1950 AMC 12 Problem 17

Attempt Problem 17 of the 1950 AMC 12 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 1950 AMC 12 solutions, or check the answer key.

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17.

The formula which expresses the relationship between

x

and

y

as shown in the accompanying table is:

\begin{array}{|c|c|c|c|c|c|} \hline x&0&1&2&3&4\\ \hline y&100&90&70&40&0\\ \hline \end{array}

y=100-10x

y=100-5x^2

y=100-5x-5x^2

y=20-x-x^2

None of these

Substitute a small nonzero table value such as

x=1

into each proposed formula

Then verify the surviving formula with

x=2

x=3

x=1,

choices A and C both give

90,

while B gives

95

and D gives

18.

Testing the two survivors at

x=2,

choice A gives

80,

whereas choice C gives

100-5(2)-5(2^2)=70,

matching the table.

Thus, the correct answer is C.

Problem 17 in other years