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Wednesday, July 18, 2012

Alphabetical Series


Alphabetical Series


    * denotes practical examples used to illustrate important points in this discussion.

Almost every test on reasoning contains questions on alphabetical series. In such a question, if it consists of a single series of alphabets/combination, the alphabets/combinations are arranged in a particular manner and each alphabet/combination is related to the earlier and the following alphabets in a particular way. The examinee is supposed to decode the logic involved in the sequence and then fill in the space containing the question mark with a suitable choice out of those given. But before we proceed to discuss the various types of questions related to alphabetical series, we will talk of some basic facts which are essential to an understanding of these types of questions.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

I. THE ALPHABET: The normal English alphabet contains 26 letters in all, as shown above

(Usually, questions on alphabet are accompanied by this normal alphabet). From A to M, the alphabet completes its first half, while the other half starts from N and ends at Z.

A-M - 1-13 (First Alphabetical Half)

N-Z –14-26 (Second Alphabetical Half)

II. EJOTY: For purpose of convenience, it is helpful to remember this simple formula called EJOTY, with the help of which you can easily find the position of any letter without much effort. But for practical purposes, you need to learn by heart the positions of different letters in the alphabet.

E    J     O    T    Y
5       10   15   20   25

Now, for instance, we wish to find the position of, say, the 17th letter from the left side. You already know that the 15th letter from the left side is O, therefore, the only thing you have to do is to find a letter which is two positions ahead of O, which is Q (The Answer). Using this simple formula, you can quickly find the position of any letter from the left side without much brain-rattling. Remembering the positions of different alphabets is basic to solving any question on alphabetical series. One of the best ways to achieve it is to practice EJOTY. Simply write down the full names of any 200 people you can imagine and do as follows:

^For example, let’s say the name of the person imagined is ZUBINA. Now from EJOTY, we know that Z stands for 26, U stands for 21, B stands for 2, I stands for 9, N stands for 14 and A stands for 1. Now add up all these positions (26+21+2+9+14+1). What you get on addition does not have any significance, but it can be a very good way to try to make out and remember the individual positions of letters in the alphabet.


III. FINDING POSITIONS: Much more commonly, you get questions in the tests which provide you alphabetical positions from the right side. Since we are used to counting from the left side i.e. A, B, C… and not Z, Y, X…, the formula we discussed earlier will be applicable with a bit of modification.  But before we proceed to discuss it, it is essential to remember one simple mathematical fact.



*Let’s say there is a row of 7 boys in which a boy is standing 3rd from left. We want to know his position from the right side.
 I          I         I        I       I       I        I  
                        1st       2nd      3rd     4th    5th    6th     7th   

You can see for yourself that the boy who was 3rd from the left is placed 5th from the right side.

The sum of both the positions is 8 (3+5), while the total number of boys is 7. This happens because we are counting a single boy twice in the calculation process. If we had subtracted 3 from 7 (as some of us might do), we would have got 4, which is obviously not the correct position from the right side. An important conclusion emerges from this discussion. If we are dealing with an alphabet and we have been given the position of any letter from either side, we will add 1 to the total no. of letters and then subtract its position from one side to get its position from the other side. For example, let’s find the position from the right of a letter which is the 9th from the left side.
   
A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z

1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26
26 25   24   23   22  21    20   19   18  17  16   15   14   13    12    11   10   9     8    7    6     5      4      3     2     1

As you can see for yourself, the 9th letter from the left side, I, comes out to be the 18th from the right side. Their sum (9+18=27) is again one more than the total number of alphabets i.e. 26. We can do this operation easily by adding one to the total number of letters (26+1=27) and then subtracting 9 from it. It gives you the letter position 18th from the right, which you can verify yourself from the above alphabet. The same procedure will be applicable if we are given an initial right position and are supposed to find it from the left side. Take for example, a letter which is placed 11th from the right side. If we want to locate its position from the left side, we will add 1 to total no. of letters and then subtract the right position from it to get its position from the left side. 27 – 11 gives you 16. Using EJOTY, you can easily conclude that the letter is P (16th from left, 11th from right).

The same logic is applicable if we are dealing with a situation in which the position of an item from the top is given to us and we want to find it from the bottom side or vice-versa.

