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Algebra Difficulty 3.3 AMC 10/12 Find the answer

In the table shown, the formula relating x and y is:
x12345y37132131\begin{array}{|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5\\ \hline y & 3 & 7 & 13 & 21 & 31\\ \hline\end{array}

Pick one

Solution

A simple method of solving the problem is trying each of the answer choices.
One can plug in values of x and y for each, because many x-values and their single corresponding y-values are given.

Choice A works for (1,3) and (2,7) but fails to work on (3,13) because 3*4=12 and 12-1=11, not 13.
Choice B doesn't work for (2,7) because it would be 8-4+2+2=8, not 7.
Choice C actually works for all five pairs, being 1+1+1=3, 4+2+1=7, 9+3+1=13, 16+4+1=21, and 25+5+1=31.
Thus, the answer is (C)\boxed{\bf{(C)}}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.