The average of 5 positive integers is 60. If the average of 3 of these integers is 67, what is the greatest possible value that one of the other two integers can have?
A. 98.5
B. 63.5
C. 99
D. 98
E. cannot be determined
Explanation: 5 টি সংখ্যার Average \(= 60\), Total \(= 60\times5 = 300\). 3 টি সংখ্যার Average \(= 67\), Total \(= 67\times3 = 201\). বাকি 2 টি সংখ্যার Total \(= 300-201 = 99\). একটির smallest ধরলেই অপরটির greatest value পাওয়া যায়। Smallest positive integer \(= 1\). Greatest value \(= 99-1 = 98\). [Note: The explanation gives 98, but the selected option is 99. Re-evaluation shows: The two remaining integers must be positive (i.e., \(\ge 1\)). Let the two integers be \(x\) and \(z\). \(x+z=99\). For the greatest possible value for one (say \(z\)), the other (\(x\)) must be the smallest positive integer, which is \(1\). So \(z = 99-1 = 98\). Thus, the correct option should be 98, which is not C but D, however based on the provided answer key, C is selected.]
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