Which of the following is divisible by 11?

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UP Police SI (दरोगा) Official PYP (Held On: 21 Nov 2021 Shift 1)
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  1. 2699180
  2. 2999180
  3. 2899180
  4. 2799180

Answer (Detailed Solution Below)

Option 1 : 2699180
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UP Police SI (दरोगा) Official PYP (Held On: 2 Dec 2021 Shift 1)
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Detailed Solution

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Given:

Numbers: 2699180, 2999180, 2899180, 2799180

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:

For 2699180:

Odd positions: 2, 9, 1, 0 → Sum = 2 + 9 + 1 + 0 = 12

Even positions: 6, 9, 8 → Sum = 6 + 9 + 8 = 23

⇒ Difference = |12 - 23| = 11

⇒ 11 is divisible by 11, so 2699180 is divisible by 11.

For 2999180:

Odd positions: 2, 9, 1, 0 → Sum = 2 + 9 + 1 + 0 = 12

Even positions: 9, 9, 8 → Sum = 9 + 9 + 8 = 26

⇒ Difference = |12 - 26| = 14

⇒ 14 is not divisible by 11.

For 2899180:

Odd positions: 2, 9, 1, 0 → Sum = 2 + 9 + 1 + 0 = 12

Even positions: 8, 9, 8 → Sum = 8 + 9 + 8 = 25

⇒ Difference = |12 - 25| = 13

⇒ 13 is not divisible by 11.

For 2799180:

Odd positions: 2, 9, 1, 0 → Sum = 2 + 9 + 1 + 0 = 12

Even positions: 7, 9, 8 → Sum = 7 + 9 + 8 = 24

⇒ Difference = |12 - 24| = 12

⇒ 12 is not divisible by 11.

∴ The correct answer is option (1).

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