JEE Main 2022 · 24 Jun · Shift 2 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

The sum of all the elements of the set $\{\alpha\in\{1,2,\dots,100\}:\mathrm{HCF}(\alpha,24)=1\}$ is ______.

Your answer

Answer and worked solution

Official answer: 1633

Coprime to 24 means not divisible by 2 or 3.

Inclusion-exclusion. Total $5050$ ; multiples of 2 sum to $2550$ ; of 3, $3\cdot\frac{33\cdot34}2=1683$ ; of 6, $6\cdot\frac{16\cdot17}2=816$ .

Sum. $5050-2550-1683+816=1633$ .

Answer: 1633

JEE Main 2022 · 24 Jun · Shift 2, Mathematics question 24