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# A team scored an average (arithmetic mean) of a points for the first x

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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22 Aug 2018, 00:09
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Difficulty:

45% (medium)

Question Stats:

79% (01:43) correct 21% (02:20) wrong based on 42 sessions

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A team scored an average (arithmetic mean) of a points for the first x games of the season, and it scored an average of b points for all y games of the season, where a, b, x, and y are integers and y > x > 0. What was the team's average score for the games played after the first x games?

A. (by-ax)/(y-x)

B. (ax+by)/(x+y)

C. (ax+by)/(2y)

D. (by-ax)/(x+y)

E. y/b - x/a

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Re: A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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22 Aug 2018, 00:14
The number of games played after the x games is y-x.

Only option A has the denominator as y-x.

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WE: Supply Chain Management (Energy and Utilities)
Re: A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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22 Aug 2018, 00:20
Bunuel wrote:
A team scored an average (arithmetic mean) of a points for the first x games of the season, and it scored an average of b points for all y games of the season, where a, b, x, and y are integers and y > x > 0. What was the team's average score for the games played after the first x games?

A. (by-ax)/(y-x)

B. (ax+by)/(x+y)

C. (ax+by)/(2y)

D. (by-ax)/(x+y)

E. y/b - x/a

Sum of points scored in the 1st 'x' games=Avg of a games * 'a' no of games=ay
Total sum of points=Avg of y games * y no of games=by
So, sum of points scored after x games = by-ax
# of games played after x games = y-x
Average = Sum of points scored after x games/Total no of games after x games=$$\frac{(by-ax)}{(y-x)}$$

Ans. (A)
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Re: A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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22 Aug 2018, 00:24

Solution

Given:
• A team scored an average (arithmetic mean) of ‘a’ points for the first x games of the season.
• It scored an average of ‘b’ points for all y games of the season.
• Also, a, b, x, and y are integers and y > x > 0.

To find:
• The team's average score for the games played after the first x games.

Approach and Working:
Average score in the first x games is ‘a’.
• Hence, total score in the first x games = ax

Average score in all y games is ‘b’.
• Hence, total score in all y games = by

• Therefore, total score in the last (y – x) games = by – ax
• Hence, average in the last (y – x) games = (by – ax)/(y – x)

Hence, the correct answer is option A.

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Re: A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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23 Aug 2018, 21:24
EgmatQuantExpert wrote:

Solution

Given:
• A team scored an average (arithmetic mean) of ‘a’ points for the first x games of the season.
• It scored an average of ‘b’ points for all y games of the season.
• Also, a, b, x, and y are integers and y > x > 0.

To find:
• The team's average score for the games played after the first x games.

Approach and Working:
Average score in the first x games is ‘a’.
• Hence, total score in the first x games = ax

Average score in all y games is ‘b’.
• Hence, total score in all y games = by

• Therefore, total score in the last (y – x) games = by – ax
• Hence, average in the last (y – x) games = (by – ax)/(y – x)

Hence, the correct answer is option A.

Hi EgmatQuantExpert,

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Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: A team scored an average (arithmetic mean) of a points for the first x  [#permalink]

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23 Aug 2018, 21:54
Bunuel wrote:
A team scored an average (arithmetic mean) of a points for the first x games of the season, and it scored an average of b points for all y games of the season, where a, b, x, and y are integers and y > x > 0. What was the team's average score for the games played after the first x games?

A. (by-ax)/(y-x)

B. (ax+by)/(x+y)

C. (ax+by)/(2y)

D. (by-ax)/(x+y)

E. y/b - x/a

It's a weighted average problem. Use Avg = (C1*w1 + C2*w2)/(w1 + w2)
Let U be the average of (y - x) games.

b = [ax + U(y - x)]/y

U = (by - ax)/(y - x)

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Re: A team scored an average (arithmetic mean) of a points for the first x &nbs [#permalink] 23 Aug 2018, 21:54
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