CAT 2018 Slot 1 — DILR Question 1
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.
What best can be said about the number of satellites serving C?
Answer & solution
- A
Cannot be more than 800
- B
Must be at least 100
Must be between 450 and 725
- D
Must be between 400 and 800
Let number of satellites exclusively serving B be ‘10x’ and number of satellites serving O be ‘z’.
∴ number of satellites exclusively serving C = number of satellites exclusively serving S = 3a
As the number of satellites serving C = number of satellites serving S, the number of satellites serving C and B but not S = number of satellites exclusively serving S and B but not C = y (assume).
∴ 10x + 2y + 100 + 6x + 2z
= 1600 ⇒ 8x + y + z
= 750 … (i)
From (1), 10x + 2y + 100
= 6x + 2y + 2z + 200
∴ z = 2x – 50 … (ii)
Thus, the minimum value that ‘x’ can takes is 25.
From (i) and (ii),
10x + y = 800 ⇒ y = 800 – 10x
Thus, the maximum value that ‘x’ can takes is 80.
The number of satellites serving
C = 3x + y + z + 100 = 3x + (800 – 10x) + (2x – 50) + 100 = 850 – 5x
As value of ‘x’ is between 25 and 80, value of (850 – 5x) must be between 450 and 725.
Hence, option (c).