QUESTION

CSAT

Medium

Maths

Prelims 2025

Consider the following statements:

I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150% can have its number of factors unchanged.

Which of the statements given above is/are correct ?

Select an option to attempt

Explanation

Statement I is correct:

Example: Take $n = 2$ Increasing it by 50% gives: $2+1=3$

Number of factors: $d(2)=2$ and $d(3)=2$ .

So the number of factors remains the same.

Statement II is correct: Example: Take $n=2$ .

Increasing it by 150% gives: $2+3=5$ .

Number of factors: $d(2)=2$ and $d(5)=2$ .

So the number of factors remains the same.

Trusted by 2L aspirants

Practice UPSC Prelims PYQs Smarter

Track accuracy & weak areas
See past trends & repeated themes

Start Practicing Now

Year-wise Prelims PYQs

2025 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013

Crack UPSC with your
Personal AI Mentor

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

Start Now

Download App

Explanation

Practice UPSC Prelims PYQs Smarter

Year-wise Prelims PYQs

Crack UPSC with your Personal AI Mentor

Download the App

Crack UPSC with your
Personal AI Mentor