In a family of three generation there are eight members. How many married couples are there in the family?
Statement I. R is son of P. S is sibling of R and has only one son. V is grandson of Q.
Statement II. U has no siblings. W is daughter in law of U. P is sibling of T.
Statement III. Q is sister-in-law of T has no siblings. U is brother-in-law of R.
Correct Answer :
If the data in all the statement I, II and III are necessary to answer the question.
Solution :
Correct Answer: If the data in all the statement I, II and III are necessary to answer the question.
To determine the number of married couples in the family of eight members spanning three generations, let us analyze the information provided in Statements I, II, and III together step-by-step.
1. Analyzing Statement I:
- R is the son of P.
- S is a sibling of R and has only one son.
- V is the grandson of Q.
Statement I gives information about generations and some parent-child relationships, but it does not specify all 8 members nor all marriage connections.
2. Analyzing Statement II:
- U has no siblings.
- W is the daughter-in-law of U.
- P is a sibling of T.
Statement II gives isolated relations about U, W, P, and T, but does not connect them fully to Statement I.
3. Analyzing Statement III:
- Q is the sister-in-law of T (who has no siblings).
- U is the brother-in-law of R.
Statement III provides crucial bridge connections between the individuals in Statements I and II.
4. Combining Statements I, II, and III:
- Total members = 8.
- From Statement III: T has no siblings. Since P is a sibling of T (Statement II), T is married to someone whose sibling is Q, or Q is married to T's sibling (P). Specifically, Q is the sister-in-law of T.
- U has no siblings (Statement II) and is the brother-in-law of R (Statement III). Thus, U must be married to R's sibling, which is S.
- Since U and S are married, they form 1 married couple. W is the daughter-in-law of U, which means W is married to the only son of S and U (who is V, the grandson of Q). This forms the 2nd married couple (V and W).
- Q is in the top generation (grandparent to V). Q is married to P (since T has no siblings, Q being sister-in-law to T means Q is married to P). P and Q form the 3rd married couple.
- Thus, combining all three statements, we uniquely determine all relations and identify the married couples in the family.
Therefore, the data in all three statements (I, II, and III) are necessary to answer the question.
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