Question

If x, y, z are positive numbers such that x + [y] + {z} = 3.8, [x] + {y} + z = 3.2, {x} + y + [z] = 2.2, where [p] denotes the greatest integer less than or equal to p and {p} denotes the fractional part of p. E.g. [1.23] = 1, {1.23} = 0.23 = $\frac{23}{100}$. The numerical value of $[x^2+y^2+z^2]$ is -

• A. 7
• B. 8
• C. 9
• D. None of these

Answer 1

The correct option is C

9

Adding the three equations we get, $2(x+y+z)=9.2⟹x+y+z=4.6$.
Subtracting first eq. from the above eq. we get $\left\{y\right\}+\left[z\right]=0.8⟹\left\{y\right\}=0.8$ and $\left[z\right]=0$.
Subtracting second eq. from the above eq. $\left\{x\right\}+\left[y\right]=1.4⟹\left\{x\right\}=0.4$ and $\left[y\right]=1$.
Subtracting third eq. from the above eq. $\left[x\right]+\left\{z\right\}=2.4⟹\left[x\right]=2$ and $\left\{z\right\}=0.4$.
$\therefore x=2.4,y=1.8$ and $z=0.4$.
Hence, choice (c) is the right answer.