When 15 is appended to a list of integers, the mean is increased by 2.

We can solve it in 30 secs using the basic concept of what mean is - the value that can replace all values in a list.
When a new value 15 is added, the mean increases by 2. It means 15 has enough extra (above mean) to give 2 to each member of the list and itself.
When a new value 1 is added, the mean decrease by 1. It means 1 has enough deficit (below mean) to take away 1 from each member of the list and still be 1 less.
Looking at the difference between 15 and 1, we can say that we will likely have 4 or 5 numbers in the original list.

Say if we have 4 numbers in the original list, 15 has 10 extra (2 for each of the 4 members and for itself) and hence original mean must be 5. When we add 15, the mean becomes 7 and now we have 5 numbers in the list.
Now when 1 is added to the list, it is 6 less than the mean 7 and hence all 5 numbers give 1 to it to bring it up to 6 and the avg reduces to 6. It works.
Hence, we had 4 numbers in the list. The numbers given are very manageable so that we don't need to do much calculation, the hallmark of a good GMAT question.

Answer (A)

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