Let x be four digit number, then gcd (x,18)=3 This implies x is divisible by 3 but not divisible by 9 . The 4-digit numbers which is an odd multiple of 3 are 1005, 1011, 1017, ...... 9999 These are 1499 in counting i.e. total number of 4-digit numbers which is odd multiple of 3 are 1499. Now, The 4-digit numbers which is an odd multiple of 9 are, 1017, 1035, ...999 These, are total 499. Then, required 4-digit numbers =1499−499=1000