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प्रश्न
If 31z5 is a multiple of 9, where z is a digit, what is the value of z? You will find that there are two answers for the last problem. Why is this so?
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उत्तर
If a number is a multiple of 9, then the sum of its digits will be divisible by 9.
Sum of digits of 31z5 = 3 + 1 + z + 5 = 9 + z
Hence, 9 + z should be a multiple of 9.
This is possible when 9 + z is any one of these numbers 0, 9, 18, 27, and so on …
However, since z is a single digit number, this sum can be either 9 or 18. Therefore, z should be either 0 or 9.
संबंधित प्रश्न
If 24x is a multiple of 3, where x is a digit, what is the value of x?
(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, 12, 15, 18…. But 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)
If 31z5 is a multiple of 3, where z is a digit, what might be the values of z?
Which of the following statement is true?
If a number is divisible by 3, it must be divisible by 9.
31×5 divisible by 3?
If the sum of digits of a number is divisible by three, then the number is always divisible by ______.
If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is ______.
Number of the form 3N + 2 will leave remainder 2 when divided by 3.
Write the smallest digit and the greatest digit in the blank space of the following number so that the number formed is divisible by 3:
4765 ______ 2
Why is 872 NOT divisible by 3?
The digit sum of 91 is 10. Therefore, 91 is:
