Manisha is a kindergarten class teacher who planned a schedule for the incoming batch of students. The classes were supposed to be held from Monday to Friday. Each day has four slots named A, B, C, and D in that order. Slot A starts from 8:00, Slot B from 09:00, slot C from 10:00, and slot D from 11:00. The classes are English, Counting, Dancing, Painting, Singing and Physical Education.
There are 3 types of categories in which classes are distributed. The details of the category are as follows::
a) Compulsory: Classes which happen 4 days a week
b) Optional: Classes which happen 2 times a week
c) Necessary: Classes which happen once a week.
Each of the 3 categories has at least 1 of the 6 subjects in them.
Furthermore, the following things are known:
  1. No subject happened in the same slot or the same day twice. None of the subjects belonging to the Optional category happened on Friday.
  2. Every day exactly 1 slot had to be free. Slot A had classes on all days.
  3. Overall 3 classes each happened in the B and C slots throughout the week. 
  4. Painting was taught on Wednesday's C slot. Exactly one of the optional subjects was not taught on consecutive days.
  5. Counting was taught on Monday. The Singing class did not happen on Tuesday.
  6. There were 2 instances where the free period was in the same slot as the preceding day.
  7. Physical Education only happened in the A slot. Slot D of Monday was a free slot
  8. Week started with teaching English.  Dance was not taught on Thursday.
  9. On a particular day, Singing happened after a free slot
  10. On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day.
 
Q. Which of the following can not be a subject of the Optional Category?
  • a)
    Painting
  • b)
    Counting
  • c)
    Dance
  • d)
    Singing
Correct answer is option 'C'. Can you explain this answer?

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Answers

Deepti Jindal
Feb 02, 2022
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.
Then a+b+c = 6 ....(I)
Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.
when c= 1, then b=3 and a = 2
when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.
Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.
Let us start by filling in the known information.
> Painting was taught on Wednesday C slot
>Slot D of Monday was a free slot
> Week starts with teaching English

> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot
>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects
Thus Dance is not a subject of Optional Category.

The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.Then a+b+c = 6 ....(I)Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.when c= 1, then b=3 and a = 2when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.Let us start by filling in the known information.> Painting was taught on Wednesday C slot>Slot D of Monday was a free slot> Week starts with teaching English> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjectsThus Dance is not a subject of Optional Category.
The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.Then a+b+c = 6 ....(I)Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.when c= 1, then b=3 and a = 2when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.Let us start by filling in the known information.> Painting was taught on Wednesday C slot>Slot D of Monday was a free slot> Week starts with teaching English> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjectsThus Dance is not a subject of Optional Category.