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
[This Question was asked as TITA]

• A. 18
• B. 21
• C. 23
• D. 28

Answer 1

The Correct Option is C

Given that,
\(x+9=z=y+1 \) and \(x+y<z+5\)
\(⇒ (z-9)+(z-1)<z+5\)
\(⇒ z<15\)
Hence the maximum value of \(z=14\), max of \(x=5\) and max of \(y=13\)
Required answer, \(2x+y=2×5+13=23\)

So, the correct option is (C): \(23\)

Answer 2

Given:
Equation 1. \(x+9=z\)
Equation 2. \(y+1=z\)
Equation 3. \(x+y\lt z+5\)
Now From equation 1 and 2:
\(x=z-9\)
\(y=z-1\)
Now put these expressions for x and y in equation 3
\((z-9)+(z-1)\lt z+5\)
\(2z-10\lt z+5\)
\(z\lt15\)
Now, the maximum possible value can't be 15 or greater than 15. So, less than 15 is 14.
\(z=14\)
We need to maximize
\(2x+y\)
\(2(z-9)+(z-1) \;=\;3z-19\)
Now put the value of z
\(3(14)-19 =23\)

So, the correct option is (C): 23