Digital Root Calculation: Finding the Roll Number
The question asks to identify the roll number whose digital root is 9. The digital root is calculated by summing the digits of a number repeatedly until a single-digit number is obtained.
Calculating Digital Roots for Each Option
We determine the digital root for each roll number provided:
Option 1: 987654
- Sum of digits: $9 + 8 + 7 + 6 + 5 + 4 = 39$
- Summing the digits of 39: $3 + 9 = 12$
- Summing the digits of 12: $1 + 2 = 3$
- The digital root for 987654 is 3.
Option 2: 888888
- Sum of digits: $8 + 8 + 8 + 8 + 8 + 8 = 48$
- Summing the digits of 48: $4 + 8 = 12$
- Summing the digits of 12: $1 + 2 = 3$
- The digital root for 888888 is 3.
Option 3: 765431
- Sum of digits: $7 + 6 + 5 + 4 + 3 + 1 = 26$
- Summing the digits of 26: $2 + 6 = 8$
- The digital root for 765431 is 8.
Option 4: 999999
- Sum of digits: $9 + 9 + 9 + 9 + 9 + 9 = 54$
- Summing the digits of 54: $5 + 4 = 9$
- The digital root for 999999 is 9.
Conclusion
By calculating the digital root for each option, we find that the roll number 999999 is the one with a digital root equal to 9.
Similar Questions
- Which of these is both an Integer and a Whole number?
- Which of the following is a non-zero number that belongs to every set: Whole, Integer, Rational, and Real?
- What is the smallest number that must be added to 2378 to make it a perfect square?
- Which of the following is a perfect square and an Integer?
- The set of real numbers includes which of the following?
In the following examples, a number is coded as three digits — representing the remainders when the number is divided by 3, 7, and 11, respectively.
Example 1: $53 \rightarrow 53 \div 3 = 17 \text{ R} 2$, $53 \div 7 = 7 \text{ R } 4$, $53 \div 11 = 4 \text{ R } 9 \rightarrow \text{ Code: } 2, 4, 9$
Example 2: $68 \rightarrow 68 \div 3 = 22 \text{ R} 2$, $68 \div 7 = 9 \text{ R } 5$, $68 \div 11 = 6 \text{ R } 2 \rightarrow \text{ Code: } 2, 5, 2$
By following this method, which is the least number which would have the code - 2, 2, 2?- Which roll number has only prime digits?
- A student was asked to find the sum of first 20 odd numbers. His answer was 400. Correct?
- Which roll number is a perfect cube?
Which of the following statement is TRUE for Whole Numbers?
Important Questions from Number System
Consider the following statements :
1. (25)! + 1 is divisible by 26
2. (6)! + 1 is divisible by 7
Which of the above statements is/are correct ?
If the sum S is divided by 8, what is the remainder ?
If the sum S is divided by 60, what is the remainder ?
Find the sum of squares of the greatest value and the smallest value of K in the number so that the number 45082K is divisible by 3.
How many composite numbers are there from 53 to 97 ?
