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Question 8 : 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

1. 6
2. 4
3. 7
4. 5

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### Explanatory Answer

a + $$frac{b + c}{2}$ = 5 ---> 2a + b + c = 10 b + $\frac{a + c}{2}$ = 7 ---> 2b + a + c = 14 Solving these two, we get b – a = 4 b = a + 4 Substituting this in the first equation 2a + a + 4 + c = 10 3a + c = 6 Given all three as positive integers, maximum value we can get for a = 1 Ex: When substituting a = 2, c = 0$Not possible)
So a = 1, then b = 5
Sum of a + b = 6

The question is "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"

##### Hence, the answer is, "6"

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