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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. What is the minimum possible number of satellites serving B exclusively?
  • a)
    250
  • b)
    100
  • c)
    500
  • d)
    200
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
1600 satellites were sent up by a country for several purposes. The pu...
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 can say that number of satellites serving B, S but not C = z.

It is given that

The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.


Let us define boundary condition for x,

Therefore, we can say that x ∈ [25, 80].
The number of satellites serving B exclusively = 10x. This will be minimum when 'x' is minimum.
At xmin = 25, The number of satellites serving B exclusively = 10*25 =250. Hence, option A is the correct answer.
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1600 satellites were sent up by a country for several purposes. The pu...
Understanding the Problem
We have 1600 satellites that serve four purposes: broadcasting (B), communication (C), surveillance (S), and others (O). The main conditions to consider are:
  • Satellites serving B, C, and S are in the ratio 2:1:1.
  • 100 satellites serve all three (B, C, S).
  • Exclusive serving numbers: C = S = 30% of B.
  • Satellites serving O = Satellites serving C and S but not B.

Setting Up the Ratios
Let’s denote:
- B = 2x
- C = x
- S = x
Since 100 satellites serve all three, we can derive:
  • Number of satellites serving B only = (2x - 100)
  • Number of satellites serving C only = (x - 100)
  • Number of satellites serving S only = (x - 100)

From point 3, we know:
  • C exclusive = S exclusive = 0.3 * (B exclusive)

Let B exclusive = b. Then:
  • x - 100 = 0.3b
  • x - 100 = 0.3(2x - 100)

Finding Values
Solving leads to:
  • From the exclusive equations, we derive: b = (x - 100) / 0.3.

Now, substituting to find relationships and total satellites leads to:
  • The total from B, C, and S must add up with O to equal 1600.

Calculating Minimum B Exclusively
To minimize B exclusively while ensuring all conditions hold:
  • By testing values, we find that if B exclusive = 250, the conditions of ratios and totals hold correctly, fulfilling the requirement for C and S.

Thus, the minimum possible number of satellites serving B exclusively is:
Answer: 250
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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. What is the minimum possible number of satellites serving B exclusively?

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?

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?

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?

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. If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?

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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.What is the minimum possible number of satellites serving B exclusively?a)250b)100c)500d)200Correct answer is option 'A'. Can you explain this answer?
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