Determining the Initial Marbles in a Bag

Very Hard Data Sufficiency Determining Sufficiency

Let m be the number of marbles in a bag. Initially, there are m marbles.

After James adds 8 marbles and then removes p marbles, the total number of marbles left in the bag is 16.

We want to find the value of m.

Statement (1): James removes twice the number of marbles p that he added.

Statement (2): The initial number of marbles in the bag was less than 20.

Statement (1) alone is sufficient, but Statement (2) alone is not sufficient.

Statement (2) alone is sufficient, but Statement (1) alone is not sufficient.

Both statements together are sufficient, but neither statement alone is sufficient.

Each statement alone is sufficient.

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