document.write( "Question 1119714: A person applying for the position of college registrar submitted the following report to the college president on 101 students: 31 take math, 28 take chemistry; 42 take psychology; 9 take math and chemistry; 10 take chemistry and psychology; 6 take math and psychology; 4 take all three subjects; and 20 take none of these courses. What is wrong with this scenario? \n" ); document.write( "

Algebra.Com's Answer #735323 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "If the data is correct, then the following identity must be in place:\r\n" );
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document.write( "    M + C + P - MC - CP - MP + MCP + 20 = 101.     (1)    <<<---=== It is the GLOBAL balance equation \r\n" );
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document.write( "(where M = 31, C = 28, P = 42, 9 = MC, 10 = CP, 6 = MP, 4 = MCP, with obvious abbreviations).\r\n" );
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document.write( "But if you substitute the values into the formula (1), your left side will be 100; not 101.\r\n" );
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document.write( "It means that the data is FALSE.\r\n" );
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document.write( "But this check does not give the answer which part is wrong.\r\n" );
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document.write( "Everything might be wrong.\r\n" );
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document.write( "But the minimal correction is to assume that the number 20 is wrong.\r\n" );
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document.write( "If to replace it with 21 (instead of 20), the balance will be correct.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you are interested to learn more on the subject, read these two lessons\r
\n" ); document.write( "\n" ); document.write( " - Counting elements in sub-sets of a given finite set\r
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