Page 54 - NUMINO Challenge_D2
P. 54
Basic Concepts Finding the Maximum and Minimum
Out of 8 students, there are 6 students who like math and 4 students who
like science. The maximum and minimum numbers of students who like both
subjects can be found as shown below.
In the case where the maximum In the case where the minimum
number of students like both subjects, number of students like both
all the students who like science also subjects, there is no one who does
like math. not like both math and science.
Total (8) Total (8)
Math (6)
Math (6) Science (4)
Science (4)
Therefore, a maximum of four students and a minimum of two students like
both subjects.
Example Out of 30 students in John’s class, there are 20 students who have
a dog, and 15 students who have a cat. What is the maximum and
minimum number of students who have both a dog and a cat?
Class Notes
In the case where the maximum number of students have Total 30
both a dog and a cat, all the students who have a dog also 30 Dogs
25 Cats
have a , as shown on the right. Therefore, a
maximum of students have both a dog and a cat.
In the case where the minimum number of students have Total 30
both a dog and a cat, there are students who do not 20 Dogs 15 Cats
have both a dog and a cat. In this case, (the number of
students who have both a dog and a cat) (the number of
students who have a dog) (the number of students who
have a cat) (the total number of students) 20 (students).
Therefore, a minimum of students have both a dog and a cat.
51Reasoning
Out of 8 students, there are 6 students who like math and 4 students who
like science. The maximum and minimum numbers of students who like both
subjects can be found as shown below.
In the case where the maximum In the case where the minimum
number of students like both subjects, number of students like both
all the students who like science also subjects, there is no one who does
like math. not like both math and science.
Total (8) Total (8)
Math (6)
Math (6) Science (4)
Science (4)
Therefore, a maximum of four students and a minimum of two students like
both subjects.
Example Out of 30 students in John’s class, there are 20 students who have
a dog, and 15 students who have a cat. What is the maximum and
minimum number of students who have both a dog and a cat?
Class Notes
In the case where the maximum number of students have Total 30
both a dog and a cat, all the students who have a dog also 30 Dogs
25 Cats
have a , as shown on the right. Therefore, a
maximum of students have both a dog and a cat.
In the case where the minimum number of students have Total 30
both a dog and a cat, there are students who do not 20 Dogs 15 Cats
have both a dog and a cat. In this case, (the number of
students who have both a dog and a cat) (the number of
students who have a dog) (the number of students who
have a cat) (the total number of students) 20 (students).
Therefore, a minimum of students have both a dog and a cat.
51Reasoning
