CAT 2001 | Question: 142

Question

In a family gathering there are two males who are grandfathers and four males who are fathers. In the same gathering there are two females who are grandmothers and four females who are mothers. There is at least one grandson or a granddaughter present in this gathering. There are two husband-wife pairs in this group. These can either be a grandfather and a grandmother, or a father and a mother. The single grandfather (who wife is not present) has two grandsons and a son present. The single grandmother (whose husband is not present) has two granddaughters and a daughter present. A grandfather or a grandmother present with their spouses does not have any grandson or granddaughter present. What is the minimum number of people present in this gathering?

• A. $10$
• B. $12$
• C. $14$
• D. $16$

 

Answer 1

Ans 2) 12

2 males who are grandfathers

4 males who are fathers (2 grandfather also father)

So, only father but not grandfather =2 male

Similarly,

 2 females who are grandmothers

 4 females who are mothers (2 grand mother are also mother)

So, only mother but not grandmother =2 female

3 gathering possible here

1> (1 grand father, 2 gandson,1son, 1 daughter or daughter in law)

2> (1 grand mother, 2 grand daughter,1 daughter , 1 son or son in law)

3> (1 grand father , 1 grand mother)

Sum up all the gathering of  1> , 2> , 3> . It will be 12

Comments

i guess it should be 12 only right ...

if you see your ans there are 3 pair of hasband wife and according to question there should be only 2 pair of couple rt ,,

so there should be  set1.(grand father grand mother  (son/ wife or daughter/ hasband),2nd set. (grand father , (son ), 2grand son) ,3rd set (grand mother , (daughter ), 2 grand daughter )

now we can check all the conditions given in questions

1)2 grand father one from 1 set and one from 2nd set

2)4 fathers , 2 from set 1, (gf also a father, there son / son in law) , 2 from set2 (gf, son )  

3)2 grand mother( 1 frome set 1 ) one from set 2nd.

4) 4 mothers , similar way 2 from set 1  , 2  from set 3 (daughter, grand mother)

5) 2 pair of husband wife . from set 1(grand father ,grand mother), and their (son/daughter , son in law / daughter in law)

so total 12 members

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yes grand father are also father , similarly gm also mother

So, 12 answer

thank u @Sonam

edited

check now:)