If x and y are non-negative integers such that x + 9 = z, y + 1 = z and x + y < z + 5, then the maximum possible value of 2x + y equals

CAT 2020 Question Paper (Slot 2) Question 72

Question 72

If x and y are non-negative integers such that $$x + 9 = z$$, $$y + 1 = z$$ and $$x + y < z + 5$$, then the maximum possible value of $$2x + y$$ equals

Correct Answer: 23

Solution

We can write x=z-9 and y=z-1 Now we have x+y< z+5

Substituting we get z-9+z-1<z+5 or z<15

Hence the maximum possible value of z is 14

Maximum value of "x" is 5 and maximum value of "y" is 13

Now 2x+y = 10+13=23

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