Let U = {1, 2, ..., 81} and A = {x ∈ U | x is a perfect square}. How many numbers divisible by 9 belong to A′?
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Answer and explanation
Correct answer: 6
The numbers from 1 to 81 divisible by 9 are 9, 18, 27, 36, 45, 54, 63, 72, and 81, so there are 9 such numbers. Among them, 9 = 3², 36 = 6², and 81 = 9² are perfect squares and therefore belong to A. Removing these three from the nine multiples leaves 9 − 3 = 6 numbers in A′.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The numbers from 1 to 81 divisible by 9 are 9, 18, 27, 36, 45, 54, 63, 72, and 81, so there are 9 such numbers. Among them, 9 = 3², 36 = 6², and 81 = 9² are perfect squares and therefore belong to A. Removing these three from the nine multiples leaves 9 − 3 = 6 numbers in A′.
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.
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