•  Linearly Increasing Same Digit Numbers

Identify the pattern

Identifying correct pattern is the key to apply a trick successfully. If you make mistake in identifying the pattern, you may calculate to wrong answer. Thus, request you to pay special attention in identifying the correct pattern

Pattern to apply this trick –

A + AA + AAA + AAAA + …… + AAAAA(ntimes)
Where A is any digit from 1 to 9

Example

9 + 99
or
3 + 33 + 333 + 3333
or
4 + 44 + 444 + 4444 + 44444

All of these are example of adding linearly increasing same digit numbers. Because all of the numbers in a particular question are made from same digit and numbers of digits in a number is exactly more than 1 than the preceding number. e.g. if we consider first example ( 9 + 99 ), both numbers in this question are made from same digit i.e. 9 and number of digits in 2nd number(99) is exactly more by 1 than the preceding number(9).

Quick Answer Trick –

You may get a direct question of this kind in competitive exam or you may need to solve this kind of pattern as part of some other question. In both of these cases, solving this type of problem with trick is most time efficient. Remember time & accuracy is the key to crack a competitive exam.

Step 1. count the digits in largest number. let’s say it is n.
Step 2. Answer = A*(123…n)

Explanation with example :

Ex-1 : 4 + 44 +444 = ?
Identify the pattern :
Given question is addition of linearly increasing same digit(4) numbers
largest number = 444, thus number of digits in largest number = 3
Therefore, Answer = 4*(123) = 492

Ex-2 : 6 + 66 + 666 + 6666 + 66666 + 666666 + 6666666 = ?
Identify the pattern :
Given question is addition of linearly increasing same digit(6) numbers
largest number = 6666666, thus number of digits in largest number = 7
Therefore, Answer = 6*(1234567) = 7407402

Practice Questions:

Q1. 3 + 33 + 333 + 3333 + 33333 = ?

Q2. 5 + 55 + 555 + 5555 = ?

Q3. 9 + 99 + 999 + 9999 + 99999 + 999999 = ?

Q4. 8 + 88 + 888 = ?

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