Directions: Analyze the details provided below to answer the following question.

Eight professionals completed their project submissions across four consecutive months—March, April, May, and June—on two specific dates of each month: the 7th and 22nd.

M finished her submission in a month containing 31 days. Exactly four professionals submitted between M and T, with T submitting after M. T did not submit on the final available date. One person submitted between T and B. The count of individuals who submitted prior to B equals the count of individuals who submitted after W. L made his submission on an odd-numbered date during a 30-day month. Three professionals submitted between L and Q. Q submitted in the same month as K. J submitted after E but before N.

Which of the following professionals completed their project submission on May 7th?

Correct Answer: J

To determine which professional submitted their project on May 7th, we can analyze the given conditions step-by-step by mapping out the eight available submission dates across the four months:

1. March 7 (31 days)
2. March 22 (31 days)
3. April 7 (30 days)
4. April 22 (30 days)
5. May 7 (31 days)
6. May 22 (31 days)
7. June 7 (30 days)
8. June 22 (30 days)

Step 1: Position of M and T
M submitted in a month with 31 days (March or May). Exactly 4 professionals submitted between M and T, and T submitted after M.

$\mathrm{Position\; of\; T}-\mathrm{Position\; of\; M}=5$

- If M submitted on March 7th (Position 1), then T submitted on May 22nd (Position 6).
- If M submitted on March 22nd (Position 2), then T submitted on June 7th (Position 7).
- (M cannot submit in May because Position 5 + 5 = 10, which exceeds the 8 available slots).

Step 2: Position of B and W
Exactly one person submitted between T and B.

$|\mathrm{Position\; of\; B}-\mathrm{Position\; of\; T}|=2$

The count of individuals who submitted prior to B equals the count of individuals who submitted after W. If B is at Position 8 (June 22nd), there are 7 people before B, which means there must be 7 people after W. This places W at Position 1 (March 7th).

Step 3: Position of L, Q, and K
L made his submission on an odd-numbered date (7th) during a 30-day month (April or June). Thus, L is either on April 7th (Position 3) or June 7th (Position 7).
Three professionals submitted between L and Q, which means:

$|\mathrm{Position\; of\; L}-\mathrm{Position\; of\; Q}|=4$

So, L and Q occupy Positions 3 and 7 in some order.
Q submitted in the same month as K:
- If Q were on June 7th (Position 7), K would have to be on June 22nd (Position 8), which is occupied by B.
- Therefore, Q must be on April 7th (Position 3), which makes K occupy April 22nd (Position 4) in the same month (April).
- This leaves L on June 7th (Position 7).

Step 4: Finalizing the Schedule
With Q at Position 3 and K at Position 4, B is confirmed at Position 8 (June 22nd). Consequently, T is at Position 6 (May 22nd) and M is at Position 1 (March 7th).

Step 5: Placing E, J, and N
We are given that J submitted after E but before N.

$\mathrm{Date\; of\; E}<\mathrm{Date\; of\; J}<\mathrm{Date\; of\; N}$

The remaining open dates are Position 2 (March 22nd), Position 5 (May 7th), and Position 8 (June 22nd):
- March 22nd (Position 2): E
- May 7th (Position 5): J
- June 22nd (Position 8): N

Complete Schedule:
- March 7th: M (and W)
- March 22nd: E
- April 7th: Q
- April 22nd: K
- May 7th: J
- May 22nd: T
- June 7th: L
- June 22nd: B (and N)

Therefore, J completed their project submission on May 7th.