Question

using divisibility test determine which of the following numbers are divisible by 11 :-
a) 5445
b) 10824
c) 7138965
d) 70169308
e) 10000001
f>901153




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Answer 1

Answer:

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A number is divisible by 11 when the alternating sun of the digits and then subtracted are divisible by 11 or equal to 0.

a) 5445

5+4 = 9

4+5 = 9

9-9 = 0

So, 5445 is divisible by 11

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b) 10824

1+8+4 = 13

0+2 = 2

13-2 = 11

So, 10824 is divisible by 11

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c) 7138965

7+3+9+5 = 24

1+8+6 = 15

24-15 = 9

So, 7138965 is not divisible by 11

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d) 70169308

7+1+9+0 = 17

0+6+3+8 = 17

17-17 = 0

So, 70169308 is divisible by 11

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e) 10000001

1+0+0+0 = 1

0+0+0+1 = 1

1-1 = 0

So, 10000001 is divisible by 11

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f) 901153

9+1+5 = 15

0+1+3 = 4

15-4 = 11

So, 901153 is divisible by 11

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Answer 2

Solution:

We will be using the concepts of divisibility by 11 to solve this.

A number is divisible by 11 if the difference between the sum of the digits at odd places and the sum of the digits at even places is divisible by 11.

(a) Given number = 5445

Sum of the digits at odd places = 5 + 4 = 9 and sum of the digits at even places = 4 + 5 = 9

Difference = 9 – 9 = 0, which is divisible by 11.

Therefore, the number 5445 is divisible by 11.

(b) Given number = 10824

Sum of the digits at odd places = 4 + 8 + 1 = 13 and  Sum of the digits at even places = 2 + 0 = 2

Difference = 13 – 2 = 11, which is divisible by 11.

Therefore, the number 10824 is divisible by 11.

(c) Given number = 7138965

Sum of the digits at odd places = 5 + 9 + 3 + 7 = 24 and Sum of the digits at even places = 6 + 8 + 1 = 15

Difference = 24 – 15 = 9, which is not divisible by 11.

Therefore, the number 7138965 is not divisible by 11.

(d) Given number = 70169308

Sum of digits at odd places = 0 + 9 + 1 + 7 = 17 and Sum of all the digits at even places = 8 + 3 + 6 + 0 = 17

Difference = 17-17 = 0, which is divisible by 11.

Therefore, the number 70169308 is divisible by 11.

(e) Given number = 10000001

Sum of all the digits at odd places = 1 + 0 + 0 + 0 = 1 and Sum of the digits at even places = 0 + 0 + 0 + 1 = 1

Difference = 1 – 1 = 0, which is divisible by 11.

Therefore, the number 10000001 is divisible by 11.

(f) Given number = 901153

Sum of all the digits at odd places = 9 + 1 + 5 = 15 and Sum of the digits at even places = 0 + 1 + 3 = 4

Difference = 15 - 4 = 11, which is divisible by 11.

Therefore, the number 901153 is divisible by 11.