How many of the following numbers are divisible by 3 but NOT by 9?
5826, 5964, 6039, 6336, 6489, 6564, 6867 and 6960
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4.
A number is divisible by 3 if the sum of its digits is divisible by 3.
and
A number is divisible by 9 if the sum of its digits is divisible by 9.
Now, let's check each number.
5826:
⇒ Sum of digits = 5 + 8 + 2 + 6 = 21
⇒ 21 is divisible by 3 but not by 9.
5964:
⇒ Sum of digits = 5+9+6+4=24
⇒ 24 is divisible by 3 but not by 9.
6039:
⇒ Sum of digits = 6 + 0 + 3 + 9 = 18
⇒ 18 is divisible by both 3 and 9.
6336:
⇒ Sum of digits = 6 + 3 + 3 + 6 = 18
⇒ 18 is divisible by both 3 and 9.
6489:
⇒ Sum of digits = 6 + 4 + 8 + 9 = 27
⇒ 27 is divisible by both 3 and 9.
6564:
⇒ Sum of digits = 6 + 5 + 6 + 4 = 21
⇒ 21 is divisible by 3 but not by 9.
6867:
⇒ Sum of digits = 6 + 8 + 6 + 7 = 27
⇒ 27 is divisible by both 3 and 9.
6960:
⇒ Sum of digits = 6 + 9 + 6 + 0 = 21
⇒ 21 is divisible by 3 but not by 9.
Numbers divisible by 3 but not by 9 are 5826, 5964, 6564, and 6960.
Thus, 4 numbers are divisible by 3 but not by 9.