Comprehension
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:
1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
2. The number of satellites serving all three of B, C, and S is 100.
3. 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.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.
1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
2. The number of satellites serving all three of B, C, and S is 100.
3. 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.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.
Question: 1
What best can be said about the number of satellites serving C?
What best can be said about the number of satellites serving C?
Updated On: Sep 30, 2024
- Must be between 450 and 725
- Cannot be more than 800
- Must be between 400 and 800
- Must be at least 100
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The Correct Option is C
Solution and Explanation
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.
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Question: 2
What is the minimum possible number of satellites serving B exclusively?
What is the minimum possible number of satellites serving B exclusively?
Updated On: Sep 30, 2024
- 100
- 200
- 500
- 250
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The Correct Option is D
Solution and Explanation
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.
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Question: 3
If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
Updated On: Sep 30, 2024
- At most 475
- Exactly 475
- At least 475
- No conclusion is possible based on the given information
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The Correct Option is A
Solution and Explanation
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
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Question: 4
If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
Updated On: Sep 30, 2024
- The number of satellites serving C cannot be uniquely determined.
- The number of satellites serving B is more than 1000 .
- All 1600 satellites serve B or C or S.
- The number of satellites serving B exclusively is exactly 250.
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The Correct Option is A
Solution and Explanation
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.
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