What is the largest 5-digit number, which leaves the remainder 7, when divided by 18 as well as by 11 ? 

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CDS Elementary Mathematics 16 April 2023 Official Paper
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  1. 99981
  2. 99988
  3. 99997
  4. 99999

Answer (Detailed Solution Below)

Option 3 : 99997
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Detailed Solution

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Concept:

Divisibility rule of 11: The given number can only be completely divided by 11 if the difference between the sum of digits at the odd position and the sum of digits at the even position in a number is 0 or 11.

Calculation:

Let the required number be n.

According to the question, 

n the remainder 7 when divided by 11. Therefore, n - 7 will be completely divisible by 11.

Now, let's check the options

Option:1   99981 - 7 = 99974 which is not divisible by 11.

Option:2   99988 - 7 = 99981 which is not divisible by 11.

Option:3   99997 - 7 = 99990 which is divisible by 11.

Option:4   99999 - 7 = 99992 which is not divisible by 11.

∴ The required value is 99997.

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