Set Theory Questions for CAT:
The following article contains questions from Venn DIagrams and Set Theory for CAT. This is a very scoring topic in CAT Quantitative Aptitude and students can expect at least one group question (around 2-3 questions) from this topic.
Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?
D. None of these
How many even integers n, where 100≤n≤200 , are divisible neither by seven nor by nine?
There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
Fifty college teachers are surveyed as to their possession of colour TV, VCR and tape recorder. Of them, 22 own colour TV, 15 own VCR and 14 own tape recorders. Nine of these college teachers own exactly two items out of colour TV, VCR and tape recorder; and, one college teacher owns all three. How many of the 50 teachers own none of the three, colour TV, VCR or tape recorder?
1) Answer (C)
Let the number of days in the vacation be x
They played tennis for x-14 days
They did yoga for x-24 days
So, they did yoga or played tennis for x-14+x-24 = 2x-38 days
2x – 38 = 22
=> x = 30
2) Answer (C)
Between 100 and 200 both included there are 51 even nos. There are 7 even nos which are divisible by 7 and 6 nos which are divisible by 9 and 1 no divisible by both. hence in total 51 – (7+6-1) = 39
There is one more method through which we can find the answer. Since we have to find even numbers, consider the numbers which are divisible by 14, 18 and 126 between 100 and 200. These are 7, 6 and 1 respectively.
3) Answer (C)
Number of people owning exactly 2 articles = 9
Number of people owning exactly 3 articles = 1
Applying AUBUC formula, we get
AUBUC = 22+15+14 – 9 -2*(1)=40
Number of people who do not own any article = 50-40 = 10
4) Answer (B)
We know that x + y + z = T and x + 2y + 3z = R, where
x = number of members belonging to exactly 1 set = 70
y = number of members belonging to exactly 2 sets
z = number of members belonging to exactly 3 sets = 10
T = Total number of members
R = Repeated total of all the members = (40+50+60) = 150
Thus we have two equations and two unknowns. Solving this we get y = 25
So, 25 people belong to exactly 2 clubs.
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