In the six digit number 8()6()4(), the symbol () stands for the same digit. How many of the six digit numbers that can be formed by replacing () with a digit are divisible by 9 ?
Answers
Answer:
806040
836343
866646
896949
Step-by-step explanation:
8+0+6+0+4+0=18 is divisible by 9
8+3+6+3+4+3=27 is divisible by 9
8+6+6+6+4+6=36 is divisible by 9
8+9+6+9+4+9=45 is divisible by 9
Solution :-
Let us assume that, () is denoted by x .
So, six digit number is 8x6x4x .
we know that,
- When sum of all digits is divisible by 9 , the given number is also divisible by 9 .
then,
→ (8 + x + 6 + 4 + x) ÷ 9 = Remainder 0
→ (18 + 3x) ÷ 9 = Remainder 0
Putting value of x from 0 to 9 we get,
- x = 0, => (18 + 3 * 0) = 18 ÷ 9 = Remainder 0 .
- x = 1, => (18 + 3 * 1) = 21 ÷ 9 ≠ Remainder 0 .
- x = 2, => (18 + 3 * 2) = 24 ÷ 9 ≠ Remainder 0 .
- x = 3, => (18 + 3 * 3) = 27 ÷ 9 = Remainder 0 .
- x = 4, => (18 + 3 * 4) = 30 ÷ 9 ≠ Remainder 0 .
- x = 5, => (18 + 3 * 5) = 33 ÷ 9 ≠ Remainder 0 .
- x = 6, => (18 + 3 * 6) = 36 ÷ 9 = Remainder 0 .
- x = 7, => (18 + 3 * 7) = 39 ÷ 9 ≠ Remainder 0 .
- x = 8, => (18 + 3 * 8) = 42 ÷ 9 ≠ Remainder 0 .
- x = 9, => (18 + 3 * 9) = 45 ÷ 9 = Remainder 0 .
therefore, Possible values of x are ,
- x = 0, 3, 6 and 9 .
hence, Possible Four six digits numbers are,
- 806040
- 836343
- 866646
- 896949
Total four six digit numbers can be formed by replacing () with a digit are divisible by 9 .
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