P, Q, R, S, T and U are six members of a family. R is the spouse of Q. U is the mother of T and S is the daughter of U. P 's daughter is T and R 's son is P. There are two couples in the family. Which one of the following is correct?
- AQ is the grandfather of T
- BQ is the grandmother of T
- CR is the mother of P
- DT is the granddaughter of QCorrect
Explanation
Let's construct the family tree step-by-step:
-
"R is the spouse of Q." -> Q - R (This is our first couple).
-
"R's son is P." -> P is male. R and Q are the parents of P. So far: Q - R (couple) | P (male)
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"P's daughter is T." -> T is female. P is a parent of T. So far: Q - R (couple) | P (male) | T (female)
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"U is the mother of T." -> U is female. Since P is already a parent of T, U must be the spouse of P. (This is our second couple). So far: Q - R (couple 1) | P (male) - U (female) (couple 2) | T (female)
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"S is the daughter of U." -> S is female. S is also a child of P and U, making S the sibling of T. Final Family Tree: Q - R (Couple 1) | P (male) - U (female) (Couple 2) | T (female) S (female)
All 6 members (P, Q, R, S, T, U) are accounted for, and there are exactly two couples (Q-R and P-U).
Now let's evaluate the options:
A) Q is the grandfather of T Q is a grandparent of T (Q is P's parent, P is T's parent). However, we do not know Q's gender from the given information. Q could be male (grandfather) or female (grandmother). So, this is not necessarily correct.
B) Q is the grandmother of T Similar to A, we do not know Q's gender. So, this is not necessarily correct.
C) R is the mother of P R is a parent of P. We do not know R's gender. R could be male (father) or female (mother). So, this is not necessarily correct.
D) T is the granddaughter of Q From the family tree, Q is a grandparent of T. T is P's daughter, which means T is female. A female grandchild is a granddaughter. Therefore, T is the granddaughter of Q, regardless of Q's gender. This statement is definitively correct.
The final answer is D

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