# CAT 2020 Quant Question [Slot 2] with Solution 17

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

Option: 23
Solution:

Given $x + 9 = z = y + 1$ and $x + y < z + 5$

$\Rightarrow (z - 9) + (z - 1) < z + 5$

$\Rightarrow z < 15$

Hence the maximum value of $z = 14,\max$ of $x = 5$ and $\max$ of $y = 13$

Required answer, $2x + y = 2 \times 5 + 13 = 23$

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