Question

P, Q, R, S, W, X, Y, Z are seated around a circle facing the centre. The husband of Z is second to the right of Q who sits between two males. X sits second to the left of the daughter of S. X is the sister of Y and not an immediate neighbour of Z's husband. Only one person sits between P and X. P is the father of Y. S (brother of Z) sits to the immediate left of his mother. Only one person sits between Z's mother and W. Only one person sits between Z and Y. Y is the mother of R and not an immediate neighbour of W. Which of the following is true?

• A. R is the cousin of W.
• B. Q is the mother of Z.
• C. Z sits third to the left of her daughter.
• D. No female is an immediate neighbour of R.

Hint:

In circular family-seating puzzles, lock the role edges first (e.g., "husband of Z second right of Q", "S left of his mother"), then place gendered roles ("between two males"). Finally, use "exactly one person between" constraints to force a unique ring.

Answer 1

The Correct Option is B

Step 1: Decode fixed relations and genders.
Z is female; S is Z's brother $\Rightarrow$ S is male.
X is sister of Y $\Rightarrow$ X, Y are females.
P is the father of Y $\Rightarrow$ P is male.
Y is the mother of R $\Rightarrow$ Y female, R child.
Let the husband of Z be one of the males. 

Step 2: Start with the "Q and Z's husband" condition.
"The husband of Z is second to the right of Q" and "Q sits between two males."
Place $Q$ and ensure both neighbours of $Q$ are males; put $Z$'s husband two seats to $Q$'s right. 

Step 3: Use the S-mother and “daughter” clues.
"S sits to the immediate left of his mother" $\Rightarrow$ the person to the right of $S$ is Z's mother.
"X sits second to the left of the daughter of $S$" and "X$\,\not\,$adjacent to Z's husband". Together with "Only one person between $P$ and $X$" fixes $X$ and hence $S$'s daughter as $W$ (female). 

Step 4: Complete the circle consistently.
A unique consistent arrangement (up to rotation) is: \[ \boxed{P \;-\; Y \;-\; X \;-\; Z \;-\; W \;-\; S \;-\; Q \;-\; R \;-\; (back~to~P)} \] with all facing the centre, and $P$ is the husband of $Z$.
Check all clues: $Q$ between two males $(S,R)$; Z's husband ($P$) is second right of $Q$; $X$ is second left of $W$ (the daughter of $S$); $X$ is not adjacent to $P$; exactly one between $P$ and $X$; exactly one between $Z$ and $Y$; $Y$ not adjacent to $W$; $S$ is immediately left of his mother $Q$; exactly one between $Q$ (Z's mother) and $W$. All satisfied. 

Step 5: Evaluate the options.
(a) $R$ and $W$ are not cousins (from the family tree, $W$ is $S$'s daughter; $R$ is $Y$'s child; $Y$ is (most naturally) $P$-$Z$'s daughter) $\Rightarrow$ False.
\(\hspace{2cm}\) Even without assuming mothers, the arrangement makes (a) not necessarily true.
(b) From Step 4, the mother of $S$ and $Z$ is $Q$ $\Rightarrow$ True.
(c) Z is not third to the left of her daughter (neither $Y$ nor $X$ fits) $\Rightarrow$ False.
(d) $R$ has $Q$ (female) as one neighbour $\Rightarrow$ False.
Hence (b) is correct.

Answer 2

Start instead from the "S sits immediately left of his mother" clue and the gender clues, then check every option against the arrangement this builds.

1. Fix genders first: Z is female (has a husband); S is Z's brother, so S is male; X is sister of Y, so X and Y are female; P is father of Y, so P is male; Y is mother of R.
2. Place S and his mother: S sits immediately left of his mother, and only one person sits between Z's mother and W — this anchors the mother's seat and fixes W two seats away from her.
3. Fit in Q and Z's husband: Q sits between two males, and Z's husband sits second to Q's right; combined with "only one person between P and X" and "X not adjacent to Z's husband," X's seat and P's seat get fixed, showing that Z's husband must be P.
4. Close the circle: Working around with the remaining "one person between Z and Y" and "Y not adjacent to W" clues gives the unique order \(P-Y-X-Z-W-S-Q-R\), in which Q sits immediately left of S and is Z's mother.

Checking the options against this arrangement: (a) R and W are not cousins on this family tree; (c) Z is not third to the left of her daughter; (d) R does have a female neighbour (Q); only (b), that Q is the mother of Z, holds.

the correct answer is Q is the mother of Z.