M07-07

Question

After 6 games, Team A had an average (arithmetic mean) of 61.5 points per game. If the team scored 47 points in the 7th game, how many more points does the team need to score in 8th game to surpass a total of 500 points?

A. 85
B. 84
C. 83
D. 74
E. 62

Show Answer

Official Answer

A

A. 85
B. 84
C. 83
D. 74
E. 62

Bunuel · Accepted Answer

Official Solution:

After 6 games, Team A had an average (arithmetic mean) of 61.5 points per game. If the team scored 47 points in the 7th game, how many more points does the team need to score in 8th game to surpass a total of 500 points?

A. 85
B. 84
C. 83
D. 74
E. 62

Show Answer

Official Answer

A

A. 85
B. 84
C. 83
D. 74
E. 62

After 6 games with an average of 61.5 points per game, Team B has accumulated:  61.5*6 = 369  points. Adding the 47 points from the 7th game gives:  369 + 47 = 416  points in total.
 
To surpass a total of 500 points, Team B needs to score at least:  501 - 416 = 85  points in the next game.

Answer: A

patto · Answer

I think this is a  high-quality  question and I agree with explanation. I liked the phrase at the end of the question. It's a good trick!!

AndrewN · Answer

Whenever an  average  or  arithmetic mean  problem comes up, and I have seen official questions in which the latter may not be defined, I find it useful to consider a basic way to derive an average: avg. = \frac{sum}{# items} 
That may seem obvious, but standardized tests are good at presenting such a simple concept in disguise. I came across a question on a different test that was something like the following:

In a certain rating system, a user may assign a value of 1-100, inclusive, to something. After 10 ratings, the average score for Acme Corp. was 85.0. What is the lowest possible score the business can receive on the 11th rating and still end up with a 90 average after 20 ratings?

Seems simple enough, but that 11th rating in particular can look daunting. How can we separate the 11th rating from, say, the 16th, or the 19th? If you have read the problem, you might want to figure it out before reading any further. Done? All right, then let us continue our discussion with a few key insights.

1) The question is still based on nothing more than finding an average.
 Key point : Make sure you know what the question is asking.

2) You have information on the first 10 ratings.
 Key point : See what you can figure out based on those ratings. Here, 85 = \frac{sum}{10} 
A little quick handiwork, similar to the process you can use to solve the above problem, yields  850 = sum

3) You can calculate the missing portion of the latter 10 ratings using the same basic  average  equation.
 Key point : Run the  average  equation again to figure out the "target" total.  90 = \frac{sum}{20} 
Once again, algebraic manipulation yields  90 * 20 = sum , or  1800 = sum

4) You can answer the question.
 Key point : If 1800 points are needed to earn an average of 90 after 20 ratings, and after 10 ratings, there are only 850 points, then another 1800 - 850, or 950 points are needed. Thus, from the latter 10 ratings, if all of them were ratings of 100  except for the lowest , then that would produce 9 * 100, or 900 points, and the 11th rating (or whatever arbitrary number the question asked about) could be as low as 50 to make up the rest.

Good luck with your studies.

- Andrew

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

bumpbot · Answer

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M07-07

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