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Seven cars $\text{P, Q. R, S, T, U and V}$ are parked in a row not necessarily in that order. The cars $T$ and $U$ should be parked next to each other. The cars $S$ and $V$ also should be parked next to each other, whereas $P$ and $Q$ cannot be parked next to each other. $Q$ and $S$ must be parked next to each other. $R$ is parked to the immediate right of $V$. $T$ is parked to the left of $U$.

Based on the above statements, the only $\text{INCORRECT}$ option given below is:

- There are two cars parked in between $Q$ and $V$.
- $Q$ and $R$ are not parked together.
- $V$ is the only car parked in between $S$ and $R$.
- Car $P$ is parked at the extreme end.

Migrated from GO Electrical 1 year ago by Arjun

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Best answer

- The cars $T$ and $U$ should be parked next to each other.

This means we can park these two cars in two ways, either $TU$ or $UT.$ - The cars $S$ and $V$ also should be parked next to each other.

This means we can park these cars also in two ways, either $SV$ or $VS.$ - The cars $P$ and $Q$ cannot be parked next to each other.

This means we can not park the cars as $PQ$ or $QP.$ - The cars $Q$ and $S$ must be parked next to each other.

This means we can park these two cars in two ways, either $QS$ or $SQ.$ - $R$ is parked to the immediate right of $V$.

This means we can park these two cars in only one way $VR.$ - $T$ is parked to the left of $U$.

This is not “immediately left” but combining with statement $1,$ “immediately left” follows. So, we can park these two cars in only one way $TU.$

Now we can combine the statements $(2)\;\& (4)$ and get two possible ways for cars $Q,S$ and $V.$

- $QSV$
- $VSQ$

But $VSQ$ is not possible because it violates statement $5.$

Now, using statement $5,$ we get the possible car parking sequence $QSVR.$

Now, we can check each and every option.

- There are two cars parked in between $Q$ and $V$, it is incorrect because only $S$ is in between $Q$ and $V.$
- $Q$ and $R$ are not parked together, it is correct.
- $V$ is the only car parked in between $S$ and $R,$ it is correct.
- Car $P$ is parked at the extreme end.

For this option, we can consider all possible combinations of car parking which are only four as given below. $(P$ cannot come near $Q$ due to statement $3)$- $QSVR\; {\color{DarkBlue} {\color{Red} {P}}\; {TU}}$
- $QSVR\; {\color{DarkBlue} \; {TU}}\;{\color{Red} {P}}$
- ${\color{DarkBlue} {TU}}\; QSVR\; {\color{Red} {P}}$
- ${\color{Red} {P}}\;{\color{DarkBlue} {TU}}\; QSVR\; $

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