Must be A.

4 numbers must be less than or equal to 15 and 4 numbers must be greater than or equal to 15 (because median = 15)

Now, the mean is 15. Hence, the numbers must add up to 135.

Option E is eliminated because it does not satisfy the condition of median. We get the smallest number as 16, which is greater than median. Therefore, it is impossible.

Option D: If 27 is the largest number, 15 is the smallest numbers; then all other numbers upto median must be 15. That would add up to 75. Summing that up with 27 gives us 102. Thus, we need to fit in the next three numbers which are greater than the median (15), however, their total must not be more than 135-102 = 33. This is impossible.

Similar calculations show that Option B and Option C also don't satisfy the condition.

Option A: If 23 is the largest number, the smallest number is (23+3)/2=13. If all numbers upto the median are 13, then they would add up to 52, plus the median i.e 15 would give 67. The largest number is 23. Therefore, the sum is 67+23=90. 135 - 90 = 45. Fitting three numbers greater than or equal to 15 and adding up to 45 is possible. Therefore, A is the answer.

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"Success is a lousy teacher. It seduces smart people to think they can't lose" - Bill Gates.