There are four prime numbers written in ascending order. The product of first three is 385 and that of last three is 1001. The last number is:

Answer: Option A

Answer: Option C

Explanation:

Required digit is = \begin{aligned}
(4)^{102} + (4)^{103} \end{aligned}
as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0

Answer: Option A

Explanation:

Although it is a simple question, but the trick is to save time in solving this.
Rather than multiplying it we can do as follows:
586645 * (10000 - 1) = 5866450000 - 586645 = 5865863355

Answer: Option D

Explanation:

Trick: Above equation can be solved by using following formula
\begin{aligned}
(a^2 + b^2) = \frac{1}{2}((a+b)^2 + (a-b)^2)
\end{aligned}

Answer: Option B

Explanation:

\begin{aligned} \frac{abc}{bcd} = \frac{385}{1001} => \frac{a}{d} = \frac{5}{13} \end{aligned}So d = 13