书学讨论：狗87 V2

200 people.  X only choose A. Y only choose B. Z choose both A and B.  N choose neither.

200 = X + Y + Z + N.
A = X + Z (A is a known number)
B = Y + Z (B is a known number)

The stimulus asks for X

1) Z = N.  Then
200 = X + Y + 2Z.  
A = X + Z (A is a known number)
B = Y + Z (B is a known number)

But this won't help us since if you add the 2nd and 3rd equation, you would get the same equation (A +B has to equal 200, though).  Insufficient.

2) X = 2Y.  Then
200 = 2Y + Y + Z + N = 3Y + Z + N
A = 2Y + Z (A is a known number)
B = Y + Z (B is a known number)

From the 2nd and 3rd equations, you get Y = (A - B).  Then X = 2* (A - B).  Sufficient.