# The total number of 4-digit numbers whose greatest common divisor with 18 is 3, is________ Option: 1 1000 Option: 2 900 Option: 3 700 Option: 4 800

Let N be the four-digit number gcd(N,18) = 3

Hence N is an odd integer that is divisible by 3 but not by 9.

4 digit odd multiples of 3 1005, 1011,......., 9999 ⇒ 1500

$\\\text{becaues,}\\9999= 1005+(n-1)\times 6\\\Rightarrow n=1500$

4 digit odd multiples of 9 1017, 1035,......., 9999 ⇒ 500

$\\\text{becaues,}\\9999= 1017+(n-1)\times 18\\\Rightarrow n=500$

Hence the number of such N = 1000

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