How many of the following numbers are divisible by 3 but NOT by 9?
5826, 5964, 6039, 6336, 6489, 6564, 6867 and 6960

The correct option is 4.

To find how many of the given numbers are divisible by 3 but not by 9, we can use the divisibility rules for 3 and 9:
1. Divisibility Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
2. Divisibility Rule for 9: A number is divisible by 9 if the sum of its digits is divisible by 9.
Therefore, a number is divisible by 3 but NOT by 9 if the sum of its digits is a multiple of 3 but not a multiple of 9.

Let us calculate the sum of the digits for each of the given numbers:

1. 5826:
Sum of digits = 5 + 8 + 2 + 6 = 21
Since 21 is divisible by 3 (21 = 3 × 7) but not by 9, 5826 is divisible by 3 but not by 9.

2. 5964:
Sum of digits = 5 + 9 + 6 + 4 = 24
Since 24 is divisible by 3 (24 = 3 × 8) but not by 9, 5964 is divisible by 3 but not by 9.

3. 6039:
Sum of digits = 6 + 0 + 3 + 9 = 18
Since 18 is divisible by 9, 6039 is divisible by 9.

4. 6336:
Sum of digits = 6 + 3 + 3 + 6 = 18
Since 18 is divisible by 9, 6336 is divisible by 9.

5. 6489:
Sum of digits = 6 + 4 + 8 + 9 = 27
Since 27 is divisible by 9, 6489 is divisible by 9.

6. 6564:
Sum of digits = 6 + 5 + 6 + 4 = 21
Since 21 is divisible by 3 (21 = 3 × 7) but not by 9, 6564 is divisible by 3 but not by 9.

7. 6867:
Sum of digits = 6 + 8 + 6 + 7 = 27
Since 27 is divisible by 9, 6867 is divisible by 9.

8. 6960:
Sum of digits = 6 + 9 + 6 + 0 = 21
Since 21 is divisible by 3 (21 = 3 × 7) but not by 9, 6960 is divisible by 3 but not by 9.

Thus, there are exactly 4 numbers (5826, 5964, 6564, and 6960) that are divisible by 3 but not by 9.