Logical Reasoning Discussion

**Common Information**

A retail major has a warehouse (W) located at (16, 10) in a town having roads laid on a square grid parallel to the *x* and *y* axes. There are five retail supermarkets (M, N, O, P and Q) located respectively at (4, 4), (6, 16), (16, 24), (20, 16) and (26, 4).

Q. |
What is the ordering of the supermarkets from the nearest to the farthest from the warehouse? |

✖ A. |
P, M, N and Q, O |

✖ B. |
P, N and Q, O, M |

✔ C. |
P, O, N and Q, M |

✖ D. |
P, O, M, N and Q |

**Solution:**

Option(**C**) is correct

$\because$ The town has roads laid on a square grid parallel to the *x* and *y* axes the distance between any two points (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}) is given by the following relation.

*d* = âˆ£*x*_{1} - *x*_{2}âˆ£ + âˆ£*y*_{1} - *y*_{2}âˆ£

The co-ordinates of M is (4, 4) and that of N is (6, 16).

Distance between M and N = âˆ£4 - 6âˆ£ + âˆ£4 - 16âˆ£ = 2 + 12 = 14

Hence the table,

Table below can be scrolled horizontally

M | N | O | P | Q | W | |
---|---|---|---|---|---|---|

M | 0 | 14 | 32 | 28 | 22 | 18 |

N | 14 | 0 | 18 | 14 | 32 | 16 |

O | 32 | 18 | 0 | 12 | 30 | 14 |

P | 28 | 14 | 12 | 0 | 18 | 10 |

Q | 22 | 32 | 30 | 18 | 0 | 16 |

W | 18 | 16 | 14 | 10 | 16 | 0 |

From the table, we get that the supermarkets in increasing order of distance from the warehouse are P, O, N/Q, M.

Hence, **option C** is the correct choice.