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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.
Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
  • a)
    At most 475
  • b)
    Exactly 475
  • c)
    No conclusion is possible based on the given information
  • d)
    At least 475
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
1600 satellites were sent up by a country for several purposes. The p...
It is given that a satellite serving either B, or C, or S does not serve O. So we can say that it's basically 3 satellites broadcasting (B), communication (C), surveillance (S) which can have intersections. Those satellites which are not part of any category are placed in others. We can draw the Venn diagram as follows.
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.
Let '10x' be the number of satellites exclusively serving B. Then, the number of satellites exclusively serving C and S = 0.30*10x = 3x
Let 'y' be the number of satellites serving others(O).
Let 'z' be the number of satellites serving B, C but not S. Since the numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1. Therefore, we can say that the number of satellites serving B, S but not C = z.
It is given that 
⇒10x + 2z + 2y + 6x = 1600 
⇒8x + z + y = 750 ... (1) 
The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
10x + 2z + 100      2
⇒Z + 100 + 3x + y = 1
⇒10x + 2z +100 = 2(z + 100 + 3x + y)
⇒4x = 100 + 2y
⇒2x = 50 + y
⇒Y = 2x - 50 …(2)
We can substitute this in equation (1) 
⇒8x + z + 2x - 50 = 750
⇒z = 800 - 10x ... (3)
Let us define boundary condition for x, 
⇒2x - 50 ≥ 0 
⇒x ≥ 25 
Also, 800 - 10x ≥ 0 
⇒x ≤ 80 
Therefore, we can say that x ∈[25, 80].
It is given that at least 100 of the 1600 satellites were serving O. 
⇒2x - 50 ≥ 100 
⇒x ≥ 75 
The number of satellites serving S = 100 + 800 - 10x + 2x - 50 + 3x = 850 - 5x 
At xmin = 75, the number of satellites serving S = 850 - 5*75 = 475 
At xmax = 80, the number of satellites serving S = 850 - 5*80 = 450
Hence, we can say that the number of satellites serving S must be from 425 to 475. Therefore, we can say that option A is the correct answer.
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1600 satellites were sent up by a country for several purposes. The p...
Given Information

- 1600 satellites in total
- Purposes: broadcasting (B), communication (C), surveillance (S), others (O)
- Ratios: B:C:S = 2:1:1
- Satellites serving B, C, and S = 100
- Satellites exclusively serving C = Satellites exclusively serving S = 30% of satellites exclusively serving B
- Satellites serving O = Satellites serving C and S but not B
Analysis

- Let the number of satellites serving B exclusively be 10x
- Number of satellites serving C exclusively = Number of satellites serving S exclusively = 3x
- Number of satellites serving O = Number of satellites serving C and S but not B = 100 - (10x + 3x + 3x)
Solving for x

- 10x + 3x + 3x + 100 - 16x = 100
- 16x = 100
- x = 6.25
Calculating Number of Satellites

- Satellites serving B = 10x = 62.5
- Satellites serving C = Satellites serving S = 3x = 18.75
- Satellites serving O = 100 - (10x + 3x + 3x) = 100 - 100 = 0
Conclusion

- If at least 100 satellites were serving O, the number of satellites serving S can be calculated as follows:
- Satellites serving S = 18.75 + 100 (as at least 100 satellites are serving O) = 118.75
- Therefore, the number of satellites serving S is at most 475. Hence, option A is the correct answer.
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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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer?
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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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer?.
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If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer?, a detailed solution for 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice 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.Q. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?a) At most 475b) Exactly 475c) No conclusion is possible based on the given informationd) At least 475Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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