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Year

CAT 2018

Section

Data

Topic

Venn Diagrams

Difficulty

Hard

Question

Slot-1

Read the passage and answer the questions below.

Passage:

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,CB, C, and SS (though may be not exclusively) are in the ratio 2:1:12: 1: 1.

  2. The number of satellites serving all three of BB, CC, and SS is 100 .

  3. The number of satellites exclusively serving CC is the same as the number of satellites exclusively serving SS. This number is 30%30 \% of the number of satellites exclusively serving BB.

  4. The number of satellites serving OO is the same as the number of satellites serving both CC and SS but not BB.

Question 1

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

Must be at least 100

Cannot be more than 800

Must be between 450 and 725

Must be between 400 and 800

Question 2

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

250

100

500

200

Question 3

If at least 100 of the 1600 satellites were serving 0 , what can be said about the number of satellites serving SS ?

At most 475

Exactly 475

No conclusion is possible based on the given information

At least 475

Question 4

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

The number of satellites serving B exclusively is exactly 250

The number of satellites serving B is more than 1000

The number of satellites serving C cannot be uniquely determined

All 1600 satellites serve B or C or S

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