GATE ECE 2017 Set 2 | GA | Question: 7

Question

Each of $P, Q, R, S, W, X, Y$and $Z$ has been married at most once . $X$ and $Y$ are married and have two children $P$ and $Q$. $Z$ is the grandfather of the daughter $S$ of $P$. Further , $Z$ and $W$ are married and are parents of $R$. Which one of the following must necessarily be FALSE?

• A. $X$ is the mother-in-law of $R$
• B. $P$ and $R$ are not married to each other
• C. $P$ is a son of $X$ and $Y$
• D. $Q$ cannot be married to $R$

Comments

This question requires analytical thinking.

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This is a bad aptitude question. You can't deduce anything from the provided facts and have to make huge leaps in logic to get the answer.

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yes , how can anyone marry there brother or sister ? This question is wrong. Option B and D both are correct.

Answer 1

Let $\to$ represent the child relation.

• $\{X,Y\} \to P, Q$
• $P \to S$
• $\{Z,W\}\to R$
• Further $P's$ spouse is the child of $Z$ so that $S$ become the grand daughter of $Z.$

1.  $X$ is the mother-in-law of $R$ -- possible if $R$ is married to either $P$ or $Q.$
2. $P$ and $R$ are not married to each other -- $P$ has only $R$ to marry as $Q$ is a sibling and $S$ daughter, but $P$ can also be married to anyone not mentioned in the question. So, this is possible.
3. $P$ is a son of $X$ and $Y$ -- possible as $P$ can either be a son or daughter of $X$ and $Y.$
4. $Q$ cannot be married to $R$ -- FALSE as $Q$ can be married to $R.$ 

Correct Option: D

Comments

Sir, a small correction is required: 

1. X is the mother-in-law of R -- possible if R is married to either P or Q.

2. P and R are not married to each other -- P has only R to marry as Q is a sibling

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Thanks 👍

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P can also be married to anyone not mentioned in the question

I think the person cannot be anyone, he/she must be son/daughter of Z and W.

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If Q can be married to R then shall we assume that Z&W can have other children not mentioned in the question?

Because it is clearly mentioned that Z is grandfather of P's daughter. So it is mandatory for P to be married to a child of Z&W.

Please clarify.

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Hear in question clearly mention is that “ Z is the grandfather of the daughter S of P”

final conclusion → p is married (but  P can not married with Q due: both parents are same.)

so,P only married with R .(because No further details is given so we assume that like.)

ANS : P and R Not married to each other is FALSE.

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who else could P be married to there is  no one left .  everyones role is already mentioned.

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"either $P$ or $P'$s spouse is the child of $Z$"

but it is given that $P$ is the child of $X$ and $Y$ and everyone is married atmost once. so, it will be not the case that previously $Z$ and $X$ or $Y$ were married and now $Z$ and $W$ are married (to make $P$ child of both $Z$ and $X$ or $Y$), so P can not be a child of $Z$ and $W$. he/she can only be son-in-law or daughter-in-law of $Z$ and $W$.

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@GateUser001 and @comder_ASHU

although "$P$ and $R$ Not married to each other" is FALSE means "$P$ and $R$ are married to each other" can be true but it is not always true either. the question talks about $P, Q, R, S, W, X, Y, Z$ but it does not mean that in the whole universe (universe in a sense like we use universal set in set theory) only these people exist and they have to marry with each other only. the question does not deny anywhere that $Z$ and $W$ do not have any other children so we are free to assume both the facts,

1. $Z$ and $W$ have only child as $R$.
2. $Z$ and $W$ have a child as $R$.

so, in a case where $R$ has siblings then any one of them can also be married to $P$ instead of $R$. 

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@anujs,

"either P or P's spouse is the child of Z"

Edited.

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@anujs @Shaik Masthan 

Sir,

If one of X or Y is related to Z as brother or sister, then also S can become grand daughter of Z.

It is not necessary that child of Z is spouse of P?

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I don't think, we should assume it, as there's no such direct reference given in the question.

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@Shaik Masthan Sir, I mean it can be the possibility na?

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@Teja25, I don't seen such possibilities in analytical thinking. Eventhough that possibility exist in the real life. 

I may be wrong.

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I think option B is true, because A\Q  Z is grandfather of S and also parent of R.
AND the most important part of the question, Each of P,Q.R,S,W,X,Y and Z has been married at most once.
hence Option D is true but we want necessarily false.

 

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But for Z to be grandfather of S, P should be married to R right?

Answer 2

https://gateoverflow.in/139221/gate-ece-2017