E is the Answer
Statement (1) alone only provides us information about when A and C cannot meet. It does not provide any information about when each of the pilots ARE able to meet. While we know that A and C cannot meet together, it is possible that some combination of three pilots would be able to meet together (such as ABD or CBE). Statement (1) alone therefore does not provide enough information to be able to definitively answer this question YES or NO.
Statement (2) alone provides us with specific information about when B and E can meet. However we are not provided with information as to whether one of the other pilots --A, C or D -- will be able to join them for the meeting. Thus, statement (2) alone is not sufficient to answer this question
In analyzing statements (1) and (2) together, it is helpful to list the 10 possible ways that 3 of the pilots could meet:
1. ABC
2. ABD
3. ABE
4. ACD
5. ACE
6. ADE
7. BCD
8. BCE
9. BDE
10. CDE
Statements (1) and (2) taken together preclude pilots A or C from meeting with pilots B and E. This is due to the fact that pilots B and E can only meet for two straight hours from 10:30 PM to 12:30 AM starting on either Monday, Tuesday, Wednesday, or Thursday night while pilots A and C can never meet during the AM hours of any weekday (leaving the 12:00 AM to 12:30 AM slot impossible). This eliminates 8 of the 10 possibilities (1, 2, 3, 5, 6 because A can't meet with B or E and 7, 8, 10 because C can't meet with B or E.)
In addition, since pilot A cannot meet with pilot C, possibility 4 is also eliminated.
Thus, the only possibility that remains is #9: BDE. The question stem states that D is able to meet at any time that B cannot. It may be tempting to use this information to conclude that B and D are not able to meet together. However, while we know for sure that D is able to meet at any time that B cannot, this does not preclude the possibility that D is ALSO able to meet at times when B can meet. Given that we don't know whether or not D can meet at the same time that B and E can meet - we do not have enough information to evaluate whether pilots B, D, and E will be able to meet together.
Therefore, the correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient.
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