Shortcuts in Reasoning for Competitive Exams – Alphabet & Number Test
Alphabet & Number Test
As we know that English alphabet is a group of English letters, hence the problems based on alphabet are the problems based on English letters.
Types of Problems
(1) General series of alphabet
(2) Random series of alphabet
(3) Problems of word formation
(4) Problems of letter gap
(5) Finding Digits after rearrangement.
1. GENERAL SERIES OF ALPHABET
EXAMPLE 1. Which of the following
options is seventh to the right of the 13th letter from the left in a forward Alphabet series?
Solution. 1st of all we will write the forward alphabet series as given below:
From the above series it is clear that M is the 13th letter from left and to the right ofM (13th letter from left), T is the 7th letter.
Here, we have solved this problem with a general method. But this type of problem can also be approached through quicker method that will help you save some extra consumed time.
If both the directions are same then subtraction of numbers takes place.
If the directions are opposite then addition of numbers takes place.
SHORTCUT METHOD FOR ABOVE EXAMPLE:
Now, for solving the example we apply this rule. As we want to find out the 7th letter to the right of the 13 th letter from the left, the directions are opposite and thus shortcut (b) will be applied here. Hence, we add 7 + 13 = 20. Therefore, the answer will be 20th from left. Also, 20th from left less mean 26 – 20 + 1 = 7th from right. We can easily see,
20th letter from left = T
Also 7th letter from right = T
After solving the example, you must have noticed that the above mentioned trick is to calculate the actual position of the required letter before going to search for it.
mth element to be counted from left to right of a series of x characters is equal to (x + l – m)th element to be counted from right to left of that series. This rule can be better illustrated by an example which is given below:
Let us take the forward order alphabet series,
As we know that English alphabet has 26 characters, hence, we have x = 26.
Now suppose, we have to find out the position of K in the above given series counting from right to left.
Position of ‘ K’ in the English alphabet from left to right is 11. Thus m = 11
Position of K in the above given series from right to left would be (26 + 1 -11 ) = 16
How to solve problems when letters are dropped or deleted at regular intervals?
EXAMPLE 2. If every 3rd letter from left to right of English alphabet is deleted, then what would be the 6th letter from left in the new series obtained?
Solution. General method:
Here, deleted letters have been encircled and we find the new series as given below:
It is clear, that 6th letter from left in the new series is H.
No doubt, above general method gives the correct answer. But we need to save extra consumed time and this is the reason we go for a quicker approach.
As per the example, every third letter is deleted in the original series. It does mean that we are left of two letters after every deletion. Here, ‘2 ’ is the key digit for us and we have to find out 6th letter from the left in the new obtained series. Therefore, we have to find a digit which is just less than 6 but divisible by 2. For this question the digit just less than 6 and divisible by 2 is 4. Now, we follow the operation given below:
6th letter from the left in the new series =
= 8th letter from the left in the original series, which is it.
In the same manners, we can find out any letter at a particular position in the new obtained series.
16th letter from the left in the new obtained series =
= 23rd letter from the left in the original series which is W. 18th letter from the left in the new obtained series
= 26th letter from the left in the original series which is Z.
The sample example can be asked in following way also.
“If every third letter from left to right in English alphabet is dropped (or deleted), then find out the 13th letter from right in the new obtained series”.
To solve this, we find first of all the number of letters in the new obtained series. As every third letter is dropped, hence we have
letters in the new series.
Point to be noted here that we divide 26 by 2 as every 3rd letter is dropped and
after division we take approximate value of
in round figure (approximate value of will be 8).
As per the example we have to find out 13 th letter from right in the newly I obtained series. This loss mean (18+ 1 -13) = 6th letter from left which is H.
Note that : This shortcut approach can also be applied to the dropping of every 4th, [5 th, 6th, 7th and so on letters from left to right at regular intervals.
How to solve problems based on the backward (reversed) alphabet series?
Solution . While solving problems based on general series of alphabet, we come across the various cases. In some cases we see that whole alphabet series is reversed but in some other cases 1st half of the series is reversed, or second half of the series is reversed or many segments of the alphabet series are reversed.
Let us take a case when a forward order alphabet series get reversed in three segments. In 1st segment 8 letters get reversed; in 2nd segment the next 8 letters get reversed and in the 3 rd segment the remaining 10 letters get reversed. Just see the presentation given below:
Now if you are asked to find out the 4th letter from left in the new obtained scries, then through general method, we simply do counting from left in the new series and find out our required answer as ‘E’ because ‘E’ is at 4,h position from left in the new obtained series. But while solving such type of problems, we have to do some time consuming formalities like (a) writing the original series (b) writing and reversing the letters of original series as per the question says and (c) counting them to get the required answer. Such time consuming processes can be avoided if we go through “Remember” and solve the question with shortcut approach.
It is clear that 4th letter from left in the new obtained series falls into first segment which has 8 letters. Hence, 4th letter in the new obtained series = (8+l-4) = 5th letter from the left in the original series. As we know that exact position of 5th letter from left in the original alphabet series is the position of E. Hence, E is our required answer.
If we have to find out 18th letter from left in the new obtained series, then that will be l6 + (10+l-2) = 25th letter from left in the original alphabet series (why?) which is Y.
