CMA Foundation · Fundamentals of Business Mathematics and Statistics · Set Theory, including Venn Diagram
The set A is written in set-builder form as A = {x : x is a whole number, 3 < x ≤ 12 and x is a multiple of 3}. How many elements does A have, and what is their sum?
The set contains the multiples of 3 greater than 3 and not exceeding 12, namely 6, 9 and 12. It therefore has 3 elements and their sum is 27. The number 3 is excluded because the condition is strictly greater than 3.
- A3 elements, sum 27
- B4 elements, sum 30Correct
- C3 elements, sum 18
- D4 elements, sum 36
Explanation
Whole numbers greater than 3 and up to 12 that are multiples of 3 are 6, 9 and 12. That gives 3 elements, not 4... recheck: 3 is excluded since 3 < x, so A = {6, 9, 12}, with 3 elements and sum 27. Option 1 is therefore the correct one, and the 4-element options wrongly include 3.
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