Question

V is product of first $41$ natural numbers $A=V+1$. The number of primes among $A+1,A+2,A+3,A+4,.....,A+39,A+40$ is

• A. $1$
• B. $2$
• C. $3$
• D. $0$

Answer 1

The correct option is D $0$

Substituting $V+1$ for each $A$ in the given numbers, we get
$V+2,V+3,...,V+41$
So each given number is of the form $V+k$ where $k$ is one of the first $41$ natural number and $k$ is not equal to 1.
We know that $V$ is divisible by any of the first 41 natural numbers.
Now since a given number is $V+k$ and $V$ is divisible by any of the $k$'s , then $V+k$ must be divisible by $k$
Therefore , no given number must be a prime.
Thus gives us $0$ as the correct answer.