CAT 2018 Set-1 | Question: 38

Question

$1600$ satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.

The following facts are known about the satellites:

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio $2:1:1$.
2. The number of satellites serving all three of B, C, and S is $100$.
3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is $30\%$ of the number of satellites exclusively serving B.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.

If the number of satellites serving at least two among B, C, and S is $1200$, which of the following MUST be FALSE?

• A. The number of satellites serving C cannot be uniquely determined.
• B. The number of satellites serving B is more than $1000$.
• C. All $1600$ satellites serve B or C or S.
• D. The number of satellites serving B exclusively is exactly $250$.