 How Cheenta works to ensure student success?
Explore the Back-Story

# Sum of digits | PRMO 2019 | Question 20 Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits.

## Sum of digits - PRMO 2019

Consider the set E of all natural numbers n such that when divided by 11,12,13 respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If N is the largest number in E, find the sum of digits of N.

• is 107
• is No largest value
• is 840
• cannot be determined from the given information

### Key Concepts

Largest Number

Divisibility

Integer

PRMO, 2019, Question 20

Elementary Number Theory by David Burton

## Try with Hints

First hint

here N can be of the form (13)(12)(11)(k)+29

Second Hint

where k belongs to an integer

Final Step

then no largest value.

## Subscribe to Cheenta at Youtube

Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits.

## Sum of digits - PRMO 2019

Consider the set E of all natural numbers n such that when divided by 11,12,13 respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If N is the largest number in E, find the sum of digits of N.

• is 107
• is No largest value
• is 840
• cannot be determined from the given information

### Key Concepts

Largest Number

Divisibility

Integer

PRMO, 2019, Question 20

Elementary Number Theory by David Burton

## Try with Hints

First hint

here N can be of the form (13)(12)(11)(k)+29

Second Hint

where k belongs to an integer

Final Step

then no largest value.

## Subscribe to Cheenta at Youtube

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Knowledge Partner  