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&nbsp;addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

CAT 2020 Question Paper | CAT Verbal Ability Slot 1

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

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A.
7
B.
5
C.
4
D.
6

Option D is the correct answer.

Explanatory Answer

A + (B+C)/2 = 5 à 2A + B + C = 10 - Eq 1
B + (A+C)/2 = 7 à A + 2B + C = 14 - Eq 2
Subtracting, Eq2 – Eq1
B = 4 + A
Adding Eq 1 and Eq 2
3(A+B) + 2C = 24 – Eq 3
Now since A B C are positive and B = 4 + A hence A+B cannot be equal to 4
In Eq 3 all components have to be even thereby eliminating 5 and 7.
Hence A+B = 6.