The number/character present in any particular situation is called the number of cards/letters. These types of questions are usually asked in all examinations. In this type of question, a series of numbers/letters have been given, in which you have to find the total number of that number/character after finding a particular number/character according to the prescribed conditions given in the question, Two types of questions are asked under this chapter.

**Type 1 **

Under the number series, such questions are asked which are related to the points series which have to be calculated according to the given condition.

** Example: **How many such numbers are there in the series in which 7 is right before the number 8 but not immediately followed by number 5?

7 8 3 7 8 5 1 2 7 8 3 3 4 7 8 2 5 6 6 8 3

(a) one (b) two (c) three (d) four

** Solution: **(c) According to the question, there are three 8 in the series, where 7 is right before the number 8 but not immediately followed by number 5.

**Type 2 **

Based on the alphabetical series, such questions are asked which are related to the Alphabet Series which must be solved according to the given condition.

** Example: **How many K are there in the series of the following letters where K is immediately followed by T but not immediately preceded by N?

Z K T L K N K T F G Z H K T K N G H J L N K T T

(a) None (b) one (c) two (d) three (e) more than three

** Solution: **(c) According to the question, there are two K in series, where K is immediately followed by T but not immediately preceded by N.

**Type 3 **

Under the Mixed Question, a number or pairs of five / six / seven numbers are given, you have to find the answer after rearranging the terms given in the question.

** Example 1.** The number of first and fifth digits is mutually changed in number 89123647. Similarly, the places of second and sixth and subsequent points are also mutated. Which of the following will be the fourth digit from the right edge of the rearrangement?

(a) 4 (b) 8 (c) 1 (d) 2 (e) None of these

** Solution: **(b) Number given = 89123647

The new number created after change = 36478912

So the fourth digit from the right is 8.

** Example 2. **Number 6492758 should be decorated in ascending order, how many digits will remain unchanged?

(a) one (b) two (c) three (d) none of these

** Solution: (b)**

6 4 9 2 7 5 8 2 4 5 6 7 8 9

Hence the points of two digits 4 and 7 will remain unchanged.

** Example 3. **How many pairs of digits are there in number 561234, among which there are as many numbers in the number as if arrange the digits in ascending order?

(a) None (b) one (c) two (d) three (e ) More than three

** Solution:** (e) More than three

** Example 4. **The second and third digits of each of the numbers given below are swipe with each other. Then the first and last digits of the new numbers are swipe with each other. Now, which is the largest number of those five numbers?

184 372 526 438 273

(a) 184 (b) 372 (c) 526 (d) 438 (e) 273

Resolution: (a) 184 ** ⇒** 148, 372 ⇒ 327, 526 ⇒ 562, 438 ⇒ 483, 273 ⇒ 237

Re: on exchange of first and last digits of new numbers.

148 ⇒ 841, 327 ⇒ 723, 562 ⇒ 265, 483 ⇒ 384, 237 ⇒ 732

So the largest number = 841 i.e. 184

** Example 5. **In the number series from 1 to 30, If the numbers which contain only one number as ‘2’ and those which are divided by 2 are deleted, then how many remaining numbers will be left?

(a) 12 (b) 14 (c) 13 (d) 10

** Solution: **(d) The total numbers from 1 to 30 are as follows.

Total number divided by 2 and a number as 2 = 20

Thus the remaining numbers = 30 – 20 = 10.

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