Hi, there. This is a tricky question, and I'm happy to help with it.
Prompt:
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 greatest number of representatives, did Country A send at least 10 representatives?
So, we have a list of six numbers, no two the same. The sum of the list is 75, and A is the second-highest number on the list. We want to know, A >= 10?
Statement #1: One of the 6 countries sent 41 representatives to the congress.
Suppose one country sent 41 delegate --- the other five combined sent the other 34.
So, 41 is the highest number in our set of six. The next highest is A. Here's a set of the remaining five numbers where A is greater than ten . . .
{1, 2, 3, 4, 24}
and here's a list of five numbers where A is less than ten . . .
{4, 6, 7, 8, 9}
Both of those have a sum of 34. Therefore, with this statement, we can construct lists to answer the prompt either way. This means, this statement does not provide a means for definitively determining an answer to the prompt question. Statement #1 is
insufficient.
Statement #2: Country A sent fewer than 12 representatives to the congress.
Could we make a list in which the second-greatest number was less than 12, but greater than or equal to 10?
Yes, the list {7, 8, 9, 10, 11, 30} has a sum of 75, and the second greatest number A is less than 12 but greater than or equal to 10.
Could we make a list in which the second-greatest number was less than 12, and also less than 10?
Yes, the list {1, 2, 3, 4, 5, 60} has a sum of 75, and the second greatest number A is less than 10.
Therefore, with this statement, we can construct lists to answer the prompt either way. This means, this statement does not provide a means for definitively determining an answer to the prompt question. Statement #2 is
insufficient.
Both Statements Combined:
We must impose the conditions that the max = 41 and A, the second-greatest number, is less than twelve. Will A be greater than or equal to 10?
Example one: {4, 5, 6, 8, 11, 41} ---> "yes" to prompt question
Example two: {4, 6, 7, 8, 9, 41} ---> "no" to prompt question
Both satisfy the combined conditions, and give opposite answer to the prompt. Combined, the statements are still
insufficient.
Answer =
E
Does that make sense? Please let me know if you have any further questions.
Mike
