Sets are the most fundamental concepts of mathematics. It is a collection of elements or objects. If the member of the sets are just numbers, then the ‘set notation’ is used which is comprised of brackets.

Such as, R = {1, 2, 3, 4, 5, 6, 7, 8}; where R is the set that contains eight members that are numbers.

The favorite topic of GMAT in the section of sets is overlapping sets.

An overlapping set is a set that shares it’s boundaries with two or more different sets. The simplest form of overlapping set is a Venn diagram, depicting two overlapping circles.

When two sets shares some common properties, these properties are said to be overlapping.

**Set operations:**

Intersection of two sets:

**Overlapping of two sets:**

A U B

**Questions: At a certain school, 75% of students receive fewer than 6 hours of sleep and report feeling tired during their studies. At the same time 70% of students who receive for more hours of sleep report no feelings of tiredness. If 80% of students receive fewer than 6 hours of sleep, what percent of students report no feelings of tiredness during their shifts?**

- 6
- 14
- 19
- 20
- 81

Solution: 80% of students receive fewer than 6 hours of sleep.

20% of students receive more than 6 hours of sleep.

As, 75% receive fewer than 6 hours of sleep and are tired.

So, 5% of students who receive less than 6 hours of sleep are not tired.

Percent of students who receive for more hours of sleep and are not feeling tired = 0.7

Percent of students who report no feeling of tiredness = 4 + 15 = 19%

**Question: 50% of rooms in a certain hotel have AC and marble flooring. 15% of rooms without AC have marble flooring. If 40% do not have marble flooring, what percent of rooms with AC have marble flooring?**

- 10%
- 16.66%
- 40%
- 50%
- 83.33%

Solution: As 40% of rooms do not have marble flooring, 60% of rooms will have marble flooring.

Let the number of rooms without AC = x%

x = 40%

40% of rooms do not have AC.

So, 60% of rooms have AC.

Percent of rooms with AC having marble flooring =50/60*100=83.33%

More on Sets and Venn Diagram.

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