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| − | ==Problem==
| + | #REDIRECT [[2021_Fall_AMC_12B_Problems/Problem_3]] |
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| − | At noon on a certain day, Minneapolis is <math>N</math> degrees warmer than St. Louis. At <math>4{:}00</math> the temperature in Minneapolis has fallen by <math>5</math> degrees while the temperature in St. Louis has risen by <math>3</math> degrees, at which time the temperatures in the two cities differ by <math>2</math> degrees. What is the product of all possible values of <math>N?</math>
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| − | <math>(\textbf{A})\: 10\qquad(\textbf{B}) \: 30\qquad(\textbf{C}) \: 60\qquad(\textbf{D}) \: 100\qquad(\textbf{E}) \: 120</math>
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| − | ==Solution 1==
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| − | Let the temperature of Minneapolis at noon be <math>M</math> and let the temperature of St. Louis at noon be <math>S</math>. Then <math>M = N + S</math> and <math>|(M-5)-(S+3)| = 2 \implies |M-S-8| = |2|</math>.
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| − | Substituting <math>M</math> into the second equation we have <math>|N - 8| = 2 \implies N = 10, 6</math>.
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| − | The product of all possible values of N is therefore <math>10\cdot6=60=\boxed{C}</math>
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| − | ~KingRavi
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| − | == Solution 2 ==
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| − | <cmath>
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| − | \begin{align*}
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| − | | N - 5 - 3 | = 2 .
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| − | \end{align*}
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| − | </cmath>
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| − | Hence, <math>N = 10</math> or 6.
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| − | Therefore, the answer is <math>\boxed{\textbf{(C) }60}</math>.
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| − | ~Steven Chen (www.professorchenedu.com)
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| − | ==Video Solution by Interstigation==
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| − | https://youtu.be/p9_RH4s-kBA?t=291
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| − | ==See Also==
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| − | {{AMC10 box|year=2021 Fall|ab=B|num-a=5|num-b=3}}
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| − | {{MAA Notice}}
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