112 lines
6.6 KiB
HTML
112 lines
6.6 KiB
HTML
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<h2>Luxury Hampers</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 236</h3><span style="width:300px;color:#666;">Published on Saturday, 14th March 2009, 09:00 am; Solved by 586</span></div>
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table.p236, table.p236 th, table.p236 td {
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table.p236 th { background-color: rgb(193,218,249); }
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table.p236 td { background-color: rgb(255,255,255); }
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</style>
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<p>Suppliers 'A' and 'B' provided the following numbers of products for the luxury hamper market:</p>
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<p><center><table class="p236">
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<tr><th>Product</th><th style="text-align:center">'A'</th><th style="text-align:center">'B'</th></tr>
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<tr><td>Beluga Caviar</td><td>5248</td><td>640</td></tr>
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<tr><td>Christmas Cake</td><td>1312</td><td>1888</td></tr>
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<tr><td>Gammon Joint</td><td>2624</td><td>3776</td></tr>
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<tr><td>Vintage Port</td><td>5760</td><td>3776</td></tr>
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<tr><td>Champagne Truffles</td><td>3936</td><td>5664</td></tr>
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</table></center></p>
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<p>Although the suppliers try very hard to ship their goods in perfect condition, there is inevitably some spoilage - <i>i.e.</i> products gone bad.</p>
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<p>The suppliers compare their performance using two types of statistic:<ul>
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<li>The five <i>per-product spoilage rates</i> for each supplier are equal to the number of products gone bad divided by the number of products supplied, for each of the five products in turn.</li>
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<li>The <i>overall spoilage rate</i> for each supplier is equal to the total number of products gone bad divided by the total number of products provided by that supplier.</li></ul>
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</p>
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<p>To their surprise, the suppliers found that each of the five per-product spoilage rates was worse (higher) for 'B' than for 'A' by the same factor (ratio of spoilage rates), <var>m</var>>1; and yet, paradoxically, the overall spoilage rate was worse for 'A' than for 'B', also by a factor of <var>m</var>.</p>
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<p>There are thirty-five <var>m</var><img src='images/symbol_gt.gif' width='10' height='10' alt='>' border='0' style='vertical-align:middle;' />1 for which this surprising result could have occurred, the smallest of which is 1476/1475.</p>
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<p>What's the largest possible value of <var>m</var>?<br />
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Give your answer as a fraction reduced to its lowest terms, in the form <var>u</var>/<var>v</var>.</p>
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