CAT 2018 Set-1 | Question: 37

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 at least $100$ of the $1600$ satellites were serving O, what can be said about the number of satellites serving S?

• A. At most $475$
• B. Exactly $475$
• C. At least $475$
• D. No conclusion is possible based on the given information