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

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

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

Answer

Explanation:

Finding the pattern:
To find the remainder when the number X is divided by 9, we need to first observe the pattern in the given number sequence. We notice that the sum of the digits of each number in the sequence from 101 to 150 is constant at 3. This is because for each number, the hundreds place digit is always 1, so the sum of the digits will always be 1 + the tens place digit + the units place digit, which is always equal to 3.

Applying divisibility rule:
According to the divisibility rule of 9, a number is divisible by 9 if the sum of its digits is divisible by 9. In this case, the sum of the digits of each number in the sequence is 3, which is divisible by 9.

Conclusion:
Since the sum of the digits of each number in the sequence is divisible by 9, the entire number X will also be divisible by 9. Therefore, the remainder when X is divided by 9 is 0.

Final Answer:
The remainder when the number X is divided by 9 is 0.

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