2011 AMC 10B Problem 2

Below is the professionally curated solution for Problem 2 of the 2011 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10B solutions, or check the answer key.

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Concepts:mean work backwards

Difficulty rating: 870

Josanna's test scores to date are $90, 80, 70, 60,$ and $85.$ Her goal is to raise her test average at least $3$ points with her next test. What is the minimum test score she would need to accomplish this goal?

$80$

$82$

$85$

$90$

$95$

Solution:

Her current average is $\dfrac{90+80+70+60+85}5 = 77,$ and the sum of her scores is $385.$ The desired average is then $80,$ so the sum of scores required is $80\cdot 6.$ Therefore, the answer is $80\cdot 6-385 = 95.$

Thus, the correct answer is E .

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