If U = {1, 2, ..., 33} and A = {x : x is divisible by 3}, how many even elements are in A'?
Answer and explanation
Correct answer: 11
The even numbers from 1 through 33 are 2, 4, ..., 32, so there are floor(33/2) = 16 of them. An even number that is also divisible by 3 is a multiple of 6. The multiples of 6 up to 33 are 6, 12, 18, 24, and 30, giving 5 numbers. Therefore the number of even elements not divisible by 3, and hence in A', is 16 − 5 = 11. Option B is correct.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The even numbers from 1 through 33 are 2, 4, ..., 32, so there are floor(33/2) = 16 of them. An even number that is also divisible by 3 is a multiple of 6. The multiples of 6 up to 33 are 6, 12, 18, 24, and 30, giving 5 numbers. Therefore the number of even elements not divisible by 3, and hence in A', is 16 − 5 = 11. Option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
