CAT 2018 Slot 1 — DILR Question 3
Answer the following question based on the information given below.
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:
- The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2 : 1 : 1.
- The number of satellites serving all three of B, C, and S is 100.
- 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.
- The number of satellites serving O is the same as the number of satellites serving both Cand 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?
Answer & solution
- A
Exactly 475
At most 475
- C
At least 475
- D
No conclusion is possible based on the given information
Number of satellites serving S = 3x + y + z + 100 = 3x + (800 – 10x) + (2x – 50) + 100
= 850 – 5x
2x – 50 ≥ 100 ⇒ x ≥ 75 ⇒ (–5x) ≤ (–375)
∴ 850 – 5x ≤ 850 – 375 = 475
Thus, the number of satellites serving S can be at most 475.
Hence, option (b).