Question

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is _______.

Answer 1

The correct answer is 150
$∵ x ∈ [100, 999], x ∈ N$
Then
$\frac{x}{2} ∈ [ 50,499 ], \frac{x}{2} ∈ N$
Number whose G.C.D with 18 is 1 in this range have the required condition.
There are 6 such number from 18 × 3 to 18 × 4.
Similarly from 18 × 4 to 18 × 5….., 26 × 18 to 27 × 18
The extra numbers are 53, 487, 491, 493, 497 and 499.
∴ Total numbers = 24 × 6 + 6 = 150