CAT 2018 Question Paper Shift 1 Solved Paper

It is given that the satellites serving either B, C or S do not serve O.
From (1), let the number of satellites serving B, C and S be 2K, K, K respectively.
Let the number of satellites exclusively serving B be x.
From (3), the number of satellites exclusively serving C and exclusively serving S will each be 0.3x
From (4), the number of satellites serving $\mathit{O}$ is same as the number of satellites serving only $\mathit{C}$ and $\mathit{S}$. Let that number be $\mathit{y}$.
Since the number of satellites serving $\mathit{C}$ is same as the number of satellites serving $\mathit{S}$, we can say that
(number of satellites serving only $\mathit{B}$ and $\mathit{C})+0.3\mathit{x}+100+\mathit{y}=($ number of satellites serving only $\mathit{B}$ and $\mathit{S})+$ $0.3\mathit{x}+100+\mathit{y}$
Let the number of satellites serving only $\mathit{B}$ and $\mathit{C}=$ the number of satellites serving only $\mathit{B}$ and $\mathit{S}$ $=\mathit{Z}$
Therefore, the venn diagram will be as followsGiven that there are a total of 1600 satellites
$1.6\mathit{x}+2\mathit{y}+2\mathit{z}=1500$............(1)
Also $\mathit{K}=0.3\mathit{x}+\mathit{z}+\mathit{y}+100$
Satellites serving $\mathit{B}=2\mathit{K}=\mathit{x}+2\mathit{z}+100$
$0.4\mathit{x}=2\mathit{y}+100$
$\mathit{x}=5\mathit{y}+250$....(2)
Substituting ( 2 ) in (1), we will get
$1.6\left(5\mathit{y}+250\right)+2\mathit{y}+2\mathit{z}=1500$
$10\mathit{y}+2\mathit{z}=1100$
$\mathit{Z}=550-5\mathit{y}$..........(3)
The number of satellites serving at least two of $\mathit{B},\mathit{C}$ or $\mathit{S}=$ number of satellites serving exactly two of
$\mathit{B},\mathit{C}$ or $\mathit{S}+$ Number of satellites serving all the three
$=\mathit{z}+\mathit{z}+\mathit{y}+100$
$=2\left(550-5\mathit{y}\right)+\mathit{y}+100$
$=1200-9\mathit{y}$
Given that this is equal to 1200
$1200-9\mathit{y}=1200$
$\Rightarrow \mathit{y}=0$
If $\mathit{y}=0,\mathit{x}=5\mathit{y}+250=250$
$\mathit{z}=550-5\mathit{y}=550$
No. of satellites serving $\mathit{C}=\mathit{k}=\mathit{z}+0.3\mathit{x}+100+\mathit{y}$
$=550+0.3\times 250+100+\mathit{y}$
$=725$
No. of satellites serving $\mathit{B}=2\mathit{k}=2\times 725=1450.$
From the given options, we can say that the option "the number of satellites serving $\mathit{C}$ cannot be uniquely determined" must be FALSE