JEE Main 2022 · 26 Jun · Shift 1 · Mathematics Q27

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MathematicsInteger+4 / -1Question 27 of 90

Let $A=\{n\in\mathbb N:\text{H.C.F.}(n,45)=1\}$ and Let $B=\{2k:k\in\{1,2,\dots,100\}\}$ . Then the sum of all the elements of $A\cap B$ is ______.

Your answer

Answer and worked solution

Official answer: 5264

Even numbers 2 to 200 not divisible by 3 or 5.

Inclusion-exclusion. All evens: 10100. Multiples of 6: $6\cdot\frac{33\cdot34}2=3366$ . Multiples of 10: $10\cdot\frac{20\cdot21}2=2100$ . Multiples of 30: $30\cdot\frac{6\cdot7}2=630$ .

Sum. $10100-3366-2100+630=5264$ .

Answer: 5264

Topics:Arithmetic progression Sets and operations

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JEE Main 2022 · 26 Jun · Shift 1, Mathematics question 27