Problems based on Numbers Test 5

Concept:The unit digit of a product depends only on the unit digits of its factors.The unit digit of powers repeats in a fixed cycle.Explanation:Unit digit of $(8267)^{153}$ is the unit digit of $7^{153}$.The cycle of unit digits for powers of $7$ is $7, 9, 3, 1$, repeating every $4$ powers.Since $153 \div 4$ leaves remainder $1$, the unit digit is the first digit of the cycle: $7$.Unit digit of $(341)^{72}$ is $1^{72}=1$.Multiply the unit digits: $7 \times 1 = 7$.So, the unit digit of the product is $7$.Answer:$7$, so option C is correct.