The sum of all integers from $1$ to $100$ that are divisible by $2$ or $5$ is...........

Out of $500$ car owners investigated,$400$ owned car $A$ and $200$ owned car $B$,and $50$ owned both car $A$ and car $B$. Is this data correct?

Consider a three-digit number $N = 100x + 10y + z$,where $x, y, z$ are the digits at the hundreds,tens,and units places respectively. The number satisfies the following properties:
$I$. If its digits in the units place and tens place are interchanged,the number increases by $36$.
$II$. If its digits in the units place and hundreds place are interchanged,the number decreases by $198$.
If the digits in the tens place and hundreds place are interchanged,then the number:

Let $S = \{(x, y, z) : x, y, z \in \mathbb{Z}, x + 2y + 3z = 42, x, y, z \geq 0\}$. Find the number of elements in $S$.

In a class of $30$ pupils,$12$ take needle work,$16$ take physics,and $18$ take history. If all the $30$ students take at least one subject and no one takes all three,then the number of pupils taking exactly $2$ subjects is:

An electronic assembly consists of two subsystems $A$ and $B$. Past testing procedures data show that probabilities of failure are $P(A \text{ fails}) = 0.2$, $P(B \text{ fails alone}) = 0.15$, and $P(A \cap B \text{ fail}) = 0.15$. Then the probability that $A$ fails alone is equal to