Question

2. If 24x is a multiple of 9, where x is a digit, what is the value of x?
3. If 34y2 is a multiple of 3, where y is a digit, what might be the value of y?
4. If 4125 is a multiple of 3, where z is a digit, what might be the value of z?
5. If 273x6 is a multiple of 3, where x is a digit, what might be the value of x
Divisibility by 6
A number N is divisible by 6, if it is divisible both by 2 and 3.​

Answer 1

AnswerIf the number is divisible by 2 and 3, then it satisfy the divisibility rule of 6.

If the number is divisible by 2 and 3, then it satisfy the divisibility rule of 6.Example: 306 is divisible by both 2 and 3.

If the number is divisible by 2 and 3, then it satisfy the divisibility rule of 6.Example: 306 is divisible by both 2 and 3.Since the last digit is even, it is divisible by 2

If the number is divisible by 2 and 3, then it satisfy the divisibility rule of 6.Example: 306 is divisible by both 2 and 3.Since the last digit is even, it is divisible by 2The sum of the digits 3+0+6=9, which is multiple of 3.

5.Since 31z5 is a multiple of 3 ,the sum of its digits must be a multiple of 3 i.e. 3+1+z+5=9+z.

Since 31z5 is a multiple of 3 ,the sum of its digits must be a multiple of 3 i.e. 3+1+z+5=9+z.Hence 9+z is a multiple of 3

Since 24x is a multiple of 3, its sum of digits 6+x is a multiple of 3;

So, 6+x is one of these numbers: 0,3,6,9,13,15,18,….

Since x is a digit, it can only be that 6+x=6 or 9 or 12 or 15.

Therefore, x=0 or 3 or 6 or 9.

Thus, x can have any of four different values.