Multiple choice

[CAT 1998] A number is formed by writing first 54 natural numbers in front of each other as 12345678910111213... Find the remainder when this number is divided by 8.

  1. 1

  2. 7

  3. 2

  4. 0
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C Correct answer
Explanation

The number ends in ...5354. A number is divisible by 8 if its last three digits are divisible by 8. The last three digits are 354. 354 / 8 = 44 with a remainder of 2.

AI explanation

To find the remainder when dividing by 8, only the last three digits of the number are needed. The number is formed by writing first 54 natural numbers consecutively, ending with 5354. The last three digits are 354; dividing 354 by 8 gives a quotient of 44 and a remainder of 2, so the remainder is 2.

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