Satellite Classifications and Venn Diagrams

CAT 2018 Slot 1 · DILR · Medium · Venn Diagrams

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Passage / data set

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.

Question 1 of 4

What best can be said about the number of satellites serving C?

  1. A.

    Must be between 400 and 800

  2. B.

    Cannot be more than 800

  3. C.

    Must be at least 100

  4. D.

    Must be between 450 and 725

Answer

D

Explanation

By setting up set equations, the minimum and maximum boundaries for CC evaluate to 450 and 725 respectively.

Question 2 of 4

What is the minimum possible number of satellites serving B exclusively?

  1. A.

    100

  2. B.

    200

  3. C.

    250

  4. D.

    500

Answer

C

Explanation

The non-negativity conditions of overlapping regions dictate that the minimum value for exclusively B is 250.

Question 3 of 4

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

  1. A.

    At least 475

  2. B.

    No conclusion is possible based on the given information

  3. C.

    Exactly 475

  4. D.

    At most 475

Answer

C

Explanation

Plugging O≥100O \ge 100 into the bounds forces the number of satellites serving S to be uniquely fixed at 475.

Question 4 of 4

If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?

  1. A.

    All 1600 satellites serve B or C or S

  2. B.

    The number of satellites serving C cannot be uniquely determined

  3. C.

    The number of satellites serving B exclusively is exactly 250

  4. D.

    The number of satellites serving B is more than 1000

Answer

B

Explanation

When satellites serving at least two equals 1200, the system fixes all regional values, making C uniquely determinable. Hence B must be false.

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