Question

if 37zy is a multiple of 3,where z is a digit whatmight be the possible values of z,y?

Answer 1

Answer :

Given : 37zy is a multiple of 3 and z and y are digits .

We know If sum of all digits of number is divisible by three than whole number also divisible by 3 .

So,
3 + 7 + z + y

= z + y + 10

And if we take z = 2 and y = 0 , then

= 2 + 0 + 10 = 12 ( that is divisible by 3 , so 3720 also divisible by 3 )

Or

We take z = 2 and y = 3 , then

= 2 + 3 + 10 = 15 ( that is divisible by 3 , so 3723 also divisible by 3 )

Or

we take z = 2 and y = 6 , then

= 2 + 6 + 10 = 18 ( that is divisible by 3 , so 3726 also divisible by 3 )

Or

we take z = 2 and y = 9 , then

= 2 + 9 + 10 = 21 ( that is divisible by 3 , so 3729 also divisible by 3 )

Or

We take z = 3 and y = 2 , then

= 3 + 2 + 10 = 15 ( that is divisible by 3 , so 3732 also divisible by 3 )

Or

we take z = 3 and y = 5 , then

= 3 + 5 + 10 = 18 ( that is divisible by 3 , so 3735 also divisible by 3 )

Or

We take z = 3 and y = 8 , then

= 3 + 8 + 10 = 21 ( that is divisible by 3 , so 3738 also divisible by 3 )

Or

We take z = 4 and y = 1 , then

= 4 + 1 + 10 = 15 ( that is divisible by 3 , so 3741 also divisible by 3 )

Or

We take z = 4 and y = 4 , then

= 4 + 4 + 10 = 18 ( that is divisible by 3 , so 3744 also divisible by 3 )

Or

We take z = 4 and y = 7 , then

= 4 + 7 + 10 = 21 ( that is divisible by 3 , so 3747 also divisible by 3 )

Or

We take z = 5 and y = 0 , then

= 5 + 0 + 10 = 15 ( that is divisible by 3 , so 3750 also divisible by 3 )

Or

We take z = 5 and y = 3 , then

= 5 + 3 + 10 = 18 ( that is divisible by 3 , so 3753 also divisible by 3 )

Or

We take z = 5 and y = 6 , then

= 5 + 6 + 10 = 21 ( that is divisible by 3 , so 3756 also divisible by 3 )

Or

We take z = 6 and y = 2 , then

= 6 + 2 + 10 = 18 ( that is divisible by 3 , so 3762 also divisible by 3 )

Or

We take z = 6 and y = 5 , then

= 6 + 5 + 10 = 21 ( that is divisible by 3 , so 3765 also divisible by 3 )

And so on