Question

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

• A. 6
• B. 5
• C. 7
• D. 4

Answer 1

Answer: (A)

6

Answer 2

The correct answer is (A): $6$

Given $A, B$ and $C$ are positive integers such that $A+\frac{B+C}2 = 5$...(1)

$B+\frac{A+C}{2} = 7$...(2)

$(2)-(1) ⇒ \frac{B}{2}-\frac{A}{2} = 2 ⇒ B-A = 4$

The least value for $A=1$ in which case $B=5$.

Hence $A+B = 6$