Question

A two-digit number $\overline{ab}$ is called almost prime if one obtains a two-digit prime number by changing at most one of its digit $a$ and $b.$ (For example, $18$ is an almost prime number because $13$ is a prime number). Then the number of almost prime two-digit numbers is

• A. $56$
• B. $75$
• C. $87$
• D. $90$

Answer 1

The correct option is D $90$

There exists at least one prime number among any ten consecutive integers. More precisely, there exists at least one prime number between $10$ to $19$, $20$ to $29$,......,$90$ to $99$.

So, for any number, we replace the unit digit such that it will become prime. So, all two digit numbers are almost prime.