The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is
Answer: 1000
Solutions · 1
Official solution
gcd(x,18)=3 means x is an odd multiple of 3 that is not a multiple of 9 (since 18=2×32).
4-digit odd multiples of 3: from 1005 to 9999, giving 1499 numbers.
4-digit odd multiples of 9: from 1017 to 9999, giving 499 numbers.
\[\text{Required} = 1499-499 = 1000\]