Set theory

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# Set theory

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Directions (Q. 1-4): Study the following information carefully and answer the questions given
below it:
There are 2500 residents in a village. 1,375 residents from this village speak only their local language. 200
residents of the village speak the local language as well as English. The number of residents in the village who speak
the local language as well as Hindi is 625. 300 residents of the village speak all the three languages ie, English, Hindi
and the local language.
1. The number of residents who speak English as one of the languages forms what per cent of the total residents
in the village?
1) 12 2) 8 3) 20
4) 18 5) None of these
2. The number of residents who speak only the local language forms what per cent of the total number of
residents in the village?
1) 45 2) 55 3) 58
4) 40 5) None of these
2. The number of residents who speak Hindi as one of the languages is approximately what per cent of the
number of residents who speak only the local language?
1) 67 2) 70 3) 61
4) 59 5) 63
3. What is the ratio of the number of residents who speak all the three languages to the number of residents who
speak the local language as well as Hindi?
1) 12 : 55 2) 10 : 25 3)14 : 55
4) 12 : 25 5) None of these
4. If 25 more people who can speak all the three languages come to reside in the village and 45 more people who
can speak the local language and Hindi come to reside in the village, what would be the difference between
the number of residents who can speak all the three languages and the number of residents who can speak
the local language and Hindi?
1) 325 2) 330 3) 340
4) 355 5) None of these

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How do we represent these in a Venn Diagram?

1) Either A or B

2) Either A or B, but not both

3) A or B

As per CAT and other competitive exams

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In a class of 60, along with English as a common subject, students can opt to major in Mathematics. Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60, However, the combined average mart in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?

1. 30

2. 25

3. 20

4. 15

5. None of the above

PFA the solution :

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