IV. Still another type of question concerns finding the midpoint between two letters in the alphabet. For instance, let’s talk of a case which requires us to find the mid-point between the 11th letter and the 17th letter from the left side.

A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z

1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26
26 25   24   23   22  21    20   19   18  17  16   15   14   13    12    11   10   9     8    7    6     5      4      3     2     1




You can see that there are five letters between these two positions i.e.  L, M, N, O and P. Obviously, the midpoint of 5 items is the third item from either side, whether counted from the left or the right. It comes out to be N, which is the correct answer. But frankly speaking, so much labour is not exactly required in solving such questions. Let’s let the cat out of the bag. In such questions, if the positions are given from the same side (i.e. either both are from left or both are from right), simply add up the two positions, get their average and you have the answer. In this case, the two positions are 11 and 17 from left. Adding them and averaging them gives you 14. Recollect the EJOTY formula and you immediately come up with the letter which is 14th from the left side (preceding O). The same procedure will be applicable if you are given a case in which both the positions are counted from the right side. Remember that the answer you get will be from the same sides which you have been given. Let’s make this thing clearer by taking a practical example.

*Consider a case in which we have to find the mid-point between the 13th and the 19th letter from the right side.

Adding the two positions gives us 32, the average of which is 16. So we get the mid-point, which is 16th from the right side (the same as the sides given in the question). Now we have to convert this position into a position from the left. Applying the logic discussed earlier, we subtract 16 from 27 and get 11th  from the left, which is obviously K. You can verify this answer by looking up the above alphabet. In fact, for such questions, one should have so much practice that one does not need to look up the alphabet, which proves to be time-consuming.

A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z

1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26
26 25   24   23   22  21    20   19   18  17  16   15   14   13    12    11   10   9     8    7    6     5      4      3     2     1

Now let us consider the third case in which we have to find the mid-point between two alphabetical positions, one of which is given from the left and the other from the right.

*Take, for instance, a case in which we have to find the mid-point between the 6th position from the left side and the 11th position from the right side. The first thing we have to do is to convert the right position into a left position to make the data comparable in nature. Doing so gives us 16. Now add up 16 and 6 (because now both are from the same side), average them, apply EJOTY and you get the correct answer. 


IV. REVERSING: Many questions concerning reversing of the alphabet are a part of reasoning tests. Consider this question:

*What will the 11th letter of the following alphabet if the second half of the alphabet is written in reverse order?

A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z

1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26
26 25   24   23   22  21    20   19   18  17  16   15   14   13    12    11   10   9     8    7    6     5      4      3     2     1

The most important thing to remember in a question like the above is to determine where the required position falls, i.e. in the first or the second half. In this case, the answer falls in the first half. Therefore, if the second half is written in reversed order, it will have no impact on the position of our letter. This can be likened to reversing the tail of an elephant and asking if it would have an impact on its trunk. The answer is obviously no. So in this case, we have to simply decide the 11th letter from the left side, which is K, by using our EJOTY.

Now have a look at this question

*What will be the 12th letter from the right side if the first half of the alphabet is written in reverse order?

Now examine it carefully. This question is pretty much the same as the earlier one. The examiner has cleverly phrased his question so as to trap you. If you want to count from the right side and the answer falls in the first half from the right side (the normal second half is now your first half because you have started counting from this side), reversing the first half of a normal alphabet will have no impact on the right answer. So now the question can be rephrased like finding the 12th letter from the right side. The correct answer as you can find quite comfortably is O.


Now try solving this one.




*Which letter will be the 17th from the left side if the second half of the normal alphabet is reversed?

Now this is posing a bit difficult problem. Your answer will fall in the second half (because the first half is complete when you are at position 13 from left). So the letters A-M remain the same while from N-Z are written like Z, Y, X till N. In effect, we can count 13 letters from A-M and then simply add four letters from the behind of the alphabet. You can see for yourself that the fourth letter from the rear side is W, which is the correct answer. But we have solved this question by looking at the above alphabet. Let’s solve it the faster way without looking up the alphabet.

Since only the 2nd half is being reversed, we can easily skip the first 13 letters, which will assume to have been counted in a normal way. The question is how to find the 17th letter from the left with the reversed second half. Simply count the fourth letter from the right side (which is obviously the 23rd from the left side), which if added to the figure 13, makes it the 17th from left. Refer to the following figure for clarity.  Applying our earlier procedure, the 4th from right is W; we get the same correct answer.

