# CAT 2020 Quant Question [Slot 1] with Solution 23

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

1. 6
2. 5
3. 7
4. 4
Option: 1
Solution:

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

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

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

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

Hence $A + B = 6$

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