Question

If 64y8 is exactly divisible by 3, then the least value of y is:

• A. 0
• B. 1
• C. 9
• D. 3

Answer 1

The correct option is A

0

$\because$ 64y8 is exactly divisible by 3

Then, the sum of its digits must be divisible by 3

$\therefore$ 6 + 4 + y + 8 or 18 + y is divisible by 3

Hence 18 + y = 3 , 6 , 9, 12, 15 , 18 , 21 ....( Multiple of 3 )

If 18 + y = 3 ; y = -15

If 18 + y = 6 ; y = -12

If 18 + y = 9 ; y = -9

If 18 + y = 12; y = -6

If 18 + y = 15 ; y = -3

If 18 + y = 18 ; y = 0

If 18 + y = 21 ; y = 3

If 18 + y = 24 ; y = 6

Hence the possible values of y can be 0 , 3 , 6 , 9... ( Since y cannot have a negative value as well it cannot have a double digit number.

Hence the least value of y = 0