Question 4 the day : April 25, 2003

The question for the day is from the topic of Number Systems and number theory and is a question on test of divisibility.

Question:
10²⁵ - 7 is divisible by

1. 2
2. 3
3. 9
4. Both (2) and (3)

Correct Answer - 3. Correct choice is (2)

Explanatory Answers

10²⁵ - 7 = (10²⁵ - 1) - 6

The number 10²⁵ - 1 = 99.....9 (25 digits) is divisible by 3 and 4.

Therefore, (10²⁵ - 1) - 6 = (24 nines and unit digit is 3) 99.......93.

This number is only divisible by 3 (from the given choices).

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