CAT 2020 Slot 1 QA Question 23: 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

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

Accepted Answer

Translate the two statements into equations.

$A + \dfrac{B + C}{2} = 5$
$\Rightarrow 2A + B + C = 10$ ---- (1)

$B + \dfrac{A + C}{2} = 7$
$\Rightarrow A + 2B + C = 14$ ---- (2)

Subtracting (1) from (2),

$B - A = 4$
$\Rightarrow B = A + 4$

Substitute this into (1).

$2A + (A + 4) + C = 10$
$\Rig

Let AAA, BBB and CCC be three positive integers such that the sum of AAA and the mean of BBB and CCC is 5. In addition, the sum of BBB and the mean of AAA and CCC is 7. Then the sum of AAA and BBB 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