Advertisements
Advertisements
Question
Given that the number \[\overline{{67y19}}\] is divisible by 9, where y is a digit, what are the possible values of y?
Advertisements
Solution
\[\text{ It is given that }\overline{{67y19}}\text{ is a multiple of 9 }. \]
\[ \therefore (6 + 7 + y + 1 + 9)\text{ is a multiple of 9 .} \]
\[ \therefore (23 + y)\text{ is a multiple of 9 . }\]
\[23 + y = 0, 9, 18, 27, 36 . . . \]
\[\text{ But }x\text{ is a digit . So, }x\text{ can take values }0, 1, 2, 3, 4 . . . 9 . \]
\[23 + y = 27\]
\[ \Rightarrow y = 4\]
APPEARS IN
RELATED QUESTIONS
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)
Which of the following statement is true?
If a number is divisible by 3, it must be divisible by 9.
Which of the following statement is true?
If a number is divisible by 9, it must be divisible by 3.
Find which of the following numbers are divisible by 3:
(i) 261
(ii) 777
(iii) 6657
(iv) 2574
28×6 a multiple of 3?
There are some flowering trees in a garden. Each tree bears many flowers with the same number printed on it. Three children took a basket each to pick flowers. Each basket has one of the numbers, 3, 4 or 9 on it. Each child picks those flowers which have numbers divisible by the number on his or her basket. He/She takes only 1 flower from each tree. Can you tell which numbers the flowers in each basket will have?
Check the divisibility of 15287 by 3.
Let abc be a three digit number. Then abc + bca + cab is not divisible by ______.
If x + y + z = 6 and z is an odd digit, then the three-digit number xyz is ______.
Why is 872 NOT divisible by 3?
