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The average (arithmetic mean) weight of the three male members of the

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The average (arithmetic mean) weight of the three male members of the  [#permalink]

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The average (arithmetic mean) weight of the three male members of the Basie High School wrestling team is 280 pounds. After four female wrestlers join the team, the average weight of the team is decreased by one seventh. What is the average weight of a female wrestler?

A. 280
B. 270
C. 240
D. 210
E. 140

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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 02:50
Bunuel wrote:
The average (arithmetic mean) weight of the three male members of the Basie High School wrestling team is 280 pounds. After four female wrestlers join the team, the average weight of the team is decreased by one seventh. What is the average weight of a female wrestler?

A. 280
B. 270
C. 240
D. 210
E. 140


Option D 210

The weight of the three male members is 280 X 3 = 840

the total weight after addition of the females is 240 x 7= 1680 ( After deducting 1/7th of 280, ie, 40)

hence, the weight of females is 1680- 840= 840

therefore, average is 210.
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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 04:01
Don't you think the question lacks clarity.

What is the average weight of a female wrestler /wrestlers?

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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 04:13
Weighted averages
Let the average weight of 4 females be Y kgs
(280*3 + y*4)/ 7 = 240

Y=210 kgs


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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 04:35
Bunuel wrote:
The average (arithmetic mean) weight of the three male members of the Basie High School wrestling team is 280 pounds. After four female wrestlers join the team, the average weight of the team is decreased by one seventh. What is the average weight of a female wrestler?

A. 280
B. 270
C. 240
D. 210
E. 140


One seventh of 280 is 40 so average goes down by 40 to 240. Now just use weighted average:

3/4 = (Wg - 240) / (240 - 280)
Wg = 210

Answer (D)
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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 05:10
Bunuel wrote:
The average (arithmetic mean) weight of the three male members of the Basie High School wrestling team is 280 pounds. After four female wrestlers join the team, the average weight of the team is decreased by one seventh. What is the average weight of a female wrestler?

A. 280
B. 270
C. 240
D. 210
E. 140


\(Average = \frac{Total.Weight}{People}\), Average of three males: \(280 = \frac{Total.Weight}{3}\) and the Total Weight of three males: \(280*3=840\)

Average of three males and four females: \((1-1/7)*280=240\), Total Weight of all team: \(240*7=1680\)

\(Average.Females = \frac{(Total.Weight.Team - Total.Weight.Males)}{Females}\); \(Average.Females: \frac{(1680-840)}{4}=210\)

(D) is the answer.
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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 06:00
Let the female avg be f
(840+4f)/7=(280-40)
f=210


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Re: The average (arithmetic mean) weight of the three male members of the  [#permalink]

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New post 20 Dec 2017, 09:01
Bunuel wrote:
The average (arithmetic mean) weight of the three male members of the Basie High School wrestling team is 280 pounds. After four female wrestlers join the team, the average weight of the team is decreased by one seventh. What is the average weight of a female wrestler?

A. 280
B. 270
C. 240
D. 210
E. 140


Try Plugging In the answer choices:

Start with centre (C) = 240 (average wt. of female wrestler

So, (280 x 3 + 240 x 4)/7 = 1800/7 = 257. 14 approx; say 257

Now 280 - 257 = 23

but 23 is not 1/7th of 280 So eliminate

As 1/7th of 280 is 40, we need a smaller number to increase the difference from 23 to 40.

Try (D) 210,


So, (280 x 3 + 210 x 4)/7 = 1680/7 = 240

280 - 240 = 40, and 40 is 1/7th of 280

So answer (D)
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Re: The average (arithmetic mean) weight of the three male members of the &nbs [#permalink] 20 Dec 2017, 09:01
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