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Question:

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

Explanation:

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).