Which set is B = {x ∈ N : x² is a two-digit number and x < 10}?
Answer and explanation
Correct answer: B = {4, 5, 6, 7, 8, 9}
Since x is a natural number and x < 10, the possible values are 1 through 9. A two-digit square must be at least 10 and at most 99. The first natural number whose square is at least 10 is 4, because 3² = 9 but 4² = 16. Every value from 4 through 9 has a square between 16 and 81, so each qualifies. Therefore B = {4, 5, 6, 7, 8, 9}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
B = {4, 5, 6, 7, 8, 9}
Why is this the correct answer?
Since x is a natural number and x < 10, the possible values are 1 through 9. A two-digit square must be at least 10 and at most 99. The first natural number whose square is at least 10 is 4, because 3² = 9 but 4² = 16. Every value from 4 through 9 has a square between 16 and 81, so each qualifies. Therefore B = {4, 5, 6, 7, 8, 9}, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Sets and their representations.
