QJEEM22Mabfde: JEE Main 2022 Mathematics - Class 11 JEEM22Mabfde Solution: The total number of 3-digit numbers, whose greatest common…

$$\because$$ x $$\in$$ [100, 999], x $$\in$$ N

Then $$\frac{x}{2}$$ $$\in$$ [50, 499], $$\frac{x}{2}$$ $$\in$$ N

Number whose G.C.D. with 18 is 1 in this range have the required condition. There are 6 such number from 18 $$\times$$ 3 to 18 $$\times$$ 4. Similarly from 18 $$\times$$ 4 to 18 $$\times$$ 5 ......., 26 $$\times$$ 18 to 27 $$\times$$ 18

$$\therefore$$ Total numbers = 24 $$\times$$ 6 + 6 = 150

The extra numbers are 53, 487, 491, 493, 497 and 499.