https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&feed=atom&action=history
1998 AHSME Problems/Problem 2 - Revision history
2024-03-28T16:29:46Z
Revision history for this page on the wiki
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https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&diff=56532&oldid=prev
Nathan wailes at 18:28, 5 July 2013
2013-07-05T18:28:37Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 18:28, 5 July 2013</td>
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Nathan wailes
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&diff=41266&oldid=prev
Talkinaway: /* Solution */
2011-08-08T20:47:34Z
<p><span dir="auto"><span class="autocomment">Solution</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:47, 8 August 2011</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If we want <math>\frac{A+B}{C+D}</math> to be as large as possible, we want to try to maximize the numerator <math>A+B</math> and minimize the denominator <math>C+D</math>.  Picking <math>A=9</math> and <math>B=8</math> will maximize the numerator, and picking <math>C=0</math> and <math>D=1</math> will minimize the denominator.   </div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>If we want <math>\frac{A+B}{C+D}</math> to be as large as possible, we want to try to maximize the numerator <math>A+B</math> and minimize the denominator <math>C+D</math>.  Picking <math>A=9</math> and <math>B=8</math> will maximize the numerator, and picking <math>C=0</math> and <math>D=1</math> will minimize the denominator.   </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Checking to make sure the fraction is an integer, <math>\frac{A+B}{C+<del class="diffchange diffchange-inline">S</del>} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>.</div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Checking to make sure the fraction is an integer, <math>\frac{A+B}{C+<ins class="diffchange diffchange-inline">D</ins>} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME box|year=1998|num-b=1|num-a=3}}</div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{AHSME box|year=1998|num-b=1|num-a=3}}</div></td></tr>
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Talkinaway
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&diff=41265&oldid=prev
Talkinaway at 20:47, 8 August 2011
2011-08-08T20:47:18Z
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<td colspan="2" style="background-color: #fff; color: #222; text-align: center;">Revision as of 20:47, 8 August 2011</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> \mathrm{(A) \  }13 \qquad \mathrm{(B) \  }14 \qquad \mathrm{(C) \  } 15\qquad \mathrm{(D) \  }16 \qquad \mathrm{(E) \  } 17 </math></div></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><math> \mathrm{(A) \  }13 \qquad \mathrm{(B) \  }14 \qquad \mathrm{(C) \  } 15\qquad \mathrm{(D) \  }16 \qquad \mathrm{(E) \  } 17 </math></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f8f9fa; color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">[[</del>1998 <del class="diffchange diffchange-inline">AHSME Problems/Problem 2</del>|<del class="diffchange diffchange-inline">Solution]]</del></div></td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">==Solution==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">If we want <math>\frac{A+B}{C+D}</math> to be as large as possible, we want to try to maximize the numerator <math>A+B</math> and minimize the denominator <math>C+D</math>.  Picking <math>A=9</math> and <math>B=8</math> will maximize the numerator, and picking <math>C=0</math> and <math>D=1</math> will minimize the denominator.  </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">Checking to make sure the fraction is an integer, <math>\frac{A+B}{C+S} = \frac{17}{1} = 17</math>, and so the values are correct, and <math>A+B = 17</math>, giving the answer <math>\boxed{E}</math>.</ins></div></td></tr>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">== See also ==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color: #222; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">{{AHSME box|year=</ins>1998|<ins class="diffchange diffchange-inline">num-b=1|num-a=3}}</ins></div></td></tr>
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Talkinaway
https://artofproblemsolving.com/wiki/index.php?title=1998_AHSME_Problems/Problem_2&diff=39333&oldid=prev
BOGTRO: Created page with "== Problem 2 == Letters <math>A,B,C,</math> and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integ..."
2011-06-06T19:51:24Z
<p>Created page with "== Problem 2 == Letters <math>A,B,C,</math> and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integ..."</p>
<p><b>New page</b></p><div>== Problem 2 ==<br />
Letters <math>A,B,C,</math> and <math>D</math> represent four different digits selected from <math>0,1,2,\ldots ,9.</math> If <math>(A+B)/(C+D)</math> is an integer that is as large as possible, what is the value of <math>A+B</math>?<br />
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<math> \mathrm{(A) \ }13 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ } 15\qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ } 17 </math><br />
<br />
[[1998 AHSME Problems/Problem 2|Solution]]</div>
BOGTRO