In fact, while finding out 18th letter, we can easily see that 18th letter is the 2nd letter of 3rd segment and hence it will be not affected by 1st two segments having 8 letters each. In other words to find out 18th letter in the new obtained series, we have to find out the 2nd letter in the 3rd segment. This is the reason we find out the 2nd letter in the 3rd segment and then add the 16 letters of 1st two segment to get the 18th letter in the new obtained series. From this, we find that 18th letter from left in the new, obtained series is the 25th letter from left in the original series. As 25th letter from left in the original series is Y. So, (Y) will be our required answer.
Readers are advised to practice such type of problems as you much as possible and after a certain time will notice that you have got a skill to solve such problems Un a few seconds and that too, without the use of pen and paper.
How to solve if positions of letters are interchanged?
There is no any rule for such type of problems. Only the hard practice can given you a skill to solve such questions in a quick time.
EXAMPLE 3. If A and C interchange their places, B and D interchange their places, F and H interchange their places and so on, then which letter will be 5th to the left of Q?
Solution. As per the question the interchanges take place as follows:
Here we can see that Q interchanges with S. Then to left of Q, the 5th letter would be P because P interchanges with N.
How to find the Middle Letter?
Case I : Remember that if mth and nth letter from the left in the English, alphabet are given then.
middle letter = from the left.
EXAMPLE 4. Which letter will be midway between 8th letter from the left and 16th letter from the left in the English alphabet?
Solution. Here,m = 8 and n = 16
then middle letter =
= 12th letter from left in the alphabet
Case II: Remember that if mth and nth letter from the right in the English alphabet are given then Middle letter
Letter from the left in the English alphabet
EXAMPLE 5. Which letter will be midway between 8th letter from the right and 16th letter from the right in the English alphabet
Solution. Middle letter =
letter from left in the alphabet.
or middle letter = (27 – 12) = 15th letter from left = 0
Note : In case I and case II (m +n) must be divisible by 2.
Case III . Remember that if the mth letter. from the left and the nth letter from the right are given then middle letter th letter from the left in the alphabet
EXAMPLE 6. Which letter will be midway between 8th letter from the left and 15th letter from the right?
Solution . Here, m = 8 and n = 15
letter from left in the English alphabet = J.
Note : In case III (m – n) + 27 must be divisible by 2.
2 . RANDOM SERIES OF ALPHABET
This series is not in the proper sequence and letters take their position in the series in jumbled manner. Further, there is also a possibility that all the 26 letters of English alphabet are not available in the series. Even same letters may be repeated in the series.
EXAMPLE 7. How many letters in the following series are immediately preceded by B but not immediately followed by D?
Only the two times A fulfill the given condition and those A have been marked with the correct sign (✓). Those not fulfilling the condition have been marked with the cross sign (x). Required answer is 2.
3 . PROBLEMS ON WORD FORMATION
In such problems, a word is given and you have to find out the number of words to be formed out of some letters drawn from that particular word.
EXAMPLE 8. How many meaningful words can be formed from the 3rd, 4th, 6th and 8th letter of the word ‘CONTROVERSIAL’?
Now, from letters N, T, O and E. two words ‘NOTE’ and ‘TONE’ can be formed.
4 . PROBLEMS OF LETTER GAP
EXAMPLE 9. How many pairs of letters are there in the word ‘DREAMLAND’ which have as many letters between them as in the English alphabet?
Solution. Here, we are asked to solve problem according to English alphabet. In this case we have to count both ways. It does mean that we have to count from left to right and from right to left. Let us see the following presentation:
The above presentation makes it clear that the required pairs of letters are 4. (Pairs: DA, EA, ML and LN)
EXAMPLE 10. How many pairs of letters are there in the word ‘DREAMLAND’ which have the same number of letters between them as in the English alphabet in the same sequence.
Solution. Here, we are asked to solve problems according to the alphabetical sequence. It does mean that we have to do counting only from left to right. Let us, see the following presentation:
The above presentation makes it clear that the required pair of letters is only 1 (Pair: LN)
5 . FINDING DIGITS AFTER REARRANGEMENT
In this type of problems, a specified order or pattern is used to rearrange the positions of digits of the number. Then, either the number of those digits is found out whose positions remain unchanged after rearrangement or the digit at particular place from left or right of the number is to be found out.
Following questions are based on the
five three-digit numbers given below:
713 361 458 932 724
EXAMPLE 11. If the positions of the first and the third digits are interchanged in each of these numbers, then which of these will be an even number.
Solution. According to the question,
So, here only one number is even i.e.,854.
EXAMPLE 12. What is the difference between the sum of the three digits of the highest and that of the second highest number?
Solution. Highest number = 932
Second highest number = 724 So, the required difference = (9 + 3 + 2) – (7 + 2 + 4)
= 14-13 = 1
EXAMPLE 13. If all the three digits are arranged in ascending order (from left to right) within the number, in each of these numbers, then which of these will be second lowest ?
Solution . According to the question,
So, the second lowest number will be 137.
EXAMPLE 14. If the positions of the second and the third digits are interchanged in each of these numbers, then which of these will be exactly divisibly by 2 ?
Solution. According to the question,
So, two numbers will be exactly divisible by 2, i.e., 316 and 742.
EXAMPLE 15. If the following numbers are arranged in descending order, then what will be the square of the digits sum of the third number from the right end of the new arrangement ?
Solution. According to the question,
Now, digits sum of the 3rd number from the right = 7 + 1+3 = 11
∴ Square of the digits sum = ( 11 )2 = 121.