A   B    C    D    E    F    G    H    I    J    K    L    M    Z    Y    X    W    V    U    T    S    R    Q    P    O    N   



1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26


Now let’s consider a case in which the entire alphabet is reversed.


*What would be the 16th letter from the left side if the normal English alphabet is written in reverse order?


A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z



1    2     3    4     5    6      7    8     10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26

26 25   24   23   22  21    20   19   18  17  16   15   14   13    12    11   10   9     8    7    6     5      4      3     2     1

Obviously the alphabet will look like Z, Y X… from the left if we reverse the whole of it. Now just imagine that what was on the left earlier has become on the right now. So A will go to the right extreme, followed by B and so on. In reality, what was 16th from the left earlier has now become the 16th from the right side. So if this 16th from right can be converted to the left side i.e. 11 and we already know from EJOTY that the 11th letter from left is K.



V. LEFT-RIGHT-LEFT: Consider the following question:

*What will be the 5th letter to the right of the 9th letter from the left side?
A   B    C    D    E    F    G    H    I    J    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z



1    2     3    4     5    6      7    8     9  10   11   12   13   14    15    16   17   18  19   20  21   22    23    24    25   26

Go to the end of the question. It asks you to start counting from left and arrive at the 9th from the left which is I. Now starting from I, we are to find the 5th letter to its right as per the statement, which is N.

In reality N is placed at the 14th from left which is a figure you can get by adding the numbers in the question (9+5).


Rule No. 1: Whenever we are given two opposite directions, i.e., left-right or right-left, we will add up those two numerals and will count from the direction given at the end of the question.

Now examine this one:

* What will be the 11th letter to the left of 23rd letter from the left side?

Repeating the procedure followed in the earlier case, we will get the answer, i.e., L. In reality, L is the 12th letter from left and this 12 has been obtained by subtracting the smaller numeral from the bigger one given in the question.


Rule No. 2: Whenever we are given two same directions, i.e., right-right or left-left, we will subtract the smaller numeral from the bigger one and will count from the direction given at the end of the question

Try this one: What will be the 9th letter to the right of 19th from the right side? (Subtract and then find the letter counting from left)


VI. MULTIPLE ALPHABETICAL SEQUENCES: Have a look at the following poser

ADH: MSZ :: GQA : ?

The components of all the sequences are related to their preceding and the following components in a specific manner. To simplify the things, we will assign the respective alphabetical positions to the letters. 

A    D    H  : M    S    Z :: G    Q    A :    ?  ?  ?
                                    1      4   8      13   19  26    8    17    1

                                    +3    +4    +5   +6   +7  +8    +9  +10    

As you can see from the above illustration, the difference between the consecutive components is increasing by one position each time. So, the question requires you to determine the next three letters working with the same logic. It is here that your EJOTY formula will prove handy. Applying it, you can readily find the answer, which turns out to be LXK.

PRACTICE QUESTIONS

1. What will be the 12th letter to the right of 10th from the left side?       

    a. V   b. T   c. U   d. W


2. What will be the 9th letter to the left of 16th from the right side?      

    a. D b. C c. B d. A


3. What will be the 19th letter to the right of 3rd from the left side?

   a. U  b. T  c. W d. V



4. What will be the 11th letter to the left of 13th from the right side?        

    a. C  b. D  c. B  d. E


5. What will be the 18th letter from the left if the first half of the alphabet is reversed?
a.    R  b. V c. I  d. Q


6. What will be the 13th letter from the right side if the first half of the normal alphabet is reversed?    

a.    A  b. Z  c. N  d. M


7. What will be the 16th letter from the left side if the second half is written in reverse order?   
a. C   b. X   c. L   d. None of these


8.  What will be the 21st letter from the right side if the first half of the alphabet is reversed?    

a.    H   b. R   c. F   d. None of these

 9. What will be the 16th letter to the right of the 8th letter from the left if the entire alphabet is written in reverse order?        
     a. C  b. B  c. X  d. None of these




10. Which alphabet will be mid-way between the 7th and the 11th letters counting from the left end of a normal alphabet?

    a. H   b. R   c. D   d. I

11. Which alphabet will be mid-way between the 17th and the 5th letters counting from the right end of a normal alphabet?    


