Directions (Q.1 –5) : Study the following information carefully and answer the…

In a multi-clue logical puzzle, convert every clue into a constraint on profession, income order, marital status, or gender, and lock in only the facts that are logically forced by those constraints. When a question asks for a minimum ("at least") count of some attribute, only the members whose attribute is actually pinned down by a clue can be counted — anyone whose gender (or other attribute) is never stated by any clue must be left undetermined rather than assumed.

1. Assign the directly-given professions: R = Doctor (clue IV), Q = Teacher (clue VII), P = Banker (clue VII). T is married to the Chartered Accountant, so T herself is not the Chartered Accountant (clue V); W is married to Q (clue VII). That leaves Lawyer, Engineer, Architect and Chartered Accountant for S, T, V and W.

2. No lady can be the Lawyer or the Engineer (clue VI), and T is female (clue V calls her "she"), so T cannot hold either of those two posts — T must be the Architect. The two married couples are therefore (Q, W) and (T, the Chartered-Accountant-holder), so the Chartered Accountant must be S or V, never W (whose spouse is Q, not T).

3. V cannot be the Lawyer (clue VIII), so V is the Engineer or the Chartered Accountant. Checking every way of placing Lawyer, Engineer and Chartered Accountant among S, V and W against the earning clues — R earns more than the Engineer and the Lawyer (clue IV); Lawyer earns more than Chartered Accountant, who earns more than Banker (clue VIII); W earns more than S and P (clue VII); Q earns less than P (clue VII); T earns the least of all seven (clue V) — rules out V holding the Lawyer post and W holding the Chartered Accountant post, but leaves three different placements of the remaining three posts among S, V and W that are all fully consistent with every earning clue: no single clue forces one unique placement.

4. In every one of those three consistent placements, though, the Chartered Accountant is always S or V (never W), and the Lawyer and Engineer posts are always held by the other two of {S, V, W}. So across all three placements, S, V and W between them always occupy the Lawyer, Engineer and Chartered Accountant posts — only which one of them holds which post changes.

5. Fix the genders that follow in EVERY one of those placements: clue VI bars a lady from the Lawyer or Engineer post, so whichever of S, V or W holds either post is male. And whichever of S or V holds the Chartered Accountant post is married to T (clue V) — since these puzzles pair each married couple as one male with one female and T is female, that person is male too. Clue VII also directly calls W "he", confirming W is male on its own regardless of which post he ends up holding.

6. So no matter which of the three consistent placements is the intended one, all three of S, V and W come out definitely male, and Q and T come out definitely female — Q because she is W's spouse and W is male, T because clue V states it directly. No clue anywhere fixes the gender of R (the Doctor) or P (the Banker).

Profession-and-gender mapping across every clue-consistent placement:

Because the exact split of the Lawyer, Engineer and Chartered Accountant posts among S, V and W is not uniquely pinned down by the clues, several different profession assignments and income orders are consistent with the passage — but every one of them keeps R's and P's genders unstated and forces the same three members (S, V and W) male. Cross-checking each of the three consistent placements against clues (IV)-(VIII) confirms none of them ever assigns a gender to R or P, and all three assign a male gender to S, V and W without exception.

Since the question asks for the minimum ("at least") number of male members, the guaranteed count is the number of members whose gender is forced to be male in every clue-consistent scenario — that is S, V and W, forced by the ladies-cannot-be-Lawyer-or-Engineer rule together with the opposite-gender-couple pairing with the relative explicitly called "she". R and P remain gender-undetermined, so three is the guaranteed minimum.