1. Must be between 450 and 725

2. Cannot be more than 800

3. Must be between 400 and 800

4. Must be at least 100

1. 100

2. 200

3. 500

4. 250

1. At most 475

2. Exactly 475

3. At least 475

4. No conclusion is possible based on the given information

1. The number of satellites serving C cannot be uniquely determined

2. The number of satellites serving B is more than 1000

3. All 1600 satellites serve B or C or S

4. The number of satellites serving B exclusively is exactly 250

**Explanation**:

It is given that the satellites serving either B, C or S do not serve O.

From (1), let the number of satellites serving B, C and S be 2K, K, K respectively. Let the number of satellites exclusively serving B be x.

From (3), the number of satellites exclusively serving C and exclusively serving S will each be 0.3x

From (4), the number of satellites serving O is same as the number of satellites serving only C and S. Let that number be y.

Since the number of satellites serving C is same as the number of satellites serving S, we can say that

(number of satellites serving only B and C) + 0.3x + 100 + y = (number of satellites serving only B and S) +

0.3x + 100 + y

Let the number of satellites serving only B and C = the number of satellites serving only B and S

= Z

Therefore, the venn diagram will be as follows

Given that there are a total of 1600 satellites

=> x + z + 0.3x + z + 100 + y + 0.3x + y = 1600 1.6x + 2y + 2z = 1500 (1)

Also K = 0.3x + z + y +100

Satellites serving B = 2K = x + 2z + 100

=> 2(0.3x + z + y + 100) = x + 2z + 100 0.4x = 2y + 100

x = 5y + 250 (2)

Substituting (2) in (1), we will get 1.6 (5y + 250) + 2y + 2z = 1500

10y + 2z = 1100

Z = 550 – 5y (3)

Question 35:

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.

Question 36:

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.

Question 37:

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

Question 38:

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

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