A two-digit number overline{ab} is called alm | vedclass

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(D) two-digit number $\overline{ab}$ is almost prime if it can be transformed into a prime number by changing at most one digit.Every two-digit number

Vedclass · Accepted Answer

$90$

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(D) two-digit number $\overline{ab}$ is almost prime if it can be transformed into a prime number by changing at most one digit.Every two-digit number $\overline{ab}$ can be written as $10a + b$,where $a \in \{1, 2, \dots, 9\}$ and $b \in \{0, 1, \dots, 9\}$.There are $90$ two-digit numbers in total,ranging from $10$ to $99$.Any prime number $p$ (where $10 \le p \le 99$) is itself an almost prime number because we can change zero digits to obtain a prime.For any non-prime two-digit number,we check if it can be changed into a prime by altering one digit.Since there are many primes ending in $1, 3, 7, 9$,almost every two-digit number can be converted into a prime by changing the units digit $b$.For example,any number $\overline{a0}, \overline{a2}, \overline{a4}, \overline{a5}, \overline{a6}, \overline{a8}$ can be changed to a prime by modifying the last digit.Exhaustive checking shows that all $90$ two-digit numbers satisfy this condition.Thus,the total count is $90$.

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

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