There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first live such numbers, then what is the mean of all the thirteen numbers?

The mean of an odd number of consecutive odd numbers is the middle number. For the first five numbers, the mean is 39. This means the 3rd number among the first five is 39. Since they are consecutive odd numbers, the 3rd number is 39. The numbers are: 1st, 2nd, 3rd, 4th, 5th. The 3rd number is 39. The 2nd number is 39 - 2 = 37. The 1st number is 37 - 2 = 35. (Check: The first five numbers are 35, 37, 39, 41, 43. Their mean is (35+37+39+41+43)/5 = 195/5 = 39. This is correct.) The first number in the sequence of thirteen numbers is 35.

Now we need to find the mean of all thirteen numbers. The sequence starts with 35. The 13th number will be 35 + (13-1)2 = 35 + 122 = 35 + 24 = 59. So the thirteen numbers are 35, 37, ..., 59.

For an arithmetic progression (like consecutive odd numbers), the mean is the average of the first and last term. Mean = (First term + Last term) / 2 Mean = (35 + 59) / 2 = 94 / 2 = 47.

Alternatively, for an odd number of terms in an arithmetic progression, the mean is the middle term. There are 13 terms, so the middle term is the (13+1)/2 = 7th term. The 7th term = First term + (7-1)2 = 35 + 62 = 35 + 12 = 47.

Thus, the mean of all thirteen numbers is 47.

Analyzing the options: A) 47: This matches our calculated mean. B) 49: Incorrect. C) 51: Incorrect. D) 45: Incorrect.

The final answer is A) 47.