Question ID: #384
The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is
Solution:
Total number of 3-digit numbers = $999 – 99 = 900$.
Number of 3-digit numbers divisible by 2 and 3 (i.e., divisible by 6):
$$ \frac{900}{6} = 150 $$
Number of 3-digit numbers divisible by 4 and 9 (i.e., divisible by 36):
$$ \frac{900}{36} = 25 $$
Therefore, the number of 3-digit numbers divisible by 2 and 3 but not by 4 and 9 is:
$$ 150 – 25 = 125 $$
Ans. (125)
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