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Directions for Questions: 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 th e number of satellites serving both C and S but not B.
(2018)
Q. What is the minimum possible number of satellites serving B exclusively?
  • a)
    500
  • b)
    250
  • c)
    200
  • d)
    100
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Directions for Questions: 1600 satellites were sent up by a country fo...
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 C and S but not B. Let the 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
∴ The number of satellites serving only B and C = the number of satellites serving only B and S = Z (let)
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   …(i)
Also k = 0.3x + z + y +100
and 2k = x + 2z + 100
⇒ 2(0.3x + z + y + 100) = x + 2z + 100
⇒  0.4x = 2y + 100
⇒ x = 5y + 250 …(ii)
From equation (i) and (ii) we will get
1.6 (5y + 250) + 2y + 2z = 1500
Z = 550 – 5y … (iii)
From (ii), the number of satellites serving B exclusively = 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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Directions for Questions: 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 th e number of satellites serving both C and S but not B.(2018)Q. What is the minimum possible number of satellites serving B exclusively?a)500b)250c)200d)100Correct answer is option 'B'. Can you explain this answer?
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Directions for Questions: 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 th e number of satellites serving both C and S but not B.(2018)Q. What is the minimum possible number of satellites serving B exclusively?a)500b)250c)200d)100Correct answer is option 'B'. 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 Directions for Questions: 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 th e number of satellites serving both C and S but not B.(2018)Q. What is the minimum possible number of satellites serving B exclusively?a)500b)250c)200d)100Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions for Questions: 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 th e number of satellites serving both C and S but not B.(2018)Q. What is the minimum possible number of satellites serving B exclusively?a)500b)250c)200d)100Correct answer is option 'B'. Can you explain this answer?.
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