Difference between revisions of "1951 AHSME Problems/Problem 41"
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| + | ==Problem== | ||
| + | |||
| + | The formula expressing the relationship between <math>x</math> and <math>y</math> in the table is: | ||
| + | <cmath> \begin{tabular}{|c|c|c|c|c|c|}\hline x & 2 & 3 & 4 & 5 & 6\\ \hline y & 0 & 2 & 6 & 12 & 20\\ \hline\end{tabular} </cmath> | ||
| + | |||
| + | <math> \textbf{(A)}\ y = 2x-4\qquad\textbf{(B)}\ y = x^{2}-3x+2\qquad\textbf{(C)}\ y = x^{3}-3x^{2}+2x</math> | ||
| + | <math> \textbf{(D)}\ y = x^{2}-4x\qquad\textbf{(E)}\ y = x^{2}-4 </math> | ||
| + | |||
| + | ==Solution== | ||
| + | Just plug the <math>x,y</math> pair <math>(6,20)</math> into each of the 5 answer choices: | ||
| + | |||
| + | (A): <math>2(6)-4=8\ne20</math> | ||
| + | |||
| + | (B): <math>6^2-3(6)+2=20</math> | ||
| + | |||
| + | (C): <math>6^3-3(6^2)+2(6)=120\ne20</math> | ||
| + | |||
| + | (D): <math>6^2-4(6)=12\ne20</math> | ||
| + | |||
| + | (E): <math>6^2-4=32\ne20</math> | ||
| + | |||
| + | The only one that works is <math>\boxed{\textbf{(B)}}</math>. | ||
| + | |||
== See Also == | == See Also == | ||
{{AHSME 50p box|year=1951|num-b=40|num-a=42}} | {{AHSME 50p box|year=1951|num-b=40|num-a=42}} | ||
Latest revision as of 10:14, 19 April 2014
Problem
The formula expressing the relationship between 
and 
in the table is:
![\[\begin{tabular}{|c|c|c|c|c|c|}\hline x & 2 & 3 & 4 & 5 & 6\\ \hline y & 0 & 2 & 6 & 12 & 20\\ \hline\end{tabular}\]](http://latex.artofproblemsolving.com/8/a/5/8a58f83b5a41d890678d7b79e2498967c3a40ec5.png)
Solution
Just plug the 
pair 
into each of the 5 answer choices:
(A): 
(B): 
(C): 
(D): 
(E): 
The only one that works is 
.
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 40 |
Followed by Problem 42 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
