Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if country A sent the second highest number of representative, did country A send at least 10 representatives?

1. One of the six countries sent 41 representatives to the congress.
2. Country A sent fewer than 12 representatives to the congress.

Let the 6 countries be A, B, C, D, E and F.

The question stem asks whether A≥10.
Plug in A=10 (which satisfies statement 2 and is at least 10) and A=9 (which also satisfies statement 2 but is NOT at least 10).
To save time, let F=41, which satisfies statement 1.

Case 1: Total = 75, F=41, A=10.
Remaining representatives for B, C, D and E = 75-41-10 = 24.
The following combination works for B, C, D and E:
B=9
C=8
D=6
E=1.
Thus, it's possible that A=10.

Case 2: Total = 75, F=41, A=9.
Remaining representatives for B, C, D and E = 75-41-9 = 25.
The following combination works for B, C, D and E:
B=8
C=7
D=6
E=4.
Thus, it's possible that A<10.

Since it's possible that A=10 or that A<10, the two statements combined are INSUFFICIENT.

The correct answer is E.

Guru,

Are you saying that DS problems HAVE to yield the same answer? I would answer that Stmt 1 is sufficient, but Stmt 2 is not. Maybe my logic is flawed in assuming that the point of DS isn't, necessarily, to actually solve the problem, but rather to figure out if there is enough information given to solve the problem. This problem asks if country A sent at least 10reps, you can answer that question with just Stmt 1, but just Stmt 2 is not sufficient.