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.

Abhijit K wrote: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 sent the second greatest number of representatives, 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.

Looking at Statement 1, one country sends 41 representatives. 75-41 = 34. So there are 34 to be allocated among the rest. If A sent the second greatest number, then A could not have sent 41.

To find the maximum value of A, allocate the smallest numbers possible to the other four, 1, 2, 3 and 4.

Add them up to get 10. 34 - 10 = 24 = A So in this case A > 10.

To see if A can also be below 10, make A 9 and see if the rest can take the remaining representatives.

34 - 9 = 25. 8 + 7 + 6 + 4 = 25.

So if one country sent 41 representatives, A can have sent 24 or 9 and Statement 1 is insufficient.

Statement 2 says that A is less that 12. We already know that A can be less than 10. Can A be 10 or 11?

If we reduce one of these, 8 + 7 + 6 + 4 = 25, by two, we can change A to 11. So A can be less than 12 and either greater than or less than 10. So Statement 2 is insufficient.

Also, when analyzing Statement 2, we continued using the assumption that one of the countries sent 41 representatives. So we don't need to do any further work to find that the two statements combined are also insufficient.

Choose E.