a.    P  b. J c. Q   d. K

12. Which alphabet will be mid-way between the 8th and the 11th letters counting from the left end of a normal alphabet?



a.    S  b. Q c. P  d. indeterminate answer
 

13. Which letter will be 2 positions ahead of the letter which is mid-way between the 7th letter and the 19th letter from the right end?       



a.    P b. O  c. Q   d. M

 14. Which letter will be three positions left of the mid-point between the 5th and the 7th letters from the right side?          


     a. C     b. K  c. P   d. R

 15. Which letter will be the 8th letter to the right of the 11th letter from the left side if the first and the second halves are reversed separately?     



   a. None of these b. U  c. X   d. S




16. Which alphabet, if counting is done from both the left and the right sides, will be mid-way between the 12th from the left side and the 11th from the right side?

a. W b. D     c. N   d. M


17. If MDX: NWC:: KTR: ?        

a.    PGI   b.  LGI c. PHI d. OHJ


18. JHFC: BGGK:: PMRO: ?

a.    ORMQ     b. None of these   c. NSLQ    d. MSLQ


19. If ADCE: 259161, RTOPQ:: ?          

a.    289256225400324   b. 324289256225400  c. 256225225400324  d. None of these


20. If EVS: DXP, LRT: ?       

    a. KTQ b. KPQ     c. MUW   d. None of these



Key and Expls


1.   A.

10+12= 22nd from left.


2.C

16+9= 25th from right i.e. 2nd from left


         3.D

22nd from left. Use EJOTY.


4.A

24th from right i.e. 3d from left


5.A
The reversal of the first half will not impact our answer as it falls in the second half.


6.C
The reversal of the first half will not impact our answer as it falls in the second half.


7.B
A-N gives us 13 letters from left. The rest have to be from right i.e. 3rd from right i.e. 24th from left is the answer.


8.A
The reversal of the first half will impact our answer as it falls in the first half. Z-N gives us the first 13 letters. The rest eight have to come from A….M. So counting with EJOTY, the 8th from left is H.


9.C
In a nutshell, after reversal, we need to count the 3rd letter from left i.e. X.


10.D
Averaging 11 and 7 gives us 9 i.e. I.

11.A
17th and 5th from right correspond to 10th and 22nd from left. Averaging them yields 16 i.e. P.

12.D
11th and 8th from right correspond to 16th and 19th from left. Averaging them yields 17.5 i.e. non-existent letter.


13.A
7th and 19th from right correspond to 20th and 8th from left. Averaging them yields 14 i.e. N. Two places ahead of N is P.


14.D
5th and 7th from right correspond to 22nd and 20th from left. Averaging them yields 21 i.e. U, which has R three places to its left.


15.B
We need to find the 21st letter from the left side.


16.C
Averaging 12 and 16 yields 14.


17.A

M D X : N   W  C    :: K     T    R    :   P     G    I

14 4 25  14   4    25     11    20   18      11    20   18   
 
     From left     From right   From left      From right



18.C
    BECOMES (REVERSE ORDER)   BECOMES (REVERSE ORDER)

J   H    F   C : B   G   G  K    :: P    M   R   O : N  S  L  Q
              +1 -1  +1 -1           +1  -1  +1   -1

    Becomes (REVERSE ORDER) BECOMES (REVERSE ORDER)

19.A
Squaring respective alphabetical positions and putting them in a reverse order.

A   D   C   E: 25  9  16  1         :: R    T O     P    Q : 289  256  225  400 324
                     12  42  32 52                                                     18202   152  16172    

20.A
E   V    S : D  X   P     ::    L   R    T:      K   T   Q      
5   22   19 : 4  24 16     ::   12   18   20     11  20  17
     
-1   +2  -3 -1   +2   -3
         Becomes   Becomes
 







2 comments:

  1. very informative post indeed.. being enrolled in http://www.wiziq.com/course/4870-ias-general-studies-and-csat-prelims-question-bank,I was looking for such articles online to assist me.. and your post helped me a lot :)

    ReplyDelete
  2. very good.. i used to count alphabets every time. but now i ll remember EJOTY. thanks. going to check ur blog in detail. really appeciate your hard work in making all this. thanks again.

    ReplyDelete

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