Question

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

• A. $11$
• B. $13$
• C. $17$
• D. $19$

Answer 1

The correct option is B

$13$

Finding the last prime number:

Let $a,b,candd$ be four prime numbers in ascending order.

Prime Factorization of $385=5\times 7\times 11$

Prime Factorization of $1001=7\times 11\times 13$

Last prime number: $$\begin{gathered} a\times b\times c=385=5\times 7\times 11.......\left(1\right) \\ b\times c\times d=1001=7\times 11\times 13.......\left(2\right) \end{gathered}$$

$\Rightarrow a=5,b=7,c=11\mathrm{and}d=13$

So, the first prime number is $\mathbf{5}$ and the last prime number is$\mathbf{13}$.

Final answer: Hence, option (b) is correct.