Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
The digit in the unit place of the number represented by $\left(7^{95}-3^{58}\right)$ is
(a)0
(b)4
(c)6
(d)7
Answer
Answer (as printed): B
Explanation
Unit digit of $7^{4}$ is 1. So, the unit digit of $\left(7^{4}\right)^{23}$ is 1. ∴ Unit digit of $7^{95}=$ Unit digit of $\left(7^{92} \times 7^{3}\right)=(1 \times 3)=3$. Unit digit of $3^{4}$ is 1. So, the unit digit of $\left(3^{4}\right)^{14}$ is 1. ∴ Unit digit of $3^{58}=$ Unit digit of $\left(3^{56} \times 3^{2}\right)=(1 \times 9)=9$. Hence, the unit digit of $\left(7^{95}-3^{58}\right)=(13-9)=4$.
Explanation as extracted from the printed page; notation may be imperfect.