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CAT 2020 Slot 2 QA Question & Solution

AlgebraMedium

Question

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

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

Hence, now: $\quad 2x+y = 10 + 13 = 23$