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VENN DIAGRAM- 2 Variable || Logical Reasoning || CAT 2021 || 14 October

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Question 1

Direction: A class of students were discussing about how they spent a weekend. Some of them went camping, while the others stayed at hostel. All the students who went camping participated in at least one of two activities - playing PUBG and trekking. All the students who stayed at hostel participated in at least one of two activities - playing PUBG and watching movies. The following information is known about the number of students who

participated in each activity:

1) The number of students who went for a trek was twice the total number of persons who participated in exactly two activities, among the entire group of students.

2) The number of students who played PUBG among those who went camping was 11 less than the number of students who watched movies.

3) The total number of students who played PUBG among the entire group of students was 20 more than the number of students who went for a trek.

4) The sum of the number of students who played PUBG among the entire group of students and the number of students who watched movies was 94.

5) The total number of students who participated in exactly two activities was 22, which was four less than the number of students who participated only in trekking.

What is the total number of students in the class?

Question 2

Direction: A class of students were discussing about how they spent a weekend. Some of them went camping, while the others stayed at hostel. All the students who went camping participated in at least one of two activities - playing PUBG and trekking. All the students who stayed at hostel participated in at least one of two activities - playing PUBG and watching movies. The following information is known about the number of students who

participated in each activity:

1) The number of students who went for a trek was twice the total number of persons who participated in exactly two activities, among the entire group of students.

2) The number of students who played PUBG among those who went camping was 11 less than the number of students who watched movies.

3) The total number of students who played PUBG among the entire group of students was 20 more than the number of students who went for a trek.

4) The sum of the number of students who played PUBG among the entire group of students and the number of students who watched movies was 94.

5) The total number of students who participated in exactly two activities was 22, which was four less than the number of students who participated only in trekking.

Among the students who stayed at hostel, how many students played PUBG?

Question 3

Direction: A class of students were discussing about how they spent a weekend. Some of them went camping, while the others stayed at hostel. All the students who went camping participated in at least one of two activities - playing PUBG and trekking. All the students who stayed at hostel participated in at least one of two activities - playing PUBG and watching movies. The following information is known about the number of students who

participated in each activity:

1) The number of students who went for a trek was twice the total number of persons who participated in exactly two activities, among the entire group of students.

2) The number of students who played PUBG among those who went camping was 11 less than the number of students who watched movies.

3) The total number of students who played PUBG among the entire group of students was 20 more than the number of students who went for a trek.

4) The sum of the number of students who played PUBG among the entire group of students and the number of students who watched movies was 94.

5) The total number of students who participated in exactly two activities was 22, which was four less than the number of students who participated only in trekking.

What is the difference between the number of students who went camping and the number of students who stayed at hostel?

Question 4

Direction: A class of students were discussing about how they spent a weekend. Some of them went camping, while the others stayed at hostel. All the students who went camping participated in at least one of two activities - playing PUBG and trekking. All the students who stayed at hostel participated in at least one of two activities - playing PUBG and watching movies. The following information is known about the number of students who

participated in each activity:

1) The number of students who went for a trek was twice the total number of persons who participated in exactly two activities, among the entire group of students.

2) The number of students who played PUBG among those who went camping was 11 less than the number of students who watched movies.

3) The total number of students who played PUBG among the entire group of students was 20 more than the number of students who went for a trek.

4) The sum of the number of students who played PUBG among the entire group of students and the number of students who watched movies was 94.

5) The total number of students who participated in exactly two activities was 22, which was four less than the number of students who participated only in trekking.

What is the total number of students who played only PUBG?

Question 5

Direction: A class of students were discussing about how they spent a weekend. Some of them went camping, while the others stayed at hostel. All the students who went camping participated in at least one of two activities - playing PUBG and trekking. All the students who stayed at hostel participated in at least one of two activities - playing PUBG and watching movies. The following information is known about the number of students who

participated in each activity:

1) The number of students who went for a trek was twice the total number of persons who participated in exactly two activities, among the entire group of students.

2) The number of students who played PUBG among those who went camping was 11 less than the number of students who watched movies.

3) The total number of students who played PUBG among the entire group of students was 20 more than the number of students who went for a trek.

4) The sum of the number of students who played PUBG among the entire group of students and the number of students who watched movies was 94.

5) The total number of students who participated in exactly two activities was 22, which was four less than the number of students who participated only in trekking.

What is the number of students who watched only movies?

Question 6

Direction: A shopkeeper sells only two items – pens and pencils. On a certain Tuesday, the shopkeeper sold only pens to 40% of the customers. The number of customers that bought only pencil was 20 more than the number of customers that bought both pencil and pen. The number of customers that bought only pencil is 5/4th of the number of customers that bought only pens.

What was the total number of customers that shopped from the shopkeeper on Tuesday?

Question 7

Direction: A shopkeeper sells only two items – pens and pencils. On a certain Tuesday, the shopkeeper sold only pens to 40% of the customers. The number of customers that bought only pencil was 20 more than the number of customers that bought both pencil and pen. The number of customers that bought only pencil is 5/4th of the number of customers that bought only pens.
Find the number of customers that bought pens on Tuesday.

Question 8

Direction: A shopkeeper sells only two items – pens and pencils. On a certain Tuesday, the shopkeeper sold only pens to 40% of the customers. The number of customers that bought only pencil was 20 more than the number of customers that bought both pencil and pen. The number of customers that bought only pencil is 5/4th of the number of customers that bought only pens.
The number of customers that bought only pencil are what percentage of total number of customers on Tuesday?

Question 9

Direction: A shopkeeper sells only two items – pens and pencils. On a certain Tuesday, the shopkeeper sold only pens to 40% of the customers. The number of customers that bought only pencil was 20 more than the number of customers that bought both pencil and pen. The number of customers that bought only pencil is 5/4th of the number of customers that bought only pens.
The number of customers that bought only pen are how much less than the number of customers that bought pencils on Tuesday?

Question 10

Direction: A shopkeeper sells only two items – pens and pencils. On a certain Tuesday, the shopkeeper sold only pens to 40% of the customers. The number of customers that bought only pencil was 20 more than the number of customers that bought both pencil and pen. The number of customers that bought only pencil is 5/4th of the number of customers that bought only pens.
What is the number of customers who bought both pen and pencil?
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