If N5921 is divisible by 11, find the value of the smallest natural number N.

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  1. 6
  2. 9
  3. 7
  4. 8

Answer (Detailed Solution Below)

Option 4 : 8
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यूपी पुलिस SI (दरोगा) सामान्य हिंदी मॉक टेस्ट
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Detailed Solution

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Given:

Number N5921 is divisible by 11.

Formula Used:

A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is divisible by 11.

Calculation:

Let the number be N5921 where N is the unknown digit.

Digits in odd positions: N, 9, 1

Digits in even positions: 5, 2

Sum of digits in odd positions = N + 9 + 1 = N + 10

Sum of digits in even positions = 5 + 2 = 7

For divisibility by 11:

Difference = (N + 10) - 7

⇒ Difference = N + 3

For divisibility by 11:

⇒ N + 3 ≡ 0 (mod 11)

⇒ N ≡ -3 (mod 11)

⇒ N ≡ 8 (mod 11) [Since -3 + 11 = 8]

Smallest natural number N = 8

Answer: The smallest natural number N is 8.

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