GATE Mechanical 2019 Set 1 | GA | Question: 10

Question

$M$ and $N$ had four children $P$, $Q$, $R$ and $S$. Of them, only $P$ and $R$ were married. They had children $X$ and $Y$ respectively. If $Y$ is a legitimate child of $W$, which of the following statements is necessarily FALSE?

• A. $M$ is the grandmother of $Y$
• B. $R$ is the father of $Y$
• C. $W$ is the wife of $R$
• D. $W$ is the wife of $P$

Comments

I think, here it’s imp. to understand the line mentioned: “They had children X and Y respectively”, (note the word respectively) which means that P had child X, and R had child Y.

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$\text{If Y is a $\underline{\text{legitimate}}$ child of W means ? }$

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@umeshshelke , 

"A legitimate child is one born to parents who are legally married to each other"

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@buriburizaemon got it! Thanks, dear.

Answer 1

$M$ and $N$ had four children $P$, $Q$, $R$ and $S$.

It means $M$ and $N$ are couple.

Only $P$ and $R$ were married. 

They had children $X$ and $Y$ respectively.

It means child of $P$ is $X$ and child of $R$ is $Y.$

If $Y$ is a legitimate child of $W$ we can conclude that $W$ and $R$ are couple.

• A. $M$ is the grandmother of $Y-$ Possible, can also be grand father.
• B. $R$ is the father of $Y-$ Possible, can also be mother.
• C. $W$ is the wife of $R-$ Possible, can also be husband.
• D. $W$ is the wife of $P{\color{Red}{-\text{False}}},$ $W$ is either wife of $R$ or husband of $R.$

So, the correct answer is $(D).$

Comments

It means M and N are couple.

 How you can say they are couples may be they are not. what if M is father of P and Q and N is father of R and S..??

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@Kiyoshi because, in the Q. it's written “M and N had four children P, Q, R and S.”

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M and N are couples. They have children P,Q,R,S and only P and R are married and have children X and Y respectively. W is married to R. that's why W can never be the wife of P that's why D is the correct answer. 

Answer 2

M-N[ husband and wife]

      |

P       Q        R-W        S

|                       |

X                    Y

option D.   W is the wife of P