Question:medium

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
[This Question was asked as TITA]

Updated On: Jan 15, 2026
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The Correct Option is C

Solution and Explanation

Given:

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

Step 1: Express $x$ and $y$ in terms of $z$.

From $x + 9 = z$, we have $x = z - 9$.
From $z = y + 1$, we have $y = z - 1$.

Step 2: Substitute into the inequality.

$x + y < z + 5$ 
$\Rightarrow (z - 9) + (z - 1) < z + 5$ 
$\Rightarrow 2z - 10 < z + 5$ 
$\Rightarrow z - 10 < 5$ 
$\Rightarrow z < 15$

Step 3: Determine the maximum possible integer value of $z$.

Since $z<15$, the maximum integer value for $z$ is $14$.

Step 4: Calculate the corresponding values for $x$ and $y$.

$x = z - 9 = 14 - 9 = 5$ 
$y = z - 1 = 14 - 1 = 13$

Step 5: Compute the required expression.

$2x + y = 2 \times 5 + 13 = 10 + 13 = \mathbf{23}$

Answer: (C): $23$

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