What is the remainder when 90 + 9 + 92.........................+ 98�

1.	What is the remainder when 90 + 9 + 92.........................+ 98 is divided by 6 ?
Answer» Correct Answer - Option 2 : 1 Given: 90 + 9 + 92.........................+ 98. Formula used: a⁰ = 1 (where a = any number) Calculations: 6 is an even multiple of 3. When any even multiple of 3 is divided by 6, it will leave a remainder of 0. Or in other words, it is perfectly divisible by 6. On the contrary, when any odd multiple of 3 is divided by 6, it will leave a remainder of 3. For e.g when 9 an odd multiple of 3 is divided by 6, you will get a remainder of 3. 9 is an odd multiple of 3. And all powers of 9 are odd multiples of 3. Therefore, when each of the 8 powers of 9 listed above is divided by 6, each of them will leave a remainder of 3. ⇒ The total value of the remainder $= 3 + 3 + . . . . + 3 (8 remainders) = 24$ $= 3 + 3 + . . . . + 3 (8 remainders) = 24$ 24 is divisible by 6 and 1 will reminder. ∴ The remainder when $9^{1} + 9^{2} + 9^{3} + . . . . + 9^{8}$ $= 3 + 3 + . . . . + 3 (8 remainders) = 24$

What is the remainder when 90 + 9 + 92.........................+ 98 is divided by 6 ?

Answer» Correct Answer - Option 2 : 1

Given:

90 + 9 + 92.........................+ 98.

Formula used:

a⁰ = 1 (where a = any number)

Calculations:

6 is an even multiple of 3. When any even multiple of 3 is divided by 6, it will leave a remainder of 0. Or in other words, it is perfectly divisible by 6.

On the contrary, when any odd multiple of 3 is divided by 6, it will leave a remainder of 3. For e.g when 9 an odd multiple of 3 is divided by 6, you will get a remainder of 3.

9 is an odd multiple of 3. And all powers of 9 are odd multiples of 3.
Therefore, when each of the 8 powers of 9 listed above is divided by 6, each of them will leave a remainder of 3.

⇒ The total value of the remainder $= 3 + 3 + . . . . + 3 (8 remainders) = 24$

$= 3 + 3 + . . . . + 3 (8 remainders) = 24$ 24 is divisible by 6 and 1 will reminder.

∴ The remainder when $9^{1} + 9^{2} + 9^{3} + . . . . + 9^{8}$

= 3 + 3 + . . . . + 3 (8 remainders) = 24

What is the remainder when 90 + 9 + 92.........................+ 98 is divided by 6 ?

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