Question : How many of the following numbers are divisible by 3 but not by 9?
5826, 5964, 6039, 6336, 6489, 6564, 6867, and 6960
Option 1: 5
Option 2: 3
Option 3: 4
Option 4: 6
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Correct Answer: 4
Solution :
Given: 5826, 5964, 6039, 6336, 6489, 6564, 6867, and 6960.
We know, a number is divisible by 3 if the sum of the digits of the number is divisible by 3.
Also, a number is divisible by 9 if the sum of the digits of the number is divisible by 9.
5 + 8 + 2 + 6 = 21 is divisible by 3 but not by 9,
So, 5826 is divisible by 3 but not by 9.
5964 = 24 is divisible by 3 but not by 9,
So, 5964 is divisible by 3 but not by 9.
6039 = 18 is divisible by 3 and 9 both.
So, 6039 is divisible by 3 and 9.
6 + 3 + 3 + 6 = 18 is divisible by 3 and 9 both.
So, 6336 is divisible by 3 and 9 both.
Similarly, we get,
6489 is divisible by 3 and 9 both.
6564 is divisible by 3 but not by 9.
6867 is divisible by 3 and 9 both.
6960 is divisible by 3 but not by 9.
Therefore 5826, 5964, 6564, and 6960 are divisible by 3 but not by 9.
Hence, the correct answer is 4.
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