The Mean, Median and Mode of seven numbers are 8, 7 and 6 respectively. Two of the numbers are 8 and 10. If the smallest of the seven numbers is 4, find the largest of the seven numbers.

Sure, let's solve this step by step:

1. We know that the mean of the seven numbers is 8. The mean is calculated by adding all the numbers together and dividing by the number of numbers. So, the sum of all seven numbers is 8 * 7 = 56.

2. We know that two of the numbers are 8 and 10, and the smallest number is 4. So, the sum of the remaining four numbers is 56 - 8 - 10 - 4 = 34.

3. We know that the median of the seven numbers is 7. The median is the middle number when the numbers are arranged in ascending order. Since there are seven numbers, the fourth number is the median. We already have the first number (4) and the second and third numbers (which must be 6 because the mode is 6 and there must be at least two 6s). So, the remaining numbers must be greater than 7.

4. Therefore, the sum of the last three numbers is 34 - 6 - 6 = 22. Since these three numbers are all greater than 7, and they must be integers, the only possible values for them are 8, 7, and 7.

5. Therefore, the largest of the seven numbers is 10.