CAT 2018 Slot 1 — DILR Question 4
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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
Answer & solution
- A
All 1600 satellites serve B or C or S
- B
The number of satellites serving B is more than 1000
The number of satellites serving C cannot be uniquely determined
- D
The number of satellites serving B exclusively is exactly 250
The number of satellites serving at least two among B, C and S is 1200
i.e., 2y + z + 100 ≥ 1200
⇒ 1600 – 20x + 2x – 50 ≥ 1100
⇒ 450 ≥ 18x
⇒ 25 ≥ x
Earlier we have seen that the minimum value of ‘x’ is 25
∴ x = 25
[1]: z = 2x – 50 = 0 ⇒ All satellites serve B or C or S. Therefore, statement 1 is true.
[2]: The number of satellites serving B = 10x + 2y + 100 = 10(25) + 2(800 – 10x) + 100
= 1450
Therefore, statement 2 is true.
[3]: The number of satellites serving C
= 3x + y + z + 100 = 3x + (800 – 10x) + (2x – 50) + 100 = 850 – 5x = 725
Therefore, statement 3 is false.
[4]: The number of satellites serving B exclusively = 10x = 10 × 25 = 250
Therefore, statement 4 is true.
Hence, option (c).