X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.a)2b)3c)4d)5Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Solution:

We need to find the remainder when the number X is divided by 9.

To find the remainder of a number when divided by 9, we need to sum up the digits of the number until we get a single digit number. This single digit number is the remainder when the original number is divided by 9.

Let us add the digits of the number X:

1 + 0 + 1 + 1 + 0 + 2 + 1 + 0 + 3 + 1 + 0 + 4 + 1 + 0 + 5 + 1 + 0 + 6 + 1 + 0 + 7 + 1 + 0 + 8 + 1 + 0 + 9 + 1 + 1 + 0 + 0 + 1 + 1 + 1 + 0 + 2 + 1 + 1 + 3 + 1 + 1 + 4 + 1 + 1 + 5 + 0

= 51

Now, we need to sum up the digits of 51:

5 + 1 = 6

Therefore, the remainder when X is divided by 9 is 6.

Hence, option A (2) is incorrect, and the correct answer is option A (6).

Answer

The divisibility rule for 9 is sum of the digits is to be divisible by 9. So

We calculate separately, sum of the digits in hundreds place, tenths place, and units place.

Sum of the digits in hundreds place: 1 x 50 = 50

Sum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105

Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225

So total = 380

So remainder = 380 / 9 = 2

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