A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P's daughter and Q is R's mother-in-law. T is an unmarried male and S is a male.
Which one of the following is correct?
Let's break down the information to construct the family tree:
1. **Members:** P, Q, R, S, T, U (6 members)
2. **Generations:** Two generations
3. **Gender distribution:** 3 males, 3 females
4. **Marital status:** Two married couples, two unmarried siblings
Now, let's use the specific clues:
* **U is P's daughter:** This means U is female. P is in the first generation, U in the second.
P (Gen 1)
|
U (Female, Gen 2)
* **Q is R's mother-in-law:** This means Q is female. Q has a child who is married to R. So, Q is in the first generation, and her child and R are in the second.
Q (Female, Gen 1)
|
Child (Gen 2) -- R (Gen 2)
* **T is an unmarried male:** T is male and unmarried. He must be in the second generation as an unmarried sibling.
* **S is a male:** S is male.
Let's consolidate the known genders:
U = Female
Q = Female
T = Male
S = Male
We need one more female and one more male to reach 3 males and 3 females. The remaining members are P and R.
Let's assume P and Q are the married couple in the first generation.
P -- Q (Female)
Since Q is R's mother-in-law, Q's child is married to R.
P and Q have children in the second generation. U is P's daughter.
Consider the gender of P:
If P is female, then P(-) -- Q(-), which is not possible for a married couple.
Therefore, P must be male.
So, P (Male) -- Q (Female) is the first married couple.
Now we have P (Male), Q (Female), U (Female), T (Male), S (Male).
The remaining member is R. To balance the genders (3 males, 3 females), R must be female.
So, R = Female.
The family structure is taking shape:
Generation 1: P (Male) -- Q (Female) (Couple 1)
Generation 2: Their children U, T, S (and R, who is married into the family)
From "Q is R's mother-in-law," Q's child is married to R (Female).
The children of P and Q are U (Female), T (Male), and S (Male).
* U (Female) cannot be married to R (Female).
* T is an unmarried male. So T cannot be married to R.
* Therefore, S (Male) must be the child of P and Q who is married to R (Female).
So, S (Male) -- R (Female) is the second married couple.
Now, let's verify all conditions with the derived family tree:
Generation 1: P (Male) -- Q (Female)
Generation 2:
S (Male) -- R (Female)
U (Female, unmarried sibling)
T (Male, unmarried sibling)
* **Members:** P, Q, R, S, T, U - All accounted for.
* **Genders:** P(M), Q(F), S(M), R(F), U(F), T(M). (3 Males, 3 Females) - Correct.
* **Generations:** P,Q in Gen 1; S,R,U,T in Gen 2 - Correct.
* **Married couples:** (P, Q) and (S, R) - Two couples. Correct.
* **Unmarried siblings:** U and T - Two unmarried siblings. Correct.
* **U is P's daughter:** U is the daughter of P and Q. Correct.
* **Q is R's mother-in-law:** Q is S's mother, and S is married to R. So Q is R's mother-in-law. Correct.
* **T is an unmarried male:** Correct.
* **S is a male:** Correct.
The family tree is consistent with all given information.
Now, let's evaluate the options:
A) R is U's husband
R is female, U is female. R is S's wife. This is incorrect.
B) R is S's wife
R is female, S is male, and they are married in our derived tree. This is correct.
C) S is unmarried
S is married to R. This is incorrect.
D) None of the above
Since option B is correct, this is incorrect.
The final answer is B.
The final answer is B
