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Question 76
Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is
Solution
Given
A+(B+C)/2=5 => 2A+B+C=10....(i)
(A+C)/2 +B=7 => A+2B+C=14.....(ii)
(i)-(ii)=> B-A=4 => B=4+A.
Given, A, B, C are positive integers
If A=1=>B=5 => C=3
If A=2=>B=6 => C=0 but this is invalid as C is positive.
Similarly if A>2 C will be negative and cases are not valid.
Hence, A+B=6.
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