CAT 2020 Question Paper | Quants Slot 1

CAT Questions

This problem is from Linear Equations. If there's one topic that you should consider nailing during your CAT preparation, that is Linear and Quadratic Equations. Mastering this topic can be enormously helpful for your CAT preparation as it has its application everywhere in the CAT Quantitative Ability Section. This question looks like solving simultaneous linear equations, but sometimes even a simple condition written in the question matters a lot! Will you be able to find that catch? Let's see!

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

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Video Explanation

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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

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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"