Question
CSATHardPrelims 2020Maths

How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?

Explanation

A prime number is a number that can only be completely divided by 11 and itself.

Given the digits 11, 22, 33, 44, and 55, we are tasked with forming five-digit prime numbers. We know that if the sum of the digits of a number is divisible by 33, the number itself is also divisible by 33.

The sum of the given digits is 1+2+3+4+5=151+2+3+4+5=15, which is divisible by 33.

Therefore, any number formed using these five digits will always be divisible by 33, meaning it cannot be a prime number.

Thus, no five-digit prime number can be formed using these five digits without repetition.

More questions fromMaths

Trusted by 2L aspirants

Practice UPSC Prelims PYQs Smarter

Practice Now
  • Track accuracy & weak areas
  • See past trends & repeated themes
Start Practicing Now

PYQs by Papers

Crack UPSC with your
Personal AI Mentor

An AI-powered ecosystem to learn, practice, and evaluate with discipline

SuperKalam
SuperKalam is your personal mentor for UPSC preparation, guiding you at every step of the exam journey.

Download the App

Get it on Google PlayDownload on the App Store
Follow us

ⓒ Snapstack Technologies Private Limited