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The average (arithmetic mean) of 100 measurements is 23,

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Carcass
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The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   23 Jan 2017, 08:44
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The average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27.

Quantity A
Quantity B
The average of the 150 measurements
25


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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B
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sandy
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   26 Jan 2017, 18:15
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Explanation

When the average of 100 measurements is 23, find the sum:

sum of 100 numbers/100 = 23 or sum of 100 numbers = 2300.

When the average of 50 measurements is 27, find the sum:

sum of 50 numbers/50 = 27 or sum of 50 numbers = \(50 \times 27\)=1350.

Total of 150 numbers = \(2300 + 1350\)= \(3650\).

Average of 150 number =\(\frac{3650}{150}\)=\(24.55\).

Clearly quantity B is greater. Hence option B is correct.
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   17 Sep 2017, 05:01
sandy wrote:
Explanation

When the average of 50 measurements is 27, find the sum:

sum of 50 numbers/50 = 27 or sum of 50 numbers = \(50 \times 50\)=1350.


It should be \(50 \times 27\)=1350
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   17 Sep 2017, 05:39
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IlCreatore wrote:
sandy wrote:
Explanation

When the average of 50 measurements is 27, find the sum:

sum of 50 numbers/50 = 27 or sum of 50 numbers = \(50 \times 50\)=1350.


It should be \(50 \times 27\)=1350


Yup, Fixed it!
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   25 Oct 2017, 16:17
I think this question sucks. I would have gotten a 19/20 if it werent for this question. Doesn't ADDITIONAL 50 measurements making it 27, I thought this wording meant they added 50 measurements to 100, so that 150 = mean of 27. I was thinking they could also be saying just a different 50 measurements the mean was 27 but it said ADDITIONAL....
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   29 Apr 2018, 19:34
I got confused because of this word "ADDITIONAL" it made me calculate the next average as 27= X/150 !
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   13 Oct 2018, 21:01
option B
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   18 Mar 2021, 15:52
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You can think about it in terms of weight. Since the two averages are equal distance from the 25, the 100's average will have more weight than the 50's. average and will pull the average of the 150 numbers to the left.
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   18 Mar 2021, 22:03
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Carcass wrote:

The average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27.

Quantity A
Quantity B
The average of the 150 measurements
25


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Col. A: \(\frac{(100)(23) + (50)(27)}{(100 + 50)} = \frac{3650}{150} = 24.33\)

Col. B: \(25\)

Hence, option B
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   23 Apr 2021, 10:20
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Carcass wrote:

This question is a part of PowerPrep Question Collection



The average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27.

Quantity A
Quantity B
The average of the 150 measurements
25



One approach here is to use weighted averages

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

Let group A be the 100 measurements with an average of 23
Let group B be the 50 measurements with an average of 27

We get:
Weighted average of groups combined = (100/150)(23) + (50/150)(27)
= (2/3)(23) + (1/3)(27)
= 46/3 + 27/3
= 73/3
= 24 1/3

So we get:
QUANTITY A: 24 1/3
QUANTITY B: 25

Answer: B
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink] New post   07 Jul 2022, 09:30
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Carcass wrote:

This question is a part of PowerPrep Question Collection



The average (arithmetic mean) of 100 measurements is 23, and the average of 50 additional measurements is 27.

Quantity A
Quantity B
The average of the 150 measurements
25


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



Solution:

We are given that the average of 100 measurements is 23, and the average of 50 additional measurements is 27.

We need to determine whether The average of the 150 measurements (Quantity A) is greater than 25.

We can create a weighted average:

(100 x 23 + 50 x 27)/150 = (2,300 + 1,350)/150 = 3,650/150 = 24.33

Since 25 > 24.33, we see that Quantity B is greater than Quantity A.

Answer: B
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Re: The average (arithmetic mean) of 100 measurements is 23, [#permalink]
07 Jul 2022, 09:30
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