If A = {x ∈ ℤ : x is divisible by 3 and x² < 30}, how many elements does A have?
Answer and explanation
Correct answer: 3
The inequality x² < 30 implies −√30 < x < √30, so the possible integers range from −5 to 5. Among these, the integers divisible by 3 are −3, 0, and 3. Therefore A = {−3, 0, 3}, which has three distinct elements. Zero is included because 0 = 3 × 0, so it is divisible by 3. Hence option A is correct; the other counts omit or add valid elements.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
The inequality x² < 30 implies −√30 < x < √30, so the possible integers range from −5 to 5. Among these, the integers divisible by 3 are −3, 0, and 3. Therefore A = {−3, 0, 3}, which has three distinct elements. Zero is included because 0 = 3 × 0, so it is divisible by 3. Hence option A is correct; the other counts omit or add valid elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
