Let A = {x : x ∈ N, x is a factor of 100, and x > 25}, where N = {1, 2, 3, ...}. How many elements does A have?
Answer and explanation
Correct answer: 2
The governing concept is selecting members of a finite set using conditions. The positive factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Applying x > 25 removes every factor up to and including 25, leaving A = {50, 100}. Therefore A has 2 elements and option A is correct. The strict inequality is why 25 is excluded.
Frequently asked questions
What is the correct answer to this question?
2
Why is this the correct answer?
The governing concept is selecting members of a finite set using conditions. The positive factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Applying x > 25 removes every factor up to and including 25, leaving A = {50, 100}. Therefore A has 2 elements and option A is correct. The strict inequality is why 25 is excluded.
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.
