A small radio station was jointly owned by two partners unti

Let the senior partner be A and junior be B

Total shares of A = 1200 (sold shares) + x (exchanged shares)
Total shares of B = y (sold shares) + 800 (exchanged shares)
Sold Shares = 1200 + y ----------------------{1}
Exchanged shares = x + 800 ---------------{2}

Total shares = 1200 + x + y + 800 -------> 2000 + x + y

what is the greatest possible number of shares the senior partner exchanged? --------> What is greatest possible integer value does x can take ?

(1) Before the acquisition, the partners jointly owned 4,000 shares of the radio station. ----------> Total shares = 4000 = 2000 + x + y -------> 2000 = x+y ---------> x can be 1999 max. Sufficient.

(2) Fewer than half of the station’s shares were sold. ---------> Fewer than half of the (2000 + x + y) shares were sold.

We know from the {1} that sold shares are equal to (1200 + y) ---------> So \(1200 + y < \frac{2000+x+y}{2}\) ---------->

-----> \(2400 + 2y < 2000 + x + y\) --------> \(400 < x - y\) ---------> \(x - y > 400\) -----> x can take any value. Hence Not sufficient.
Choice A

Though B will never help to answer, Can anyone enlighten how will A help to reach the answer?

If i apply the same logic you used for option 'a' then since in option 'b' it is mentioned that "Fewer than half of the station’s shares were sold" .My main goal is to maximize 'x' and 2000 + x + y=4000 which is the total number of shares so if again i put y=1 then x=1999 which is the maximum value that x can take .Also the other condition "Fewer than half of the station’s shares were sold" i.e 1201 is satisfied. So the answer should be D.

This is exactly how I solved this but the following explanation by Kaplan made me question my solution;

This Value question asks for the greatest possible number of shares a senior partner exchanged during an acquisition. Let’s call that number x. For sufficiency, we need to be able to answer the question with a single value.

We’re told that the senior partner sold 1,200 shares; if a statement tells us how many shares he had to start with, we’ll know how many he exchanged (x = [total owned by senior partner] – 1,200). But the question asks about the greatest possible number of shares he exchanged. This suggests we won’t learn the actual amount and will have to think about how the number of shares is limited.

Since we’re interested in the senior partner holding as many shares as possible, we want the junior partner to have as few as possible. The junior partner exchanges 800, but we aren’t told how many he sells. He must sell some, so the smallest possible number he sells is 1. Therefore, the smallest possible number of station shares held by the junior partner is 801.

This means that [total owned by senior partner] = [total of all radio station shares] – 801. To answer the question, we need the total of all the radio station’s shares. From that, we can calculate the number of shares owned by the senior partner, and from that we can calculate how many he exchanged.

Evaluate the Statements:

Statement (1): This statement gives us exactly what our analysis of the question stem told us that we need—the total shares of the radio station. Statement (1) is Sufficient to answer the question. Eliminate choices (B), (C), and (E).

Statement (2): We are told that fewer than half the initial shares were sold, and 1,201 is the smallest possible number of shares that were sold, so the total number of shares is larger than 2,402. But we still don’t know the exact number of shares, so Statement (2) is Insufficient to answer the question. Eliminate choice (D).

Therefore, Choice (A) is correct.

Hey, I totally get that to minimize the holdings of the the second person you assumed it to be 1.
But my question here is can we even do that in gmat?