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Divisibility Tests for 11

Which of the ...

Question

Which of the following statements are correct regarding the number $12, 375$ :
$I .$ divisible by $3$
$I I .$ divisible by $11$
$I I I .$ divisible by $9$

I, I I a n d I I I

are correct.

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I a n d I I

are correct.

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I I a n d I I I

are correct.

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I a n d I I I

are correct.

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Solution

The correct option is A $I, I I a n d I I I$ are correct.
The sum of digits is $1 + 2 + 3 + 7 + 5 = 18$ .
As the sum is a multiple of $9$ , the number is divisible by $3$ and $9$ .
The sum of digits in odd places is $1 + 3 + 5 = 9$ .
The sum of digits in even places is $2 + 7 = 9$ .
Sum of digits at odd places $= 1 + 3 + 5 = 9$
Sum of digits at even places $= 2 + 7 = 9$
Difference of Sum $= 9 - 9 = 0$
As the difference between the sum of digits at even and odd places is $0$ , So, the number is divisible by $11$ .
Therefore, the number is divisible by $3, 11$ and $9$ .

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12, 375

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a_{1} a_{2} a_{3} a_{4} a_{5}

a_{1} + a_{2} + a_{3} + a_{4} + a_{5}

9.

a_{1} - a_{2} + a_{3} - a_{4} + a_{5}

9.

Find which of the following numbers are divisible by 11 :

(i) 2563 (ii) 8307 (iii) 95635

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