Number System MCQs with Answers & Explanations

**Method 1: Using Algebra**

For a number to be divisible by 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

Step-by-step solution: 1. Add the ones place: 8 + 9. 2. Add the tens and hundreds to get 477. 3. Therefore, 408 + 69 = 477.

Step-by-step solution: 1. Recognize that division asks how many times 7 fits into 42. 2. 42 = 7 * 6. 3. So, 42 / 7 = 6.

Step-by-step solution: 1. Recognize that division asks how many times 15 fits into 75. 2. 75 = 15 * 5. 3. So, 75 / 15 = 5.

Step-by-step solution: 1. Recognize that division asks how many times 7 fits into 63. 2. 63 = 7 * 9. 3. So, 63 / 7 = 9.

Step-by-step solution: 1. Multiply 22 by 15. 2. Break the multiplication into tens and ones for clarity. 3. Combine partial products to get 330.

Step-by-step solution: 1. Align the numbers vertically. 2. Subtract the ones, tens, and hundreds to obtain 314. 3. Confirm the result: 412 - 98 = 314.

Step-by-step solution: 1. Recognize that division asks how many times 7 fits into 49. 2. 49 = 7 * 7. 3. So, 49 / 7 = 7.

Step-by-step solution: 1. Multiply 15 by 12. 2. Break the multiplication into tens and ones for clarity. 3. Combine partial products to get 180.

Step-by-step solution: 1. Add the ones place: 0 + 5. 2. Add the tens and hundreds to get 265. 3. Therefore, 180 + 85 = 265.

Step-by-step solution: 1. Add the ones place: 0 + 5. 2. Add the tens and hundreds to get 445. 3. Therefore, 360 + 85 = 445.

Step-by-step solution: 1. Add the ones place: 6 + 3. 2. Add the tens and hundreds to get 229. 3. Therefore, 156 + 73 = 229.

Step-by-step solution: 1. Recognize that division asks how many times 7 fits into 35. 2. 35 = 7 * 5. 3. So, 35 / 7 = 5.

Step-by-step solution: 1. Add the ones place: 0 + 5. 2. Add the tens and hundreds to get 385. 3. Therefore, 300 + 85 = 385.

Step-by-step solution: 1. Add the ones place: 8 + 9. 2. Add the tens and hundreds to get 417. 3. Therefore, 348 + 69 = 417.

Step-by-step solution: 1. Recognize that division asks how many times 7 fits into 56. 2. 56 = 7 * 8. 3. So, 56 / 7 = 8.

Step-by-step solution: 1. Align the numbers vertically. 2. Subtract the ones, tens, and hundreds to obtain 326. 3. Confirm the result: 428 - 102 = 326.

Step-by-step solution: 1. Add the ones place: 2 + 1. 2. Add the tens and hundreds to get 273. 3. Therefore, 192 + 81 = 273.

Step-by-step solution: 1. Recognize that division asks how many times 11 fits into 77. 2. 77 = 11 * 7. 3. So, 77 / 11 = 7.