QUESTION

CSAT

Easy

Maths

Prelims 2017

Certain 3-digit numbers have the following characteristics:

  1. All the three digits are different.
  2. The number is divisible by 7.
  3. The number on reversing the digits is also divisible by 7.

How many such 3-digit numbers are there?

Select an option to attempt

Explanation

Step 1: General Form of the Number Let the three-digit number be represented as: N=100a+10b+cN = 100a + 10b + c where a, b, c are the digits, and $a

eq 0$ since it's a 3-digit number.

Step 2: Divisibility by 7 The number N=100a+10b+cN = 100a + 10b + c must be divisible by 7. This gives the first condition.

Step 3: Reversing the Digits The number formed by reversing the digits is: N=100c+10b+aN' = 100c + 10b + a This number must also be divisible by 7.

Step 4: Possible Numbers To find such numbers, we need to check for numbers that satisfy both N and N' being divisible by 7. After checking possible numbers, we find that there are 4 such numbers.

Answer: The number of such 3-digit numbers is 4. Correct answer: 4

Trusted by 2L aspirants

Practice UPSC Prelims PYQs Smarter

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

Crack UPSC with your
Personal AI Mentor

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

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