Explanation:

Let’s break it down, statement by statement:

- There are 7 people, 7 months: Jan, Mar, Apr, May, Jun, Jul, Aug. Each person has a unique month.

- P’s birthday is in January. That’s locked.

- R is right in the middle: 3 people before, 3 after. So R is 4th from the top.

- Only one person between S and R.

- Q’s birthday is in a 31-day month, but not August (March, May, July are left).

- Two people between Q and V.

- T's before U.

- Q’s birthday is not before R (means Q is after R).

Now let's lay it out:

| 1. Jan | 2. Mar | 3. Apr | 4. May | 5. Jun | 6. Jul | 7. Aug |

|-----------|-----------|-----------|-----------|-----------|-----------|-----------|

| P | | | R | | | |

- Since Q's month is 31 days, but not August, Q can be in March, May, or July. But Q is after R (May is R, so only July possible).

- Q’s only possible spot is July (position 6).

- Two persons between Q and V, so V can be in March (position 2) or April (position 3).

- Let’s check both cases.

Case 1: V in March

| 1. Jan | 2. Mar | 3. Apr | 4. May | 5. Jun | 6. Jul | 7. Aug |

|--------|--------|--------|--------|--------|--------|--------|

| P | V | | R | | Q | |

But only one person between S and R, so S can be in April or June:

- If S is in April, S (3), R (4).

- That works.

Let’s fill remaining names: T and U, with the condition T before U.

Left: June and August (5 and 7).

So assign T in June (5) and U in August (7).

That gives us:

| 1. Jan | 2. Mar | 3. Apr | 4. May | 5. Jun | 6. Jul | 7. Aug |

|--------|--------|--------|--------|--------|--------|--------|

| P | V | S | R | T | Q | U |

All conditions satisfied.

Now let's check who is last: In August, U.

So, the correct answer is:

- Option 1, U

Just to quickly lock in the explanation:

- Every clue fits.

- T comes before U as required.

- Q is after R.

- Two between Q (July) and V (March).

- Only one between S (April) and R (May).

- P is January.

- U’s birthday is last (August).

You nailed it.