document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982656>Question 982656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a quiz game of 20 questions, each correct answer earns 5 points. Each incorrect answer reduces the score by 2 points. Omitted questions scored 0 points. Jana has a total score of 59 points. How many questions did she omit? </SPAN>\n" );
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document.write( "A quick informal solution using logical reasoning and some simple mental arithmetic -- if a formal algebraic solution is not required.<br><BR>\n" );
document.write( "Each correct answer earns 5 points; the total points earned for the correct answers is a multiple of 5.<br><BR>\n" );
document.write( "Each incorrect answer loses 2 points; the total points lost for the correct answers is an even number.<br><BR>\n" );
document.write( "Jana's score was 59, an odd number.  That means the number of correct answers has to be odd, making the total for the correct answers an odd multiple of 5 -- that is, a number with units digit 5.<br><BR>\n" );
document.write( "So 59 has to be some even number less than a number with units digit 5.<br><BR>\n" );
document.write( "The first possibility is 59 = 65-6, which means 13 correct answers an 3 wrong answers.<br><BR>\n" );
document.write( "The next possibility is 59 = 75-16; but that requires far more than 20 questions on the test.<br><BR>\n" );
document.write( "ANSWER: 13 right, 3 wrong; that means 4 questions were unanswered.<br><BR>\n" );
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