What is the ten’s digit of 7^195?
A) 3
B) 4
C) 5
D) 6
E) 7
Solution
This question is based on the cyclicity concept in number theory.
Ten’s digit of powers of 7 follows a cyclic pattern as depicted:
7^1 = 07 7^5 = 16807
7^2 = 49 7^6 = 117649
7^3 = 343 7^7 = 823543
7^4 = 2401 7^8 = 5764801
Every fourth power of 7 has its ten’s place repeated.
Now, let’s break 195 (power of 7) into multiple of 4
195 = 48 * 4 + 3
The 7^195 will have its tens digit the same as 7^3 has, i.e. 4
Correct Answer: B
About the Author
GyanOne is an educational services firm focused on premium GMAT coaching, application advisory (with a focus on ISB applications), and interview preparation for B-school admissions. GyanOne operates in the New Delhi region of India and has top global B-school alumni with a minimum score of 770 on the GMAT, as instructors. All GyanOne counsellors are professionally trained top B-school alumni with an experience of 100+ MBA applications behind them.