CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

The question is about finding the Last two Digits. We need to find out the last two digits of a number which is ultimately the remainder when that number is divided by 100. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 4: What are the last two digits of the number 7⁴⁵?

1. 07
2. 23
3. 49
4. 43

Explanatory Answer

Method of solving this CAT Question from Number Theory - Digits: Remainder when we divide a number by 100 is nothing but the last two digits of the number.

The last two digits of 7¹ are 07.
The last two digits of 7² are 49.
The last two digits of 7³ are 43.
The last two digits of 7⁴ are 01.

The last two digits of powers of 7 go in a cycle - 07, 49, 43, 01.

So, the last two digits of 7⁴⁵ are 07.

The question is "What are the last two digits of the number 7⁴⁵?"

Hence the answer is "07"

Choice A is the correct answer.