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Assignment Sets

In these sets we assign elements to places. Making rough sketches can be a big help to solve these questions and the best sketch to use is a grid.

 

Example: A radio station will schedule five programs—A, B, C, D, and E—to be aired Monday through Friday, one program each evening, in an order that conforms to the following restrictions:

  • Program D must be aired before Program A.
  • Programs C and D must be aired on consecutive evenings.
  • Program E may not be the second program to be aired.

The way in which we tackle a game is two-fold.

 

Step 1 would be to draw the diagram.

 

M      T      W     Th    F

 

Step 2: Symbolize the rules. In the above game the rules can be symbolized as below.


1. D < A

2. CD or DC

3. E cannot be on Tuesday.


M      T      W     R      F

        Not E

 

By making this diagram we are able to visualise the conditions and solve the questions quickly.

 

 


A very common set that states that there are five or six different people let us say – A, B, C, D, E and F live in six different houses in six different cities. You have to correctly find which house and in which city each of the given people resides in. For this, you are given a number of statements or clues to help you make the correct match.

 

This type of question might appear time consuming, but remember that such types of questions are usually in the form of 'caselets' -- that is a set of three or four linked questions, so if you get the correct sequence, you actually end up with the answers to three questions at one go.

 

Take your time setting up your diagram before you start attempting the questions. Explore the rules. Make sure you understand what the rules say and consider what they don't say. Draw any conclusions you can.

 

Question 1
 

Examples


Six books—on history, English, algebra, ceramics, Spanish, and philosophy—are arranged on a shelf, with a bookend at the either ends.

The history book is next to a bookend.
The English book is next to the algebra book.
At least one book separates the English and ceramic books, and the English and Spanish books.
The ceramics book and the Spanish book are next to each other.
At least two books separate the English and philosophy books.
 

Solution
 

Step 1 would be to have the diagram in place.

 
        [1     2      3      4      5      6]
 
Step 2: Symbolize the rules. In the above game the rules can be symbolized as below.
 
1.  Either [H, or H]
2. EA or AE
3. NOT EC, NOT ES
4. SC or CS
5. NOT E ↔ P, NOT E – P
 

 

 

Question 2

Examples
 

If the history book is next to the English book, which of the following must be true?

(A) The philosophy book is next to a bookend.
(B) The ceramics book is next to a bookend.
(C) The Spanish book is next to the algebra book.
(D) The philosophy book is next to the ceramics book.
(E) The algebra book is next to the ceramics book.
 

Solution


In this question, we have to make an assignment based on the data in the question and the rules. Given below is one possible allocation along with the steps
 
1. Based on the question data, we can put History next to either of the bookends. Let us keep it in position 1, knowing that the other possibility was keeping it in position 6.
 
Bookend   1      2      3      4      5      6      Bookend
                        H             
 
2.  Now in the question it is given that the history book is next to the English book, so place the English book in slot 2. (Slot 0 is already occupied by the bookend)
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E     
 
3.  Now rule 2 states that E ↔ A, so A has to go in slot 3.
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E      A     
 
4. Rule 5 states that NOT E ↔ P, NOT E – P. So slot 4 cannot have P. In case it cannot have P, the only options that remain are S or C.
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E      A      S/C  

5.     Rule 4. S ↔ C. So whatever we choose for slot 4, the remaining of the two has to be fitted into slot 5.
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E      A      S/C   S/C  
 
6.     Now the only book that remains is P, which has to be fitted into slot 6.
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E      A      S/C   S/C   P     
 
Having done this assignment, we look at the options and find that the only one that fits in is the first.

 

 

 

 

 

Question 3

 

Examples


Which of the following books can be next to a bookend?

I.   Philosophy
II.  English
III. Ceramics
 
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
 
1. Bookend ↔ H
2. E ↔ A
3. NOT E ↔ C, NOT E ↔ S
4. S ↔ C
5. NOT E ↔ P, NOT E – P
 

Solution


In the previous question we have seen that P can be next to a bookend. Now we will try to tackle the remaining two options and see if we can have an assignment with E or C as being near a Bookend. Please note that in both cases the other bookend perforce has to have H adjacent to it.
 
Bookend   1      2      3      4      5      6      Bookend
                        H                                      E     
 
Bookend   1      2      3      4      5      6      Bookend
                        H                              A      E     
 
Bookend   1      2      3      4      5      6      Bookend
                        H                      Not P        A      E     
 
Bookend   1      2      3      4      5      6      Bookend
                        H              S/C   S/C   A      E     
 
Bookend   1      2      3      4      5      6      Bookend
                        H      P      S/C   S/C   A      E     

 
There seems to be an assignment possible with E near the bookend. Now we will check with C.
 
Bookend   1      2      3      4      5      6      Bookend
                        H                                      C     
Bookend   1      2      3      4      5      6      Bookend
                        H                              S      C     
 
Bookend   1      2      3      4      5      6      Bookend
                        H                      Not E        S      C     
 
Bookend   1      2      3      4      5      6      Bookend
                        H      E/A   E/A           A      C    
 
 
Here, we run into a problem. As only P can fit into slot 4, we find that by doing that we are violating rule 5. So we cannot have C near the bookend. So the answer is option 3.

 

 





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