Repeated addition of two or more digits number to obtain a single digit is called a digit sum. Since a single digit is obtained the digit sum can only be any integer from 1 to 9. Eg: Digit sum of 58798 → 5 + 8 + 7 + 9 + 8 = 37 → 3 + 7 = 10 → 1 + 0 = 1 is 1.
Digit sum can also be calculated by dividing a number by 9, the remainder obtained is the digit sum of that number. Eg: 58798 ÷ 9 gives remainder 1 which is the digit sum.
Please note: If no reminder is obtained, then the digit sum is 9 or sometimes called as 0. Eg: 58797 ÷ 9 gives no reminder, hence the digit sum is 0 or 9
Digit Sum method is a Vedic Mathematic Approach of reverse Engineering used by ancient mathematicians for determining the accuracy of complex calculations. This method is very useful in Objective Based Competitive exams which help in determining the correct option from a given set of options by skipping the calculation involved in the question. The application of the method is very vast it can be used in basic to advanced arithmetic operations consisting of multiplication, division, addition, subtraction, squares, square roots, cube roots, etc., which we have discussed in the examples section.
The method is used in Objective-based Competitive Exams where you have to select an option as the correct answer to a question. The digit sum method may drastically increase the question-solving speed saving considerable time.
The method helps in solving arithmetical calculations only, thus before applying DSM, one should reach the final equation (equation on simplifying gives correct answer) and then calculate the digit sum of the final equation. The logic behind the DSM is that the digit sum of the final equation is always equal to the digit sum of the correct option (its value) i.e.
► If your final equation is 148 x 4,654 x 782 the value of which is 538,635,344
► With the help of DSM, you don't need to completely solve the final equation to determine the correct answer instead you can simply calculate the digit sum of 148 x 4,654 x 782 which is calculated as 5. Now you can calculate the digit sum of all the given options. The correct option i.e. 538,635,344 will also have the digit sum as 5 and accordingly, you can select the correct answer.
However, there is a chance that two options in a question have the same digit sum, in such case DSM fails.
Since DSM may fail when two or more options (of which one is correct) have the same digit sum, it is advised before calculating the digit sum of the final equation we should first calculate the digit sum of the given options, if digit sum of all the options is different when can proceed with DSM and calculate the Digit Sum of the final equation and determine the correct option.
Please Note: Theoretically DSM may appear complex but it is very handy; once you go through the example section you will start developing an interest in it.
We can calculate the digit sum of most of the expressions comprising addition, subtraction, multiplication, division, decimal, root, etc. arithmetical operations in it, provided it does not have any unknown variable in it. Like we cannot calculate the digit sum of equation 35y + 7852 x 1736, as the variable 'y' is unknown. Apart from this, there are some rules set for calculating the digit sum of any expression which we have discussed in the next section.