In a certain notation system for directions and distances between points: - $P@Q$ means $P$ is East of $Q$ and the distance between $P$ and $Q$ is either $4 ext{ m}$ or $15 ext{ m}$. - $P\#Q$ means $P$ is West of $Q$ and the distance between $P$ and $Q$ is either $7 ext{ m}$ or $18 ext{ m}$. - $P&Q$ means $P$ is North of $Q$ and the distance between $P$ and $Q$ is either $4 ext{ m}$ or $15 ext{ m}$. - $P\%Q$ means $P$ is South of $Q$ and the distance between $P$ and $Q$ is either $7 ext{ m}$ or $18 ext{ m}$. Given the following relations: - $J&K\#L\%M$ - $B&N\#M$ - $BN

Question

In a certain notation system for directions and distances between points:

- $P@Q$ means $P$ is East of $Q$ and the distance between $P$ and $Q$ is either $4 	ext{ m}$ or $15 	ext{ m}$.
- $P\#Q$ means $P$ is West of $Q$ and the distance between $P$ and $Q$ is either $7 	ext{ m}$ or $18 	ext{ m}$.
- $P&Q$ means $P$ is North of $Q$ and the distance between $P$ and $Q$ is either $4 	ext{ m}$ or $15 	ext{ m}$.
- $P\%Q$ means $P$ is South of $Q$ and the distance between $P$ and $Q$ is either $7 	ext{ m}$ or $18 	ext{ m}$.

Given the following relations:

- $J&K\#L\%M$
- $B&N\#M$
- $BN < MN < KL$
- $JK > ML$

Four of the following pairs are similar in a certain way. Identify the pair which does NOT belong to the group:

(a) $BM$

(b) $BL$

(c) $NL$

(d) $KN$

(e) $JM$

Accepted Answer

**Solution:**

1. According to the given notation:
   - $P@Q$ means $P$ is to the East of $Q$ with distance either $4 	ext{ m}$ or $15 	ext{ m}$.
   - $P\#Q$ means $P$ is to the West of $Q$ with distance either $7 	ext{ m}$ or $18 	ext{ m}$.
   - $P&Q$ means $P$ is to the North of $Q$ with distance either $4 	ext{ m}$ or $15 	ext{ m}$.
   - $P\%Q$ means $P$ is to the South of $Q$ with distance either $7 	ext{ m}$ or $18 	ext{ m}$.

2. The given relations are:
   - $J&K\#L\%M$ means:
     - $J$ is North of $K$,
     - $K$ is West of $L$,
     - $L$ is South of $M$.

- $B&N\#M$ means:
     - $B$ is North of $N$,
     - $N$ is West of $M$.

3. The inequalities $BN < MN < KL$ and $JK > ML$ provide relative distances.

4. Now, consider the pairs given:
   - $BM$, $BL$, $NL$, $KN$, and $JM$.

5. Among these, four pairs share a common directional or distance property based on the given notation and relations.

6. The pair $KN$ does not fit the pattern formed by the other pairs in terms of direction and distance constraints.

**Answer:** $KN$

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