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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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
  • a)
    The number of satellites serving B exclusively is exactly 250
  • b)
    The number of satellites serving B is more than 1000
  • c)
    The number of satellites serving C cannot be uniquely determined
  • d)
    All 1600 satellites serve B or C or S
Correct answer is option 'C'. 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 the number of satellites serving at least two among B, C, and S is 1200.
⇒800 - 10x + 800 - 10x + 2x -50 + 100 = 1200
⇒18x = 450
⇒x = 25
We can determine the number of satellites in each of the following categories. Hence, option C is definitely false. Therefore, we can say that option C is incorrect.
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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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?a) The number of satellites serving B exclusively is exactly 250b) The number of satellites serving B is more than 1000c) The number of satellites serving C cannot be uniquely determinedd) All 1600 satellites serve B or C or SCorrect answer is option 'C'. 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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?a) The number of satellites serving B exclusively is exactly 250b) The number of satellites serving B is more than 1000c) The number of satellites serving C cannot be uniquely determinedd) All 1600 satellites serve B or C or SCorrect answer is option 'C'. 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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?a) The number of satellites serving B exclusively is exactly 250b) The number of satellites serving B is more than 1000c) The number of satellites serving C cannot be uniquely determinedd) All 1600 satellites serve B or C or SCorrect answer is option 'C'. 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 the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?a) The number of satellites serving B exclusively is exactly 250b) The number of satellites serving B is more than 1000c) The number of satellites serving C cannot be uniquely determinedd) All 1600 satellites serve B or C or SCorrect answer is option 'C'. Can you explain this answer?.
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If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?a) The number of satellites serving B exclusively is exactly 250b) The number of satellites serving B is more than 1000c) The number of satellites serving C cannot be uniquely determinedd) All 1600 satellites serve B or C or SCorrect answer is option 'C'. 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. 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