1 = 13.375, since I need to round the numerator down, ans = 13.333, or A
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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2
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
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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2
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 $$= \frac{96 + 60 + 4}{12} = 8 + 5 + \frac{4}{12} = 13\frac{1}{3}$$

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

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Bunuel wrote:
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) $$16\frac{1}{2}$$

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

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

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The total weight of packages on Monday = 12 $$\frac{3}{8}$$ * 8 = 99 pounds

The total weight of packages on tuesday = 15 $$\frac{1}{4}$$ * 4 = 61 pounds

Average = Total weight / Number of packages = $$\frac{(99+61)}{12}$$ = 13 $$\frac{1}{3}$$ pounds
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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(2*12 3/8)+(1*15 1/4)=40 pounds
40/3=13 1/3 pounds average
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Joined: 12 Aug 2015
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GRE 1: Q169 V154 On Monday, a person mailed 8 packages weighing an average  [#permalink]

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This Question is giving us mean of two data and asking us for the combined average.

Using $$Mean = Sum/#$$

Sum(8) = $$\frac{99}{8}*8=99$$
Sum(4)=$$\frac{61}{4}*4=61$$

Hence combined average =$$\frac{99+61}{12}= \frac{40}{3}$$
Hence A

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GMAT 1: 580 Q36 V32 GMAT 2: 660 Q39 V41 GRE 1: Q159 V160 Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Using the weighted average formula =
weight of x (x) + weight of y (y) = weight of x and y (x+y)

In this situation, x =8, weighting of x = 12 3/8; y = 4, weighting of y = 15 1/4

substitute in the formula to find
99 + 61 = weight of x and y (8 +4)
99 + 61 = weight of x and y (12)
(99+61)/12 = weight of x and y
= 13 1/3
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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Bunuel wrote:
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) $$16\frac{1}{2}$$

Practice Questions
Question: 16
Page: 154
Difficulty: 600

This is how i solved

the ratio of Packets on Mon : Tuesday = 8 : 4

avg of monday = 12 3/8 or 99/8 and Tuesday = 15 1/4 or 61 /4

We have a formula for weighted avg ie

8 /12 * 99/8 + 4/12 * 61 /4

=99 /12 + 61 /12 = 160 /12 = 13 1/3 ans choice A
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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I know this question without this fraction and I’m complete lost WHERE this fraction come frommm?
On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of pounds, and on Tuesday, 4 packages weighing an average of 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

I could find the result of entire number but I still don’t get where this fraction come from!
I have to use the weighted average calculation right?

Posted from my mobile device
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On Monday, a person mailed 8 packages weighing an average  [#permalink]

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I think the fastest approach is to combine the balancing method and approximation.

You have 4 packages with weight of 15 pounds - approximately - and 4 packages with weight of 12 - approximately - pounds. The average of the two weights is (15+12)/2=13.5 {you will get the same if you calculate (4*15+4*12)/8 }

But then, you still have 4 packages with weight close to 12 pounds so the average will be definitely less than 13.5. Only A fits.

Originally posted by rencsee on 05 Dec 2019, 09:23.
Last edited by rencsee on 05 Dec 2019, 10:14, edited 1 time in total.
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Re: On Monday, a person mailed 8 packages weighing an average  [#permalink]

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letsamf wrote:
I know this question without this fraction and I’m complete lost WHERE this fraction come frommm?
On Monday, a person mailed 8 packages weighing an average (arithmetic mean) of pounds, and on Tuesday, 4 packages weighing an average of 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

I could find the result of entire number but I still don’t get where this fraction come from!
I have to use the weighted average calculation right?

Posted from my mobile device

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.
Attachments 4D1A0A49-DC08-4EFE-8ABD-AA1797E92D1F.jpeg [ 2.45 MiB | Viewed 126 times ] Re: On Monday, a person mailed 8 packages weighing an average   [#permalink] 05 Dec 2019, 10:10
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