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UPSC Prelims

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

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CSAT 2023

Q27 2023, Number System: Divisibility Rules

A number N is formed by writing 9 for 99 times, what is the remainder if N is divided by 13?

9 को 99 बार लिख कर कोई संख्या N बनाई जाती है । यदि N को 13 से विभाजित किया जाए, तो शेषफल क्या होगा?

Explanation Please wait..

Any digit repeated (P - 1) times is divisible by P, where P is a prime number > 5.

Number = 9999 …… 99 times

The number 9 repeated 12 times is divisible by 13.

In 99 digits, 12-digit long numbers can be written for 96 times (12*8 = 96)

The number 9 repeated 96 times is divisible by 13.

The remainder when dividing 9 repeated 96 times by 13 is 0.

Hence, we only need to find out the remainder when we divide the remaining three digits by 13.

The remainder when dividing the number 999 by 13 is 11.

Therefore, the correct option is (a).

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