Direction: Read the information given below and answer the questions.
(i) In a family of six persons and , there are two married couples.
(ii) is grandmother of and mother of .
(iii) is wife of and mother of .
(iv) is grand daughter of .
Which of the following is necessarily true?
- Ais brother of .
- Bhas two grandsons.
- Chas two daughters.
- DNone of the above
Solution & Step-by-step Explanation
Let us systematically chart out the family hierarchy based on the clues:
1. From (ii) and (iii): is the mother of . is married to ( is the wife, so is the husband). This gives us our first married couple: and .
2. From (iii), is the mother of ( is female since she is a granddaughter). Since is the grandmother of and mother of , and are siblings (children of and ).
3. From (iv), is the granddaughter of . Since is her paternal grandmother, must be her paternal grandfather. This gives us our second married couple: and .
Let's look closely at the children of and , who are and :
* is confirmed to be female ().
* The gender of is not specified anywhere in the statements. could be male or female.
Reviewing options:
* \text{OPT_A}: Not necessarily true, because could be a sister of .
* \text{OPT_B}: Not necessarily true, because 's gender is unknown.
* \text{OPT_C}: Not necessarily true, because could be a son.
* \text{OPT_D}: Correct, since none of the specific statements are absolute truths.
1. From (ii) and (iii): is the mother of . is married to ( is the wife, so is the husband). This gives us our first married couple: and .
2. From (iii), is the mother of ( is female since she is a granddaughter). Since is the grandmother of and mother of , and are siblings (children of and ).
3. From (iv), is the granddaughter of . Since is her paternal grandmother, must be her paternal grandfather. This gives us our second married couple: and .
Let's look closely at the children of and , who are and :
* is confirmed to be female ().
* The gender of is not specified anywhere in the statements. could be male or female.
Reviewing options:
* \text{OPT_A}: Not necessarily true, because could be a sister of .
* \text{OPT_B}: Not necessarily true, because 's gender is unknown.
* \text{OPT_C}: Not necessarily true, because could be a son.
* \text{OPT_D}: Correct, since none of the specific statements are absolute truths.