document.write( "Question 1125943: A set of 7 positive integers has a unique mode of 1, a mean of 5, and a median of 6. What is the largest possible value for any of the integers in the set. \n" ); document.write( "

Algebra.Com's Answer #742293 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "There is one error in the analysis of the problem by the other tutor, leading to the wrong answer to the question.

\n" ); document.write( "The mean of the 7 numbers is 5, so their sum is 35.
\n" ); document.write( "The median is 6, so the 4th number is 6; there are 3 numbers smaller than (or equal to) 6 and 3 larger than (or equal to) 6.
\n" ); document.write( "Since we want to find the largest possible value for the largest number, the smallest 3 numbers should all be 1.
\n" ); document.write( "So the first 4 numbers are 1, 1, 1, and 6. Their sum is 9, so the sum of the other 3 numbers must be 26.
\n" ); document.write( "Again since we want to find the largest possible value for the largest number, the first two of the three numbers larger than or equal to 6 should be as small as possible. Since the unique mode is 1 and there are 3 of them, we can only have one more 6.
\n" ); document.write( "So the first two numbers after the median are 6 and 7. The sum of the first 6 numbers is then 1+1+1+6+6+7=22, so the largest possible value for the largest number in the set is 35-22 = 13. \n" ); document.write( "

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