Logical Reasoning Discussion

**Common Information**

The regular mathematics faculty could not teach because of being sick. As a stop gap arrangement, different visiting faculty taught different topics on 4 different days in a week. The scheduled time for class was 7:00 am with maximum permissible delay of 20 minutes. The monsoon made the city bus schedules erratic and therefore the classes started on different times on different days.

Mr. Singh didn’t teach on Thursday. Calculus was taught in the class that started at 7:20 am. Mr. Chatterjee took the class on Wednesday, but he didn’t teach probability. The class on Monday started at 7:00 am, but Mr. Singh didn’t teach it. Mr. Dutta didn’t teach ratio and proportion.

Mr. Banerjee, who didn’t teach set theory, taught a class that started five minutes later than the class featuring the teacher who taught probability. The teacher in Friday’s class taught set theory. Wednesday’s class didn’t start at 7:10 am. No two classes started at the same time.

Q. |
The option which gives a possible correct class time – week day combination is: |

✖ A. |
Wednesday – 7:10 am, Thursday – 7:20 am, Friday – 7:05 am |

✖ B. |
Wednesday – 7:20 am, Thursday – 7:15 am, Friday – 7:20 am |

✖ C. |
Wednesday – 7:05 am, Thursday – 7:20 am, Friday – 7:10 am |

✖ D. |
Wednesday – 7:10 am, Thursday – 7:15 am, Friday – 7:05 am |

✔ E. |
Wednesday – 7:20 am, Thursday – 7:05 am, Friday – 7:10 am |

**Solution:**

Option(**E**) is correct

It is given that Mr. Chatterjee took the class on Wednesday.

Also the class on Monday which started at 7:00 am was not taken by Mr. Singh

∴ It has to be taken either by Mr. Dutta or Mr. Banerjee.

But Mr. Banerjee taught a class that started five minutes later than the class of probability.

∴ The class on Monday starting at 7:00 am was taken by Mr. Dutta.

∴ Mr. Singh didn’t take a class on Thursday

∴ His class has to be on Friday.

We also know that the teacher in Friday’s class taught set theory.

∴ The information that we have till now can be represented as:

Table below can be scrolled horizontally

Professor | Timing | Subject | Day |
---|---|---|---|

Mr. Singh | set theory | Friday | |

Mr. Chatterjee | Wednesday | ||

Mr. Dutta | 7:00 am | Monday | |

Mr. Banerjee | Thursday |

The class on Calculus started at 7:20 am.

Now this class cannot be taken by Mr. Singh as he is teaching set theory, not by Mr. Dutta also as his class is starting at 7:00 am, not even by Mr. Banerjee as his class is starting 5 mins after the class on Probability and the timing on probability has to be one from 7: 10 am and 7:20 am.

∴ The class on Calculus started at 7:20 am was taken by Mr. Chatterjee.

We also know that Mr. Dutta didn’t take a class on ratio and proportion.

The class on ratio and proportion was taken by Mr. Banerjee.

∴ The class on probability was taken by Mr. Dutta.

∴ The class by Mr. Banerjee was taken at 7:05 am as the class on probability was taken at 7:00 am.

∴ The class by Mr. Singh was taken at 7:10 am.

Table below can be scrolled horizontally

Professor | Timing | Subject | Day |
---|---|---|---|

Mr. Singh | 7:10 am | Set theory | Friday |

Mr. Chatterjee | 7:20 am | Calculus | Wednesday |

Mr. Dutta | 7:00 am | Probability | Monday |

Mr. Banerjee | 7:05 am | Ratio and proportion | Thursday |

Referring the above table we can say that the only possible correct class time – week day combination is:

Wednesday – 7:20 am, Thursday – 7:05 am, Friday – 7:10 am.

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