Question

Adam took a surprise test of the students of his class on a topic which was taught in the class two weeks earlier. The test consisted of seven questions out of which students needed to attempt only five questions. Shane, a student of his class attempted five questions and copied these five questions on a notebook so that he could solve these questions at his home, and verify whether he answered these questions correctly or not. Help Shane in verifying the answer to these questions.

What is the unit digit of $7^{333}\times 5^{11}\times 4^{234}\times 3^{11}$.

• A. $0$
• B. $1$
• C. $7$
• D. $5$

Answer 1

The correct option is A $0$

In the question there is at least one power of $5$ and at least one power of $4$ .

Now, $5\times 4=20$, i.e., the unit digit is $0$ .

So, no matter what the other numbers are, the unit digit of $7^{333}\times 5^{11}\times 4^{234}\times 3^{11}$ will be $0$

Alternatively,

Unit digit of $7^1=7$

Unit digit of $7^2=9$

Unit digit of $7^3=3$

Unit digit of $7^4=1$

Unit digit of $7^5=7$

So, we can see that the unit digit of the powers of $7$ will start repeating after a cycle of four powers.

Thus, the unit digit of $7^{333}=7$

Similarly, we can find the pattern of the unit digit of other numbers and can find that the unit digit of $5^{11}$ is $5$, the unit digit of $4^{234}$ is $6$ and the unit digit of $3^{11}$ is $7$ .

Thus, the unit digit of $7^{333}\times 5^{11}\times 4^{234}\times 3^{11}$ is equal to the unit digit of $7\times 5\times 6\times 7=0$

Hence, option $A$ is the correct answer.