1999 AMC 8 Problem 16

Attempt Problem 16 of the 1999 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1999 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

16.

Tori’s mathematics test had 7575 problems: 1010 arithmetic, 3030 algebra, and 3535 geometry problems. Although she answered 70%70\% of the arithmetic, 40%40\% of the algebra, and 60%60\% of the geometry problems correctly, she did not pass the test because she got less than 60%60\% of the problems right.
How many more problems would she have needed to answer correctly to earn a 60%60\% passing grade?
11
55
77
99
1111
Answer: B
Concepts:percentage
Small hint:
Compute Tori’s current correct answers by category
Big hint:
Compare that total with 60%60\% of 7575
Solution:
She answered 10⋅0.7=7 10 \cdot 0.7 = 7 arithmetic questions correctly. She answered 30⋅0.4=12 30 \cdot 0.4 = 12 algebra ones correctly. She also got 35⋅0.6=2135 \cdot 0.6 = 21 geometry questions correctly.
This means she got a total of 7+12+21=40 7 + 12 + 21 = 40 questions correct.
As such, in order to get a 60%,60\%, Tori must have answered 75⋅0.6=45 75 \cdot 0.6 = 45 questions correctly. This means that she would have needed to answer an additional 45−40=545 - 40 = 5 questions correctly.
Thus, B is the correct answer.
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