The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is
The sum of all the elements of the set {α ∈ {1, 2, …, 100} : HCF(α, 24) = 1} is
Correct Answer: 1633
Solution and Explanation
The correct answer is 1633
The numbers upto 24 which gives g.c.d. with 24 equals to 1 are 1, 5, 7, 11, 13, 17, 19 and 23.
Sum of these numbers is 96
There are four such blocks and a number 97 is there upto 100.
∴ Complete sum
= 96 + (24 × 8 + 96) + (48 × 8 + 96) + (72 × 8 + 96) + 97
= 1633
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
1. Union of Sets:
- The union of sets lists the elements in set A and set B or the elements in both set A and set B.
- For example, {3,4} ∪ {1, 4} = {1, 3, 4}
- It is denoted as “A U B”
2. Intersection of Sets:
- Intersection of sets lists the common elements in set A and B.
- For example, {3,4} ∪ {1, 4} = {4}
- It is denoted as “A ∩ B”
3.Set Difference:
- Set difference is the list of elements in set A which is not present in set B
- For example, {3,4} - {1, 4} = {3}
- It is denoted as “A - B”
4.Set Complement:
- The set complement is the list of all elements present in the Universal set except the elements present in set A
- It is denoted as “U-A”