# Quantitative Aptitude For Bank Exam|Simplification-Digital Root /Sum Hello! Friends, in this article we will discuss one important concept of Quantitative aptitude, that is Digital Root Or Digital Sum. Questions from Simplification are asked in every exam like IBPS PO, SBI PO, IBPS RRB, IBPS Clerk, SBI Clerk, IBPS RRB, SSC CGL, SSC CGL, SSC MTS , NICL AO, LIC AAO, SBI Associate Clerk, SBI Associate PO  and others. Solving simplification questions using conventional method is tedious and time taking. Here using “Digital Root” method made very easy to solve Simplification questions and save lot of time. In this article, we will discuss Digital root and solve few simplification questions from bank exams. In our previous article we discussed “How to prepare for any IBPS exam”.

##### What is Digital Root?

The Digital root of a number is the value obtained by an iterative process of summing digits, on each iteration  use the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.

##### How to Find Digital Root?

To find Digital root of a number, add all its digits. If this sum is more than 9, add the digits of this sum. The single digit obtained at the end is the Digital root of the number. Digital root of a number can be any number from 1 to 9.

For example, Digital sum of 462486 is 4 + 6 + 2 + 4 + 8 + 6 = 30 = 3 + 0 = 3.

Similarly, the digital sum of 65536 is 7, because 6 + 5 + 5 + 3 + 6 = 25 and 2 + 5 = 7.

##### IS there any Short cut method of finding Digital Root?

There is a short cut method of finding Digital root of any number. The process is called “Casting out 9’s. The presence of Number 9 and Number 0 does not affect the Digital sum if they are not added. In this method you do not need to add 9 to find Digital Root.

For example, Digital Sum of 1249 is 1 + 2 + 4 + 9 = 16 = 7

If we ignored “9” and find digital root of 1249. we get the same result By adding 1, 2 and 4.

We can use the method casting out “9” in a different way. If there is no 9’s in any number but adding pair of digits we get number 9, then we can ignore that pair or pairs and calculate digital root by rest of the digits.

For example, Digital Sum of 7486352 is 7 + 4 + 8 + 6 + 3 + 5 + 2 = 35 = 8

In this example we get three pairs of digits( 6 & 3, 4 & 5, 7 & 2)  by adding them we get 9.

We can cancel all the digits, we are left with the digit 8, so Digital root is 8.

##### Properties of digital root
• When we add 9 to a number, it does not change the digital root of the number

For example, Digital Sum of 417 = 4 + 1 + 7 = 12 = 3

Now if we annex 9 to this number 4179= 4 + 1 + 7 + 9 = 21 = 3

Now if we annex 9 to this number, we get same result.

Hence we observe that adding 9 does not change the digital Sum of that number.

• When you multiply any number by 9,the digital Sum always be 9

For example, 7 x 9 = 63 = 9 or 11 x 9= 117 = 9

• When you divide any number by 9,the digital sum of that number will be the reminder

For example, 13 ÷ 9 reminder is 4 which is same as digital sum of 13 (1 + 3 = 4)

And 47 ÷ 9 reminder is 2 which is again same as 4 + 7 = 11 = 2.

Hence we observe that dividing by 9 does not change the digital sum of any number.

##### Simplification question asked in recent exam

1. 84368 + 65466 – 72009 – 13964 = ?

(a) 61481    (b) 62921 (c) 63861   (d) 64241  (e) None of these

Solution:  Replacing the number with their digital sum we get

2 + 9 – 9 – 5 = – 3

After solving we get “ -3 ” so digital sum is 9-3=6 Option ” c ” has the same digital sum so answer is 63861.

2. 12 % of 555 + 15 % of 666 = ?

(a) 166.5  (b) 167.5 (c) 168.5  (d) 169.5  (e) None of these

Solution: In this question you have to find digital sum of 12% and 15%. As percentage does not affect digital sum of any number hence digital Sum of 12% is same as digital sum of 12.

Replacing the number with their digital sum we get

3 * 6 + 6 * 9 = 9

Option ” a ” has the same digital sum so answer is 166.5.

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