Question

What best can be said about the number of satellites serving C?

• A. Must be between 450 and 725
• B. Cannot be more than 800
• C. Must be between 400 and 800
• D. Must be at least 100
• A. 100
• B. 200
• C. 500
• D. 250
• A. At most 475
• B. Exactly 475
• C. At least 475
• D. No conclusion is possible based on the given information
• A. The number of satellites serving C cannot be uniquely determined.
• B. The number of satellites serving B is more than 1000 .
• C. All 1600 satellites serve B or C or S.
• D. The number of satellites serving B exclusively is exactly 250.

Answer 1

The Correct Option is C

The correct answer is (C):
The number of satellites serving C = z + 0.3x + 100 + y
= (550 – 5y) + 0.3(5y + 250) + 100 + y = 725 – 2.5y
This number will be maximum when y is minimum.
Minimum value of y is 0.
Therefore, the maximum number of satellites serving C will be 725.
From ③, z = 550 – 5y
Since the number of satellites cannot be negative,
z ≥ 0 ⇒ 550 - 5y ≥ 0
y ≤ 110
Maximum value of y is 110. When y = 110,
the number of satellites serving C will be 725 – 2.5 × 110 = 450. This will be the minimum number of satellites serving C.
The number of satellites serving C must be between 450 and 725.

Answer 2

The correct answer is (D):
From 2, the number of satellites serving B exclusively is x = 5y + 250
This is minimum when y is minimum.
Minimum value of y = 0.
The minimum number of satellites serving B exclusively = 5 × 0 + 250 = 250.

Answer 3

The correct answer is (A):
Given that at least 100 satellites serve 0; we can say in this case that y ≥ 100.
Number of satellites serving s = 0.3x + z +100 + y=725 – 2.5y
This is minimum when y is maximum, i.e. 110, (from③)
Minimum number of satellites serving = 725 – 2.5 ×100 = 450.
This is maximum when y is minimum, i.e., 100 in this case.
Maximum number of satellites serving = 725 – 2.5 ×100 = 475
Therefore, the number of satellites serving S is at most 475

Answer 4

The correct answer is (A):
The number of satellites serving at least two of B, C or S = number of satellites serving exactly two of B, C or S + Number of satellites serving all the three = z + z + y + 100 = 2(550 – 5y) + y + 100 = 1200 – 9y.
Given that this is equal to 1200
1200 – 9y = 1200
=> y = 0
If y = 0, x = 5y + 250 = 250
z = 550 – 5y = 550
No. of satellites serving C = k = z + 0.3x + 100 + y
= 550 + 0.3 × 250 + 100 + y
= 725
No. of satellites serving B = 2k = 2 × 725 = 1450.
From the given options, we can say that the option “the number of satellites serving C cannot be uniquely determined” must be FALSE.