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2010 UNCO Math Contest II Problems/Problem 7

Revision as of 15:18, 19 October 2014 by Timneh (talk | contribs) (Created page with "== Problem == <math>P</math> and <math>Q</math> are each <math>2</math>-digit <math>\underline{prime}</math> numbers (like <math>73</math> and <math>19</math>), and all four dig...")
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Problem

$P$ and $Q$ are each $2$-digit $\underline{prime}$ numbers (like $73$ and $19$), and all four digits are different. The sum $P+Q$ is a $2$-digit number made up of two more different digits ($P+Q$ is not necessarily prime). Further, the difference $P-Q$ consists of yet two more different digits (again, $P-Q$ is not necessarily prime). The number $R$ is a two digit $\underline{prime}$ number which uses the remaining two digits. What is $R$?


Solution

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