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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 the number of satellites serving both C and S but not B.
(2018)
Q. What best can be said about the number of satellites serving C?
  • a)
    Must be between 450 and 725
  • b)
    Must be at least 100
  • c)
    Cannot be more than 800
  • d)
    Must be between 400 and 800
Correct answer is option 'A'. 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)
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.
∴ The maximum number of satellites serving C will be 725.
From (iii), 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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Most Upvoted Answer
Directions for Questions: 1600 satellites were sent up by a country fo...
Solution:

Given,
- Total number of satellites = 1600
- Ratio of satellites serving B, C, and S = 2:1:1
- Number of satellites serving all three of B, C, and S = 100
- Number of satellites exclusively serving C = Number of satellites exclusively serving S = 0.3 x Number of satellites exclusively serving B
- Number of satellites serving O = Number of satellites serving both C and S but not B

Let's solve the question step by step.

Step 1: Find the number of satellites serving B, C, and S.

Let the number of satellites serving B, C, and S be 2x, x, and x respectively. Then, the total number of satellites serving B, C, or S would be 4x, and the number of satellites serving all three of B, C, and S would be 100.

Therefore,

4x - 100 = Number of satellites serving only B or only C or only S

Step 2: Find the number of satellites exclusively serving B, C, and S.

Let the number of satellites exclusively serving B, C, and S be a, b, and c respectively. Then,

- a + b + c + 100 = Number of satellites serving B, C, or S (since 100 satellites serve all three purposes)
- a = 0.3a + b + 0.3b + c (since the number of satellites exclusively serving C is the same as the number of satellites exclusively serving S, and this number is 30% of the number of satellites exclusively serving B)
- Total number of satellites serving B, C, or S = 4x = a + b + c + 100

Simplifying the above equations, we get

- a + b + c = 700
- 1.6a + 0.6b + c = 4x - 100

Step 3: Find the number of satellites serving O.

Let the number of satellites serving both C and S but not B be y. Then,

- Number of satellites serving O = y
- Number of satellites serving C and/or S but not B = 2x - 100 - y (since 100 satellites serve all three purposes)

Now, the total number of satellites can be expressed as:

Total number of satellites = Number of satellites exclusively serving B + Number of satellites exclusively serving C + Number of satellites exclusively serving S + Number of satellites serving both C and S but not B + Number of satellites serving O

Substituting the values we have derived, we get

1600 = a + 0.7a + 0.7a + 700 + 2x - 100 - y + y

Simplifying, we get

- 3.1a = 2x + 200

Step 4: Find the range of the number of satellites serving C.

We know that the number of satellites serving C and/or S but not B = 2x - 100 - y. Also, a + b + c = 700.

Therefore,

- Number of satellites serving C = x + 2a + b + y
- Number of satellites serving C = x + 0.7a + 0.3a + 0.3b + y
- Number of
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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 the number of satellites serving both C and S but not B.(2018)Q. What best can be said about the number of satellites serving C?a)Must be between 450 and 725b)Must be at least 100c)Cannot be more than 800d)Must be between 400 and 800Correct answer is option 'A'. 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 the number of satellites serving both C and S but not B.(2018)Q. What best can be said about the number of satellites serving C?a)Must be between 450 and 725b)Must be at least 100c)Cannot be more than 800d)Must be between 400 and 800Correct 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 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 the number of satellites serving both C and S but not B.(2018)Q. What best can be said about the number of satellites serving C?a)Must be between 450 and 725b)Must be at least 100c)Cannot be more than 800d)Must be between 400 and 800Correct 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 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 the number of satellites serving both C and S but not B.(2018)Q. What best can be said about the number of satellites serving C?a)Must be between 450 and 725b)Must be at least 100c)Cannot be more than 800d)Must be between 400 and 800Correct answer is option 'A'. Can you explain this answer?.
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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.(2018)Q. What best can be said about the number of satellites serving C?a)Must be between 450 and 725b)Must be at least 100c)Cannot be more than 800d)Must be between 400 and 800Correct answer is option 'A'. Can you explain this answer?, a detailed solution 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. 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