When a number is divided by 13, the remainder is 10. When the same number is divided by 17, the remainder is 8. What is the number?  Options :329336348353

The problem can be solved using the Chinese Remainder Theorem.

Step 1: Write down the given conditions. We have two conditions: a) When the number is divided by 13, the remainder is 10. b) When the same number is divided by 17, the remainder is 8.

Step 2: Write these conditions in the form of equations. Let's denote the unknown number as x. Then we can write: a) x ≡ 10 (mod 13) b) x ≡ 8 (mod 17)

Step 3: Solve these equations. We are looking for a number that satisfies both of these conditions. We can start by checking the given options.

Option 1: 329 329 divided by 13 gives a remainder of 3, not 10. So, this option is incorrect.

Option 2: 336 336 divided by 13 gives a remainder of 9, not 10. So, this option is incorrect.

Option 3: 348 348 divided by 13 gives a remainder of 10, which satisfies the first condition. 348 divided by 17 gives a remainder of 8, which satisfies the second condition. So, this option is correct.

Option 4: 353 353 divided by 13 gives a remainder of 1, not 10. So, this option is incorrect.

So, the number that satisfies both conditions is 348.